Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
MOTION SAMPLE BOOKLET CLASS X • ELECTRICITY • CHEMICAL REACTIONS AND EQUATIONS • NUTRITION • REAL NUMBER • WORK LIFE & LEISURE Copyright © reserved with Motion Edu. Pvt. Ltd. and Publications All rights reserved. No part of this work herein should be reproduced or used either graphically, electronically, mechanically or by recording, photocopying, taping, web distributing or by storing in any form and retrieving without the prior written permission of the publisher. Anybody violating this is liable to be legally prosecuted. Corporate Head Off ice 394 - Rajeev Gand hi Na gar Kota, (Raj .) Ph. No. : 08003899588, 0744-2209671 IVRS No : 0744-2439051, 52, 53, www. motioniitjee.com , info@motio niitjee.com CLASS - X THEORY AND EXERCISE BOOKLET CONTENTS ELECTRICITY S.NO. TOPIC PAGE NO. THEORY .............................................................................................. 5 – 21 SOLVED EXAMPLE ............................................................................. 22 – 29 EXERCISE - I ....................................................................................... 30 – 33 EXERCISE -II ....................................................................................... 34 – 38 CHEMICAL REACTIONS AND EQUATIONS S.NO. TOPIC PAGE NO. THEORY .............................................................................................. 39 – 60 SOLVED EXAMPLE ............................................................................. 61 – 70 EXERCISE - I ....................................................................................... 71 – 73 EXERCISE -II ....................................................................................... 74 – 77 NUTRITION S.NO. TOPIC PAGE NO. THEORY .............................................................................................. 78 – 86 SOLVED EXAMPLE ............................................................................. 87 – 87 EXERCISE - I ....................................................................................... 88 – 89 EXERCISE -II ....................................................................................... 90 – 90 THEORY AND EXERCISE BOOKLET CONTENTS REAL NUMBERS S.NO. TOPIC PAGE NO. THEORY .............................................................................................. 91 – 92 SOLVED EXAMPLE ............................................................................. 93 – 97 EXERCISE - I ....................................................................................... 98 – 102 EXERCISE -II ....................................................................................... 103 – 103 EXERCISE -III ...................................................................................... 104 – 109 WORK, LIFE AND LEISURE S.NO. TOPIC PAGE NO. THEORY .............................................................................................. 110 – 117 EXERCISE - I ....................................................................................... 118 – 119 EXERCISE -II ....................................................................................... 120 – 120 Page # 5 ELECTRICITY ELECTRICITY ELECTRIC CHARGE (A) (B) Definition: Electric charge may be defined as the intrinsic property of certain fundamental particles (electron, proton, etc) due to which they produce electric and magnetic effects. Charge on a Macrobody: Excess or deficiency of electrons in a body is equal to the charge on a macrobody. A body having excess of electrons in negatively charge and a body having deficiency of electrons is positively charged. From the study of atomic structure, we know that an atom consists of a central part called nucleus and around the nucleus there are a number of electrons revolving in different paths or orbits. The nucleus contains protons and neutrons. A proton is a positively charged particle while a neutron has no charge. Therefore, the nucleus of an atom bears a positive charge. An electron is a negatively charged particle having negative charge equal to the positive charge on a proton. Normally, the number of electrons is equal to the number of protons in an atom. Therefore, an atom is neutral as a whole; the negative charge on electrons cancelling the positive charge on protons. This leads to the conclusion that under ordinary conditions, a body is neutral i.e. it exhibits no charge. When this equity or balance is disturbed by removing or supplying electrons, the body acquires a net charge. The body will acquire a positive or negative charge depending upon whether electrons are removed from it or added to it. (C) Types of Electric Charge: There are two types of charges. They are: (i) Positive charge: A body having deficiency of electrons. (ii) Negative charge: A body having excess of electrons. (D) Charging of a Body: There are a number of methods to charge a body as: (i) Charging by friction (ii) Charging by conduction (iii) Charging by induction etc. We will discuss charging by friction in detail: Whenever two bodies (at least one non conductor) are rubbed against each other, heat is produced due to friction present between them. Due to this heat produced, electrons in both the bodies are excited. The body having more electron affinity attracts some of the electrons from other body. Both the bodies develop equal and opposite charges by this method. S.No. (E) Positive charge Negative Charge 1 Glass Rod 2 Fur or woolen clot h Ebonit e, Amber, Rubber rod 3 Woolen coat Plast ic seat 4 Woolen carpet Rubber shoes 5 Nylon or Acet at e Clot h 6 Dry hair Comb Silk clot h Properties of Electric Charge: (i) Like charges repel and unlike charges attract each other. (ii) Charge is a scalar quantity. (iii) Charge is always quantized. (iv) Charge is conserved. (v) Charge is always associated with mass. : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] Page # 6 (F) ELECTRICITY Unit of Charge: The charge on an electron is so small that it is not convenient to select it the unit of charge. In practice, coulomb is used as the unit of charge, i.e. SI unit of charge is coulomb abbreviated as C. One coulomb of charge is equal to the charge on 625 × 10 16 electrons. 1 coulomb = charge on 625 × 1016 electrons or 6.25 × 1018 electrons Thus, when we say that a body has a positive charge of one coulomb (i.e + 1C) it means that the body has a deficit of 625 × 10 16 electrons from the normal due share. Newton's Thought If a neutral body is made positively charged, is there any change in its mass? Explanation In charging any neutral body, the mass of a body changes, though the change is extremely small or negligible. If a neutral body is made positive, it means electrons are removed from it. Thus, the mass of body decreases. STATIC AND CURRENT ELECTRICITY (A) (B) Static Electricity: A branch of physics which deals with the study of the electric charges at rest and their effects is known as electrostatic or static electricity. Current Electricity: A branch of physics which deals with the study of the electric charges in motion and their effects is known as current electricity. ELECTRIC FIELD AND ELECTRIC POTENTIAL (A) Electric Field: Electric field due to a given charge is defined as the space around the charge in which electrostatic force of attraction or repulsion due to charge can be experienced by any other charge. If a test charge experiences no force at a point, the electric field at that point must be zero. Electric field intensity at any point is the strength of electric field at that point. It is defined as the force experienced by unit positive charge placed at that point. If F is the force acting on a test charge +q0 at any point r, then electric field intensity at this point is given by E F q0 Electric field is a vector quantity and its S.I. unit is Newton per coulomb or N/C. (B) Electric Potential: The electric potential at a point in an electric field is defined as the amount of work done in moving a unit +ve charge from infinity to that point, without acceleration or without a change in K.E. against the electric force Mathematically. V W q Since work is measured in joule and charge in coulomb, therefore electric potential is measured in joule per coulomb (J/C). This unit occurs so often in our study of electricity, so it has been named as volt, in honour of the scientist Alessandra Volta (the inventor of the voltaic cell). 1 V olt 1 jo ule 1 cou lom b Potential is a scalar quantity, therefore it is added algebraically. For a positively charged body potential is positive and for a negatively charged body potential is negative. Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) Page # 7 ELECTRICITY (C) Electric Potential Difference: Consider a charge Q placed at a point P. Let A and B be two other points (B being closer to A) as shown in figure. Q B q A P From infinity If a charge q is brought from infinity to A, work WA will be done. The potential at A will then be, VA WA q If charge q is brought from infinity to B, the work done will be WB. The potential at B will then be, VB WB q The quantity V B – VA is called the potential difference between points A and B in the electric field of charge Q. Mathematically we have, VB VA WB WA q q Electric potential difference is also measured in volt. ELECTRICITY The source of all electricity is charge. As charge is the basis of all electrical phenomena, we need to know the amount of charge on a body. It is measured in coulombs. The coulomb is the SI unit of charge and its symbol is C. Matter is generally made of protons, electrons and neutrons. Each proton carries a charge of 1.6 × 10 –19 coulomb, and each electron carries an equal negative charge. Neutrons do not carry any net charge. Normally, a body has equal number of protons and electrons, and is therefore, electrically neutral. In certain situations, the balance of charges in a body is disturbed. For example:- when a glass rod is rubbed with a silk cloth, some electrons get transferred from the glass rod to the silk. The silk cloth, which gains electrons, becomes negatively charged. And the glass rod, which is left with more protons than electrons, becomes positively charged. Charged particles or objects can exert forces on each other. While like (similar) charges repel each other, unlike charges attract. Another important thing about charged particles is that they can flow, i.e., they can move in a particular direction. This flow of charged particles is called an electric current. Charged particles such as electrons are present in all substances. But they do not flow on their own. For flow of charges, there has to be a potential difference. POTENTIAL DIFFERENCE AND THE FLOW OF CHARGE Charges q A B The potential difference between two points A and B is the work done per unit charge in taking a charge from B to A. We express this mathematically as V VA – VB W q Here, V is the potential difference between the points A and B, and V A and VB are the potentials at these points. The potential at infinity is chosen as zero. : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] Page # 8 ELECTRICITY If B be the reference point, the potential at B is V B = O. From Equation, the potential at A is V A = W/q. So, the potential at a point is the work done per unit charge in taking a charge to that point from a chosen reference point. Equation may also be written as W= qV. The work done on the charge q is stored as the electric potential energy (U) of the group of charges. So, U = qV UNIT OF POTENTIAL DIFFERENCE The unit of potential difference (and potential) is the volt, whose symbol is V. One volt is the potential difference between two points in a current carrying conductor when 1 joule of work is done to move a charge of 1 coulomb from one point to the other. 1 J oule 1 Co ulomb 1 volt or 1 V 1 J C –1 The potential difference between two points is sometimes also called the voltage. FLOW OF CHARGE Consider two identical metallic spheres P and N, carrying equal amounts of positive and negative charges respectively. A positive charge is to be taken from B to A. It is attracted by the negatively charged sphere N and repelled by the positively charged sphere P. So, to move the charge towards A, one has to apply a force on it towards the left. Thus, the work done is positive. Hence, the potential difference VA – V B is positive. This means V A > V B' As one moves towards P, the work done increases; so, the potential increases. And on moving towards N, the potential decreases. So, the potential of P is higher than that of N. In general, the potential of a positively charged body is taken as higher than that of a negatively charged body. + – + + + + A + P Repulsion B + + + – – Attraction – N – – – – What happens when a free-to-move charge is placed between the spheres? A positive charge will move towards the negatively charged sphere. And a negative charge will move towards the positively charged sphere. That is, a free positive charge moves towards lower potential. And a free negative charge moves towards higher potential. If the two spheres are connected by a metal wire, electrons from the negatively charged sphere (at a lower potential) will flow to the positively charged sphere (at a higher potential). Eventually, the flow of electrons causes the charges on the spheres to become balanced. When that happens, the spheres no longer carry a net charge, and therefore, have equal potential. So, the flow of electrons stops. So we can say that a potential difference causes charges to flow. + + + + Electrons + + + Higher potential (a) – – – – – – – Lower potential (b) Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) Page # 9 ELECTRICITY A CELL PROVIDES A CONSTANT POTENTIAL DIFFERENCE The potential difference provided by things like charged spheres reduces to zero quickly once charges start to flow. So, we have to use cells to provide constant potential difference for a long time. Cells have chemicals inside. Reactions in the cell cause positive and negative charges to gather separately. This creates a potential difference between the terminals of the cell. The terminal at a higher potential is called the positive terminal and the one at a lower potential is called the negative terminal. The cells that we commonly use are called dry cells (Figure). In a common dry cell, the small metallic cap at one end is the positive terminal, while the flat metallic plate at the other end is the negative terminal. It provides a potential difference of 1.5 V. A cell is represented by the symbol shown in fig (b). The larger line represents the positive terminal, while the shorter line represents the negative terminal. A COMBINATION OF CELLS IS CALLED A BATTERY Quite often, multiple cells are combined to get a potential difference that is higher than that of a single cell. For example, we connect two 1.5V cells to get a potential difference of 3V (Figure (c)) This is shown using symbols in Figure (d). + – 1.5V Negative terminal Positive terminal (a) 1.5V – + A battery of two cells to provide 3 volts (b) (c) (d) ELECTRIC CURRENT Consider a metallic wire ACB connected across a cell of potential difference V. Since the end A is connected to the positive terminal, it is at a higher potential than the end B. In metals, some electrons are loosely bound to the atoms, and can move within it. These are called free electrons. In the metallic wire, these electrons (negative charges) move from the low-potential side B to the high-potential side A. After reaching A, they enter the cell. The chemical reactions in the cell drive these electrons to the negative terminal. From there, they re-enter the wire at the end B. Thus, there is a continuous flow of electrons in the wire from B to C to A. We say that there is an electric current in the wire. In a metal, the flow of negative charges constitutes the current. Direction of current C A B Current in a wire connected to a cell An electric current can also be a flow of positive charges. So, a flow of charge is called an electric current.By convention, the direction of current is taken as the direction of flow of positive charges. Thus, the direction of current is opposite to the direction of flow of negative charges. So, when a wire is connected to a cell, the current in the wire is from the positive-terminal end to the negative-terminal end. : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] Page # 10 ELECTRICITY MEASUREMENT OF CURRENT The charge passing per unit time through a given place(area) is the magnitude of the electric current at that place. Thus, i Q t Here Q is the charge that passes through a place in time t. Unit of current From Equation, we find that current is charge divided by time. The SI unit of charge is the coulomb and that of time is the second. The SI unit of current, therefore, is coulomb / second. This unit is called the ampere, whose symbol is A. Thus, if one coulomb of charge passes through a place in one second, the current there is 1 ampere. CONDUCTORS AND INSULATORS Materials that conduct electricity easily are called good conductors or simply, conductors. And, materials that do not conduct electricity easily are called insulators. All metals conduct electricity because they have some loosely bound free electrons, which flow when a potential difference is applied. However, some metals conduct electricity better than others. Silver is the best conductor. But because of the high cost of silver, electric wires are made of copper, or in some cases aluminium. Most nonmetallic solids do not conduct electricity. Although diamond and graphite are both forms of carbon (a nonmetal), graphite is a conductor while diamond is an insulator. Insulators do not conduct electricity because their electrons are tightly bound to the atoms. Rubber, plastics, wood, glass and porcelain are some examples of insulators. Insulators have many uses. For example, they are used as protective covers on electric wires and electrician's tools. Certain liquids also conduct electricity. While distilled water is an insulator, addition of certain salts, acids or bases allows it to conduct electricity. Under normal circumstances, gases do not conduct electricity. ELECTRIC CIRCUITS AND MEASURING INSTRUMENTS A closed path in which a current can flow is called an electric circuit. An electric circuit may have one or more electric elements such as bulbs (or lamps), cells, switches (or plug keys), metal wires, etc. Each element of a circuit has a specific function to play. For example, wires can be used to connect one element to the next. And a plug key or a switch can be used to either complete or break the closed path, thereby starting or stopping the current in the circuit. Some common circuit elements and their symbols are shown in Figure. + Bulb (lamp) Plug key (OFF) Switch (OFF) Resistor Unconnected conductor Ammeter + Fuse Plug key (ON) Switch (ON) Variable Resistor (rheostat) Connected conductors Voltmeter Fig. Some symbols used in circuit diagrams COMMON MEASURING INSTRUMENTS The electric current in a circuit is measured by an instrument called the ammeter, and the potential difference between two points in it is measured by a voltmeter (in voltage stabilizers). In these meters, a needle moving over a graduated scale gives the value of the measured quantity. Each meter has two terminals. The terminal marked '+' is connected by a wire to the higher-potential side of a circuit, while the terminal marked '–' is connected to the lower-potential side. Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) Page # 11 ELECTRICITY USING AN AMMETER TO MEASURE CURRENT To measure the current through an element of a circuit, an ammeter is connected in such a way that the current flowing through it also flows through the element. Such a connection is called a series connection. In Figure, the current i flowing through the lamp also flows through the ammeter. The reading of the ammeter gives the current through the lamp. Note that if the ammeter is removed, there will be a gap, and the current through the circuit will stop. i + A – Ammeter in a circuit Two or more electric elements are said to be connected in series if the current flowing through one also flows through the rest. An ammeter is always connected in series in a circuit. USING A VOLTMETER TO MEASURE POTENTIAL DIFFERENCE Figure shows a circuit that has two lamps connected to a cell. We want to measure the potential difference across the lamp L2 , i.e., between the points A and B. As A is on the side of the positive terminal of the cell, its potential is higher than that of B. So, the '+' terminal of the voltmeter is connected to A, and the '–' terminal, to B. The reading of the voltmeter gives the potential difference across L2. The current flowing through the voltmeter is different from those flowing through the other elements of the circuit. Also, even if the voltmeter is removed, the current continues to flow in the circuit. Note that the potential difference across L 2 and the voltmeter is the same. Such a connection is called a parallel connection. i2 + i L1 V – i1 A L2 B Voltmeter in a circuit Two or more electric elements are said to be connected in parallel if the same potential difference exists across them. OHM'S LAW The electric current through a metallic element or wire is directly proportional to the potential difference applied between its ends, provided the temperature remains constant. If a potential difference V is applied to an element and a current i passes through it, i V or i = Thus Ohm's Law 1 V R V = iR i (A) 1ohm 1 volt 1 amp ere V (volt) Here R is a constant for the given element (metallic wire) at a given temperature and is called its resistance. It is the property of a conductor to resist the flow of charges through it. : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] Page # 12 ELECTRICITY RESISTANCE From equation, i V R So, for a given potential difference, i 1 R Thus, for a given potential difference, the current is inversely proportional to the resistance. The higher is the resistance, the lower is the current. If the resistance is doubled, the current is halved. Good conductors have low resistance, while insulators have very high resistance. UNIT OF RESISTANCE Potential difference is measured in volts, and current is measured in amperes. From Equation, R = V/ i. So, the unit of resistance is volt/ampere. This unit is called the ohm, and its symbol is . We can define one ohm as follows. If a potential difference of 1 volt is applied across an element, and a current of 1 ampere passes through it, the resistance of the element is called 1 ohm. ON WHAT DOES RESISTANCE DEPEND ? The resistance of the conductor depends on: (i) on its length (ii) on its area of cross-section (iii) on the nature of its material (iv) Resistance depends on temperature (resistance increases with increase in temperature) Resistance of a uniform metallic conductor is directly proportional to its length ( ) and inversely proportional to the area of cross-section (A). R 1 A R Combining eqs. we get Where and R or R A A (rho) is a constant of proportionality and is called electrical resistivity of the material of the conductor. RESISTIVITY ( ) : Here, is a constant for a given material at a given temperature. It is called the resistivity of the material. the resistivity of a material is the resistance per unit length of a unit cross section of the material. The SI unit of a material depends on its temperature. For metals and alloys of metals, the resistivity increases with rise in temperature. The SI unit of resistivity is m. Material Metals Alloys Semiconductors Insulators Silver Copper Aluminium Tungsten Iron Manganin Nichrome Germanium Silicon Diamond Fused quartz Resistivity 1.6 × 10 –8 1.7 × 10 –8 2.8 × 10 –8 5.8 × 10 –8 9.7 × 10 –8 48.2 × 10–8 100 × 10–8 4.7 × 10 –3 2.5 × 103 5 × 1012 1016 – 10 19 Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) Page # 13 ELECTRICITY Newton's Thought Two materials have different resistivities. Two wires of the same length are made, one from each of the materials. Is it possible for each wire to have the same resistance? Explanation Two wires of the same length are made, one from of the materials. The resistance of a wire is given by, R A cross-sectional areas of the wires are chosen so that the ratio A is the same for each. That is A 2 or 2 2 A1 A2 A1 1 This is the condition for each wire of different materials to have the same resistance when they have same length. R3 B R2 A R1 1 V1 V2 V3 V A series combination of resistors SERIES AND PARALLEL CONNECTIONS OF RESISTORS A conducting material (e.g., a wire) of a particular resistance meant for use in a circuit is called a resistor. A resistor is sometimes simply referred to as a resistance. It is represented by the symbol . Two or more resistors can be connected in series, in parallel or in a manner that is a combination of these two. 1. SERIES CONNECTION OF RESISTORS Two or more resistors are said to be connected in series if the current flowing through one also flows through the rest. The total potential difference across the combination of resistors connected in series is equal to the sum of the potential differences across the individual resistors. V V1 V2 V3 EQUIVALENT RESISTANCE IN SERIES CONNECTION Figure (a) shows three resistors of resistances R 1 , R2 and R3 connected in series. The cell connected across the combination maintains a potential difference V across the combination. The current through the cell is i. The same current i flows through each resistor. Let us replace the combination of resistors by a single resistor R eq such that the current does not change, i.e., it remains i. This resistance is called the equivalent resistance of the combination, and its value is given by Ohm's law as Req = V/i Thus V = iR eq. (a) (b) : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] Page # 14 ELECTRICITY The potential differences V1 , V2 and V3 across the resistors R1 , R2 and R3 respectively are given by Ohm's law as : V 1 = iR1 , V2 = iR2 , V3 = iR3 Since the resistors are in series, V = V 1 + V2 + V3 Substituting the values of the potential differences in the above equation, iReq = iR1 + iR2 + iR3 or iReq =i(R1 +R2 +R3) or R eq = R 1 + R 2 + R3 Similarly, for n resistors connected in series, Equivalent resistance of resistors in series : R e q = R 1 + R 2 + R 3 + .... . + R n 2. PARALLEL CONNECTION OF RESISTORS The total current flowing into the combination is equal to the sum of the currents passing through the individual resistors. i i1 i2 i3 If resistors are connected in such a way that the same potential difference gets applied to each of them, they are said to be connected in parallel. EQUIVALENT RESISTANCE IN PARALLEL CONNECTION Figure (a) shows three resistors of resistances R1, R2 and R3 connected in parallel across the points A and B. The cell connected across these two points maintains a potential difference V across each resistor. The current through the cell is i. It gets divided at A into three parts i 1 , i2 and i3 , which flow through R1 , R2 and R3 respectively. R1 i1 i2 A R2 Req B R3 i3 i i i V (a) V (b) Let us replace the combination of resistors by an equivalent resistor R eq such that the current i in the circuit does not change (Fig). The equivalent resistance is given by Ohm's law as Req = V/i. Thus, i= V Re q The currents i1 , i2 and i3 through the resistors R1, R2 and R3 respectively are given by Ohm's law as i1 = V , R1 i2 = V V , i3 = R2 R3 Since the resistors are in parallel, i = i1 + i2 + i3 Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) Page # 15 ELECTRICITY Substituting the values of the currents in the above equation, V V V V = + + R e q R1 R2 R 3 or 1 1 1 1 = + + R e q R1 R2 R 3 Similarly, if there are n resistors connected in parallel, their equivalent resistance Req is given by Equivalent Resistance of resistors in parallel : 1 1 1 1 = + +.......+ Req R1 R2 Rn For two resistances R1 and R2 connected in parallel, 1 1 1 R + R2 = + = 1 R R1 R2 R1 R 2 or R R1R2 R1 + R2 The equivalent resistance in a parallel connection is less than each of the resistances. When a resistance is joined parallel to a comparatively smaller resistance, the equivalent resistance is very close to the value of the smaller resistance. NOTE : If a resistor connected in series with others is removed or fails, the current through each resistor becomes zero. On the other hand, if a resistor connected in parallel with others fails or is removed, the current continues to flow through the other resistors. DISTRIBUTION OF CURRENT IN TWO RESISTORS IN PARALLEL Consider the circuit in fig. The resistors R 1 and R2 are connected in parallel. The current i gets distributed in the two resistors. i = i1 + i2 .....(i) Applying Ohm's law to the resistor R1 V A – VB =R1 i1 · .....(ii) And applying Ohm's law to the resistor R2 V A – VB = R2i2 From (ii) and (iii), R1i1 = R2 i2 or i2 .... (iii) R1 i R2 1 Substituting for i2 in (i), we have R1 R R + R2 i = i 1 + 1 = i1 1 i = i1 + R2 1 1 R2 R2 R 2 or i1 = R + R i 1 2 : 0744-2209671, 08003899588 | url : www.motioniitjee.com, i1 R1 i2 R2 A B i : [email protected] Page # 16 ELECTRICITY Similarly, i2 = R1 i R1 + R 2 i1 R2 = i2 R1 Thus, The current through each branch in a parallel combination of resistors is inversely proportional to its resistance. Newton's Thought Figure shows a combination of four identical bulbs joined with a battery. Compare the brightness of the bulbs shown. What happens if bulb A fails, so that it cannot conduct current? What happens if bulb C fails? What happens if bulb D fails? Explanation Bulbs A and B are connected in series across the emf of th battery, whereas bulb C is connected by itself across the battery. This means the voltage drop across C has the same magnitude as the battery voltage, whereas this same voltage is split between bulbs A and B. As a result, bulb C will glow more brightly than either of bulbs A and B, which will glow equally brightly. bulb D has a wire connected across it i.e., a short circuit, so that potential difference across bulb D is zero and it doesn't glow. If bulb A fails, B goes out, but bulb C will glow. If bulb C fails, there is no effect on the other bulbs. If bulb D fails we cannot detect this event, because bulb D was not glowing initially; also, there is no effect on the other bulbs. A B C D DEVICES IN SERIES AND PARALLEL You must have seen tiny bulbs strung together for decorating buildings during festivals like Diwali, and occasions like marriages, etc. These bulbs are connected in series, and the mains voltage is applied to the combination. The potential difference (V) of the mains gets divided across the bulbs (V = V1 + V 2 + V 3 + ... ). So, a small potential difference exists across each bulb, close to that required to make the bulb work. However, the same current flows through all the bulbs. So, if one bulb goes bad, the current through it stops, and this stops the current through the rest of the bulbs as well. To make the chain of lights work, we have to find and replace the defective bulb. This problem does not occur with the lights in our house. That is because in houses, lights, fans, etc., are connected in parallel. In parallel connection, the same mains voltage gets applied to each device, but the current through each is different. If one of them goes bad, the current in the other branches of the parallel connection does not stop. Another advantage of parallel connection is that, unlike series connection, each device can draw a different current, as per its requirement. Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) Page # 17 ELECTRICITY HEATING EFFECT OF ELECTRIC CURRENT When an electric current passes through a bulb, the filament gets so hot that it glows and emits light. When a current passes through the filament of an electric iron, the iron becomes very hot. This increase in temperature is due to what is called 'the heat produced due to current'.Suppose a resistor R is connected to a cell. The cell maintains a potential difference V across the resistor, driving a current i through it. So, V = iR ......(i) R i V The current through the resistor is actually a flow of negative charges (electrons). Inside the cell, the negative charges flow from the positive to the negative terminal. The cell does work = QV to take a charge through the potential difference V between its terminals. This increases the energy of the charge by QV. This increased energy gets converted to heat in the resistor. So, the energy appearing as heat is given by U = QV ......(ii) The charge that passes through the wire in time t is Q =it. ......(iii) Using (i), (ii) and (iii), we find that the heat produced in the wire in time t is U =QV = (it) (iR) =i2 Rt. From Equation the heat produced is proportional to the square of the current, if R and t remain constant. So, if the current passing for a given time through a given resistance is doubled, the heat produced becomes four times. Similarly, for a given i and t, the heat produced is proportional to R. If the same current i passes through two resistances in a given time, more heat will be produced in the larger resistance. The heat produced can also be written as. U = i2 Rt = or U= V R 2 Rt V2 t R For a given V and t, the heat produced is inversely proportional to R. So, if the same potential difference is applied across two resistances, more heat will be produced in the smaller resistance. We have seen above that the increased energy of a charge gets converted to heat in the resistor. The increase in energy comes from the work done by the cell. This uses up the chemical energy of the cell. So, the energy appearing as heat in the resistor ultimately comes at the expense of the chemical energy of the cell. Not always is the work done by a cell converted to heat. Immediately after a motor is connected to a cell, the speed of the shaft of the motor increases. A part of the work done by the cell goes into producing the increase in kinetic energy. And a part is used to overcome friction, etc. When the motor achieves a constant speed, its kinetic energy does not change. So the work done by the cell is only used to overcome friction, etc. This appears as heat. That is why the cover over a motor becomes warm on use. : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] Page # 18 ELECTRICITY APPLICATIONS OF THE HEATING EFFECT OF CURRENT The heating effect of electric current has many uses. Electric bulbs, room heaters, electric irons, immersion heaters, toasters, electric fuses and a number of other appliances work on this principle. In all of these, a wire of suitable resistance, commonly called the heating element, is connected to the power supply. The current passing through the element produces heat in it, which is used for some specific purpose. (i) Electric bulb: An electric bulb has a simple structure. It consists of a sealed glass bulb that has a tungsten filament connected to two electrical contacts. The bulb is filled with an unreactive gas like argon or nitrogen. To produce white light, the filament has to be heated to about 3000°C by passing a current through it. Obviously, the material of the filament should such that it does not melt at this temperature. Tungsten is used for the filament because its melting point is about 3400°C. The sealed glass bulb serves two purposes. First, it protects the filament from oxidation and the effects of humidity. Secondly, the small enclosed volume makes it easier to maintain the required temperature, as without it the loss of heat would be more. (ii) Fuse: A fuse is a safety device that does not allow excessive current to flow through an electric circuit. It consists of a metallic wire of low melting point, fixed between the two terminals of a fuse plug. The fuse plug fits into a fuse socket connected in the circuit. Fuses are available in various shapes. The fuse plug is used in household wiring. It is made of porcelain. A fuse is connected in series with an appliance (such as a TV) or a group of appliances (such as the lights and fans in a room). So, the current through the fuse is the same as the current through the appliance or the group of appliances. If this current exceeds a safe value, the heat produced in the fuse wire causes it to melt immediately. This breaks the circuit, preventing any damage. Figure shows examples of how a fuse is connected in circuits. Good-quality fuse wires are made of tin, as it has a low melting point. Some fuse wires are made of an alloy of tin and copper. The thickness of the fuse wire depends on the circuit in which it is to be used. If a section of the circuit is meant to carry a maximum of 5A current, the fuse wire should also be able to carry currents up to 5A. Similarly, for wiring meant for 15A, the fuse wire should be thicker, and should be able to carry currents up to 15A. 12V 12V (a) (b) DISADVANTAGES OF THE HEATING EFFECT OF CURRENT A current always produces some heat, whether we use the heat or not. If the heat produced cannot be utilized, it represents a wastage of energy. A considerable amount of energy is thus wasted in the transmission of electricity from the generating station to our homes. Sometimes, the heat produced in a device is so much that it can damage the device, unless proper cooling arrangements are made. To dissipate the heat produced in TV sets, monitors, etc., their cabinets have grills for air to pass. Certain components of a computer get so hot that they have fans to cool them. Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) Page # 19 ELECTRICITY ELECTRIC POWER Power is the rate of doing work, or the rate at which energy is produced or consumed. The electrical energy produced or consumed per unit time is called electric power. In an electric circuit, the power is P= Using U t i2 Rt t i2 R iR = V P = Vi P= V2 R The energy consumed and power are related as U = Pt. UNIT OF POWER The SI unit of energy is the joule, and that of time is the second. The SI unit of power is therefore joule/second. This unit is called the watt, whose symbol is W. RATING OF ELECTRIC APPLIANCES Take an electric bulb and see what is written on it. Apart from the name and the symbol of the company, we will find values of power and potential difference. For example, it could be 60W, 220V. It means that 220V should be applied across this bulb, and when 220V is applied, the power consumed will be 60W. We will find similar markings on all electric· appliances. For an electric appliance, the values of power and voltage taken together form what is called the rating of the appliance. From the rating of an appliance, you can easily calculate its resistance by using the equation P = V2 . R Note that higher the power rating, smaller the resistance. So, a 1000W heater has less resistance than P a 100W bulb. We can also calculate the current drawn by an appliance by using the relation i = . V KILOWATT HOUR Power is the rate of energy consumed or produced. If 1 joule of energy is used per second, the energy is used at the rate of 1 watt. In other words, if energy is used at the rate of 1 watt, the total energy used in 1 second is 1 joule. How much energy is used in 1 hour if it is used at the rate of 1000 watt? It is (1000 watt) × (3600 second) = 3,600,000 joule. This amount of energy is called 1 kilowatt hour, written in short as kWh. Thus, 1 kWh =3,600,000 J = 3.6 × 106 J. The electrical energy used in houses, factories, etc., is measured in kilowatt hours. The cost of electricity is fixed per kilowatt hour. One kilowatt hour of electrical energy is called one unit. : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] Page # 20 ELECTRICITY ELECTRICAL SAFETY (A) Earthing: Earthing means to connect the metal case of electrical appliance to the earth (at zero potential) by means of a metal wire called "earth wire". In household circuits, we have three wires, the live wire, the neutral wire and the earth wire. One end of the earth wire is buried in the earth. We connect the earth wire to the metal case of the electrical appliance by using a three-pinplug. The metal casing of the appliance will now always remain at the zero potential of the earth. We say that the appliance has been earthed or grounded. If, by chance, the live wire touches the metal case of the electric iron (or any other appliance) which has been earthed, then the current passed directly to the earth through the earth wire. It does not need our body to pass the current and therefore, we do not get an electric shock. Actually, a very heavy current flows through the earth wire and the fuse of house-hold wiring blows out or melts. And it cuts off the power supply. In this way, earthing also saves the electrical appliance from damage due to excessive current. (B) Miniature Circuit Breaker: These days a device called a miniature circuit breaker (MCB) is also used instead of or in addition of fuses, in the household electric circuits. It is a switch that automatically switches off a circuit if the current in it exceeds the specified maximum limit. COLOR CODING OF WIRES An electric appliance is provided with a three-core flexible cable. The insulation on the three wires is of different colours. The old convention is red for live, black for neutral and green for earth. The new international convention is brown for live, light blue for neutral and green (or yellow) for earth. GALVANOMETER A galvanometer is an instrument that can detect the presence of a current in a circuit. The pointer remains at zero (the centre of the scale) for zero current flowing through it. It can deflect either to the left or to the right of the zero mark depending on the direction of current. Galvanometers are of two types: (i) Moving coil galvanometer (A) (B) (ii) Moving magnet galvanometer It is used to make ammeter and voltmeter as follows: Ammeter: Ammeter is an electrical instrument which measures the strength of current in 'ampere' in a circuitry which is always connected in series in circuit so that total current (to be measured) may pass through it. The resistance of an ideal ammeter is zero (practically it should be minimum). Voltmeter: It is an electrical instrument which measures the potential difference in 'volt' between two points of electric circuit. The only difference between ammeter and voltmeter is that ammeter has its negligible (approximately zero) resistance so that it may measure current of circuit passing through it more accurately giving the deflection accordingly, while the voltmeter passes negligible current through itself so that potential difference developed due to maximum current passing through circuit may be measured. Voltmeter has very high resistance and the resistance of an ideal voltmeter is infinite. A voltmeter is always connected in parallel. V Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) Page # 21 ELECTRICITY COLOR CODING OF RESISTORS Digit Digit Multiplier Tolerance Digit Digit Digit Multiplier 4-band code Color 5-band code Digit Multiplier Black 0 0 10 (1) Brown 1 10 1 1 2 10 2 2 Red Tolerance (%) Orange 3 10 3 Yellow 4 10 4 Green 5 10 5 0.5 Blue 6 10 6 0.25 7 10 7 8 Violet Grey 8 10 White 9 10 9 Gold Silver Tolerance 10–1 –2 10 (None) 0.1 5 10 20 Note: Short trick for colors:- B B Roy of Great Britain has very good Wife. : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] Page # 22 ELECTRICITY SOLVED PROBLEMS Ex.1 A piece of wire of resistance R is cut into five equal parts. These parts are then connected in parallel. If the equivalent resistance of this combination is R', then the ratio R/R' is : (A) 1/25 (B) 1/5 (C) 5 (D) 25 Sol. Resistance of each one of the five parts = R 5 Resistance of five parts connected in parallel is given by or 1 R' R R' 1 R/ 5 1 R/ 5 1 R/ 5 1 R/ 5 1 R/ 5 1 R' or 5 R 5 R 5 R 5 R 5 R 25 R 25 Ex.2 Thus, (D) is the correct answer. Which of the following terms does not represent electrical power in a circuit : (A) I2 R (B) IR2 (C) VI (D) V2 /R Sol. Electrical power, P = VI = (IR) I = I 2R = V Ex.3 Obviously, IR2 does not Thus, (B) is the correct An electric bulb is rated will be: (A) 100 W (B) Sol. V R V2 R represent electrical power in a circuit. answer. 220 V and 100 W. When it is operated on 110 V, the power consumed 75 W (C) 50 W Resistance of the electric bulbs, R = V 2 (D) 25 W (P = V 2/R) P (2 20 )2 = 484 1 00 or R = Power consumed by the bulb when it is operated at 110 V is given by V '2 R P' = Ex.4 Sol. (1 10 )2 4 84 1 10 1 1 0 48 4 25 W (V' = 100 V) Thus, (D) is the correct answer. Two conducting wires of the same material and of equal lengths and equal diameters are first connected in series and then in parallel in an electric circuit. The ratio of the heat produced in series and parallel combinations would be : (A) 1:2 (B) 2:1 (C) 1:4 (D) 4:1 Since both the wires are made of the same material and have equal lengths and equal diameters, these have the same resistance. Let it be R. When connected in series, their equivalent resistance is given by Rs = R + R = 2R When connected in parallel, their equivalent resistance is given by 1 Rp 1 R 1 R 2 R or Rp = R 2 V2 R V2 Power (or heat produced) in series, P s = R s Further, electrical power is given by P = V2 Power (or heat produced) in parallel, Pp = R p Thus, Ps Pp V2 / R s V2 / R p Rp Rs R/ 2 2R 1 4 or Ps : Pp : : 1 : 4 Thus, (C) is the correct answer. Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) Page # 23 ELECTRICITY Ex.5 How is voltmeter connected in the circuit to measure potential difference between two points? Sol. A voltmeter is always connected in parallel across the points between which the P.D. is to be determined. Ex.6 A copper wire has a diameter of 0.5 mm and a resistivity of 1.6 × 10 –6 ohm cm. How much of this wire would be required to make a 10 ohm coil? How much does the resistance change if the diameter is doubled? Sol. D = 0.5 mm = 0.5 × 10 –3 m We are given that, Diameter of the wire, = 1.6 × 10–6 ohm cm = 1.6 × 10–8 ohm m resistivity of copper, required resistance, R = 10 ohm As R = or = A , 3. 14 4 1 0 (0 .5 1 0 –3 )2 –8 1 .6 1 0 r Since, R = Ex.7 R( D 2 / 4 ) RA = D2 / 4 D2 , R RD 2 4 r2 = [A = (D/2)2 = D2/4] m = 112.7 m 1/D2 . When D is doubled, R becomes 1 times. 4 The values of current, I, flowing in a given resistor for the corresponding values of potential difference, V, across the resistor are given below : I (ampere) : 0.5 1.0 2.0 3.0 4.0 V (volt) : 1.6 3.4 6.7 10.2 13.2 Plot a graph between V and I and calculate the resistance of the resistor. Sol. The V-I graph is as shown in fig. I (ampere) 4.0 3.0 2.65 2.0 1.25A 1.40 1.0 4V 0.5 (0,0) 1 1.6 2 3.4 5 6 6.7 7 8 9 1010.211 12 1313.2 14 V(volt) For V = 4V (i.e., 9V – 5V), I = 1.25 A (i.e., 2.65 A – 1.40 A). Therefore, R = V I 4V = 3.2 1.2 5 A The value of R obtained from the graph depends upon the accuracy with which the graph is plotted. Ex.8 When a 12 V battery is connected across an unknown resistor, there is a current of 2.5 mA in the circuit. Find the value of the resistance of the resistor. Sol. Here, V = 12 V, I = 2.5 mA = 2.5 × 10 –3 A Resistance of the resistor, R = 12V V = 2 .5 1 0 –3 A I = 4800 = 4.8 k Ex.9 A battery of 9 V is connected in series with resistors of 0.2 , 0.3 , 0.4 , 0.5 current would flow through the 12 resistor? Sol. Since all the resistors are in seies, equivalent resistance, Rs = 0.2 + 0.3 + 0.4 + 0.5 V Current through the circuit, I = R s 9V 1 3.4 + 12 and 12 . How much = 13.4 0 .67 A In series, same current (I) flows through all the resistors. Thus, current flowing through 12 = 0.67 A : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] resistor Page # 24 ELECTRICITY Ex.10 How many 176 resistors (in parallel) are required to carry 5 A in 220 V line? Sol. Here, I = 5A, V = 220 V. V I Resistance required in the circuit, R = 2 20 V 5A , Resistance of each resistor, r = 176 44 If n resistors, each of resistance r, are connected in parallel to get the required resistance R, then r n R = or 44 = 17 6 n or n = 17 6 44 = 4 Ex.11 Show how you would connect three resistors, each of resistance 6 , so that the combination has a resistance of (i) 9 (ii) 2 . Sol. (i) In order to get a resistance of 9 from three resistors, each of resistance 6 , we connect two resistors in parallel and this parallel combination (or resistance 3 ) in series with the third resistor as shown in fig. 6 6 A 6 D C B 6 A C 9 D B A B (a) (ii) In order to get a resistance of 2 from three resistors, each of resistance 6 , we connect all the three resistors in parallel as shown in fig (b) as equivalent resistance in parallel combination, i.e., R p is given by Rp = 6 6 3 = 2 . 6 A B A B 6 (b) Ex.12 Several electric bulbs designed to be used on a 220 V electric supply line, are rated 10 W. How many lamps can be connected in parallel with each other across the two wires of 220 V line if the maximum allowable current is 5 A? Sol. Resistance of each bulb, r = V2 P Total resistance in the circuit, R (2 20 )2 4 84 0 10 22 0 V 44 5A Let n be the number of bulb (each of resistance r) to be connected in parallel to obtain a resistance R. r n r 48 40 1 10 n = R 44 Ex.13 A hot plate of an electric oven connected to a 220 V line has two resistance coils A and B, each of 24 resistance, which may be used separately, in series, or in parallel. What are the currents in the three cases? Sol. Here, potential difference, V = 220 V Resistance of each coil, r = 24 (i) When each of the coils A or B is connected separately, current through each foil, i.e., Clearly, R = V or 220V 9 .2 A I = r 24 (ii) When coils A and B are connected in series, equivalent resistance in the circuit, Rs = r + r = 2r = 48 V 220V 4.6 A Current through the series combination, ie.e, I s = R 48 s (iii) When the coils A and B are connected in parallel, equivalent resistance in the circuit, Rp = r 2 24 2 12 Current through the parallel combination, ie.e, I p = V Rp 2 20 V 12 1 8.3 A Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) Page # 25 ELECTRICITY Ex.14 Compare the power used in the 2 (i) a 6 V battery in series with 1 resistor in each of the following circuits : and 2 (ii) a 4 V battery in parallel with 12 Sol. resistors, and and 2 (i) Since 6 V battery is in series with 1 6V I = 1 2 6V 3 Power used in 2 P1 Clearly, P 2 8W 8W resistors, current in the circuit, 2A resistor, P1 = I2R = (2A) 2 × 2 (ii) Since 4 V battery is in parallel with 12 V2 resistor, P2 = R Power used in 2 resistors. and 2 and 2 (4 V)2 (2 ) = 8W resistors, pd across 2 resistor, V = 4V. 8W 1 Ex.15 Two lamps, one rated 100 W at 220 V, and the other 60 W at 220 V, are connected in parallel to the electric mains supply. What current is drawn from the line if the supply voltage is 220 V? Sol. Resistance of first lamp, r1 = V2 P (2 20 )2 100 resistance of the second lamp, r2 = V2 P 4 84 (2 20 )2 60 80 6 .7 Since the two lamps are connected in parallel, the equivalent resistance is given by 1 Rp 1 r1 1 r2 r2 r 1 r2 or Rp = r 1 r2 r1 r1 r2 4 84 4 84 8 0 6.7 8 06. 7 39 04 4 2.8 12 90 .7 = 302.5 V Current drawn from the line, i.e., I = R p 2 20 V 30 2 .6 = 0.73 A Ex.16 Which uses more energy, a 250 W TV set in 1 h, or a 1200 W toaster in 10 minutes? Sol. Energy used by 250 W TV set in 1 h = 250 W × 1h = 250 Wh Energy used by 1200 W toaster in 10 min. (i.e., 1/6 h) = 1200 W × (1/6) h = 200 Wh Thus, a 250 W TV set uses more power in 1 h than a 1200 W toaster in 10 minutes. Ex.17 An electric heater of resistance 8 draws 15 A from the service mains for 2 hour. Calculate the rate at which heat is developed in the heater. Sol. Here, I = 15A, R = 8 , t = 2h Rate at which heat is developed, i.e, electric power, P = I 2 R = (15)2 × 8 = 1800 W = 1800 J/s Ex.18 Explain the following : (a) Why is tungsten used almost exclusively for filament of incandescent lamps? (b) Why are the conductors of electric heating devices, such as toasters and electric irons, made of an alloy rather than a pure metal? (c) Why is the series arrangement not used for domestic circuits? (d) How does the resistance of a wire vary with its cross-sectional area? Sol. (e) Why are copper and aluminium wires usually employed for electricity transmission. (a) Tungsten has a high melting point (3380°C) and becomes incandescent (i.e., emits light at a high temperature) at 2400 K. (b) The resistivity of an alloy is generally higher than that of pure metals of which it is made of. (c) In series arrangement, if any one of the appliances fails or is switched off, all the other appliances stop working because the same current is passing through all the appliances. (d) The resistance of a wire (R) varies inversely as its cross-sectional area (A) as R 1/A. (e) Copper and Aluminium wires possess low resistivity and as such are generally used for electricity transmission. : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] Page # 26 ELECTRICITY NCERT QUESTIONS WITH SOLUTIONS Q.1 What does an electric circuit mean ? Ans. An electric circuit is a closed and continuous path consisting of many devices like resistors, electric bulbs, etc. through which an electric current flows. Q.2 Define the unit of current. Ans. The 51 unit of current is ampere (A). Current flowing through a conductor Is said to be 1 ampere if 1 coulomb of charge flows through it in 1 second. Q.3 Calculate the number of electrons constituting one coulomb of charge. Ans. Number of electrons constituting 1 coulomb is given by, n= Q , where, Q = 1 C and e = charge of a single electron = 1.6 × 10–19 C e or n = 1C 1.6 10 19 C = 6.25 × 10 18 electrons. Q.4 Name a device that helps to maintain a potential difference across a conductor. Ans. A battery can be used to maintain a potential difference across a conductor. Q.5 Ans. What is meant by saying that the potential difference between two points is 1 V ? Potential difference between two points is 1 volt if 1 joule of work is done to carry a charge of 1 coulomb from one point to the other. Q.6 Ans. How much energy is given to each coulomb of charge passing through a 6V battery? Work done, W = QV Where, Q = 1C; V = 6V W = 1C × 6V = 6J Q.7 Ans. On what factors does the resistance of a conductor depend? The resistance (R) of a conductor depends upon (i) its length ( ): R (ii) its cross-sectional area (A): R 1 A (iii) Nature of material i.e., resistivity ( ) of its material: R (iv) Temperature: more the temperature, more will be its resistance. Q.8 Ans. Q.9 Ans. Does current flow more easily through a thick wire or a thin wire of the same material when connected to the same source? Why? The current flows more easily through a thick wire than through a thin wire. This is because the resistance R of a thick wire (large area of cross-section) is less than that of a thin wire (small area of 1 cross-section) as R . A Let the resistance of an electrical component remains constant while the potential difference across the two ends of the component decreases to half its former value. What change will occur in the current through it? We know that I = V/R, when potential difference becomes V/2, and resistance remains constant, then, current becomes 1/2 of its former value. Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) Page # 27 ELECTRICITY Q.10 Why are coils of electric toasters and electric irons made of an alloy rather than a pure metal? Ans. This is because (i) resistivity of an alloy is generally higher than that of pure metals (ii) an alloy has a high melting point and it does not oxidise at high temperatures. Q.11 (a) which among iron and mercury is a better conductor? Given, 94.0 × 10–8 m. iron = 10.0 × 10–8 m and mercury = (b) Which material is the best conductor? Ans. (a) Iron is a better conductor than mercury as resistivity ( ) for iron is less than that for mercury. (b) Silver is the best conductor because its resistivity ( ) is least. Q.12 Ans. Draw a schematic diagram of a circuit consisting of a battery of three cells of 2V each, a 5 ohm resistor, an 8 ohm resistor, and a 12 ohm resistor, and a plug key, all connected in series. I 2V2V 2V Q.13 k ( Redraw the circuit of Q. 12, putting in an ammeter to measure,the current through the resistors and a voltmeter to measure the voltage across the 12 ohm resistor. What would be the reading in the ammeter and the voltmeter? V + I A + 2V2V 2V Ans. k ( Since all the three resistances are in series, total resistance in the circuit, R = 5 + 8 + 12 = 25 Current in the circuit, I V R 2 2 2 25 6 25 0.24 A , thus, ammeter will read 0.24 A. Potential difference across 12 ohm resistor, V = I × R = 0.24 × 12 = 2.88 V Q.14 Judge the equivalent resistance when the following are connected in parallel (a) 1 10 3 and 106 . and 106 (b) 1 , Ans. (a) Approx. 1 (slightly less than 1 ) as other one (106 ) is very large as compared to 1 . In parallel combination of resistors, the equivalent resistance is lesser than the least resistance (in this case, 1 ). (b) Again, resistance is approx. 1 (slightly less than 1 ). Q.15 An electric lamp of 100 , a toaster of resistance 50 and a water filter of resistance 500 are connected in parallel to a 220V source. What is the resistance of an electric iron connected to the same source that takes as much current as in three appliances and what is current through it? Ans. Resistance of the electric lamp, R1 = 100 R3 = 500 ; resistance of toaster, R2 = 50 ; resistance of water filter, Since R1 , R2 and R3 are connected in Parallel, their equivalent resistance (Rp ) is given by 1 Rp 1 R1 1 R2 1 R3 1 100 1 50 1 500 5 10 1 500 16 500 4 125 : 0744-2209671, 08003899588 | url : www.motioniitjee.com, Rp 125 4 : [email protected] Page # 28 ELECTRICITY Current through the three appliances, i.e., V Rp I 220 125 / 4 7.04 A Since the electric iron drawing the same current when connected to the same source (220 V), its resistance must be equal to Rp. Thus, resistance of the electric iron, 125 4 31.25 Current through the electric iron, I = 7.04 A Q.16 Ans. What are the advantages of connecting electrical devices in parallel with the battery instead of connecting them in series. (a) In case of devices in parallel. if one device gets damaged (or open), all other will work as usual as the whole circuit does not break. This is not with the devices connected in series because when one device fails, the circuit breaks and all devices stop working. (b) Since potential difference across all devices is same in parallel Circuit, they will draw required current according to their resistances. This is not so in series circuit where same current flows through all the devices, irrespective of their resistances. Q.17 How can three resistors of resistances 2 , 3 (b) 1 ? Ans. (a) The get a total resistance of 4 as shown below. and 6 be connected to give a total resistance of (a) 4 from resistors of resistance 2 , 3 A and 6 , the resistors are joined B The resistors having resistances 3 and 6 are connected in parallel. This combination is connected in series with the resistor of resistance 2 . Let us check it mathematically, equivalent resistance of 3 and 6 resistors is, R1 3 6 3 6 3 6 9 Now, R1 and 2 2 resistors are in series, their equivalent resistance is Re = R1 + 2 = 2 + 2 = 4 . (b) To get a resistance of 1 below. from three given resistors of resistance 2 , 3 , 6 , are joined as shown A B They all are connected in parallel. Their equivalent resistance is given by, 1 R 1 2 1 3 1 6 3 2 6 1 6 6 1 R= Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) Page # 29 ELECTRICITY Q.18 What is (a) the highest, (b) the lowest total resistance that can be secured by combinations of four coils of resistance 4 , 8 , 12 , 24 ? Ans. (a) The highest resistance is secured when all the resistors are connected in series. The equivalent resistance is given by, Re = 4 +8 + 12 + 24 = 48 . (b) The lowest resistance is secured when all the four coils are connected in parallel. The equivalent resistance is given by, 1 Re 1 4 1 8 1 12 1 24 6 3 2 24 1 12 24 1 2 or Re = 2 Q.19 Why does the cord of electric heater not glow while the heating element does? Ans. The cord of an electric heater is made of thick copper wire and has much lower resistance than the heating element. For the same current (I) flowing through the cord and the element, heat produced in the element is much more than that produced in the cord. As a result, the element becomes very hot and glows whereas the cord does not become hot and as such does not glow. Q.20 Compute the heat generated while transferring 96000 coulombs of charge in one hour through a potential difference of 50 V. Ans. Here, charge, Q = 96000C; time, t = 1 hr potential difference, V = 50V. Heat produced, H = V I t = V × q [ q = I t] = 96000C × 50V = 4.8 × 106 J. Q.21 An electric iron of resistance 20 takes a current of 5A. Calculate the heat developed in 30s. Ans. Here, resistance, R = 20 , current, I = 5A, time, t = 30 s. Heat produced, H = I2 R t = (5)2 5 20 × 30 = 1.5 × 104 J. Q.22 What determines the rate at which energy is delivered by a current? Ans. Electric power determines the rate at which energy is delivered by a current. Q.23 An electric motor takes 5A from a 220V. Determine the power and energy consumed in 2Hr. Ans. Here, current, I = 5A; potential difference, V = 220V; time, t = 2hr = 2 × 60 × 60 = 72000 = 7.92 × 10 6 J : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] Page # 30 ELECTRICITY EXERCISE – I BOARD PROBLEMS Q.1 Define resistivity of a material. [2004] Q.2 A cylinder of a material is 10 cm long and has Q.14 connecting domestic electrical appliances in a circuit ? a cross-section of 2 cm2. If its resistance along the length be 20 , what will be its resistivity in number and units. Q.3 filaments of incandescent lamps ? Q.4 Q.15 [2004] Why is tungsten metal selected for making Why is series arrangement not used for Out of 60 W and 40 W lamps, which one has a higher resistance when in use? Q.16 [2005] An electric bulb draws a current of 0·2 A when of charge flowing through it in one hour. [2004] closed circle. What is the effective resistance diameter of this circle? Q.5 A wire of resistance 5 [2005] Q.17 is bent in the form of a circle ? Q.6 A wire of resistance 20 [2005] An electric iron draws a current of 0·5 A when the voltage is 200 volts. Calculate the amount of electric charge flowing through it in one closed circle. What is the resistance between two points at the ends of any diameter of the [2008] the voltage is 220 volts. Calculate the amount A resistance of 10 ohm is bent in the form of a between the two points at the ends of any [2008] hour. Q.18 [2004] An electric appliance draws a current of 0·4 A when the voltage is 200 volts. Calculate the is bent in the form of amount of charge flowing through it in one a closed circle. What is the effective resistance hour. [2004] between the two points at the ends of any diameter of the circle? Q.7 [2005] Q.19 flow in 1 hour through the element of an electric Why is much less heat generated in long electric bulb drawing a current of 0·2 A. cables than in filaments of electric bulbs? [2005] Q.8 Calculate the amount of charge that would Q.20 Calculate the amount of charge that would flow in 2 hours through the element of an State which has a higher resistance: a 50 W electric bulb drawing a current of 0·25 A. or a 25 W lamp bulb and how many times? [2004] [2005] Q.9 What is the power of torch bulb rated at 2·5 V and 500 mA ? Q.21 Calculate the amount of charge that would flow in 1 hour through the element of an electric [2005] iron drawing a current of 0·4 A. Q.10 Q.22 Out of the two, a toaster of 1 kW and an Q.23 electric heater of 2 kW, which has a greater resistance? [2006] 10 [2007] and are connected in series, how does the current passing through the two resistors compare ? What is meant by the statement "Potential electric circuit is 1 volt ? [2006] (ii) In a circuit if the two resistors of 5 What is the SI unit of electrical potential ? difference between two points A and B in an [2005] (i) Draw a circuit diagram to show how two resistors are connected in series. [2007] Q.13 Derive the relation R = R1 + R 2 + R 3 when resistors are joined in series. one of them has higher resistance ? [2006] Q.12 [2004] There are two electric bulbs, (i) marked 60 W, 220 V and (ii) marked 100 W ; 220 V. Which Q.11 [2004] Q.24 A bulb is rated at 5.0 V, 100 mA. Calculate its (i) power and (ii) resistance. [2006] Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) Page # 31 ELECTRICITY Q.25 An electric iron has a rating of 750 W, 220 V. Calculate Q.31 (i) State the formula showing how the current [2007] I in a conductor varies when the potential difference V applied across it is increased (i) current passing through it, and stepwise (ii) its resistance, when in use. Q.26 (ii) Show this relationship also on a schematic An electric lamp is marked 100 W, 220 V. It is used for 5 hours daily. Calculate graph. [2007] (iii) Calculate the resistance of a conductor if (i) its resistance while glowing the current flowing through it is 0·2 ampere when the applied potential difference is 0·8 (ii) energy consumed in kWh per day. Q.27 [2004] volt. Three resistors are connected as shown in Fig. Through a resistor of 5 ohm, a current of 1 ampere is flowing. Q.32 A torch bulb is rated 5·0 V and 500 mA. Calculate its (i) power (ii) resistance and (iii) [2003] energy consumed when it is lighted for 4 hours. [2005] I2 R2= 10 I1 I1 R1= 5 A B I1 I3 R2= 15 Q.33 If a 12 V ba tt ery i s co nnec ted to t he arrangement of resistances given in Fig. (with C 5 replaced by 10 and 10 , 15 replaced by 25 replaced by 5 ). Calculate (i) the (a) What is the potential difference across AB total effective resistance of the arrangement and across AC ? and (ii) the total current flowing in the circuit. [2005] (b) What is the current through the other two resistors ? 5 20 15 10 (c) What is the total resistance? Q.28 An electric bulb is rated at 200 V-100 W. What I I is its resistance? Five such bulbs burn for 4 hours. What is electrical energy consumed ? ( ) 24V Calculate the cost if the rate is 50 paise unit. [2003] Q.29 Q.34 Two electric lamps of 100 W and 25 W respectively are joined in parallel to a supply State the formula co-relating the electric of 200 V. Calculate the total current flowing current flowing in a conductor and the voltage through the circuit. [2005] applied across it. Also show this relationship Q.35 by drawing a graph. Two identical resistors, each of resistance 2 , are connected in turn (i) in series, and (ii) What would be the resistance of a conductor in parallel, to a battery of 12 V. Calculate the if the current flowing through it is 0·35 ampere ratio of power consumed in the two cases. when the potential difference across it is 1·4 volt. [2005] [2004] Q.36 Q.30 When a potential difference of 1·2 volt is applied Two identical resistors, each of resistance 10 are connected in (i) series, and (ii) in parallel, across a conductor, the current flowing through in turn to a battery of 10 V. Calculate the ratio it is 0·25 ampere. Calculate the resistance of of power consumed in the combination of the conductor. resistors in the two cases. [2004] : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] [2005] Page # 32 Q.37 ELECTRICITY In the given cir cuit , ca lculate (i ) t ota l Q.42 resistance of the circuit, and (ii) current shown by the ammeter. for studying Ohm's law. Q.43 R1=3 Two lamps, one rated 60 W at 220 V and the other 40 W at 220 V, are connected in parallel to the electric supply at 220 V. R2=2 Q + A [2007] (b) Draw a schematic diagram of the circuit [2005] R3 = 5 P (a) State Ohm's law. [2008] (a) Draw a ci rcuit diagram to show the – connections. 2.5V (b) Calculate the current drawn from the electric supply. Q.38 (i) Draw a schematic diagram of a circuit (c) Calculate the total energy consumed by consisting of a battery of five 2 V cells, a 5 resistor, a 10 resistor and a 15 the two lamps together when they operate for resistor, one hour. and a plug key, all connected in series. [2006] (ii) Calculate the current passing through the Q.44 and 'short-circuiting' as used in domestic above circuit when key is closed. Q.39 circuits. In a household, 5 tube lights of 40 W each are of an alloy than a pure metal ? W for 4 hour each day. Calculate the total energy consumed by the tube lights and press Q.40 Q.45 [2006] resistance total resistance in arm CE, (b) total current I1 A D 4 2 [2008] (b) the total current in the circuit drawn from the battery, and (c) current in each C For the circuit shown in Fig., calculate (a ) t he value o f cu rrent t hrough ea ch In the circuit shown in Fig., calculate : (a) arm, i.e., AB and CE of the circuit. [2008] (b) Why are the coils of electric toasters made used for 5 hours and an electric press of 500 in a month of 30 days. (a) Distinguish between the terms 'overloading' (c) the total effective resistance of the circuit. [2006] I2 6 I2 B + ( ) 5 I1 E I – I3 10 30 I – 3V ( ) A + 6V Q.41 (a) What is meant by 'Electric Resistance' of a conductor? [2007] (b) A wire of length L and resistance R is stretched so that its length is doubled and area of cross· section is halved. How will its : (i) resistance change ? (ii) resistivity change ? Q.46 (a) Express Ohm's law by a mathematical formula. [2004] (b) Draw a circuit diagram to verify Ohm's law. (c) Present the relationship between the voltage applied across a conductor and the current flowing through it graphically. Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) Page # 33 ELECTRICITY Q.47 State Ohm's law. Express it mathematically. (a) Name an instrument that measures electric Define SI uni t of resistance. Derive an current in a circuit. Define the unit of electric expression for the equivalent resistance of three current. resistors R1 , R2 and R3 connected in series (or (b) What do the following symbols mean in in parallel). Q.48 Q.50 [2004] [2008] circuit diagram ? (a) Express Ohm's law both by a mathematical formula and by a graph line. [2004] V (volt) (b) State SI units of (i) resistance and 1.6 1.5 (ii) resistivity. 1.2 1.0 0.8 0.5 (c) What will be the equivalent resistance of two resistors R1 and R2 0 0.1 0.2 0.3 0.4 0.5 0.6 I(A) (i) connected in series and (ii) connected in parallel. Q.49 (a) What is meant by saying that the potential difference between two points is 1 volt? Name (i) (ii) ( ) a device that helps to measure the potential difference across a conductor. [2008] (b) Why does the connecting cord of an electric heater not glow hot while the heating element does ? (c) Electrical resistivities of some substances at 20°C are given below: (c) An electric circuit consisting of a 0·5 m long nichrome wire XY, an ammeter, a voltmeter, four cells of 1·5 V each and a plug key was set up. (i) Draw a diagram of this electric circuit to study the relation between the potential difference maintained between the points 'X' Silver 1·60 × 10–8 m Copper 1·62 × 10–8 m Tungsten 5·20 × 10–8 m Iron 10·0 × 10–8 m Mercury 94·0 × 10–8 m Nichrome 100 × 10–6 m and 'Y' and the electric current flowing through XY. (ii) Graph shown in Fig. was plotted between V and I values. What would be the values of V/I ratios when the potential difference is 0·8 V, 1·2 V and 1·6 V respectively? What conclusion do you draw from these values ? Answer the following questions in relation to them : (i) Among silver and copper, which one is a better conductor? Why ? (ii) Which material would you advise to be used in electrical heating devices ? Why ? : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] Page # 34 ELECTRICITY EXERCISE – II Q.1 OLYMPIAD QUESTIONS If a charged body attracts another body, the charge on the other body :(A) must be negative (B) must be positive (C) must be zero (D) may be negative or positive or zero Q.2 1 MeV is equal to :(A) 1.6 × 10 –19 J (B) 1.6 × 10 –14 J (C) 1.6 × 10 –13 J (D) 1.6 × 10 +13 J Q.3 Q.4 Q.5 1 A man has five resistors each of value . 5 What is the maximum resistance he can obtain by connecting them ? (A) 1 (B) 5 2 1 (C) (D) 5 2 Materials which allow larger currents to flow through them are called :- (A) 106 A (C) 10 –3 A (B) 10 –6 A (D) 10 A Q.12 How many electrons constitute a current of one microampere? (A) 6.25 × 10 6 (C) 6.25 x 10 9 (B) 6.25 × 10 12 (D) 6.25 × 10 15 Q.13 The SI unit of specific resistance is :(A) ohm m (C) ohm m 2 (B) ohm m –1 (D) (ohm) –1 Q.14 T he e ffe ct i ve re si st a nce of a c ir cu it containing resistances in parallel is (A) equal to the sum of t he individua l resistances (C ) gr eat er t han a ny o f t he indi vi dua l resistances (B) Ite (D) It/e Conventionally, the direction of the current is taken as - (C) the direction of flow of molecules (D) the direction of flow of positive charge The unit of specific resistance is :(A) ohm (C) ohm-metre (B) mho (d) ohm per metre 1 volt equals :(A) 1 joule (B) 1 joule per coulomb (C) 1 coulomb per metre (D) 1 newton per coulomb Q.9 Q.11 One ampere equals :- If I is the current through a wire and e is the charge of electrons, then the number of electrons in t seconds will be given by :- (A) the direction of flow to negative charge (B) the direction of flow of atoms Q.8 (B) molecules (D) electrons (B) s ma ller than any of t he individua l resistances Ie t (C) e/It Q.7 (A) atoms (C) protons (A) Insulators (B) Conductors (C) Semiconductors(D) Alloys (A) Q.6 Q.10 Good conductors have many loosely bound- The reciprocal of resistance is conductance. If the unit of resistance is ohm, the unit of conductance will be (A) ohm (C) mho (B) volt (D) ohm metre –1 (D) sometimes greater and sometimes smaller than the individual resistances Q.15 Electric field intensity is (A) a scalar quantity (B) a vector quantity (C) neither scalar nor vector (D) sometimes scalar and sometimes vector Q.16 Electric potential is (A) A scalar quantity (B) a vector quantity (C) neither scalar nor vector (D) sometimes scalar and sometimes vector Q.17 In Co ul o mb' s l a w, t he c on st a nt proportionality k has the units (A) N (C) NC2/m2 of (B) Nm2 (D) Nm2/C 2 Q.18 The variable resistance is called :(A) resistor (C) open switch (B) rheostat (D) none of these Q.19 The law that governs the force between electric charges is called (A) Ampere's law (C) Faraday's law (B) Coulomb's law (D) Ohm's law Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) Page # 35 ELECTRICITY Q.20 A charge q is placed at the center of the line joining two equal charges Q. The system of the three charges will be in equilibrium, if q is equal to Q Q (B) – 2 4 Q Q (C) + (D) + 4 2 Q.21 The force between two electrons separated by a distance r varies as :(A) (A) r 2 (C) r –1 (B) r (D) r–2 Q.22 When the distance between the charged particles is halved, the force between them becomes (A) One-fourth (C) Double (B) Half (D) Four times Q.23 A charge q 1 exerts some force on a second charge q 2. If third charge q 3 is brought near, the force of q 1 exerted on, q 2 : (A) Decreases (B) Increases (C) Remains unchanged (D) Increases if q 3 is of the same sign as q 1 and decreases if q 3 is of opposite sign Q.24 If the charge is moved against the coulomb force of an electric field (A) Work is done by the electric field (B) Energy is used from some outside force (C) The strength of the field is decreased (D) The energy of the system is decreased Q.25 The ratio of the forces between two small spheres with constant charge (a) in air (b) in a medium of dielectric constant K is(A) 1 : K (C) 1 : K 2 (B) K : 1 (D) K 2 : 1 Q.26 Two charges are placed at a distance. If a glass slab is placed between them, force between them will be (A) Zero (C) Decreased (8) Increased (D) Remains same Q.27 If a unit positive charge is taken from one point t o a no ther over an e quipot entia l surface, then (A) Work is done on the charge (B) Work is done by the charge (C) Work done is constant (D) No work is done Q.28 If a glass rod is rubbed with silk, it acquires a positive charge because(A) Protons are added to it (C) Electrons are added to it (B) Protons are removed from it (D) Electrons are removed from it Q.29 Two resistors of resistance R 1 and R2 having R1 > R 2 are co nnecte d i n pa rallel. For e qui va l e nt r e si st a nc e R , t he co rr e ct statement is (A) R > R 1 + R 2 (B) R 1 < R < R 2 (C) R2 < R < (R1 + R2) (D) R < R1 Q.30 Two unequal resistances are connected in parallel. Which one of the statement is correct(A) The current flowing is same in both (B) M ore cur rent wi ll flow from higher resistance piece (C) The potential drop is same in both (D) The conductivity of lower resistance is less Q.31 There are 8 equal resistances R. Two are connected in parallel, such four groups are connected in series, the total resistance (A) R/2 (C) 4R (B) 2R (D) 8R Q.32 In a conductor 4 coulombs of charge flows for 2 seconds. The value of electric current will be(A) 4V (C) 2A (B) 4A (D) 2V Q.33 In a conductor, the flow of current is :(A) Flow of molecules (B) Flow of free electrons (C) Flow of positive charge (D) Flow of ions Q.34 Three resistances of magnitude 2, 3 and 5 ohm are connected in parallel to a battery of 10 volts and of negligible resistance. The potential difference across 3 resistance will be(A) 2V (C) 5V : 0744-2209671, 08003899588 | url : www.motioniitjee.com, (B) 3V (D) 10V : [email protected] Page # 36 ELECTRICITY Q.35 In the circuit shown below, the ammeter A reads 5A and the voltmeter V reads 20 V (Fig.). The correct value of resistance R is:- Q.39 What is the resistance between A and B in the given network (Fig.) ? 1 1 R A A B 2 V (A) exactly 4 (B) slightly greater than 4 (C) slightly less than 4 (D) zero Q.36 What is the current in the circuit shown (Fig.) 2 (A) 2 (B) 2 2 3 (C) (D) 3 2 Q.40 The equivalent resistance between A and B (Fig.) will be :1 A 2 2 2 2 2 B 2 I 2V (A) 1.5 A (B) 0.5 A (C) 2.5 A (D) none of these Q.37 In the circuit shown in Fig., the reading of the voltmeter V will be :- (A) 7 (B) 2 5 (C) (D) 1 3 Q.41 What is the resistance between A and B ? 2 2 12V 2 2 – + 2 A 100 2 V (A) 4V (B) 2V (C) 6V (D) 3V Q.38 Which of the following networks yields maximum effective resistance between A and B? B 4 3 (A) (B) 3 4 16 (C) (D) infinity 3 Q.42 The slope of voltage (V) versus current (I) is called :Y 2 2 (A) A V B O 2 2 2 X i (B) A B 2 2V 2 (C) I (A) resistance (B) conductance (C) resistivity (D) conductivity Q.43 The current in the adjoining circuit will be- A 30 30 B 2 30 2 2 (A) 1 A 45 (B) 1 A 15 (C) 1 A 10 (D) 1 A 5 2 B (D) A 2 Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) Page # 37 ELECTRICITY Q.44 The resistance wires are made of the material Q.50 The cost of electricity is about 30 paise per having :- unit for household use. This unit is the same ( A) L ow spe ci fi c r e si st a nc e a nd l o w as temperature coefficient of resistance. (A) ohm (B) ampere ( B) Hi gh spe ci fi c re si st a nce an d l o w (C) volt (D) kilowatt-hour temperature coefficient of resistance. ( C) Lo w sp ec i fic r e si st a nce a nd hi gh temperature coefficient of resistance. Q.51 A fuse wire should have (A) low resistance and low melting point (B) low resistance and high melting point. ( D) H igh spe ci fi c r esi st a nce a nd hi gh temperature coefficient of resistance. Q.45 The resistance between points A and B in (C) high resistance and low melting point. (D) high resistance and high melting point. Q.52 A o ne- o hm an d ha lf- o hm res ist o r a re Fig. is :- connected in parallel across a 3 volt battery. R Total energy given out per second is R R R (A) 27 J (C) 4.5 J R (A) 7 R 3 (C) 5R (B) 3R (D) 4 R 3 Q.46 Two wires of same material and same mass have their lengths in the ratio 1 : 2. Their electrical resistances are in the ratio (A) 1 : 1 (B) 1: 2 (C) 2: 1 (D) 1: 4 Q.47 A 24 V potential difference is applied across (B) 9 J (D) 3 J Q.53 Two electric lamps each of 100 watts 220 V are connected in series to a supply of 220 volts. The power consumed would be (A) 100 watts (B) 200 watts (C) 25 watts (D) 50 watts Q.54 A rheostat can be used in an electrical circuit as a (A) standard resistance (B) potential divider (C) heat controller a parallel combination of four 6-ohm resistors. The current in each resistor is (A) 1A (B) 4A (C) 16 A (D) 36 A (D) on-off switch Q.55 The potential difference between points A and B of adjoining figure is Q.48 Three resistors in parallel have an effective re s is t anc e of 1 o hm. Wh en t he y a re A B 5 connected in series their resistance is 9 ohm. The resistance of each resistor is : A 4, 4, 1 ohm (B) 6, 2, 1 ohm (C) 3, 3, 3 ohm (D) 2, 3, 4 ohm 2V 5 5 D 5 5 5 C Q.49 Fo ur 20 o hm r es ist o rs a re co nne ct e d together to form a square. The resistance (A) 2 V 3 (B) (C) 4 V 3 (D) 2 V between opposite corners will be :(A) 20 ohm (C) 24 ohm (B) 22 ohm (D) 24.8 ohm : 0744-2209671, 08003899588 | url : www.motioniitjee.com, 8 V 9 : [email protected] Page # 38 ELECTRICITY Q.56 the value of equivalent resistance between Q.59 Eight ident ical spherical mercury drops the points A and B in the given circuit, will be [NTSE] charged to a pot ential of 20V each are coalesced into a single spherical drop R R [NTSE] A (A) the internal energy of the system remains the same R R (B) the new potential of the drop is 80V (C) internal energy of the system decreases B R R (D) the potential remains the same i.e. 20V (A) 6 R (B) 4R 11 11R 4 (D) R 6 (C) Q.60 A t e chni cia n has 10 r esi st ors e ach o f resistance 0.1 . The largest and smallest resistance that he can obtain by combining these resistors are (A) 10 and 1 Q.57 Consider a simple circuit containing a battery (B) 1 and 0.1 and three identical incandescent bulbs A, B and C. Bulb A is wired in parallel with bulb B and this combination is wired in series with bulb C. What would happen to the brightness of the other two bulbs if bulb A were to (C) 1 and 0.01 burn out? [NTSE] C A B I (D) 0.1 [NTSE] respectively respectively respectively and 0.01 respectively ANSWER KEY 1. D 2. C 3. A 4. B 5. D 6. D 7. C 8. B 9. C 10. D 11. A 12. B 13. A 14. B 15. B 16. A 17. D 18. B 19. B 20. B 21. D 22. D 23. C 24. B 25. B 26. D 27. D 28. D 29. D 30. C 31. B 32. C 33. B 34. D 35. B 36. A 37. A 38. A 39. D 40. D 41. C 42. A 43. C 44. B 45. A 46. D 47. B 48. C 49. A 50. D 51. A 52. A 53. D 54. B 55. C 56. C 57. C 58. C 59. B 60. C V (A) Only bulb B would get brighter (B) Both A and B would get brighter (C) Bulb B would get brighter and bulb C would get dimmer ( D) The re w ould b e no c hange in the brightness of either bulb B or bulb C. Q.58 Three equal resistors connected in series across a source of emf dissipates 10 watts of power. What will be the power dissipated is watts if the same resistors are connected in parallel across the same source of emf? (A) 10W (B) 30W (C) 90W (D) 10 W 3 [NTSE] Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) CHEMICAL REACTIONS AND EQUATIONS Page # 39 CHEMICAL REACTIONS AND EQUATIONS INTRODUCTION We observe many chemical changes taking place in our daily life. The milk turns sour if kept for a long time at room temperature, milk changes to curd, rusting of iron, digestion of food in our body are examples of chemical changes. In such changes, the nature and the properties of the substances change and we say a chemical reaction has taken place. A chemical reaction is represented by a chemical equation which is a convenient way of describing a chemical reaction with the help of symbols of elements and formulae of chemical compounds. In this chapter, we shall discuss about chemical formulae, chemical equations, balancing of chemical equations and types of chemical reactions. Physical change :– A change in which the physical properties of the substance changes but the chemical composition does not change. The substance is restored to its original state as soon as the cause of change is withdrawn. Chemical change :– In a chemical change, at least one of the reacting substance changes into a new substances with a different composition. The new substances can not be changed back to the original substance even if the cause of change is withdrawn. DIFFERENCE BETWEEN PHYSICAL & CHEMICAL CHANGE S.No. Physical change Chemical change 1 The ident it y of the substance is The ident it y of the original maintained. substance is completely lost. 2 The change is temporary, the The change is permanent. substance returns to its original st ate as the cause of. change is withdrawn 3 No new substance is produced. A new substance is always produced. 4 Heat change may or may not occur. 5 Only the physical state or some The substance after t he change of the physical properties of the can not come back to its original substances are changed state even when the cause of change is withdrawn. 6 Eg. Iron t awa is left exposed t o Eg. Ferment ation of rice, breathing, air, melting of wax. curding of milk. Heat change may occur. CHEMICAL REACTION The processes, in which a substance or substances undergo a chemical change to produce new substance or substances, with entire new properties, are known as chemical reaction. The nature and identity of products totally changes from the reactants. Some important characteristics of chemical reactions are: (i) Change in state: The physical state of the substances normally changes. e.g (a) Formation of solid MgO from solid Mg and gaseous O 2. (b) Formation of solid Pbl(ppt) from liquid solutions of PbNO 3 and Kl. (c) Formation of H2 gas from the reaction of solid Zn with liquid H2SO 4. : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] Page # 40 (ii) CHEMICAL REACTIONS AND EQUATIONS Change in colour : In some of the chemical reactions change in colour can be observed. e.g. (a) Formation of brown rust on black iron nails. (b) Formation of yellow ppt. of lead iodide from colourless solution of PbNO3 and Kl. (iii) Evolution on a gas: In some cases, a gas may be evolved. e.g. (a) Evolution of H2 gas, in the reaction between Zn and dil HCL (b) Evolution of CO2 gas, during burning of any fuel, which contains carbon. (iv) Change in temperature: Most of the reactions are accompanied by temperature change. i.e. increase or decrease in temperature. e.g. (a) In the reaction between Zn and H 2 SO4 , flask was found to be warm. Thus rise in temperature has taken place. (b) If a reaction between barium hydroxide, Ba(OH)2 and ammonium chloride, NH4 Cl is carried out in a test tube, it is observed that bottom of test tube becomes cooler. Q. Check Your Concepts From the given exaples, identify the chemical changes. (a) Fermentation of grapes. (b) Burning of a candle. (c) Evaporation of alcohol. (d) Freezing of water. (e) Turning brown of a freshly cut apple in the air. (f) Growth of a plant. (g) Dissolution of sugar in water. (h) Fading of coloured clothes in the sun. WORD EQUATION A chemical equation which represents a chemical reaction briefly in words is called word equation. Example : For the example the word equation is Sodium + water Sodium hydroxide + Hydrogen Do You Know? Reactants:- The substance or substances which takes part in a chemical reaction are called reactants. Products:- The new substance or substances formed as a result of a chemical reaction are called products. In the above reaction sodium & water are reactants and sodium hydroxide & hydrogen are products. RULES FOR WRITING A WORD EQUATION (i) The substances taking part in chemical reaction, reactants are always written on the left hand side of arrow. (ii) The substances formed after the chemical reaction, products are always written on the right hand side of arrow. (iii) A plus sign (+) is put in between the reactants or between the products. If their number is two or more. (iv) An arrow ( ) is put between the reactants and products, the arrow shows the direction of the reaction in which the reaction proceeds. The arrow is read as "to yield" or "to form". In the word equation when symbols and chemical formulae of the reactants and products are used then it is called as chemical equation. Example : Na + H2O NaOH + H2 Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) CHEMICAL REACTIONS AND EQUATIONS Page # 41 IMPORTANT TERMS AND CONCEPTS I. Formulae of Ions 1. Valency. The number of electrons shared by an atom is called its valency. It is also called the combining capacity of an atom, e.g., Cl atom can share one valence electron, its valency is 1, Oxygen can share two valence electrons, its valency is 2. Nitrogen can share 3 valence electrons, its valency is 3, Carbon can share 4 valence electrons, therefore its valency is 4 and so on. It means if Carbon combines with Chlorine, Carbon will share four valence electrons with four Chlorine atoms, therefore the molecular formula of the covalent compound will be i.e. CCl4 is formula. Some more examples are : + 1 Charge Formula + 2 Charge Chromium (III) ion Potassium ion Manganese (II) ion Au 1 Charge Name of ion Bromide ion Chloride ion Fl uoride ion Iodide ion Sb3+ Hg 2+ 2 + Formula Br Cl F I 2 Charge Name of ion Oxide ion Sulphide ion Formula O2 S2 3 Charge Name of ion Nitride ion Phosphide ion Boride ion : 0744-2209671, 08003899588 | url : www.motioniitjee.com, Formula N3 P3 B3 : [email protected] Page # 42 CHEMICAL REACTIONS AND EQUATIONS *The elements show more than one valency. So a Roman numeral shows theft valency in a bracket. 1 Charge Formula Name of ion Hydrogen carbonate 2 Charge Name of ion CO23 HCO3 HSO4 Manganate ion O 24 Thiosulphate ion 2 3 O Phosphate ion O34 O33 O32 NO3 O 24 ClO3 Phosphite ion O24 MnO4 O72 O 33 O 33 O32 NO2 O 34 Ferricyanide ion - 4 Charge O24 O24 PO2 AlO2 [Fe(CN)6] –4 +1 Charge NH+4 2. Chemical Equations. “A chemical equation is a symbolic notation that uses formulae of compounds and symbols of elements to represent a chemical reaction”, e.g., Copper oxide reacts with Carbon to form Copper and Carbon monoxide. The reaction may be represented as CuO + C 3. Cu + Co Writing of a Chemical Equation. (i) The symbols of elements and the formulae of reacting substances (reactants) are written on the left hand side and plus (+) sign is written between them. (ii) The symbols and formulae of the substances formed (products) are written on the right hand side with a plus sign (+) between them. (iii) An arrow ( ) sign in put between the reactants and products, e. g.,, Mg + H2 SO4 MgSO4 + H2 (iv) The physical states of the reactants and products are also mentioned in a chemical equation. The notations g, l, s, aq. are written in brackets along with symbols/formulae of reactants and products. These symbols stand for gaseous, liquid, solid and aqueous solution respectively, e.g., Mg (s) + H2 SO4 (aq) MgSO4 (aq) + H2 (g) Zn (s) + H2 SO4 (aq) ZnSO4 (aq) + H2 Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) CHEMICAL REACTIONS AND EQUATIONS Page # 43 The symbol ( ) may also be used to represent a gaseous product. The symbol ( ) is used to represent the formation of a precipitate (water insoluble) or a sparingly soluble substance formed during the reaction which settles down mostly, e.g., NaCl (aq) + AgNO3 (aq) AgCl ( ) + NaNO3 (aq) (v) Sometimes, the temperature, pressure and catalyst of the reaction are indicated above and or below the arrow in the equation, e.g., CO (g) + 2H2 (g) ZnO / Cr2O3 340 atm, heat CH3 OH (g) (vi) A chemical equation represents an actual chemical reaction in which the reactants and products are known, e.g., 2 KMnO4 (s) 2 KClO3 (s) 4. heat heat MnO2 K2 MnO4 (s) + MnO2 (s) + O2 (g) 2 KCl (s) + 3 O2 (g) Balancing of chemical equation. Observe the following two chemical equations : Zn + H2 SO4 Na + H2 O ZnSO4 + H2 NaOH + H2 ……(i) …….(ii) In equation (i), the number of atoms of Zn, H, S, and O are equal on both sides, i.e., the equation is balanced. 5. Balanced Equations. The equations in which atoms of various elements on the reactant’s and the product’s side are equal. Equation (ii) is not balanced because the number of hydrogen atoms is not equal on both sides. It is called a skeleton chemical equation. 6. Reason of Balancing Equat ions. The number of atoms of elements on both sides of a chemical equation should be equal in accordance with the law of conservation of mass. 7. Balancing. The process of making atoms of various elements equal in an equation on either side is called balancing. 8. Steps in Balancing of Chemical Equations. A number of steps are involved in balancing a chemical equation, e.g., Na + H2 O NaOH + H2 Step 1: Examine the number of atoms of different elements present in unbalanced equation. Number of atoms in reactants Step 2: Pick an element to balance the equation. In the above equation Na and O are balanced, Hydrogen is not. Step : To balance Hydrogen on both sides we need to multiply H2O by 2 which makes Hydrogen atoms equal to 4 on the reactants’ side. To make Hydrogen 4 on the products’ side, multiply NaOH by 2. Now oxygen has become 2 on both sides. But Sodium atom has become two on the product’s side. Multiply Na by 2 on the reactant’s side so that they become equal on both sides. The steps are as follows : : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] Page # 44 CHEMICAL REACTIONS AND EQUATIONS (i) Na + 2H2 O (ii) Na + 2 H2 O (iii) 2 Na + 2 H2 O NaOH + H2 2 NaOH + H2 2 NaOH + H2 The equation is now balanced. Example : Fe + H2O Step 1 : Element Fe3O4 + H2 Number of atoms in reactants Step 2 : Pick up the compound which has the maximum number of atoms whether a reactant or a product, and in that compound select the element which has the highest number of atoms, e.g., we select Fe 3O4 in the above equation : To balance oxygen atoms, In reactant To equalise the number of atoms, we put the coefficient on the left side of the formula. A coefficient is a small whole number, like coefficients used in algebraic equations. You must keep in mind that we can put coefficients but we cannot change the subscripts in the formula, i.e., to balance Oxygen atoms, we can put the coefficient 4 as 4 H 2O and not H2O 4 or (H2 O)4 . Now the partly balanced equation becomes as follows : Fe (s) + 4 H2O (g) Fe 3O4 (s) + H2 (g) (Partly balanced) Step 3 : Pick up the second element to balance this partly balanced equation. Let us try to balance hydrogen atoms. bIn partly balanced equation. Atoms of Hydrogen To equalise the number of Hydrogen atoms, we use 4 as the coefficient of H 2 in the products. Fe (s) + 4H2 O (g) Fe3 O4 (s) 4H2 Step 4 : Pick up the third element to be balanced. The element which is left to be balanced is Fe. Atoms of Iron To equalise iron, we use 3 as coefficient of Fe in reactants. 3 Fe + 4 H2O Fe3O4 + 4H2 Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) CHEMICAL REACTIONS AND EQUATIONS Page # 45 Step 5 : Check the correctness of the balanced equation. Atoms The equation is balanced because atoms of all the elements are equal on both sides. This method of balancing equation is known as hit and trial method. 9. Balancing of Ionic Equations. In these equations, charge balancing is also done along with balancing of atoms on both sides of the equation, e.g., Initial Cu2+ (aq) + H2 S Balanced Cu2+ (aq) + H2S CuS (s) + H+ (aq). CuS (s) + 2 H+ (aq) We have balanced the charges. It was + 2 on LHS and we have made + 2 on RHS. Number of Hydrogen atoms, Cu and Sulphur atoms are also balanced on both sides. Do You Know? A chemical equation that conserves the amounts of all elements and electrical charges, is said to be balanced. Q. Why is it necessary to balance the chemical equation? Explanation In order to make law of conservation of mass, applicable on the given chemical equation, it is necessary to make number of atoms of all elements equal on L.H.S. & R.H.S. Thus balancing of equation is required. Q. In order to white wash a house a man mixed 10 kg of quick lime with 30 litres of water. On adding lime, he noticed that the water started boiling even when it was not being heated. Explain what is the reason behind it and write the reaction involved. Explanation When quick lime (CaO) was added to water, formation of slaked lime [Ca(0H) 2 ]has taken place, with the evolution of a large amount of heat. i.e. its an exothermic reaction, which caused solution to boil. CaO(s) + H2O( ) Ca(OH) 2(s) + heat Calcium oxide Calcium hydroxide Do You Know? In a balanced chemical equation an integer precedes the formula of each substance. This number is known as stoichiometric coefficient. If no number is there, stoichiometric coefficient is taken as 1. TYPES OF CHEMICAL REACTIONS The chemical reactions are classified into various categories depending upon the types of changes taking place. The different types of reactions are as follows : Chemical Reactions Combination Decomposition Reaction Reaction Displacement Double Oxidation Reaction Displacement and Reaction Reduction Reaction : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] Page # 46 (i) CHEMICAL REACTIONS AND EQUATIONS Combination Reaction. The reactions in which two or more substances combine to form a single new substance are called combination reaction. Combination may take place, (i) Between two or more elements. (ii) Between two or more compounds. (iii) Between elements and compounds. Some more examples of combination reactions: (a) Between two elements (i) Burning of Coal C(s) + Carbon (ii) + Hydrogen + Magnesium + Iron O 2(g) 2H2O( ) Oxygen Water O 2(s) 2MgO(s) Oxygen Magnesium oxide S(s) FeS(s) Sulphur Iron sulphide Between 2 compounds (i) Formation of Ammonium chloride NH3(g) + Ammonia (ii) HCl(g) NH4 Cl(s) Hydrogen Ammonium Chloride Chloride Formation of Calcium Carbonate CaO(s) (c) Carbon dioxide Formation of Iron sulphide Fe(s) (b) Oxygen Burning of Magnesium in air 2Mg(s) (iv) CO2(g) Formation of Water 2H2(g) (iii) O 2(g) CO2(g) CaCO3 (s) Calcium oxide + Carbon Calcium (Quick lime) dioxide carbonate Between an element and a compound (i) Reaction of carbon monoxide with oxygen 2CO(g) + O 2(g) 2CO2(g) This is also an exothermic reactions. Q. How the process of respiration help us to stay alive? Explanation The food we eat provides us the energy to stay alive. During digestion, food is broken down into simpler substances. For example, rice, potatoes and bread contain carbohydrates. These carbohydrates are broken down to form glucose. This glucose combines with oxygen in the cells of our body and provides energy. The special name of this reaction is respiration. C6 H12O6(aq) Glucose + 6O2 (aq) 6O 2(aq) Oxygen Carbon dioxide + 6H2O( ) + energy Water So, we can say that respiration is an exothermic reaction. Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) CHEMICAL REACTIONS AND EQUATIONS Page # 47 ACTIVITY - 1 Aim : To show the combination reaction between calcium oxide and water is an exothermic process. Materials Required: Quicklime (calcium oxide), water, beaker. Procedure : 1. Take 5 g of calcium oxide in a beaker. 2. Add water to it slowly. 3. Touch the beaker. 4. Note down the observations. Observation : Calcium oxide reacts with water vigorously to form calcium hydroxide with the evolution of heat. Chemical Reaction : CaO (s) + H2 O (l) Ca(OH)2 (aq) + Heat Conclusion : The reaction between CaO (Calcium oxide) and H2 O is a combination reaction. It is an exothermic process because heat is evolved. ACTIVITY - 2 Aim: To show burning of magnesium ribbon in air is a combination reaction. Materials Required: Magnesium wire, tongs, burner. Procedure : 1. Take a strip of magnesium ribbon and hold it with the help of tongs. 2. Introduce it in the flame of the burner. Observation : Magnesium ribbon bums with dazzling light and white substance is formed which is magnesium oxide. This happens due to following chemical reaction. Chemical Reaction : 2 Mg (s) + O2 (g) 2 MgO (s) Conclusion : Burning of magnesium in presence of oxygen to form magnesium oxide is a combination reaction. (ii) Decomposition Reaction. A reaction in which a single compound breaks down to produce two or more simpler substances. i.e., a compound decomposes into simpler substances. It is opposite to combination reactions. There are three ways in which decomposition reactions can be carried out, i.e., energy required in decomposition reaction can be supplied in the following ways: (i) Heat (ii) Electricity (iii) Light (1) Electrolysis. When decomposition reaction is carried out with the help of electric current, the process is called electrolysis (‘electro’ means electric, ‘lysis’ means break down), e.g., when electric current is passed through acidified water (water mixed with a few drops of acid so as to make it a good conductor), it decomposes into Hydrogen and Oxygen gases. 2 H2 O (l) electric current 2 H2 (g) + O2 (g) : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] Page # 48 CHEMICAL REACTIONS AND EQUATIONS ACTIVITY - 3 Aim : To demonstrate electrolysis of water. Materials Required : Plastic mug, drilling machine or screw driver, carbon electrodes, 6 volt battery, dil. H2 SO4 , water Procedure : 1. Take a plastic mug. 2. 3. 4. Drill two holes at the base and insert carbon electrodes as shown in figure. Fill the mug with water to its half and add a few drops of dilute sulphuric acid. Fill a graduated measuring cylinder with water and invert it in the apparatus so that one of the two electrodes is enclosed within it. 5. 6. Fill another graduated cylinder with water and invert it over the second electrode. Allow the current to pass through the voltameter and leave the apparatus undisturbed for some time. 7. The bubble formation starts at both the electrodes. 8. Observe the volume of gases collected in the inverted measuring cylinders. 9. Collect the gases in respective cylinders and test them separately. 10. Bring a match stick near each of the gases in the cylinders and note down the observation and write conclusion about the gas. Plastic Mug Hydrogen Oxygen Test tube Water Water Graphfite rod Anode Switch Rubber stopper Cathode 6V Battery Electrolysis of Water Observation : The volume of one of the gases is twice the volume of other gas. One of the gases catches fire and burns with ‘pop’ sound whereas in other gas match stick burns brightly. Conclusion : Water, on electrolysis decomposes to hydrogen gas and oxygen gas. Hydrogen gas burns explosively whereas oxygen gas helps in burning, i.e., hydrogen is highly combustible and oxygen is supporter of combustion. (2) Thermal Decomposition. When decomposition reaction is carried out by heating, it is called thermal decomposition reaction, e.g., CaCO3 (s) [Limestone] FeSO 4 (S) heat CaO (s) + CO2 (g) [Quick lime] heat Fe2O3 + SO2(g) + SO3(g) [Ferric oxide] 2Pb(NO3)2(S) Zn CO 3 (s) heat heat 2PbO + 4NO2(g) + O2(g) ZnO (s) + CO2 (g) The process of heating ZnCO3 (Calamine), an ore of zinc in absence of air to form Zinc oxide (ZnO) and CO (g) is also called calcination. Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) CHEMICAL REACTIONS AND EQUATIONS Page # 49 ACTIVITY - 4 Aim : To show heating of lead nitrate is decomposition reaction. Materials Required : A test tube, lead nitrate solid. Procedure : 1. Take lead nitrate (white powder) in a test tube and hold it in tongs. 2. Heat it over flame of burner slowly as shown in diagram. Observation : Pungent smelling brown fumes are evolved and brownish residue is left. Chemical Reaction : 2 Pb(NO3 )2 heat 2PbO (s) + 4 NO2 (g) + O2 (g) Explanation : Lead nitrate on heating decomposes to lead monoxide (brown), brown gas nitrogen dioxide (NO2 ) and oxygen gas are evolved. Conclusion : It is an example of decomposition reaction. ACTIVITY - 5 Aim : To show decomposition reaction of ferrous sulphate. Materials Required : Ferrous sulphate crystals, dry test tube, burner. Procedure : 1. Take 2 g of ferrous sulphate crystals in a dry test tube. 2. Observe the colour of ferrous sulphate crystals. 3. Heat the crystals of ferrous sulphate over the flameof a burner for some time. 4. Observe the crystals after heating for 5 minutes. Observation : The green colour of ferrous sulphate crystals changes to brownish black ferric oxide and smell of burning sulphur is observed. Chemical Reaction : 2 FeSO4 (s) heat Fe2 O3 (s) + SO2 (g) + SO3 (g) Explanation : Ferrous sulphate decomposes to form ferric oxide along with evolution of SO2 and SO3 gases. Conclusion : Heating of ferrous sulphate is a thermal decomposition reaction because ferrous sulphate breaks down into simpler compounds Fe2 O3 , SO2 and SO 3. Do You Know? The decomposition of vegetable matter into compost is also an example of an exothermic reaction. (3) Photochemical Decomposition : Chemical reaction in which a compound decomposes into simpler substances on the absorption of light energy is called photo-decomposition reaction. 2Agcl(s) sunlight Silver Chloride (White) 2AgBr(s) sunlight 2Ag(s) + Cl2 (g) Silver (Grey in colour) 2Ag(s) + Br2 (g) Silver Bromide Silver Bromine The Decomposition of a Compound with light is called “Photolysis.” All Decomposition reaction requires energy i.e. these reactions are “Endothermic reactions.” These reactions are used in extractions of metals. : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] Page # 50 CHEMICAL REACTIONS AND EQUATIONS ACTIVITY - 6 Aim : To show photochemical decomposition of silver chloride. Materials Required : AgNO3 (aq), NaCl (aq), test tubes. Procedure : 1. Take 5 ml of silver nitrate solution in a test tube. 2. Prepare sodium chloride solution in another test tube. 3. Add sodium chloride solution into test tube containing silver nitrate solution. 4. Observe the colour of silver chloride formed. Dry it with the help of filter papers and place it on the watch glass. 5. Place the watch glass under sunlight for some time. 6. Observe the colour of the silver chloride after some time. Observation : White silver chloride turns grey in sunlight because silver metal is formed. Chemical Reaction : sunlight 2 AgCl (s) 2 Ag(s) + Cl2 (g) Explanation : Silver chloride is photo-sensitive. It decomposes in presence of sunlight to form silver metal and chlorine gas. Conclusion : Decomposition of silver chloride in presence of sunlight is photochemical decomposition reaction. Other examples of photochemical reactions : Silver bromide and silver iodide also decompose in the same manner. sunlight 2 AgBr (s) sunlight 2 AgI (s) 2 Ag(s) + Br2 (g) 2 Ag (s) + I2 (g) These reactions are photochemical reactions which are used in black and white photography. Another important example of decomposition reaction in our body is digestion of food. When we eat rice, wheat or potatoes, the starch gets decomposed to simple sugar and proteins get converted into simple substances called amino acids in our body. (C6H10O5 )n + H2O C12H22 O11 + H2O Proteins Diastase Maltase Pep sin C12 H22 O11 2C6H12 O6 Amino acids We have observed all the decomposition reactions require energy either in form of heat, light or electricity for breaking down of reactants. Therefore, they are endothermic reactions. Endothermic Reactions: Those reactions in which heat is absorbed are called endothermic reactions. Do You Know? Decomposition reaction is just opposite of the combination reaction. Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) CHEMICAL REACTIONS AND EQUATIONS Page # 51 Memory Tip Thermal decomposition reaction Absorption of heat Decomposition Reactions Electro decomposition reaction (iii) Photo decomposition reaction Displacement Reactions. Those reactions in which a more reactive element displaces a less reactive element from a compound are called displacement reactions. Potassium K Sodium Na Most Reactive Barium Ba Calcium Ca Magnesium Mg Aluminium Al Zinc Zn Iron Fe Nickel Ni Tin Sn Lead Pb Hydrogen H Copper Cu Mercury Hg Silver Ag Gold Au Least Reactive These reactions mostly occur in solution form, e.g., Zn (s) + CuSO4 (aq) ZnSO4 (aq) + Cu (s) Colourless Pb + CuSO4 (aq) PbSO4 Reddish brown + Cu (s) It is a displacement reaction. Other examples are : Mg + CuSO4 MgSO4 (aq) + Zn (s) : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] Page # 52 CHEMICAL REACTIONS AND EQUATIONS It shows magnesium is more reactive than Cu because it can displace Copper from Copper sulphate solution. Mg(s) + ZnSO4 (aq) MgSO4 (aq) + Zn (s) Mg (s) + FeSO4 (aq) MgSO4 (aq) + Fe (s) These reactions show that Mg is more reactive than Zn and Fe. Zn (s) + FeSO4 (aq) ZnSO4 (aq) + Fe (s)] It shows Zn is more reactive than Fe. On the basis of the above reactions, we can conclude Mg > Zn >Fe > Pb > Cu > Ag is the order of reactivity. Zn (s) + H2 SO4 (dil.) ZnSO 4 (aq) + H2 (g) Mg (s) + H2 SO4 (dil.) MgSO4 (aq) + H2 (g) These reactions show that Zn and Mg are more reactive than Hydrogen because they displace Hydrogen from dilute acids. These are also examples of displacement reactions. ACTIVITY - 7 Aim: To show iron is more reactive than copper. Materials Required : Iron nails, copper sulphate solution, test tubes. Procedure : 1. Take blue coloured copper sulphate solution in a test tube. 2. Put iron nails in it. Observation : Colour of solution slowly changes to light green and brown coloured copper metal gets deposited over iron nails. Chemical Reaction : Fe (s) + CuSO4 (aq) Blue heat FeSO4 (aq) + Cu (s) Light green Conclusion : Iron is more reactive than copper because iron can displace copper from copper sulphate solution. It is an example of displacement reaction. Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) CHEMICAL REACTIONS AND EQUATIONS Page # 53 ACTIVITY - 8 \ Aim : To show the displacement reaction between zinc granules and dilute hydrochloric ac id or dilute sulphuric acid. Materials Required : Zinc granules, conical flask, dil. HCl or dil. H2SO 4. Procedure : 1. Take 5-6 zinc granules in a conical flask. 2. Set the apparatus as shown in figure. 3. Add dil. HCl or dil. H2SO 4 over it. 4. Observe the reaction. 5. Touch the conical flask and observe the change in temperature. Observation: The bubbles of hydrogen gas are observed. The conical flask becomes hot showing that the process is exothermic. Chemical Reaction : Zn (s) + 2 HCl (dil) ZnCl2 (aq) + H2 (g) Zn (s) + H2 SO4 (dil) ZnSO4 (aq) + H2 (g) Conclusion : The reaction between Zn and dil. HCl or dil. H2 SO4 is a displacement reaction. It is exothermic process. It shows zinc is more reactive than hydrogen, therefore it can displace hydrogen from dilute acids like HCl and H2 SO4. (iv) Double Decomposition Reactions (Double Displacement Reactions). Those reactions in which two different atoms or groups of atoms are displaced by other atoms or groups of atoms, i.e., two compounds exchange their ions and one of the products formed is insoluble, e.g., BaCl2 (aq) + Na2SO 4 (aq) Here, S O 24 BaSO 4 (s) + 2NaCl (aq) ions are displacing Cl ions and Cl ions are displacing S O24 ions. Since it involves displacement of two species, therefore, is called double displacement reactions. If one of the products formed in the reaction is insoluble, it is also called double decomposition reaction. These reactions usually occur in between ionic compounds when they are dissolved in water i.e., in aqueous solution. These reactions are fast reactions and take place within fraction of a second. : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] Page # 54 CHEMICAL REACTIONS AND EQUATIONS Other examples of double displacement reactions are AgNO3 (aq) + NaBr (aq) AgBr + NaNO3 (aq) AgNO3 (aq) + KI (aq) AgI + KNO3 (aq) FeSO 4 (aq) + 2 NaOH (aq) Fe (OH)2 + Na2SO 4 (aq) Cr2(SO4 )3 + 6 NaOH 2 Cr(OH)3 + 3 Na2 SO4 (aq) FeCl 3 + 3 NaOH Fe(OH)3 + 3 NaCl (aq) AlCl3 + 3 NaOH Al(OH)3 + 3 NaCl (aq) CuSO4 + H2 S(g) CuS + H2SO4 (aq) MnSO4 + H2 S (g) MnS + H2SO4 (aq.) NiCl2 + H2 S (g) NiS + 2 HCl (aq) Pb (NO 3 )2 + 2 HCl (aq) PbCl2 (s) + 2 HNO3 (aq) CaCO3 + 2 NaCl (aq) CaCl2 (aq) + Na2CO3 (aq) Ca(NO3 )2 + (NH4 )2 CO3 CaCO3 + 2 NH4NO3 ZnSO4 + H2S ZnS + H2SO4 (aq) ACTIVITY - 9 Aim : To show reaction between sodium sulphate solution and barium chloride solution is double displacement reaction (precipitation reaction). Materials Required : Barium chloride solution, sodium sulphate solution, two test tubes. Procedure : 1. Take sodium sulphate solution in a test tube. 2. Add few drops of solution of barium chloride. Observation : White precipitate is formed. Chemical Reaction : Na2 SO4 (aq) + BaCl2 (aq) BaSO4 + 2NaCl (aq) Conclusion : Reaction between sodium sulphate solution and barium chloride solution is double displacement reaction. Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) CHEMICAL REACTIONS AND EQUATIONS Page # 55 ACTIVITY - 10 Aim : To show the reaction between lead nitrate and potassium iodide is double decomposition reaction (precipitation reaction). Materials Required : Test tubes, lead nitrate solution, potassium iodide solution. Procedure : 1. Take lead nitrate solution in a test tube. 2. Add potassium iodide solution to it. 3. Observe the changes taking place in the solution. Observation : Yellow precipitate is formed. Chemical Reaction and Explanation : Lead nitrate reacts with potassium iodide to form lead iodide which is insoluble in water and yellow in colour. It is called precipitate. The reaction is also called precipitation reaction. Pb(NO 3)2 (aq) + 2KI (aq) PbI2 (s) + 2 KNO3 (aq) Conclusion : The reaction between lead nitrate and potassium iodide is double decomposition reaction. Since Pb is insoluble called precipitate, therefore, this reaction is also called precipitation reaction. (v) Neutralization Reactions. Those reactions in which acid or acidic oxide reacts with base or basic oxide to form salt and water are called neutralization reactions, e.g., NaOH + HNO3 NaNO3 + H2O 2 NaOH + H2 SO4 Na2SO4 + 2 H2 O KOH + HCl KCl + H2O KOH + HNO3 KNO3 + H2O 2KOH + H2 SO4 K2SO4 + 2H2O CH3COOH + NaOH CH3COONa + H2O + 2NaOH + 2H2O When salt of weak acid reacts with strong acid, it is also called neutralization reaction. Na2CO3 + 2HCl 2NaCl + H2 O + CO2 CH3COONa + HCl CH3COOH + NaCl When acidic salt reacts with base to form salt and water, it is also called neutralization reaction. NaHCO3 + NaOH Na2CO3 : 0744-2209671, 08003899588 | url : www.motioniitjee.com, + H2O : [email protected] Page # 56 (vi) CHEMICAL REACTIONS AND EQUATIONS Oxidation and Reduction (1) Oxidation. (a) It is a process in which Oxygen or an electronegative element is added. (b) It can also be defined as a process in which Hydrogen or an electropositive element is removed. (c) In terms of electronic concept, oxidation is a process in which loss of electrons takes place. 4Na + O2 2 Na2 O (Addition of oxygen) 2Mg + O2 2 MgO (Addition of oxygen) Fe Fe (Loss of electron) 2+ 3+ +e 2 Fe + 3 Cl2 2 FeCl3 (Addition of electronegative element) Hg2Cl2 Hg + HgCl2 (Removal of electropositive element) Cu 300o C CH3CH2OH CH3CHO + H2 (Removal of Hydrogn) (2) Reduction. (a) It is a process in which addition of Hydrogen or an electropositive element takes place. (b) It is also defined as a process in which Oxygen or an electronegative element is removed. (c) In electronic concept, reduction process involves gain of electrons. 2 Na + H2 2NaH (Addition of Hydrogen) CuO + H2 Cu + H2O (Removal of Oxygen and addition of hydrogen) Fe3+ + e Fe 2+ (Gain of electron) Hg + HgCl2 Hg2 Cl2 (Addition of an electropositive element) Cu + CuCl2 Cu 2Cl2 (Addition of an electropositive element) Cl2 (Removal of an electronegative element) AuCl3 AuCl + ACTIVITY - 11 Aim: To study oxidation of copper to copper (II) oxide. Method: Heat a china dish containing about 1 9 copper powder . Now answer: What do you observe? Discussion: It is observed that the brown copper powder gets coated with black copper (II) oxide. Wire gauze Tripod stand Burner Oxidation of copper to copper oxide Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) CHEMICAL REACTIONS AND EQUATIONS Page # 57 Conclusion: Copper (brown in colour) on heating combines with oxygen to form black copper (II) oxide. 2Cu(s) + Copper(Brown) O2 (g) 2CuO(s) Oxygen Copper (II) oxide (Black) Here, we can say that copper is being oxidised, as it is gaining oxygen. In the above activity if hydrogen gas is passed over product (CuO) and the black coating on the surface becomes brown because reverse reaction takes place. CuO(s) + Heat H2(g) Cu(s) + H2 O( ) Here, we can say that copper oxide is being reducing, as it is loosing oxygen and hydrogen is being oxidised. Redox Reactions : Those reactions in which oxidation and reduction take place simultaneously are called redox reactions, e.g., (i) (ii) Mn4+ + 2e Mn 2+ (Reduction) [Gain of electrons] 2 Cl Cl2 + 2e (Oxidation) [Loss of electron] Cu (s) + I2 (s) CuI2 (s) Cu (s) Cu2+ (aq) + 2e (Oxidation) [Loss of electron] I2 (s) + 2e 2I (Reduction) [Gain of electron] Cu (s) + I2 (s) CuI2 + 2e Cu (s) + I2 (s) CuI2 (s) is a Redox reaction. Oxidising Agent. It is a substance which can (i) add oxygen or an electronegative element to other materials. (ii) remove hydrogen or an electropositive element from other materials. (iii) gain electrons. Oxidising agent itself gets reduced. Reducing Agent. It is a substance which can (i) add hydrogen or an electropositive element to other materials. (ii) remove oxygen or an electronegative element from other materials (iii) lose electrons. Reducing agent itself gets oxidised. : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] Page # 58 Example 1. CHEMICAL REACTIONS AND EQUATIONS Fe + S FeS Fe Fe2+ + 2e (Oxidation) S + 2e S2 (Reduction) Fe is losing electrons, therefore, it acts as a Reducing agent. S is gaining electrons, therefore, it acts as an Oxidising agent. Fe is getting oxidised to Fe2+ (Ferrous ion) whereas S gets reduced to S2 (Sulphide ion) Example 2. Cu (s) + 2AgNO3 (aq) Cu (NO 3)2 (aq) + 2 Ag (s) Cu (s) Cu2+ 2 Ag+ + 2e 2 Ag Cu (s) + 2 Ag+ (aq) Cu2+ (aq) + 2 Ag (s) + 2e (Oxidation) (Reduction) Cu is a reducing agent because it is losing electrons whereas Ag + is an oxidising agent. Example 3. Fe 2O3 is an oxidizing agent whereas Al is a readucing agent. Example 4. Zn + CuSO4 ZnSO4 + Cu Zn is a reducing agent whereas Cu 2+ is an oxidizing agent Example 5. 2 Na + Cl2 2NaCl 2 Na 2 Na+ + 2e Cl2 + 2e 2Cl [Oxidation] Na is a reducing agent whereas Cl2 is an oxidizing agent. Example 6. H2 S is a reducing agent whereas SO2 is an oxidizing agent. Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) CHEMICAL REACTIONS AND EQUATIONS Page # 59 Memory Tip Reduction reaction Oxidation reaction Combination reaction Chemical Reaction Double displacement reaction Decomposition reaction Displacement reaction EFFECTS OF OXIDATION IN EVERYDAY LIFE Oxidation has damaging effect on metals as well as on food. The damaging effect of oxidation on metals is studied as corrosion and that on food is studied as rancidity. Thus there are two common effects of oxidation reactions are as (I) (I) Corrosion of metals (II) Rancidity of food Corrosion of metals :– Corrosion is the process of deterioration of metals as a result of its reaction with air, moisture and acids. (Present in environment) surrounding it. The corrosion causes damage to buildings, bridges, ships and many other articles especially made of iron. Rust : Iron corrode readily when exposed to moisture and gets covered with a brown flaky substance called rust. It is called rusting of iron, Rust is a hydrated Iron (III) oxide. [Fe2O3 · 2H2O] Oil Iron nail Iron nail Iron nail Tap water Rust Dry water Anhydrous calcium chloride (a) (b) Boiled water (c) Rusting of iron takes place under the following conditions – (a) Presence of air (or oxygen) (b) Presence of water (or moisture) It has been observed that (c) Presence of impurities in the metal speed up the rusting process. Pure iron does not rust. (d) Presence of electrolytes in water also speeds up the process of rusting (e) The position of the metal in the electrochemical series determines the extent of corrosion. More the reactivity of the metal, there will be more possibility of the metal getting corroded. : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] Page # 60 CHEMICAL REACTIONS AND EQUATIONS Other examples of corrosion are – (i) Copper reacts with moist carbon dioxide in the air and slowly loses its shiny brown surface and acquires a green coating of basic copper carbonate. (ii) Silver articles become black after sometime when exposed to air because it reacts with sulphur to form a coating of silver sulphide. (iii) Lead or stainless steel lose their lusture due to corrosion. (iv) Unreactive metals such as Gold, Platinum, Palladium, Titanium etc. do not corrode. Prevention of Rusting. (II) 1. The iron articles should be painted. 2. The machine parts should be oiled and greased. 3. Galvanised iron pipes are used for water supply. 4. Iron can be coated with chromium to prevent rusting. Rancidity. The oxidation of oils or fats in food, resulting into a bad taste and bad smell is called rancidity. It is caused due to prolonged exposure of food in air. Oxygen present in air oxidise fats/oil present in food and form volatile substances, which have bad odour. Do You Know? Vitamin E and Vitamin C (Ascorbic acid) are the two antioxidants occuring in natural fats. Prevention of rancidity :– (i) Rancidity can be prevented by adding antioxidants to foods containing fats and oils. Antioxidants are reducing agents so when they are added to food it do not get oxidised easily and hence do not turn rancid. The two common anti oxidants are – (a) BHA (Butylated Hydroxy Anisole) (b) BHT (Butylated Hydroxy Toluene) (ii) Rancidity can be prevented by packaging fat and oil containing foods in nitrogen gas. (iii) It can be retarted by keeping food in refrigerator. (iv) It can also be retarded by storing food in air tight containers. (v) It can be retarded by storing foods away from light. Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) CHEMICAL REACTIONS AND EQUATIONS Page # 61 SOLVED PROBLEMS Ex.1 Translate the following statements into chemical equations and then balance them. (A) Hydrogen gas combines with nitrogen to form ammonia (B) Hydrogen sulphide gas burns in air to give water and sulphur dioxide. (C) Barium chloride reacts with aluminium sulphate to give aluminium chloride and a precipitate of barium sulphate. (D) Potassium metal reacts with water to give potassium hydroxide and hydrogen gas. Sol. (A) N2(g) + 3H2(g) (B) 2H2S + 3O 2 2NH3(g) 2H2O + 2SO2 from air (C) 3BaCl2(aq) + Al2(SO 4)3(aq) 2AlCl3(aq) + 3BaSO4(s) White ppt. (D) 2K(s) + 2H2O(l) Ex.2 2KOH + H2(g) Balance the following chemical equations. (A) HNO3 + Ca(OH)2 (B) NaOH + H2SO4 Sol. Ca(NO3)2 + H2O Na2SO4 + H2O (A) 2HNO3 + Ca(OH)2 (B) 2NaOH + H2SO 4 Ex.3 Ca(NO3)2 + 2H2O Na2SO4 + 2H2O Write the balanced chemical equations for the following reactions. (A) Calcium hydroxide + Carbon dioxide (B) Zinc + Silver nitrate Calcium carbonate + water Zinc nitrate + Silver (C) Aluminium + copper chloride Aluminium chloride + Copper (D) Barium chloride + Potassium sulphate Sol. (A) Ca(OH)2 + calcium CO2 carbon hydroxide dioxide (B) Zn + 2AgNO3 zinc silver nitrate (C) 2Al + aluminium 3CuCl2 copper chloride (B) BaCl2 + Barium sulphate + Potassium chloride. CaCO3 + H2O calcium carbonate Zn(NO3)2 + 2Ag zinc nitrate silver 2AlCl3 + aluminium 3Cu copper chloride K2SO 4 BaSO4 + 2KCl barium potassium barium potassium chloride sulphate sulphate chloride : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] Page # 62 Ex.4 CHEMICAL REACTIONS AND EQUATIONS Write the balanced chemical equation for the following and identify the type of reaction in each case (A) Potassium bromide(aq) + Barium iodide(aq) (B) Zinc carbonate (s) Zinc oxide (s) + Carbon dioxide(g) (C) Hydrogen(g) + Chlorine(g) Hydrogen chloride(g) (D) Magnesium(s) + Hydrochloridc acid(aq) Sol. Potassium iodide(aq) + Barium bromide(s) (A) 2KBr(aq) + BaI2(aq) Magnesium chloride(aq) + Hydrogen(g) 2KI(aq) + BaBr2(aq) This reaction is a double-displacement reaction. (B) ZnCO 3(s) ZnO(s) + CO2(g) This reaction is a decomposition reaction (C) H2(g) + Cl 2(g) 2HCl(g) [Combination Reaction] (D) Mg(s) + 2HCl(aq.) MgCl2(aq.) + H2(g) [Displacement Reaction] Ex.5 Why should a magnesium ribbon be cleaned before burning in air? Sol. Magnesium reacts with the constituent gases of the atmosphere to form various compounds which get deposited over its surface. The ribbon is cleaned before burning to remove the layer of these compounds so that pure magnesium can burn in air. Ex.6 In the refining of silver, the recovery of silver from silver nitrate solution involved displacement by copper metal. Write down the reaction involved. Sol. 2AgNO 3(aq) + Cu(s) 2Ag(s) + Cu(NO3)2(aq) (silver nitrate) (copper) (silver metal) (copper(II) nitrate) Ex.7 A shiny brown coloured element 'X' on heating in air becomes black in colour. Name the element 'X' and the black coloured compound formed. Sol. An element on heating in air changes in its oxide. The brownish element which forms black oxide is copper. So, Name of the element Copper (Cu) Name of black compound: Copper(II) oxide, (CuO) Reaction + 2Cu(s) O2(g) copper (brown) from air Heat 2CuO(s) copper(II) oxide (black) Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) CHEMICAL REACTIONS AND EQUATIONS Page # 63 Ex.8 What happens chemically when quick lime is added or water ? Sol. Calcium hydroxide (or slaked lime) is formed accompanied by a hissing sound. So much heat is evolved during the reaction that the reaction mixture starts boiling. The chemical equation for the reaction is : CaO(s) + H 2O(aq) Ca(OH)2(s) + heat (Quick lime) Ex.9 (Slaked lime) What is an oxidation reaction ? Identify in the following reactions : (i) the substance oxidised ZnO + C Sol. (ii) the substance reduced. Zn + CO Oxidation involves the addition of oxygen or the removal of hydrogen in a chemical reaction while reduction involves the addition of hydrogen or removal of organ. In the given reaction : (i) Carbon (C) is oxidised to carbon monoxide (CO). (ii) Zinc oxide (ZnO) is reduced to zinc (Zn) Ex.10 Which gas is evolved when dilute hydrochloric acid reacts with zinc ? Write the molecular formula of the gas. Sol. Hydrogen gas is evolved. Its molecular formula is H 2. Ex.11 State any two observation in an activity which may suggest that a chemical reaction has taken place. Give examples in support of your answer. Sol. (i) In a tube take small amount of solid sodium carbonate (Na 2CO3). To this add a few drops of hydrocloric acid. (ii) A colourless and odourless gas will evolve which shows that a chemical reaction has taken place. The gas will turn lime water milky when passed through it. : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] Page # 64 CHEMICAL REACTIONS AND EQUATIONS Ex.12 Identify the type of reaction in the following examples : (i) Na 2SO4(aq) + BaCl2(aq) (ii) Fe(s) + CuSO 4(aq) (iii) 2H2(g) + O2(g) Sol. BaSO 4(s) + 2NaCl(aq) FeSO4(aq) + Cu(s) 2H 2O( ) (i) It is an example of double displacement reaction. (ii) It is an example of displacement reaction. (iii) It is an example of combination reaction. Ex.13 Solid calcium oxide was taken in a container and water was added slowly to it (i) State two observations made in the experiment. (ii) Write the name of the chemical formula of the product. Sol. (i) Water will start boiling and hissing noise will be produced. (ii) Calcium hydroxide (slaked lime) will be formed. CaO(s) + H 2O(aq) Ca(OH)2(s) + heat Calcium oxide Calcium hydroxide Ex.14 A house wife wanted her house to be white washed. She bought 10 kg of quick lime from the market and dissolved in 30 litres of water. On adding lime to water, she noticed that the water started boiling even when it was not being heated. Give reason for her observation. Write the corresponding equation and name the product formed. Sol. A supension of slaked lime also called calcium hydroxide is formed when water is added to quick lime. CaO(s) + H 2O( ) Ca(OH)2(s) + heat (Slaked lime) Since the reaction is highly exothermic, the solution started although it was not being heated. The suspension of slaked lime is allowed to cool for sometime, preferably overnight. It is then decanted and the liquid obtained is used for white washing. Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) CHEMICAL REACTIONS AND EQUATIONS Page # 65 NCERT QUESTIONS WITH SOLUTIONS Q.1 Why should a magnesium ribbon be cleaned before it is burnt in air? Ans. Magnesium is an extremely reactive metal. When stored, it reacts with oxygen to form a layer of magnesium oxide on its surface. This layer of magnesium oxide is quite stable and prevents further reaction of magnesium with oxygen. The magnesium ribbon is cleaned by sand paper for removing this layer so that the underlying metal can be exposed to air. Q.2 Write the balanced equation for the following chemical reactios. (i) Hydrogen + Chlorine Hydrogen chloride (ii) Berium chloride + Aluminium sulphate (iii) Sodium + Water Ans. (i) H2 (g) + Cl2(g) 2HCl(g) (ii) 3BaCl2(aq) + Al2 (SO4 )3(aq) (iii) 2Na(s) + 2H2O( ) Q.3 Barium sulphate + Aluminium chloride Sodium hydroxide + Hydrogen 3BaSO 3(s) + 2AlCl3 (aq) 2NaOH(aq) + H2 (g) Write a balanced chemical equation with state symbols for the following reactions. (i) Solutions of barium chloride and sodium sulphate in water react to give insoluble barium sulphate and the solution of sodium chloride. (ii) Sodium hydroxide solution (in water) reacts with hydrochloric acid solution (in water) reacts with hydrochloric acid solution (in water) to produce sodium chloride solution and water. Ans. (i) BaCl2(aq) + Na2 SO4 (aq) (ii) NaOH(aq) + HCl(aq) Q.4 BaSO 4(s) + 2NaCl(aq) NaCl(aq) + H2 O( ) A solution of a substance 'X' is used for white washing. (i) Name the substance 'X' and write its formula. Ans. (ii) Write the reaction of the substance 'X' with water. (i) The substance 'X' is calcium oxide. Its chemical foluma is CaO. (ii) Calcium oxide reacts vigorously with water to form calcium hydroxide (slaked lime). CaO(s) + Calcium oxide (Quick lime) H2O( ) Ca(OH)2 (aq) Water Calcium hydroxide (Slaked lime) Q.5 Why is the amount of gas collected in one of the test tubes is double of the amount collected in the other? Name this gas. Ans. Water (H2 O) contains two parts hydrogen and one part oxygen. Therefore, the amount of hydrogen and oxygen produced during electrolysis of water is in a 2 : 1 ratio. During electrolysis, since hydrogen goes to one test tube and oxygen goes to another, the amount of gas collected in one of the test tubes is double of the amount collected in the other. Q.6 Why does the colour of copper sulphate solution change when an iron nail is dipped in it? Ans. When an iron nail is placed in a copper sulphate solution, iron displaces copper from copper sulphate solution forming iron sulphate, which is green in colour. Fe(s) + Iron CuSO4 (aq) Copper sulphate FeSO 4(aq) + Iron sulphate (Blue colour) (Green colour) Cu(s) Copper Therefore, the blue colour of copper sulphate solution fades and green colour appears. : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] Page # 66 CHEMICAL REACTIONS AND EQUATIONS Q.7 Give an example of a double displacement reaction other than the one given in Activity 1.10. Ans. Sodium carbonate reacts with calcium chloride to form calcium carbonate and sodium chloride. Na2 CO3(aq) + CaCl2(aq) CaCO3 (s) + 2NaCl(aq) Sodium Calcium Calcium Sodium carbonate chloride carbonate chloride In this reaction, sodium carbonate and calcium chloride exchange ions to form two new compounds. Hence, it is a double displacement reaction. Q.8 Ans. Identify the substances that are oxidised and the substances that are reduced in the followiing reactions. (i) 4Na(s) + O2(g) 2Na2 O(s) + O2 (g) (ii) CuO(s) + H2(g) Cu(s) + H2O( ) (i) Sodium (Na) is oxidised as it gains oxygen and oxygen gets reduced. (ii) Copper oxide (CuO) is reduced to copper (Cu) while hydrogen (H2 ) gets oxidised to water (H2 O). Q.9 Which of the statements about the reaction below are incorrect? 2PbO(s) + C(s) 2Pb(s) + CO2(g) (a) Lead is getting reduced. (b) Carbon dioxide is getting oxidised. (c) Carbon is getting oxidised. (d) Lead oxide is getting reduced. (1) (a) and (b) Ans. (1) (a) and (b) Q.10 Fe 2O 3 + (2) (a) and (c) (3) (a), (b) and (c) 2Al + Al2O3 (4) all 2Fe The above reaction is an example of a (1) Combination reaction. (2) Double displacement reaction. (3) Decomposition reaction. (4) Displacement reaction. Ans. (4) The given reaction is an example of a displacement reaction. Q.11 What happens when dilute hydrochloric add is added to iron filings? Tick the correct answer. (1) Hydrogen gas and iron chloride are produced. (2) Chlorine gas and iron hydroxide are produced. (3) No reaction takes place. (4) Iron salt and water are produced. Ans. (1) Hydrogen gas and iron chloride are produced. The reaction is as follows: Fe(s) + 2HCl(aq) FeCl2 (aq) + H2 Q.12 What is a balanced chemical equation? Why should chemical equations be balanced ? Ans. A reaction which has an equal number of atoms of all the elements on both sides of the chemical equation is called a balanced chemical equation. The law of conservation of mass states that mass can neither be created nor destroyed. Hence, in a chemical reaction, the total mass of reactants should, be equal to the total mass of the products. It means that the total number of atoms of each element should be equal on both sides of a chemical equation. Hence, it is for this reason that chemical equations should be balanced. Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) CHEMICAL REACTIONS AND EQUATIONS Q.13 Page # 67 Translate the following statements into chemical equations and then balance them. (a) Hydrogen gas combines with nitrogen to form ammonia. (b) Hydrogen sulphide gas burns in air to give water and sulphur dioxide. (c) Barium chloride reacts with aluminium sulphate to give aluminium chloride and a precipitate of barium sulphate. (d) Potassium metal reacts with water to give potassium hydroxide and hydrogen gas. Ans. (a) 3H2 (g) + N2 (g) 2NH3(g) (b) 2H2 S(g) + 3O2 (g) 2H2 O( ) + 2SO2 (g) (c) 3BaCl2(aq) +Al2 (SO4 )3 (aq) (d) 2K(s) + 2H2O( ) Q.14 2KOH(aq) + H2 (g) Balance the following chemical equations. (a) HNO3 + Ca(OH)2 Ca(NO3 )2 + H2 O (b) NaOH + H2SO 4 Ans. Na2 SO4 + H2 O (c) NaCl + AgNO3 AgCl + NaNO3 (d) BaCl2 + H2SO4 BaSO 4 + HCl (a) 2HNO 3 + Ca(OH)2 Ca(NO3 )2 + H2 (g) (b) 2NaOH + H2 SO4 Na2 SO4 + 2H2O (c) NaCl + AgNO3 AgCl + NaNO3 (d) BaCl2+ H2 SO4 Q.15 2AlCl3 (aq) + 3BaSO4 (s) BaSO4 + 2HCl Write the balanced chemical equations for the following reactions. (a) Calcium hydroxide + Carbon dioxide (b) Zinc + Silver nitrate Zinc nitrate + Silver (c) Aluminium + Copper chloride Alumiium chloride + Copper (d) Barium chloride + Potassium sulhate Ans. (a) Ca(OH) 2 + CO2 Barium sulphate + Potassium chloride CaCO 3 + H2O (b)Zn + 2AgNO3 Zn(NO3)2 + 2Ag (c) 2Al + 3CuCl2 2AlCl3 + 3Cu (d) BaCl2 + K2 SO4 Q.16 Calcium carbonate + Water BaSO4 + 2KCl Write the balanced chemical equation for the following and identify the type of reaction in each case. (a) Potassium iodide(aq) + Barium iodide(aq) (b) Zinc carbonate(s) Zinc oxide(s) + Carbon dioxide(g) (c) Hydrogen(g) + Chlorine(g) Hydrogen chloride(g) (d) Magnesium(s) + Hydrochloric acid(aq) Ans. (a) 2KBr(aq) + BaIz (aq) (b) ZnCO 3(s) Carbon dioxide(g) Magnesium chloride(aq) + Hydrogen(g) 2KI(aq) + BaBr2 (s); Double displacement reaction ZnO(s) + CO2 (g) ; Decomposition reaction (c) H2 (g) + Cl2(g) (d) Mg(s) + 2HCl(aq) 2HCl(g) ; Combination reaction MgCl2(aq) + H2(g) ; Displacement reaction : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] Page # 68 CHEMICAL REACTIONS AND EQUATIONS Q.17 What does one mean by exothermic and endothermic reactions? Give examples. Ans. Chemical'reactions that release energy in the form of heat, light, or sound are called exothermic reaction. Example: Mixture of sodium and chlorine to yield table salt Na(s) + 1 Cl (g) 2 2 NaCl(s) + 411 kL of energy In other words, combination reactions are exothermic. Reactions that absorb energy or require energy in order to proceed are called endothermic reactions. For example: In the process of photosynthesis, plants use the energy from the sun to convert carbon dioxide and water to glucose and oxygen. Sunlight 6CO 2(g) + 6H2 O( ) C6 H12O6 (aq) + 6)2 (g Glucose Q.18 Why is respiration considerd an exothermic reaction ? Explain. Ans. Energy is required to support life. Energy in our body is obtained from the food we eat. During digestion, large molecules of food are broken down into simpler substances such as glucose. Glucose combines with oxygen in the cells and provides energy. The special name of this combustion reaction is respiration. Since energy is released in the whole process, it is an exothermic process. C6 H12O6(aq) + Glucose 6O2(g) 6CO2 (g) Oxygen Carbon dioxide + 6H2O( ) + Energy Water Q.19 Why are decomposition reactions called the opposite of combination reactions? Write equations for these reactions. Ans. Decomposition reactions are those in which a compound breaks down to form two or more substances. These reactions require a source of energy to proceed. Thus, they are the exact opposite of combination reactions in which two or more substances combine to give a new substance with the release of energy. Decomposition reaction: AB + Energy 2H2 O( ) Elect rolysis 2H2 (g) + O2 (g) Combination reaction: A + B 2H2 (g) + O2 (g) A +B AB + Energy 2H2 O( ) + Energy Q.20 Write one equation each for decomposition reactions where energy is supplied in the form of heat, light or electricity. Ans. (a) (b) Thermal decomposition: 2FeSO4(s) Fe 2O3 (g) Ferrous sulphate Ferric oxide SO2 (g) + Sulphur dioxide SO 3(g) Sulphur trioxide Decomposition by light: 2AgCl(s) Ligh t Silver chloride (c) + 2Ag(s) + Silver Cl2(s) Chlorine Decomposition by electricity: 2Al2O3 (aq) Aluminium oxide Electricity 4Al(s) Aluminium + 3O 3(g) Oxygen Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) CHEMICAL REACTIONS AND EQUATIONS Page # 69 Q.21 What is the difference betuJeen dispiacemen[ and double displacement reactions? Write equations for these reactions. Ans. In a displacement reaction, a more reactive element replaces a less reactive element from a compound. A + BX AX + B; where A is more reactive than B In a double displacement reaction, two atoms or a group of atoms shift places to form new compounds. AB + CD AD + CB For example: Displacement reaction: CuSO 4(aq) + Zn(s) ZnSO 4(aq) + Cu(s) Double displacement reaction: Na2 SO4 (aq) + BaCl2 (aq) BaSO4(s) + 2NaCl(aq) Q.22 In the refining of silver, the recovery of silver from silver nitrate solutior. involved displacement by copper metal. Write down the reaction involved. Ans. 2AgNO 3(aq) + Silver nitrate Cu(s) Cu(NO 3)2(aq) + 2Ag(s) Copper Copper nitrate Silver Q.23 What do you mean by a precipitation reaction? Explain by giving examples. Ans. A reaction in which an insoluble solid (called precipitate) is formed is called a precipitation reaction. For example: Na2 CO3(aq) + Sodium carbonate CaCl2 (aq) CaCO3 (s) Calcium chloride Calcium carbonate + 2NaCl(aq) Sodium chloride In this reaction, calcium carbonate is obtained as a precipitate. Hence, it is a precipitation reaction. Another example of precipitation reaction is: Na2 SO4(aq) + BaCl2(aq) BaSO4(s) + 2NaCl(aq) Sodium sulphate Barium chloride Barium sulphate Sodium chloride In this reaction, barium sulphate is obtained as a precipitate. Q.24 Explain the following in terms of gain or loss of oxygen with two examples each. (a) Oxidation Ans. (b) Reduction (a) Oxidation is the gain of oxygen. For example: CO 2 + H 2 (i) CO + H2O Addition of oxygen-oxidation (ii) 2Cu + O2 CuO 2 Gain of oxygen - oxidation In equation (i), H2 is oxidized to H2O and in equation (ii), Cu is oxidised to CuO. (b) Reduction is the loss of oxygen. For example: CO 2 + H 2 (i) CO + H2O Removal of oxygen - reduction (ii) CuO + H2 Cu + H2O Loss of oxygen - reduction in equation (i), CO2 is reduced to CO and in equation (ii), CuO is reduced ro Cu. : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] Page # 70 Q.25 CHEMICAL REACTIONS AND EQUATIONS A shiny brown-cloured element 'X' on heating in air becomes black in colour. Name the element 'X' and the black coloured compound formed. Ans. ‘X’ is copper (Cu) and the black-coloured ocmpound formed is copper oxide (CuO). The equation of the reaction involved on heating copper is given below. 2Cu + Heat O2 2CuO (Shiny brown in colour) (Black in colour) Q.26 Why do we apply paint on iron articles? Ans. Iron articles are painted because it prevents them from rusting. When painted, the contact of iron articles from moisture and air is cut off. Hence, rusting is prevented. Their presence is essential for rusting to take place. Q.27 Oil and fat containing food items are flushed with nitrogen. Why? Ans. Nitrogen is an inert gas and does not easily read with these substances. On the other hand, oxygen reacts with food substances and makes them rancid. Thus, bags used in packing food items are flushed with nitrogen gas to remove oxygen inside the pack. When oxygen is not present inside the pack, rancidity of oil and fat containing food items is avoided. Q.28 Explain the following terms with one example each. (a) Corrosion Ans. (b) Rancidity (a) Corrosion: Corrosion is defined as a process where materials, usually metals, deteriorate as a result of a chemical reaction with air, mOisture, chemicals, etc. For example, iron, in the presence of moisture, reacts with oxygen to form hydrated iron oxide. 4Fe + 3O2 + nH2O 2Fe2O3 .nH2O Hydrated iron oxide This hydrated iron oxide is rust. (b) Rancidity: The process of oxidation of fats and oils that can be easily noticed by the change in taste and smell is known as rancidity. For example, the taste and smell of butter changes when kept for long. Rancidity can be avoided by: (1) Storing fooo in air tight containers (2) Storing fooo in refrigerators (3) Adding antioxidants (4) Storing food in an environment of nitrogen Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) CHEMICAL REACTIONS AND EQUATIONS EXERCISE – I Page # 71 BOARD PROBLEMS Type I- Very Short Answer Questions Q.1 Why does not a wall immediately acquire a white Q.13 lead nitrate crystals are heated in a dry test tube? colour when a coating of slaked lime is applied on it? [C.B.S.E. 2010] Q.14 Q.2 What is ruet? Q.3 What is the difference b/w the following 2 Q.15 [C.B.S.E. 2011] (a) Mg + 2HCl In the reaction MnO2 + 4HCl MnCl2 + 2H2O Complete the equation:- [C.B.S.E. 2010] Fe 2O3 + 2Al MgCl2 + H 2 (b) NaOH + HCl NaCl + H 2O Q.16 Q.5 What is the role of oxidising agent in a reaction? [C.B.S.E. 2010] Q.6 What is meant by a skeletal chemical equation? [C.B.S.E. 2010] Q.7 On what basis is a chemical equation balanced? [C.B.S.E. 2010] Q.8 Balance following chemical equation:Heat Take a small amount of calcium oxide or quick lime in a beaker and slowly add water to this. Is there any change in temperature? Suggest 2 ways to check the rancidity of food articles. [C.B.S.E. 2011, 2012] Pb(NO3)2(s) [C.B.S.E. 2010] + Cl 2. Identify which one is reduced and which one is oxidized? [C.B.S.E. 2010] reactions? Q.4 What is the brown coloured gas evolved when [C.B.S.E. 2010, 2011] Q.17 Which chemical process is used for obtaining a metal from its oxide? [C.B.S.E. 2010] Type II - Short Answer Type Questions Q.18 Write balance chemical equation “during respiration combustion of glucose takes place producing carbon dioxide water and energy”. Q.19 A zinc rod is left for nearly 20 minutes in a copper sulphate solution. What change would you observe in zinc rod? Pbo(s) + NO2(g) + O2(g) [C.B.S.E. 2009] Q.20 Name a reducing agent that can be used to obtain manganese from manganese dioxide. Write balanced chemical equation for the reaction? [C.B.S.E. Delhi 2009] Q.21 Give reason, silver articles become black after sometime when exposed to air? Q.9 Writ e a balanced chemic al e quat ion to represent the following equation:- Iron reacts with stream to form Iron (II, III) oxide and Hydrogen gas.[C.B.S.E. Sample paper 2011] Q.10 Balance the following chemical equation. (i) FeCl2 + H 2S HCl + Fes (ii) HNO3 + Ca(OH)2 Ca(NO 3)2 + H 2O [C.B.S.E. 2008] Q.22 What is the role of catalyest in a chemical reaction? [C.B.S.E. 2007] What happens chemically when Quick lime is added to water? [C.B.S.E. 2010] Q.23 Name 2 salts which are used in black and white Q.11 Q.12 [C.B.S.E. 2008] photography? Give one example of each exothermic reaction and endothermic reaction? [C.B.S.E. 2010] Q.24 [C.B.S.E. 2010, 11] State the essential requriement for rusting? [C.B.S.E. 2013] : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] Page # 72 CHEMICAL REACTIONS AND EQUATIONS Type III- Long Answer Type Questions Q.25 Q.31 A brown substance “X” on heating in air forms When a water insoluble substance “X” is added a substance “Y”. When hydrogen gas is passed to dil. Hydrochloric acid, a colourless, odourless over heated “Y”. It again changes back into gas is evolved. When the gas is passed through “X”. lime water, it turns milky. Write the formula [C.B.S.E. 2010] (i) Name the substance X and Y. of gas evolved and balanced chemical equation of the reaction. (ii) Name the chemical processes occuring during both changes. Q.26 (a) Write one equation each for decomposition (iii) Write chemical equations? reaction when energy is supplied in the form of (i) Heat (ii) Light. (b) Account for following:- Q.32 (i) Paint is applied on Iron articles. Explain why:- [C.B.S.E. 2011] (i) Respiration is an Exothermic reaction. (ii) Oil and fat containing food items are flushed with nitrogen. [C.B.S.E. 2011] (ii) When blue salt of CuSO4 is heated it becomes colourless? Q.27 A green coloured hydrated salt of Iron loses its water of crystallisation and smell of burning sulphur is given. Identify the salt and write chemical equation. [C.B.S.E. 2011] Q.33 In electrolysis of water [C.B.S.E. 2012] (i) Name the gas collected at the cathod and anode respectively. Q.28 (a) Why cannot a chemical change be normally reversed? (ii) Why is the volume of one gas collected (b) Why is it always essential to balance a Name this gas? at one electrode double that at the other? chemical equation? (c) Why do diamond and graphite, 2 forms of carbon evolve different amounts heat on combustion? (iii) How will you test the evolved gases? Q.34 (d) Why does milkness disappear when CO 2 (i) CuSO4 + Zn is passed throug lime water in excess? X + YSO4 XSO4 + Y Y + XSO4 No reaction (iii) NH4Cl (a) Can a combination reaction be an oxidation reaction? [C.B.S.E. 2011] Heat BaSO4 + ZnCl2 NH3 + HCl (iv) HgCl2 + SnCl2 HgCl2 + SnCl4 (v) 2KClO3 Al2O4 + 2Fe (vi) 2All + Fe2O3 and of the 2 elements “X” and “Y” which is more reactive and why? [C.B.S.E. 2011] Q.30 ZnSO4 + Cu (ii) BaCl2 + ZnSO4 (e) Can rusting of Iron take place in distilled water? Q.29 Identify the type of reaction[C.B.S.E. 2012] Q.35 Al2O3 + 2Fe Balance the following equation [C.B.S.E. 2008] (i) H2SO4(aq.) + NaOH(aq.) Na2SO4(aq.) + H2O (l) (b) How will you test whether the gas evolved in a reaction is hydrogen? (ii) KCN(aq.) + H2SO4(aq.) K2SO4(aq.) + HCN(g) (c) Why does copper not evolve hydrogen on reacting with dilute sulphuric acid? (iv) Al2O3 + H 2SO4 (iii) HgCl2 + SnCl2 (v) Al2(SO 4)3 + NaOH Hg 2Cl2 + SnCl4 Al2(SO4)3 + H 2SO4 Al(OH)3 + Na2SO4 Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) CHEMICAL REACTIONS AND EQUATIONS Q.36 Page # 73 Identify the type of reaction (i) 2H2O Elect rolysis Q.41 2H2 + O 2 2gm of FeSO 4 Crystals were heated in a hard glass test tube and observations recorded. (a) What was the successive colour change? (ii) 2NH3 + H2SO4 (NH4)2SO4 (b) Identify liquid droplets collected on cooler (iii) AgNO 3 + Nacl NaNO3 + Agcl part of test tube. (iv) Zn(s) + 2AgNO3 (aq.) Zn(NO3)2(aq.) + 2Ag(s) (v) Ni(NO3)2(aq.) + 2NaOH(aq.) Ni(OH)2 (c) What type of odour is observed on heating FeSO 4 Crystals? + 2NaNO3(aq.) (vi) MgO(s) + C(s) CO(g) + Mg(s) Type IV- Thinking Based/Skill Based Questions Q.37 The marble statues slowly get carroded when kept in open for a long time. Give suitable explanation? Q.38 (a) Based on reactions given below, arrange the metals invloved in these reactions in decreasing order of reactivity. Give suitable explanation. (i) Zn + CuSO 4 (ii) Cu + 2AgNO 3 ZnSO4 + Cu Cu (NO3)2 + 2Ag (i) Zn + FeSO4 ZnSO 4 + Fe (ii) FE + CuSO4 FeSO 4 + Cu (b) What is the nature of reactions? Q.39 A, B and C are 3 elements which undergo chemical reactions according to following equations:A 2O3 + 2B 3CSO 4 + 2B 3CO + 2A B2O3 + 2A B2(SO4)3 + 3C A2O3 + 3C Ans. Following Questions (a) Which element is more reactive? (b) Which element is least reactive? Q.40 You are given following materials:(i) Marble chips (ii) Dil. HCl acid (iii) zinc granules Identify type of reaction when marble chips and zinc granules are added separately to acid taken in two tubes. Write chemical equation in each case. : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] Page # 74 CHEMICAL REACTIONS AND EQUATIONS EXERCISE – II Q.1 OLYMPIAD QUESTIONS The example of a physical change is Q.7 (A) milk is left at room temperature in summers (B) an Iron is heated (C) Iron tawa is left emposed to humid air (D) Food is cooked Q.2 Which of the following is/are exothermic processes (ii) In beaker “A” and “B” exothermic process has occurred. (iii) In beaker A and B endothermic process has occurred. (iv) In beaker “C” endothermic process has occured. (A) (i) and (ii) (B) (ii) and (iii) (C) (iii) and (iv) (D) (ii) and (iv) (i) Sublimation of NH4Cl (ii) Quick lime is added to water (iii) Evaporation of water (iv) Dilution of an acid Q.3 (A) (i) and (ii) (B) (ii) and (iii) (C) (iii) and (iv) (D) (ii) and (iv) Fe 2O3 + 2Al Q.8 Example of a chemical change is (A) fermentation of rice (B) breathing (C) curdling of milk (d) all of above Q.9 Which of the following is a double displacement reaction? Al2O 3 + 2Fe, is a (i) combination rxn (ii) Displacement Rxn (iii) redox Rxn (iv) Double displacement Rxn Q.4 (A) (i) and (ii) (B) (ii) and (iii) (C) (iii) and (iv) (D) (ii) and (iv) (A) (B) (C) (D) Silver Bromide, On expourse to sunlight turns grey due to (A) Formation of silver by its decomposition Which of the following is not a decomposition reacion? (A) CaCO3 CaO + CO2 (B) 2KClO3 2KCl + 3O 2 (C) Digestion of food in the body (D) H2 + Cl2 2HCl Q.11 Which of the following represent a double displacement reaction? (A) 2H2 + O 2 2H2O (B) 2Mg + O2 2MgO (C) AgNO3 + NaCl AgCl + NaNO3 (D) H2 + Cl2 2HCl Q.12 Which of the following is a displacement reaction? (A) CaCO3 CaO + CO2 (B) CaO + 2HCl CaCl2 + H 2O (C) Sublimation of silver Bromide (D) Decomposition of bromine gas from silver bromide Q.6 Water on electrolysis decomposes to hydrogen and oxygen. the mole ratio of H 2 and O2 is (A) 1 : 2 (B) 1 : 1 (C) 2 : 1 (D) 4 : 1 Which of the following gases used for storage of fresh sample of an oil for a long time (A) Nitrogen and Oxygen (B) CO 2 and Helium (C) CO2 and oxygen (d) Nitrogen and Helium 2H2 + O2 2H2O FeSO4 + Zn ZnSO4 + Fe CH4 + 2O2 2H2O + CO2 Na2SO 4 + Bacl2 BaSO4 + 2Nacl Q.10 (B) Oxidation of silver Bromide Q.5 50 ml of water was taken in a beaker A, B and C. A small amount of CuSO4, NaOH and NaCl were added to beaker A, B and C respectively. The temperature of beaker A and B increased where in beaker c decreases. The correct statement (s) is/are (i) In beaker “C” exothermic process has occurred. (C) Fe + CuSO4 (D) NaOH + HCl FeSO4 + Cu NaCl + H2O Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) CHEMICAL REACTIONS AND EQUATIONS Q.13 The reaction H 2 + Cl2 2HCl is a – (A) Decomposition reaction Page # 75 Q.20 Conversion of CaCO3 in to CaO as per following reaction is an example of – CaCO3 CaO + CO2 (A) Decomposition reaction (B) Reduction reaction (C) Oxidation reaction (D) None of these Q.21 Fe 2O3 + 2Al (B) Combination reaction (C) Double displacement reaction (D) Displacement reaction Q.14 Which of the following is a decomposition reaction? (A) NaOH + HCl is an example of – (B) NH4CNO (C) 2KClO 3 2KCl + 3O2 (B) Double displacement reaction (D) H2 + I2 Q.15 (A) Combination reaction 2HI (C) Decomposition reaction (D) Displacement reaction Which of the following statement is incorrect? (A) In oxidation, oxygen in added to a substance. (B) In reduction, Hydrogen is added to a substance. Q.16 Q.22 (A) SO2 (B) H2S (D) Reducing agent is oxidized. (C) H2O (D) S Which of the following is a combustion reaction– Q.23 (C) Burning of petrol What happens when dil hydrochloric acid is added to iron fillings? (D) None of these (B) Chlorine gas and Iron hydroxide are produced. Which of the following is a redox reaction? (C) NO reaction takes place (A) CaCO3 (D) Iron salt and water are produced. CaO + CO2 (B) H2 + Cl2 (C) CaO + 2HCl 2HCl (D) NaOH + HCl CaCl2 + H2O Q.24 NaCl + H2O Which statement is correct about the following reaction? ZnO + CO When Iron nails are added to an aquous solution of copper sulphate, a chemical change occurs, which of the following is not true about this reaction? (A) Blue colour of the solution fades. (B) Iron nails becomes brownish in colour. Zn + CO2 (A) ZnO is being oxidized (C) It is a displacement reaction. (B) CO is being reduced (D) Iron nails dissolves completly. (C) CO 2 is being oxidized (D) ZnO is being reduced Q.19 2H2O + 3S the (A) Hydrogen gas and Iron chloride are produced. (B) Melting of wax Q.18 In reaction SO2 + 2H2S reducing agent is – (C) Oxidizing agent in oxidized. (A) Boiling of water Q.17 Al2O3 + 2Fe This reaction NaCl + H2O H2NCONH2 The reaction C + O 2 CO2 + Heat is a – (A) Combination reaction (B) Oxidation reaction (C) Exothermic reaction (D) All of the above Q.25 Pot assium rea ct s wi th bromine t o form potassium bromide. [NTSE] (A) 2K + Br 2KBr (B) K2 + Br2 2 KBr (C) K 2 + Br2 (D) K2 +Br2 KBr2 : 0744-2209671, 08003899588 | url : www.motioniitjee.com, KBr : [email protected] Page # 76 Q.26 Q.27 CHEMICAL REACTIONS AND EQUATIONS A silver spoon on exposure to air reacts with the sulphur present in air to give a black material called ______. [NTSE] (A) Silver oxide (B) Silversulphide (C) Tarnish (D) Coal tar In the decomposition of sulphates by heat, which is the gas formed exclusively along with the metal oxide? Q.28 Q.33 The rate of a chemical reaction is altered by ______. [NTSE] (A) nature of reactants (B) changing temperature (C) using a catalyst (D) all the above Q.34 Which of the following is an example of a reversible reaction? [NTSE] [NTSE] (A) SO2 (B) SO3 (C) SO3 and SO2 (D) H2SO3 [NTSE] Q.36 When hydrogen sulphide gas is passed through a blue solution of copper sulphate, a black precipitate of copper sulphide is obtained and the sulphuric acid so formed remains in the solution. The reaction is an example of (A) a combination reaction [NTSE] (B) a displacement reaction (C) a decomposition reaction (D) a double decomposition reaction Q.37 In the following equations Na2CO3 + xHCl 2NaCl + CO2 + H2O the value of x is: [NTSE] (A) 1 (B) 2 (C) 3 (D) 4 Q.38 Combustion of fuel is (A) displacement reaction (B) double displacement reaction (C) oxidation reaction (D) isomerisation reaction Q.39 The reaction between acid and base to form salt and water is an example of [NTSE] (C) Liquefaction of gases to liquids (D) Decay of matter Which among the following reactions are exothermic in nature? [NTSE] (A) Bond formation (B) Bond breaking (C) Combustion of carbon (D) Both (A) and (C) The reaction P4 + 3O2 (A) synthesis reaction 2P2O3 is ____. [NTSE] (B) displacement reaction (C) decomposition reaction (D) combustion Q.32 CaO + CO2 AgCl + KNO3 NaCl + H 2O Which of the following reaction will not take place? [NTSE] (A) Zn + FeSO4 ZnSO4 + Fe (B) 2Kl + Cl2 2KCl + I2 (C) Zn + MgSO4 ZnSO4 + Mg (D) Mg + CuSO4 MgSO4 + Cu (B) Vapourisation of liquids to gases Q.31 (B) CaCO3 (C) AgNO3 + KCl (D) NaOH + HCl Fe3O4 + 4H2 Q.35 (A) Melting of solids to liquids Q.30 1237 K Which among the following is not a physical change? Q.29 (A) 3Fe + 4H2O PbO 2 + 4HCl PbCl2 + 2H 2O + Cl2. The substance undergoing oxidation is _____. [NTSE] (A) lead dioxide (B) hydrochloric acid (C) hydrogen (D) lead chloride In the equation FeCl 3 + xNaOH yNaCl + Fe(OH) 3, the value of x and y, respectively, are _____. [NTSE] (A) 3 and 1 (B) 3 and 3 (C) 2 and 3 (D) 3 and 4 [NTSE] (A) decomposition reaction (B) combination reaction (C) displacement reaction (D) double displacement Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) CHEMICAL REACTIONS AND EQUATIONS Q.40 Page # 77 Which of the following reactions are exothermic in nature? Q.47 [NTSE] FeSO4 + Cu (A) Combustion of Carbon FeSO4 + Zn ZnSO4 + Fe (B) Bond breaking (A) Zn is most reactive, Fe is least reactive (B) Fe is most reactive and cu is least reactive (C) Zn is most reactive and cu is least reactive (D) Cu is most reactions, Fe is least reactive (D) Both (A) and (C) Which of the following changes is not a physical change? [NTSE] Q.48 Choose the incorrect statement. [NTSE] (A) physical change is reversible (A) glowing of filament in bulb (B) physical change results information of new substances (B) combustion (C) chemical change is permanent (C) boiling of water (D) physical change is accompanied by energy change (D) sublimation Q.42 [NTSE] CuSO 4 + Fe (C) Bond formation Q.41 Consider the reactions The substance that looses electrons is called as: [NTSE] (A) oxidizing agent (B) reducing agent (C) catalyst (D) none of above Q.49 Which of following is fast reaction? [NTSE] (A) reaction between H 2 and O2 to form H2O (B) reaction between acid and base to form salt and water (C) hydrolysis of ester (D) hydrolysis of sugar to glucose Q.43 The process of reduction involves [NTSE] (A) removal of hydrogen (B) gain of electrons (C) addition of oxygen (D) loss of electrons Q.44 In the reaction H2S + Cl2 oxidizing agent is: (A) H2S (C) HCl Q.45 2HCl + S, the [NTSE] (B) Cl2 (D) S Select Redox reaction from the following (A) Zn + CuSO4 (B) CaO + 2HCl ZnSO4 + Cu [NTSE] CaCl2 + H 2O (C) NaOH + 2HCl NaCl2 + H 2O (D) CaCO3 CaO + CO2 Q.46 Which of the following reactins is not correct? [NTSE] (A) 2AgNO 3 + Cu Cu(NO3)2 + 2Ag (B) Cl 2 + 2KI 2KCl + I2 (C) FeSO4 + Cu CuSO4 + Fe (D) CuSO4 + Zn ZnSO4 + Cu ANSWER KEY 1. C 2. D 3. B 4. A 5. C 6. D 7. D 8. D 9. D 10. D 11. C 12. C 13. C 14. C 15. C 16. C 17. B 18. D 19. D 20. A 21. D 22. B 23. A 24. D 25. A 26. B 27. B 28. D 29. D 30. D 31. B 32. B 33. D 34. A 35. C 36. D 37. B 38. C 39. D 40. D 41. B 42. B 43. B 44. B 45. A 46. C 47. C 48. B 49. B : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] Page # 78 NUTRITION 1. NUTRITION The whole process by which an organism obtains its food is referred to as nutrition. NUTRITION It is the method of obtaining nutrients from the environment. It can be defined as the process by which the organism ingests, digests, absorbs, transports and utilises nutrients and disposes off their end products. NUTRIENT The different component of food that have distinct functions like providing energy. materials for body building, maintenance & regulation of metabolism are called nutrient. For exmple-Proteins, Minerals, Vitamin, Carbohydrates, fats. MODES OF NUTRITION Mode of nutrition Autotrophic nutrition Heterotrophic nutrition Holozoic nutrition Saprotrophic nutrition Pasrsitic nutrition (a) Autotrophic Nutrition In this type of nutrition, organisms synthesise the organic materials they require from inorganic sources. All green plants are autotrophic and use light as a source of energy for the synthesis. Autotrophs The organisms which make their own food from carbon dioxide and water in the presence of sunlight and chlorophyll are called autotrophs. These organisms are also called producers and include green plants and some bacteria. PHOTOSYNTHESIS It is the process by which green parts of the plant synthesise organic food in the form of carbohydrates from CO2 and water in the presence of sunlight. 6CO2 + 6H2O light chlorophyll C6H12O6 + 6O2 In plants and most algae it occurs in the chloroplasts and there are two principal reactions: (i) Light reaction (light-dependent) requires the presence of light energy from sunlight which is obtained by photosynthetic pigments, i.e., chlorophyll and used to bring about the photolysis of water. H2O 2H+ + 2e- (ii) Dark reaction (light-independent) i.e., this reaction is not dependent on light and during this reaction carbon dioxide is reduced to carbohydrate in a metabolic pathway known as the Calvin cycle. Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) Page # 79 NUTRITION Difference between light and dark reactions Features Requirement of light Required Light reaction Takes place inside Grana part of the chloroplast ATP and NADPH2 ATP and NADPH2 are produced by the conversion of light energy into chemical energy Sugar formation Release of oxygen No sugar formation takes place Oxygen is released Dark reaction Not required The stroma region of chloroplast ATP and NADPH2 formed during light reaction are used for the fixation of CO 2 into carbohydrate Sugar formation takes place No oxygen is released VARIOUS COMPONENTS OF PHOTOSYNTHESIS Various components necessary for the process of photosynthesis are : 1.Chlorophyll 2. Carbon dioxide 3. Sunlight 4. Water This can be demonstrated with the help of various experiments. 1. Chlorophyll Chlorophyll is green pigment present in the green leaves. Activity-1.1 SCIENCE COMES ALIVE To prove that chlorophyll is essential for photosynthesis. Apparatus Plant with variegated leaves, Apparatus for starch test i.e., iodine solution, beaker, test tubes. BLUE BLACK (STARCH) GREEN (CHLOROPHYLL) NON-GREEN COLOURLESS (NO STARCH) Fig. 1 Apparatus to show that chlorophyll is essential for phtosynthesis Procedure 1. A potted plant with variegated leaf (Coleus, Croton) is kept in darkness for two days to make the leaves starch-free. 2. A plant is then kept in sunlight for few hours. 3. A leaf is removed from the plant and tested with iodine for starch, after decolourising it first with water and then alcohol. Conclusion It is seen that the portions of leaves which are devoid of chlorophyll remain colourless (starch free) whereas the rest of the leaf turns blue-black due to the presence of starch. PRACTICE ZONE 1.1 1. Why do plants need magnesium ? 2. What type of the plants do we use in the experiment to prove that chlorophyll is necessary for photosynthesis. 3. What substance does a plant need to be able to convert glucose into proteins ? : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] Page # 80 NUTRITION 2. Carbon-Dioxide Photosynthesis has been found to takes place in a very wide range of CO2 concentration. Within the range the rate of photosynthesis will decrease or increase with decrease or increase in CO2 concentration, provided other factors are not limiting. Relatively high concentration of CO 2, reduces the rate of photosynthesis and if given for a considerable period of time, has detrimental effect on the process itself. Activity-1.2 SCIENCE COMES ALIVE To prove that carbon dioxide is necessary for the process of photosynthesis. Apparatus Two healthy potted plants, Potassium hydroxide (KOH), 2 bell jars, watch-glass, vaseline, 2 glass plates, Iodine solution, H2O and alcohol. Procedure 1. Take two healthy potted plants of same size. 2. Destarch them by keeping in a dark room for 3-4 days. 3. Now place these potted plants on separate glass sheets. 4. Place watch glass containing KOH by the side of one of the plants. KOH has the property to absorb carbon dioxide. 5. Now cover these potted plants with bell jars. 6. To make the apparatus air tight use vaseline to seal the botton of the jars to glass plates. 7. Keep this experimental setup in sunlight for 3 to 4 hours. 8. Pluck one leaf from each plant. POTTED PLANT BELL JAR BELL JAR WATCH-GLASS CONTAINING KOH NO WATCH-GLASS CONTAINING KOH A B GLASS SHEET Fig. 2 Apparatus to show that CO2 is necessary for the process of photosynthesis 9. Perform starch test for both the leaves by decolourizing leaf first in water, then in alcohol and finally testing with iodine solution. 10. Leaf which was within bell jar with KOH solution gives a negative test whereas other one gives positive test. Conclusion The experiment clearly proves the fact that carbon dioxide is absolutely essential for photosynthesis. The part of the leaf which could not show iodine test positive or manufacture starch had all the requirements for photosynthesis except CO 2, which was absorbed by KOH in the bottle. ON YOUR TIPS The light intensity where in the photosynthesising organs neither takes CO2 nor release the same is called compensation point. Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) Page # 81 NUTRITION 3. Sunlight Activity-1.3 SCIENCE COMES ALIVE To prove that light is necessary for photosynthesis-Starch Printing Test. Apparatus Ganong's light screen or two strips of black paper. A destarched plant, Apparatus for starch test. Procedure 1. Take a Ganong's light screen. It has a small metallic box with ventilating holes. To the is attached a spring handle, bearing a lid at its one end which fits over the metallic box lightly. The lid has a design within its centre. You can even use two black paper strips to cover the leaf. 2. A potted plant is kept in the dark for two days to make the leaves starch free. 3. A leaf is partly covered with a piece of black paper or by a Ganong's light screen. 4. The pot is then kept in the sunlight for few hours. 5. The leaf is then tested with jodine solution for starch. Conclusion It is seen that the starch is formed only in the exposed portion of the leaf whereas covered portion remains starch-free because light was not available to such patches for photosynthesis. STARCH FORMED BLACK PAPER NO STARCH FORMATION Fig. 3 Apparation to show that light is required for phtosythsis PRACTICE ZONE 1.1 1. Plants need magnesium to make chlorophyll. 2. Desarched potted plants with variegated leaves eg. Croton and Pothos. 3. Nitrogen. 4. Water Plants absorb water from the soil with the help of root system. The effect of water deficiency on the rate of photosynthesis is indirect one. Decrease in H2 O content of the leaves may cause partial or complete closure of stomatal opening, and hence a reduction in the rate of diffusion of CO2 . A partial drying of the cell walls cause decrease in its permeability to CO2 , Another indirect effect of water deficiency is that the accumulation of sugar within the cells increases the rate of respiration and thus decreases apparent photosynthesis (b) Heterotrophic Nutrition The type of nutrition in which organisms derive their food (nutrients) from other living organisms. In heterotrophic nutrition, the energy is derived from the intake and digestion of the organic substances, normally of plant or animal tissue. Heterotrophic mode of nutrition are of different types : (i) Saprotrophic Nutrition It refers to the mode of nutrition in which organisms obtain nutrients from the dead and decaying organic matter, e.g., fungi, yeast and bacteria are called saprophytes. (ii) Parasitic Nutrition It refers to the mode of obtaining food synthesised by others. The organism which obtains food is called the ‘parasite’ and the organism from which food is absorbed is called the ‘host’. This nutrition is observed in fungi, bacteria, a few plants like Cuscata and some animals like Plasmodium and roundworm. (iii) Holozoic Nutrition It refers to the mode of nutrition in which the complex organic matter in the form of solid food is ingested, digested and then absorbed into the cells and utilised, e.g. amoeba, frog, human beings. Heterotrophs The organisms which cannot make their food and depend directly or indirectly on autotrophs for their survival are called heterotrophs. These organisms include animals and fungi. : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] Page # 82 NUTRITION TYPE OF HETEROTROPHIC NUTRITION 1. Saprophytic or Saprotrophic Nutrition : It is a mode of heterotrophic nutrition in which food is obtained from organic remains like dead organisms, excreta, fallen leaves, broken twigs, food articles, etc. Organisms performing saprophytic nutrition are called saprophytes. · 2. Parasitic Nutrition : It is a mode of hetrotrophic nutrition in which a living organisms flourishes by obtaining food from another living organism. The lving organisms which obtains food and shelter from another organism is called parasite. The organism which provides food and shelter to a parasite is known as host. An external plant parasite is Cuscuta (Amarbel). It is a non-green plant that sends haustroria or sucking roots into host plant for obtaining food and water. 3. Holozoic Nutrition : It is a mode of heterotrophic nutrition which involves intake of solid pieces of food. Since solid food is taken in, holozoic nutrition is also called ingestive nutrition. The food may consist of another animal, plant or its parts. Depending upon the source of food, holozoic organisms are of three types – Herbivores, carnivores, omnivores. Herbivores : (L.herba-plant, vorare-to eat) They are holozoic organisms which feed on plants or plant parts, e.g., Cow, Buffalo, Deer, Goat, Rabbit, Grasshopper, Elephant, Squirrel, Hippopotamus. Carnivores : They are animals which feed on other animals. Carnivores are also called predators they hunt, kill and feed on their preys, e.g. Lion, Tiger, Leopard, Snake, Hawk. Omnivores : (L.omnis-all, vorare-to eat) They are holozoic organisms which feed on both plant and animal materials, e.g. Cockroach, Ant, Pig, Crow, Rat, Bear, Dog, Humans. NUTRITION IN AMOEBA Protozoan protests carry out holozoic nutrition through intracellular digestion. Fig. - 4 Nutrition in Amoeba ON YOUR TIPS Free-living platyhelminthes (e.g., planaria) possess both kinds of digestion. Humans have extracellular digestion. Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) Page # 83 NUTRITION Some protests can ingest food particle from any point on the surface (e.g., Amoeba) while others have fixed points for the same (e.g., Paramoecium). Protozoans like Amoeba capture food with the help of temporary finger-like processes called pseudopodia. Protozoans like (Paramoecium have small hair-like processes called cilia.) Beating of cilia creates current in water that pushes food particle through cytostome or cell mouth. The process of ingestion of solid food particle by a cell or unicellular organism is called phagocytosis. As soon as Amoeba comes in contact with a food particle or prey, it throws pseudopodia all around the same. The tips of encircling pseudopodia fuse and the prey comes to lie in a vesicle or phagosome. This method of intake of food is called circumvallation. Amoeba can also ingest food by other methods like import, circumfluence and invagination. DIGESTIVE SYSTEM OF HUMAN The organs which are responsible for ingestion, digestion, absorption, assimilation and egestion constitute the digestive system. The digestive system comprises of the alimentary canal and associated digestive glands. Digestive system Alimentary canal Mouth Buccal cavity Oesophagus Digestive Glands Stomach Intestine Small Intestine Duodenum Jejunum Large Intestine lluem Caecum Colon Rectum (A) Alimentary canal The alimentary canal is basically a long tube extending from the mouth to the anus. It is differentiated into following parts. (i) Mouth It is a transverse slit bounded by movable lips. The lips serve to close and open mouth. holding the food in between and also help in speaking. The floor of the buccal cavity has a tongue bearing taste buds. Man possess teeth on both the jaws. There are 32 teeth of four different types, namely incisors, canines, premolars and molars. Digestion may be intracellular (Paramoecium) or extracellular (multicellular animals). The process of digestion starts in the mouth cavity and continues upto the intestine. In the mouth, food gets mixed up with saliva secreted by salivary glands. Saliva contains an enzyme ptyalin which breaks polysaccharide starch into disaccharide maltose. Starch Ptyalin ( Salivary amylase) Maltose The food from the mouth cavity passes into the stomach through the oesophagus. ON YOUR TIPS Apart from the presence of food, the sight, smell or even touch of one's favourite food can initiate secretion of gastric juices. : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] Page # 84 NUTRITION (ii) Pharynx It is a short, conical region that lies after the mouth cavity. The pharynx are divided into two parts — the nasopharynx which lies behind the nasal cavities and the oropharynx which lies behind the mouth. (iii) Oesophagus (food pipe) It is a long, narrow, muscular tube which leads to the stomach, The oesophagus is a collapsible muscular tube leading from pharynx to stomach. There are no digestive glands but mucus glands are present. (iv) Stomach It is a thick, muscular and J shaped sac present on the left side of upper part of abdomen. Gastric glands are present in the wall of stomach. These releases gestric juice or digestive juice, which contains mucus. hydrochloric acid and a protein digesting enzyme called pepsin. Mucus lubricated the food and protects the inner linning of the stomach from the action of HCl. HCl creates an acidic medium, which facilitates the action of enzyme pepsin and kills the bacteria present in food. Pepsin breaks down proteins into peptides. Sphincter muscles regulate the exit of food from stomach into intestine due to peristaltic waves of stomach. Fig. -5 Human alimentary canal (v) Intestine It is the largest part of alimentary canal which is fitted into a compact space because of extensive coiling. It is distingushed into small intestine and large intestine. Small intestine The small intestine is the site of the complete digestion of carbohydrates. proteins and fats. It receives the secretions of the liver and pancrease for digestion. Food is mixed with three digestive juices (bile juice, pancreatic juice and intestinal juice) Bile juice (from the liver) provide alkaline medium and emulsifies fats (conversion of larger fat globules into smaller fat droplets) but it is non enzymatic digestive juice so has no chemical action on food. Pancreatic juice (from the pancreas) contains trypsin, pancreatic amylase and pancreatic lipase enzymes which digest the peptons, starch and fats into peptides, maltose and fatty acids and glycerol respectively. The wall of intestine secretes intestinal juice which contains enzymes for complete digestion of proteins into amino acids, carbohydrates into glucose and fat into fatty acid and glycerol. The inner lining of the small intestine has numerous finger like projections called villi which increase the surface area for absorbtion of digested food. These are richly supplied with blood vesseles. Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) Page # 85 NUTRITION Large Intestine It is much shorter and wider than small intestine and is differentiated into three regions viz., caecum, which is small rounded blind sac from which vermiform appendix arises; colon is the inverted U-shaped tube and the rectum opens to exterior through anus. (vi) Anus The rest of the material is removed from the body via anus. The exit of waste material is regulated by anal sphincter. (B) Digestive Glands Various glands associated with alimentary canal are : Fig. -6 Salivary glands of man ON YOUR TIPS On eating food of our interest, watering starts in our mouth. This water is basically the saliva which is secreted by salivary glands that get activated by eating and even seeing or thinking of good food. (i) Salivary Glands The salivary glands secrete the first of the digestive juices, the saliva. There are three pairs of salivary glands, namely the parotids, sub-maxillary and sublingual glands. (ii) Gastric Glands They are branched tubular glands which lie in the mucus membranes of the stomach. They secrete gastric juice, which is clear, acidic containing HCl, enzymes and mucus. (iii) Liver It is the largest gland in man and lies below diaphragm in the right upper part of abdomen. Liver comprises of two lobes, right and left, where the right lobe is much larger than the left lobe. The cells of liver, i.e., hepatic cells produce bile juice which flows out of liver through hepatic ducts forming common bile duct and opens into duodenum. Bile juice then flows into gall bladder through the cystic ducts. : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] Page # 86 NUTRITION Fig. -7 Liver and Pancreas and their ducts (iv) Pancreas It is a soft lobulated gland present in between the loops of duodenum. It secretes pancreatic juice containing enzymes which is poured into duodenum with the help of pancreatic duct. Table: Summary of the digestive enzymes of various glands with their secretions and end products of Digestion in Man Se cretio n ON YOUR TIPS It is the tooth decay which involves destruction of the enamel layer of the tooth by acids produced by the action of bacteria on sugar. If dental caries is not treated, it can spread to the dentine and pulp of the tooth, causing inflammation a n d i n f e c t io n o f t h e to o th . Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) Page # 87 NUTRITION N.C.E.R .T TEXT BOOK SOLUTION Q.1 Why is diffusion insufficient to meet the oxygen requirement of multicellular organisms like humans? Ans. In humans, the body organisation is multicellular and complex. The living cells are not in direct constant with environment because they are generally covered by dead cells. Air containing intracellular spaces are also absent so quick diffusion cannot occur. Cell to cell diffusion is very slow process and if it takes place in humans then passage of oxygen in whole body will take about years. Thus, diffusion is insufficient to deliver oxygen to all parts of a multicellular organisms like humans. Q.2 What criteria do we use to decide whether something is alive? Ans. The main criterion that is used to decide whether something is alive, is movement. Movements may be of different types like locomotion (running, walking), moving body parts, breathing movements, growth movements and movement of molecules in various metabolic reactions. Besides movements, other qualities found in living beings are self-built body organisation, presence of protoplasm, self repair, various vital life processes like metabolism, growth, nutrition, respiration, excretion and reproduction. All living organisms have a definite lifespan and particular life cycle. Q.3 What processes would you consider essential for maintaining life? Ans. The processes essential for maintaining life are nutrition, metabolism, respiration, circulation/transportation and excretion. Q.4 What are the differences between autotrophic nutrition and heterotrophic nutrition? Ans. In autotrophic mode of nutrition, organisms (green plants, some protists and bacteria) prepare their own food from inorganic raw materials with the help of energy obtained from sunlight whereas in heterotrophic mode of nutrition, organisms obtain food prepared by autotrophs or from other organic sources as they cannot synthesise their own food. Heterotrophic nutrition may be saprophytic, parasitic and holozoic. Q.5 Where do plants get each of the raw materials required for photosynthesis? Ans. The raw materials required for photosynthesis are carbon dioxide and water. Plants obtain water from the soil through roots and carbon dioxide from the atmosphere through stomata present on leaves. Q.6 What is the role of the acid in our stomach? Ans. Hydrochloric acid (HCl) is secreted inside the stomach. The main functions of HCl are to (i) stop the action of salivary amylase (ii) kill the microbes present in the food (iii) provide acidic medium necessary for the activation of the enzyme pepsin (iv) make food soft (v) convert pepsinogen and prorennin into active forms of pepsin and rennin. Q.7 What is the function of digestive enzymes? Ans. Digestive enzymes are hydrolytic in nature which help in digestion of carbohydrates, proteins and fats. They bring about hydrolytic splitting of complex organic substances into simple soluble and absorbable substances. For example, by the action of digestive enzymes, proteins are converted into amino acids. Q.8 How is the small intestine designed to absorb digested food? Ans. Small intestine is a long, tubular structure. Its inner wall is lined by epithelium which possess numerous finger-like projections called villi. These villi not only increase the surface area for absorption but also reach deep into the lumen of intestine for maximum absorption of digested food. Villi possess blood capillaries and lymph vessels (lacteals) for quick transport of absorbed food. : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] Page # 88 NUTRITION EXERCISE – I Q.1 PRACTISE FOR FORMATIVE ASSESSMENT CO2 and O2 balance in atmosphere is due to (A) Photorespiration (B) Photosynthesis Q.2 Q.3 (A) Water (B) Carbon dioxide (C) Both from water and carbon dioxide (D) Oxygen in air With regards to natural eating habits, a human is Q.8 (B) Deglutition (C) Peristalsis (D) Churning (B) Stomach (C) Duodenum (D) Mouth (B) Ptyalin (C) Trypsin (D) Rennin Pepsin digests (A) Proteins in stomach (B) Carbohydrates in duodenum (C) Proteins in duodenum (D) Fats in ileum If the stomach did not produce any hydrochloric acid, which enzyme will not function ? (A) Ptyalin Q.9 (D) A Granivore Saliva has the enzyme (A) Pepsin Q.7 (C) An omnivore Which of the following regions of the alimentary canal of man does not secrete a digestive enzyme ? (A) Oesophagus Q.6 (B) A carnivore Muscular contractions of alimentary canal are (A) Circulation Q.5 (D) Leaf anatomy During photosynthesis the oxygen in glucose comes from (A) An herbivore Q.4 (C) Respiration (B) Trypsin (C) Pepsin (D) Collagenase (C) In liver (D) In spleen (C) Pituitary (D) Thyroid Chief function of bile is (A) To digest fat by enzymatic action (B) To emulsify fat for digestion (C) To eliminate waste product (D) To regulate process of digestion Q.10 Where is bile produced ? (A) In gall bladder Q.11 Largest gland in human body is (A) Liver Q.12 (B) In blood (B) Pancreas The original function of the vertebrate stomach was (A) Storage (B) Digestion (C) Enzyme secretion (D) Absorption Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) Page # 89 NUTRITION FILL IN THE BLANKS 1. The whole process by which an organism obtains its food is referred to as ............. 2. Other term for autotrophic nutrition is .............. 3. .................. manufacture their food from inorganic substances in the presence of energy derived from the oxidation of simple inorganic compounds of iron, sulphur etc. 4. The process of utilization of absorbed food is known as .............. 5. Those organisms which depend on faecal matte of other organisms are known as ............... 6. Ligth reaction is also known as ............. phase. 7. The light intensity, at which the photosynthetic intake CO 2 is called .............. . 8. Ingestion of food in Amoeba takes place by the process of ............ 9. ................ is the type of digestion that occurs inside the lumen of digestive tract. 10. ................ are known as suicide bags of the cell. ANSWER KEY 1. B 2. A 3. C 4. C 5. A 8. C 9. B 10. C 11. A 12. A 6. B 7. A 3. Chemoautotrophs 8. Phagocytosis FILL IN THE BLANKS 1. Nutrition 2. a 4. Assimilation 5. Coprozoic heterotrophs 6. Photochemical phase 7. Compensation point 9. Intercellualr 10. Lysosomes : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] Page # 90 EXERCISE – II NUTRITION PRACTISE FOR SUMMATIVE ASSESSMENT Very Short Answer Type Questions Q.1 Define heterotrophic nutrition. Q.2 What are heterotrophs ? Q.3 Which types of organisms are called consumers ? Q.4 What is saprophytic nutrition ? Q.5 Define saprophyte. Q.6 Define a hervivore. Q.7 What is carnivore ? Q.8 Which type of animal is called omnivore ? Q.9 What is the mode of nutrition in Amoeba ? Q.10 What type of digestion occurs in Paramoecium ? Short Answer Type Questions Q.11 How do saprophytic organisms obtain their nourishment ? Q.12 What is the importance of saprophytes ? Q.13 What is the action of hydrochloric acid of gastric juice ? Q.14 Name a digestive juice that has no enzymes. What is the role of this juice ? Q.15 Name the various parts of large intestine. What is the role of large intestine ? Long Answer Type Questions Q.16 Explain the mechanism of nutrition of Amoeba with the help of suitable diagram. Q.17 Describe the various types of heterotrophic nutrition. Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) REAL NUMBERS Page # 91 REAL NUMBERS 1.1 BASIC CONCEPTS AND IMPORTANT RESULTS (a) Natural numbers : Counting numbers are called natural numbers. We start counting from 1, so 1 is the smallest natural number. A set of natural numbers is denoted by N. Thus, N = {1, 2, 3, ...up to the numbers as possible as we can count} (b) Whole numbers : Natural numbers together with zero are called whole numbers. A set of whole numbers is denoted by W. Thus, W = {0, 1, 2, 3, .....} All natural numbers are whole numbers but all whole numbers are not natural numbers. Only the difference between whole numbers and natural numbers is the number zero (0). (c) Integers : All positive and negative natural numbers together with zero are called integers. A set of integers denoted by Z or I. Thus, Z = {.... – 6, – 5, – 4, –3, – 2, –1, 0, 1, 2, 3, 4, 5, 6 ....} (d) Rational numbers : A number of the form rational number. For example, p , where p and q are integers and q q 0 is called a 2 3 , , 2, 0, etc., are rational number.. 7 8 The decimal expansion of a rational number is either terminating or non-terminating repeating one. (e) Irrational numbers : A number which is not a rational number, i.e., which cannot be written in the form p , p and q q 2 , – 3, 7 5, Z or I and q 1 2,1+ 0, is known as an irrational number. For example, 6 , etc., are irrational numbers. The decimal expansion of an irrational number is non-terminating and non-repeating one. (f) Real numbers : All rational and irrational numbers together make up a collection, called real numbers. Note : All natural numbers, integers, rational numbers and irrational numbers are real numbers. 1.2 EUCLID’S DIVISION ALGORITHM OR EUCLID’S DIVISION LEMMA For any two given positive integers a and b, there exist unique whole numbers q and r such that: a = b × q + r, where 0 r<b 2 5 4 1 2 Here, a is called the dividend, b the divisor, q the quotient and r is called the remainder. For example, when we divide 5 by 2, we get 2 as quotient and 1 as remainder Here 5 = 2 × 2 + 1 Dividend = Divisor × Quotient + Remainder : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] REAL NUMBERS Page # 92 Properties of Euclid’s Division Lemma : (i) If an integer c be a divisor of each of the two given integers a and b, then we say that c is a common factor of both a and b. (ii) Let P be a prime number and if a,b, are integers such that P P P , then either or is a factor.. ab a b Note : If a prime number divides a product of integers, then it necessarily divides either of the integers. Obtaining HCF by Euclid Division Lemma : Let a and b be two positive integers. If a = b × q + r, 0 r <b Then HCF (a, b) = HCF (b, r) where HCF(a, b) = Common division of a and b and HCF (b, r) = Common division of b and r. 1.3 FUNDAMENTAL THEOREM OF ARITHMETIC Every composite number can be expressed as a product of primes and this factorization is unique, apart from the order in which the prime factors occur. Note : Any number of the form an will end with the digit zero if prime factors of an would contain 5 and 2 as a prime factor, where n W. 1.4 THEOREMS ON RATIONAL NUMBERS (i) Let x be a rational number whose decimal expansion terminates. Then x can be expressed in the form p n m q , where p and q are co-prime, and the prime factorization of q is of the form 2 5 , where n, m are non-negative integer. (ii) p Let x = q be a rational number, such that the prime factorization of q is of the form 2n5 m , where n, m are non-negative integers. Then x has a decimal expansion which terminates. (iii) p Let x = q be a rational number such that the prime factorization of q is not of the form 2n5m, where n, m are non-negative integers. Then x has a decimal expansion which is non-terminating repeating (recurring). Note : HCF(p, q, r) × LCM(p, q, r) (p × q × r), where p, r and q are positive integers. p× q×r.HCF(p, q,r) LCM(p, q, r) = HCF(p, q).HCF(q,r).HCF(p,r) p × q×r.LCM(p, q,r) HCF(p, q, r) = LCM(p,q).LCM(q,r).LCM(p,r) Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) REAL NUMBERS Page # 93 SOLVED PROBLEMS Ex.1 Sol. Show that any positive odd integer is of the form 6q + 1, or 6q + 3 or 6q + 5, where q is some integer. Let us start with taking a, where a is any positive odd integer. We apply the division algorithm, with a and b = 6. Since 0 r < 6, the possible remainders are 0, 1, 2, 3, 4, 5. That is, a can be 6q or 6q + 1, or 6q + 2, or 6q + 3, or 6q + 4, or 6q + 5, where q is the quotient. However, since a is odd, we do not consider the cases 6q, 6q + 2 and 6q + 4 (since all the three are divisible by 2). Therefore, any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5. Ex.2 Sol. If a = 10 and b = 3. Then find q and r such that a = bq + r, o Clearly 10 = 3 × 3 + 1 q = 3 and r = 1 are required numbers. Ex.3 Sol. Use Euclid’s division algorithm to find the HCF of 135 and 225. We start with the larger integer, that is, 225. Then by Euclid’s division algorithm we get: 225 = 135 × 1 + 90 Now, consider the divisor 135 and the remainder 90 and apply the division algorithm again, we get : 135 = 90 × 1 + 45 Now, consider the divisor 90 and the remainder 45 and apply the division algorithm again, we get. 90 = 45 × 2 + 0 Notice that the remainder has become zero and we cannot proceed any further. The HCF of 90 and 45 is 45 and we claim that the HCF of 225 and 135 is also 45. Ex.4 An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march? Hint : Find HCF of 616 & 32 Sol. Ex.5 Sol. Ex.6 Sol. r < b. Use Euclid's division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m. Let a be any odd positive integer. We apply the division lemma with a and b = 3. Since 0 r < 3, the possible remainders are 0, 1 and 2. That is, a can be 3q, or 3q + 1, or 3q + 2, where q is the quotient. Now, (3q)2 = 9q2 which can be written in the form 3m, since 9 is divisible by 3. Again, (3q + 1) 2 = 9q 2 + 6q + 1 = 3 (3q2 + 2q) + 1 which can be written in the form 3m + 1 since 9q 2 + 6q, i.e., 3(3q2 + 2q) is divisible by 3. Lastly, (3q + 2) 2 = 9q 2 + 12q + 4 = (9q2 + 12q + 3) + 1 = 3(3q2 + 4q + 1) + 1 which can be written in the form 3m + 1, since 9q 2 + 12q + 3, i.e., 3(3q 2 + 4q + 1) is divisible by 3. Therefore, the square of any positive integer is either of the form 3m or 3m + 1 for some integer m. Express each number as product of its prime factors : (i) 140 (ii) 156(iii) 3825 (iv) 5005 (v) 7429 (i) 140 (ii) 156 140 156 70 2 35 2 5 78 2 39 2 7 So, 140 = 2 × 2 × 5 × 7 = 2 2 × 5 × 7 3 13 So, 156 = 2 × 2 × 3 × 13 = 2 2 × 3 × 13 (Rest Try your self) : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] REAL NUMBERS Page # 94 Ex.7 Sol. Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of two numbers. (i) 26 and 91 (ii) 510 and 92 (iii) 336 and 54 (i) 26 and 91 26 13 2 So, 26 = 2 × 13 91 13 7 So, 91 = 7 × 13 Therefore, LCM (26, 91) = 2 × 7 × 13 = 182 HCF (26, 91) = 13 Verification LCM × HCF = 182 × 13 = 2366 and 26 × 91 = 2366 i.e., LCM × HCF = product of two numbers. Ex.8 Sol. (Rest Try your self) Find the LCM and HCF of the following integers by applying the prime factorisation method. (i) 12, 15 and 21 (ii) 17, 23 and 29 (iii) 8, 9 and 25 (i) 12, 15 and 21 12 6 2 So, 2 3 12 = 2 × 2 × 3 = 22 × 3 15 5 3 So, 15 = 3 × 5 21 3 7 So, 21 = 3 × 7 Therefore, HCF (12, 15, 21) = 3 ; LCM = (12, 15, 21) = 2 2 × 3 × 5 × 7 = 420 (Rest Try your self) Ex.9 Given that HCF (306, 657) = 9, find LCM (306, 657). Sol. 306×657 306×657 LCM (306, 657) = HCF (306, 657) = = 22338. 9 Ex.10 Prove that square of any odd integer is of the form 8k + 1, k an integer. Sol. For any odd integer is of the form 2m + 1 and (2m + 1)2 = 4m2 + 4m + 1 = 4 m (m + 1) + 1 Now, m (m + 1) is alwyas even, say 2k, hence 4m(m + 1) = 4 × 2k (2m + 1)2 = 8k + 1 Ex.11 Check whether 6n can end with the digit 0 for any natural number n. Sol. If the number 6 n, for any natural number n, ends with digit 0, then it would be divisible by 5. That is, the prime factorisation of 6 n would contain the prime number 5. This is not possible because 6 n = (2 × 3)n = 2n × 3n ; so the only primes in the factorisation of 6n are 2 and 3 and the uniqueness of the Fundamental Theorem of Arithmetic guarantees that there are no other primes in the factorisation of 6n. So, there is no natural number n for which 6n ends with the digit zero. Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) REAL NUMBERS Page # 95 Ex.12 Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers. Sol. (i) 7 × 11 × 13 + 13 = (7 × 11 + 1) × 13 = (77 + 1) × 13 = 78 × 13 = (2 × 3 × 13) × 13 [ 78 = 2 × 3 × 13] = 2 × 3 × 13 2 Since, 7 × 11 × 13 + 13 can be expressed as a product of primes, therefore, it is a composite number. (Rest Try your self) Ex.13 Prove that Sol. 5 is irrational. Let us assume, to the contrary, that 5 is rational. So, we can find coprime integers a and b ( 0) such that a 5 = b 5b= a Squaring on both sides, we get 5b 2 = a2 Therefore, 5 divides a2. Therefore, 5, divides a So, we can write a = 5c for some integer c. Substituting for a, we get 5b 2 = 25c 2 b 2 = 5c 2 This means that 5 divides b 2, and so 5 divides b. Therefore, a and b have at least 5 as a common factor. But this contradicts the fact that a and b have no common factor other than 1. This contradiction arose because of our incorrect assumption that 5 is rational. So, we conclude that 5 is irrational. Ex.14 There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point? Sol. [Hint : Take LCM of 18 and 12] Ex.15 Prove that 3 + 2 5 is irrational. Sol. Let us assume, to the contrary, that 3 + 2 5 is rational. That is, we can find coprime integers a and b (b Therefore, 0) such that 3 + 2 5 = a b a – 3=2 5 b a–3b =2 5 b a–3b = 5 2b a 3 – = 2b 2 5 Since a and b are integers, we get But this contradicts the fact that a 3 a – 3b – is rational, and so 2b 2 2b 5 is rational. 5 is irrational. This contradiction has arisen because of our incorrect assumption that 3 + 2 5 is rational. So, we conclude that 3 + 2 5 is irrational. : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] REAL NUMBERS Page # 96 Ex.16 Show that 5 – 3 is irrational. Sol. Suppose 5 – 3 is a rational number (say p) Then 5 – 5–p= 3 =p 3 Since p is a rational number and 5 is a rational 5 – p being the difference of two rational numbers is a rational number because the set of rational numbers are closed w.r.t. the operation of subtraction. 3 is a rational number But, it is an irrational number Our supposition is wrong. Hence 5 – 3 irrational . Ex.17 Prove that the following are irrationals : (i) Sol. 1 (ii) 7 5 2 (iii) 6 2 (Try yourself) Ex.18 Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion. (i) 13 3125 23 (vi) 23 52 Sol. (i) (ii) 17 8 129 (vii) 22 57 75 (iii) 64 455 (iv) 15 1600 (v) 29 343 6 15 (ix) 35 50 (x) 77 210 (viii) 13 13 = 5 3 1 25 5 Hence, q = 5 5, which is of the form 2n 5 m (n = 0, m = 5). So, the rational number 13 has a 3 1 25 terminating decimal expansion. (ii) 17 17 = 3 8 2 Hence, q = 2 3, which is of the form 2n 5m (n = 3, m = 0). So, the rational number 17 has a terminating 8 decimal expansion. (iii) 64 64 = 5 7 13 455 Hence, q = 5 × 7 × 13, which is not of the form 2 n 5 m. So, the rational number non-terminating repeating decimal expansion. 64 has a 455 (Rest Try your self) Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) REAL NUMBERS Page # 97 Ex.19 Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions. Sol. (i) 13 3 1 25 = (ii) 13 13×2 5 416 = 0.00416 = = 55 55 ×25 10 5 17 8 = 17 23 17×53 17×5 3 2125 = = = 2.125 2 3 ×5 3 10 3 103 (Rest Try your self) Ex.20 The following real numbers have decimal expansions as given below. In each case, decide whether p they are rational, or not. If they are rational, and of the form , what can you say about the prime q factors of q? Sol. (i) 43.123456789 (ii) 0.120 1200 12000 120000.... (iii) 43.123456789 (i) 43.123456789 Since, the decimal expansion terminates, so the given real number is rational and therefore of the form p . 43.123456789 q = 43123456789 1000000000 = 43123456789 109 = 43123456789 (2×5)9 = 43123456789 29 59 Hence, q = 2 9 59 The prime factorization of q is of the form 2n 5m, where n = 9, m = 9. (ii) 0.120 1200 12000 120000.... Since, the decimal expansion is neither terminating nor non-terminating repeating, therefore, the given real number is not rational. (Rest Try your self) : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] REAL NUMBERS Page # 98 EXERCISE – I Q.1 Prove that 2 is not a rational number or there is no rational whose square is 2. 3 UNSOLVED PROBLEMS Q.14 State fundamental theorem of Arithmetic. Q.15 For any two positive integers, state the relation between the numbers, their H.C.F. and L.C.M. Q.2 Prove that 3 is irrational. Q.3 Prove that 2 + 3 is irrational. Is this result true for three positive integers? Q.16 Explain why 7 × 11 × 13 + 13 is a composite number Q.4 Prove that 2 + 3 is irrational. Q.17 Q.5 Use Euclid's division lemma to show that the If p is a rational number (q q conditi on square of any positive integer is either of the on q representation of form 3m or 3m +1 for some interger m. Q.6 Show that one and only one out of n, n + 2 or so 0), what is the t ha t t he decimal p is terminating? q Q.18 Write a rational number between 2 and 3. Q.19 Complete the missing entries in the following n + 4 is divisible by 3, where n is any positive integer. factor tree? Q.7 Use Euclid's algorithm to find the HCF of 4052 2 and 12576. 3 Box 2 Q.8 Find the HCF of 1848, 3058 and 1331. Q.9 Using Euclid's division, find the HCF of 56, 96 and 404 Q.10 7 Box 1 Q.20 Find the prime factors of 560. Q.21 Find the missing numbers in the following factorisation : Find the L.C.M and H.C.F. of 1296 and 2520 (box 4) by applying the fundamental theorem of (box 3) 2 arithmeti c me thod i.e. using t he pri me factorisation method. (box 2) 2 (box 1) 3 Q.11 Given that H.C.F. (336, 54) = 6. Find L.C.M. 5 5 (336, 54) Q.22 Q.12 Given that L.C.M. (150, 100) = 300, find H.C.F. Find the H.C.F. and L.C.M. of 17, 23, 37 by applying prime factorisation method. (150, 100). Q.23 Q.13 State Euclid's division lemma. Given that H.C.F. (14, 35) = 7, find L.C.M. (14, 35). Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) REAL NUMBERS Q.24 Page # 99 Without performing long division, state Q.31 Examine whether the following numbers are rational or irrational : 84 whether the number 455 will have a (i) 2 terminating or a non-terminating but repeating 3 2 (ii) 2 (iv) 2 3 3 3 2 decimal representation. Q.25 (iii) 3 Write down the decimal representation of 3 3 3 77 . 210 Q.32 Q.26 The following real numbers have decimal Show that p 2 – 1 is divisible by 8, where p is an odd positive interger. expansion as given below. In each case decide whether it is rational or not. If rational, Q.33 Prove that 5 is an irrational number.. Q.34 Use Euclid's division lemma to show that the what can be said about the prime factors of denominator. cube of any positive integer is of the form 9m, (i) 4.59 9m + 1 or 9m + 8. (ii) 0.13013001300013000013…… Q.35 Check whether 7n can end with digit 0, for any natural number n. (iii) 0.0 6012 Q.36 Q.27 If H.C.F. (65, 117) is expressed in the form 65m + 117n, then find the value of m. Find two irrational numbers between 0.1 and 0.12. Q.28 Find a rational number and also an irrational Find the g.c.d. of the following pairs of polynomials number between the numbers. a = 0.101001000100001……, Q.37 (x + 1)2 (x + 7) b = 0.1001000100001…… Q.29 Show that any positive odd integer is of the form 4q + 1 or 4q + 3, where q Q.30 4(x – 3) 2 (x – 1) (x + 1) 3 and 6(x – 1) 2 Q.38 (x – 2)2 (x + 3) (x – 4) and (x – 2) (x + 2) (x – 5) Z+ . Without actually performing the long division, Q.39 (2x – 7) (3x + 4) and (2x – 7)2 (x + 3) 17 will 1600 Q.40 (3x – 2)2 (2x + 3)3 (x – 1) and (3x – 2)3 (2x + state whether the rational number 3) (x – 1)3 have terminating or non-terminating but repeated decimal representation. Q.41 (x – 1) (x + 1)3 and (x – 1)3 (x + 1) : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] REAL NUMBERS Page # 100 Q.42 (x + 4)2 (x – 3)3 and (x – 1) (x + 4) (x – 3)2 Q.64 (6x4 – 13x3 + 6x2) and (8x4 – 36x3 + 54x2 – 27x) Q.43 24(x – 3) (x – 2)2 and 15(x – 2) (x – 3)3 Q.65 (x3 – x2 – x – 2) and (x3 + 3x2 – 6x – 8) Q.44 16 – 4x2 and x2 + x – 6 Q.66 (4x5 + 16x4 – 44x2 – 24x) and (2x5 – 6x3 + 2x) Q.45 xy – y and x4 y – xy Q.67 (3x3 – 14x2 + 9x + 10) and (15x3 – 34x2 + 21x – 10) Q.46 2x2 – 7x + 3 and 3x2 – 7x – 6 Q.68 4x2(x2 – a2 ) and 9x2(x3 – a3 ) Q.47 x3 + 64 and x2 – 16 Q.69 2(a2 – b2) and 3(a 3 – b 3) Q.48 x3 + 2x2 – 3x and 2x3 + 5x2 – 3x Q.70 (x2 + 3x – 4) and (x3 – 2x2 – 2x + 3) Q.49 22x(x + 1)2 and 36x2 (2x2 + 3x + 1) Q.71 12(x4 – 25) and 8(x4 + 4x2 – 5) Q.50 3 + 13x – 30x2 and 25x2 – 30x + 9 Q.72 Find the values of a and b so that the polynomial Q.51 (x3 – y3 ) and (x4 + x2y2 + y4) Q.52 2x2 + 7xy + 3y2 and 2x2 + 6xy + x + 3y Q.53 56(x6 y2 – x2y6) and 72(x5 y3 + 3y5 x3 + 2y7 x) Q.54 54(x3 + 8y3 ) and 90(x3 + 7x2 y + 16xy2 + 12y3) Q.55 (4x4 + y4) and (2x3 – xy2 – y3 ) Q.56 x3 – y3; x3 y – y4 and y2(x – y)2 (x2 + xy + y2) (i) 12(x3 + x2 + x + 1) and 18(x4 – 1). Q.57 (2x2 – 3xy)2 ; (4x – 6y)3 and (8x3 – 27y3 ) (ii) 12(3x4 – 14x3 – 5x2) and 30(3x5 + 4x4 + x3) Q.58 (4x4 + y4); (2x3 – xy2 – y3) and (2x2 + 2xy + y2) Q.59 x4 – x3 + x – 1 and x4 + x2 + 1 (i) x3 + 2x2 – 3x and 2x3 + 5x2 – 3x Q.60 (8x6 – 32x5 + 128x3 – 128x2 ) and (12x6 – 36x5 + (ii) 4(x4 – 1) and 6(x3 – x2 – x + 1) x3 + ax2 + bx – 42 is divisible by x2 – x – 6. Q.73 48x3 ) + ax2 + bx – 6 is completely divisible by x2 – 4x – 3. Q.74 (x3 – x2 – x + 1) and (x4 – 2x3 + 2x – 1) Q.62 2x y(x – y ) and 35 xy (x – y) Q.63 (x2 + 4x – 21) and (x3 + 7x2 – 9x – 63) Find the values of a and b so that the polynomial f(x) = 3x3 + ax2 – 13x + b is divisible by x2 – 2x – 3. Q.75 Q.76 Q.77 Q.61 Find the values of a and b so that the polynomial x3 Find the GCD of the polynomials Find the GCD of the polynomials : If x2 – x – 6 is the GCD of the expressions (x + 2) (2x2 + ax + 3) and (x – 3) (3x2 + bx + 8). Find the values of a and b. 2 2 2 2 Q.78 Find the GCD of the polynomials : 2(x4 – y4 ), 3(x2 + 2x2 y – xy2 – 2y3 ). Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) REAL NUMBERS Q.79 Page # 101 If (x2 – x – 2) is the GCD of the expressions Q.80 Q.88 Find the values of a and b such that the (x – 2) (2x + ax + 1) and (x + 1) (3x + bx + 2), polynomials. P(x) and Q(x) have (x + 3) find the values of a and b. (x – 2) as their HCF : Find the GCD of the polynomials : P(x) = (x2 – 4x – 21) (x2 – 4x + a) (i) p(x) = 45(2x4 – x3 – x2) and q(x) = 75(8x5 + x2). Q(x) = (x2 – 5x + 6) (x2 – 4x + b) 2 2 Q.89 (ii) p(x) = 36(3x4 + 5x3 – 2x2) and q(x) = 54(27x4 – x). If (x ) is the GCD of ax2 + bx + c and bx2 + cx + a, prove that either a = 0 or a3 + b3 + c 3 = 3abc. (iii) p(x) = 42(2x3 – 5x2 – 3x) and q(x) = 60(8x4 + x). Q.90 If (x ) is the GCD of ax2 + bx + c and cx2 + bx + a, prove that Q.81 (x + 1) (x – 4) is the g.c.d. of the polynomials a + b + c = 0 or a – b + c = 0 (x – 4) (2x2 + x – a) and (x + 1) (2x2 + bx – 12). Find a and b. Q.91 Q.82 Q.83 (x – 3) is the g.c.d. of x3 – 2x2 + px + 1 and 3x2 – 2mx – 4 have a common linear factor, x2 – 5x + q. Find the 6p + 5q. find the values of m. For what value of k, the g.c.d. of x2 + x – Q.92 (2k + 2) and 2x2 + kx – 12 is x + 4 ? Q.84 If t he po lyno mials x 2 – 4m x + 2 and If G.C.D. of (x – 5) (x2 – x – a) and (x – 4) If (x ) is the HCF of px2 + qx + c and ax2 + bx + c, prove that Q.93 (p a) = (b – q). Find the HCF (GCD) of the polynomials : (x2 – 2x – b) is (x – 4) (x – 5), find the values (i) (x – 3) (x + 5)2, (x + 5) (x + 7)2 and (x + 2) of a, b. (x + 5)3 Q.85 Find the values of k for which the g.c.d. of (ii) 2(x – 7) (x + 7) 2, 4(x – 7)2 (x + 8) and x2 – 2x – 24 and x2 – kx – 6 is x – 6. 8(x2 – 49) Q.86 Find the H.C.F. of x – 1 and x + x + x + 1. 4 3 2 (iii) x2 – 1, x4 – 1 and (x – 1)2 Q.87 Find the va lue of a and b s o that t he (iv) 4(x + 2), 8(x + 3) and 16(x + 4) polynomials P(x) and Q(x) have (x + 1) (x – 2) as their HCF : (v) 3(x + 3), 5(x + 3) (x + 5) and 7(x + 4) P(x) = (x2 + 3x + 2) (x2 + x + a) Q.94 Q(x) = (x2 – 3x + 2) (x2 – 3x + b) Fine what value(s) of k is the HCF of x2 + x – (2k + 2) and 2x2 + kx – 12, (x + 4) ? : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] REAL NUMBERS Page # 102 Q.95 If the HCF of the polynomials 37. 2(x – 1) (x + 1)2 f(x) = (x – 1) (x2 + 3x + a) and, 39. (2x – 7) g(x) = (x + 2) (x2 + 2x + b) is (x – 1) (x + 2) find a and b. Q.96 38. (x – 2) 40. (3x – 2)2 (2x + 3) (x – 1) 41. (x – 1) (x + 1) 42. (x + 4) (x – 3)2 43. 3(x – 3) (x – 2) 44. (x – 2) 45. (x – 1)y 46. (x – 3) 47. (x + 4) 48. x(x + 3) 49. 2x(x + 1) 50. (5x – 3) Find a and b so that the polynomials f(x) = (x2 + 3x + 2) (x2 + 2x + a) and g(x) = (x + 7x + 12) (x + 7x + b) may 2 51. x2 + xy + y2 52. x + 3y 53. 8xy2(x2 + y2) 54. 18(x + 2y) 2 have (x + 1) (x + 3) as their HCF. Q.97 If (x – 2) is a factor of x 2 + ax + b and 55. 2x2 + 2xy + y2 56. x3 – y3 57. 2x – 3y 58. 2x2 + 2xy + y2 59. x2 – x + 1 60. 4x2(x – 2) 61. (x – 1)2 (x + 1) 62. xy(x – y) 63. (x + 7) (x – 3)2 64. x(2x – 3) 65. (x – 2) 66. 2x(x2 – x – 1) 67. (3x – 5) 68. x2 (x – a) 69. (a – b) 70. (x – 1) 71. 4(x2 + 5) a + b = 1, find the values of a and b. 2 Q.98 If (x + 3) (x – 2) is the GCD of f(x) = (x + 3) (2 x – 3x + a) and, g(x) = (x – 2) (3x2 + 10x – b) find the values of a and b. ANSWER KEY 7. HCF = 4 8. HCF = 11 9. HCF = 4 72. a = 6, b = 13 10. HCF = 72, LCM = 45360 11. LCM = 3024 74. a = 12. HCF = 50 75. (i) 6(x + 1) (x2 + 1) 15. HCF × LCM = a × b, No 16. More than 2 factors 6, b = 11 6 (ii) 6x2(3x + 1) 76. (i) x(x + 3) (ii) 2(x2 – 1) 17. Factors of q are in the form of 2m or 5n or 2m × 5n 18. 1.5 4, b = 73. a = 77. a = 7, b = 10 78. x2 – y2 79. a = 3, b = 80. (i) 15x2(2x + 1) (ii) 18x (3x – 1) (iii) 6x(2x + 1) 4 20. 2 × 5 × 7 21. 25, 75, 150, 300 22. 1,14467 24. Non-terminating 23. 70 81. a = 1, b = 5 84. a = 12, b = 15 25. 0.3 6 26. (i) Rational (ii) Not Rational (iii) Rational 27. 0.101001000...., 0.1121231234.... 87. a = 91. m = ± 28. 0.1002, 0.100212112111.... 6, b = 82. 10 83. k = 5 85. k = 5 86. (x + 1) (x2 + 1) 4 88. a = 4, b = 21 1 2 93. (i) x + 5 (ii) 2(x – 7) (iii) x – 1 (iv) 4 (v) 1 30. Terminating 31. (i) Irrational (iii) Rational 35. Not 7 19. 21, 42 (ii) Irrational (iv) Irrational 36. m = 2, n = –1 94. 5 95. a = 2, b = 96. a = 3, b = 6 98. a = 2, b = 3. 97. a = 3 3, b = 6 Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) REAL NUMBERS Page # 103 EXERCISE – II BOARD PROBLEMS Questions Carrying 1 Mark Q.1 p If is a rational number (q q Q.14 Prove that 2 is an irrational number.. [Delhi-2009/AI-2008] Q.15 Prove that 5 is an irrational number.. 0), what is [Delhi-2009/AI-2008] condition of q so that the decimal representation of p is terminating? q [Delhi-2008] Q.16 Prove that 3 + 2 is an irrational number.. [AI-2009] Q.2 Write a rational number between 2 and 3 . [AI-2008] Q.17 Q.3 Complete the missing entries in the following factor tree : [Foreign-2008] Prove that 3 + 5 2 is an irrational number.. [AI-2009] Q.18 Show that the square of any positive odd integers is of the form 8m + 1, for some integer m. [Foreign-2009] Q.19 Prove that 7 + 3 2 is not a rational number.. [Foreign-2009] 2 3 7 Q.4 The decimal expansion of the rational number 43 , will terminate after how many places 2 4 ·5 3 of decimals? [Delhi-2009] Q.5 Find the [HCF × LCM] for the numbers 100 and 190. [AI-2009] Q.6 Find the [HCF × LCM] for the numbers 105 and 120. [AI-2009] Q.7 Write whether the rational number ANSWER KEY 1. q = 2 n × 5 m, where n and m are whole numbers. 2. 51 will 1 50 0 2 = 1.41......., One rational no. between have a terminating decimal expansion or a nonterminating repeating decimal expansion. [Foreign-2009] Q.8 The HCF and LCM of two numbers are 9 and 360 respectively. If one number is 45, write the other number. [Foreign-2009] 3 = 1.73..... 2 and 3 is 1.5. 2 3. 3 42 21 7 Questions Carrying 3 Marks 43 43 = = 0.0215 2 4 ·5 3 2 0 00 Q.9 Show that 5 – 2 3 is an irrational number.. [Delhi-2008] 4. After 4 decimal; Q.10 Show that 2 – 5. HCF × LCM = 100 × 190 = 19000 6. HCF × LCM = 105 × 120 = 12600 7. 51 1 5 00 3 is an irrational number.. [Delhi-2008] Q.11 Show that 5 + 3 2 is an irrational number.. [Delhi-2008] Q.12 Prove that 3 is an irrational number.. [Delhi -2009/AI-2008] Q.13 Use Euclid's Division Lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m. [Foreign-2008/AI-2008] 17 ; 500 = 22 × 53 (2m · 5 n). So, it 5 00 has terminating expansion. 8. Other number = : 0744-2209671, 08003899588 | url : www.motioniitjee.com, 9 3 60 45 72 : [email protected] REAL NUMBERS Page # 104 EXERCISE – III Q.1 A rational number between MULTIPLE CHOICE QUESTIONS 1 1 and is 4 3 7 (B) 0.29 24 13 (C) (D) all the above 48 An irrational number is (A) a terminating and nonrepeating decimal Q.10 (A) Q.2 Q.11 (B) a nonterminating and non repeating decimal (C) a terminating and repeating decimal Q.3 (D) a nonterminating and repeating decimal Which of the following statements is true (A) Every point on the number line represents a rational number (B) Irrational numbers cannot be represented by points on the number line Q.12 22 is a rational number 7 (D) None of these The set of real numbers does not satisfy the property of (A) multiplicative inverse Q.13 (C) Q.4 Q.5 (B) additive inverse (C) multiplicative identity (D) none of these If m is an integer, then square of any positive integer is of the form : (A) 2m + 1 (C) 3m or 3m + 1 Q.6 Q.7 Q.8 Q.9 (B) 2 m or 3m (D) 2m + 1 or 3m + 1 If 'm' is an irrational number then '2m' is (A) a rational number (B) an irrational number (C) a whole number (D) a natural number The value of 3 is (A) 0.414 (B) 2.256 (C) 1.732 (D) none The sum of a rational and an irrational number. (A) an irrational number (B) a rational number (C) an integer (D) a whole number The product of two irrationals is (A) a rational number (B) an irrational number (C) either A or B (D) neither A nor B Q.14 Q.15 The value of 1.34 4.12 is 133 371 (A) (B) 99 90 5169 5411 (C) (D) 990 990 Which of the following statements is false? (A) Every fraction is a rational number (B) Every rational number is a fraction (C) Every integer is a rational number (D) All the above An irrational number is : (A) a terminating and non-repeating decimal (B) a non-terminating and non-repeating decimal (C) a terminating and repeating decimal (D) a non-terminating and repeating decimal 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are (A) composite numbers (B) whole number (C) prime numbers (D) none of these HCF of two numbers is 113, their LCM is 56952. If one number is 904, the other number is : (A) 7719 (B) 7119 (C) 7791 (D) 7911 For what least value of n (where n is a natural number), (24)n is divisible by 8? Q.16 (A) 0 (B) –1 (C) 1 (D) no value of x possible is (A) a rational (B) an irrational (C) both (A) and (B) (D) sometimes rational, sometimes irrational Q.17 Expressing 0.358 as a rational number, we get : 358 358 (B) 100 999 355 (C) (D) None of these 990 Which of the following numbers has the terminating decimal representation ? (A) Q.18 (A) 1 7 (B) 1 3 (C) 3 5 (D) 17 6 Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) REAL NUMBERS Q.19 Page # 105 Missing numbers in the following factor tree are : x y 2 2 (A) x = 34, y = 68 Q.20 Q.28 Express 0.75 as rational number.. (A) 75 90 (B) 25 33 (C) 3 4 (D) None y (B) y = 34, x = 68 (C) y = 34, x = 34 (D) y = 68, x = 68 A lemma is an axiom used for proving : Q.29 (A) other statement (B) no statement Express 0. 358 as rational number (A) 358 1000 (B) 358 999 (C) 355 990 (D) All (C) contradictory statement (D) none of these Q.21 1 ,b 3 2 2 If a 1 , then the value of 3 2 2 a 2 + b2 is : (A) 34 (C) 36 Q.22 (C) a b a is b (B) b a b a 1 0 Q.32 (B) 0 (C) does not exist If Q.31 a b (D) Multiplicative inverse of '0' is (A) Q.25 (B) multiplication (D) none of these The additive inverse of (A) Q.24 (B) 35 (D) 37 5 = 2.236 and (D) none of these 3 = 1.732, then the value 2 7 is 5 3 5 3 (A) 14 (B) 14.39 (C) 14.392 (D) 16 A rational number can be expressed as a terminating decimal if the denominator has factors (A) 2 or 5 (B) 2, 3 or 5 (C) 3 or 5 (D) none of these Express 0.75 as rational number. Q.33 of Q.26 Q.27 Which of the following statements is true? (A) 5 7 (B) 11 13 (C) 5 7 (D) 5 7 The set of all irrational number is closed for (A) addition (C) division Q.23 Q.30 (A) (C) 75 99 (B) 75 90 3 4 (D) None 7 9 9 11 11 13 7 9 5 7 11 13 7 9 9 11 9 11 11 13 7 9 9 11 ______ is a series of well defined steps, which gives a procedure for solving a type of problem. (A) Theorem (B) Statment (C) Algorithm (D) None of these Euclid's division algorithm can be applied to : (A) only positive integers (B) only negative integers (C) all integers (D) none of these Expressing 0.625 as a rational number, we get : (A) 62 .5 1000 (B) 5 8 (C) 625 100 (D) None of these Q.34 A rational number in its standard from can be expressed as a terminating decimal, if the denominator has factors : (A) 2 or 5 (B) 2, 3 or 5 (C) 3 or 5 (D) None of these Q.35 0 .36 as a fraction in the simplest form is : (A) 36 90 (B) 36 100 (C) 11 30 (D) 33 90 : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] REAL NUMBERS Page # 106 Q.36 0.254 as a fraction in the simplest form is 14 (A) 55 (C) Q.37 Q.38 42 165 Q.40 Q.41 Representation of 3 .6 as a fraction in the simplest form is : (A) 11 13 (B) 11 3 (C) 36 10 (D) 3 11 5 6 is : (A) 16 1000 (B) 16 99 (C) 16 100 (D) 8 50 0.1010010001 …… is : (A) a rational number (B) a repeating decimal number (C) an irrational number (D) both (A) and (C) 5 The value of 4 – is 1 (A) 40 31 (B) 4 9 (C) 1 8 (D) 31 40 (A) 3 2 (B) 3 2 (C) 1 2 (D) 1 2 If 6 = 2.449 then the value of to (A) 1.225 (C) 0.613 (B) 0.816 (D) 2.449 IV. 17 8 (A) 2 (B) 4 (C) 9 (D) 16 Q.48 The quotient of (3 2 3 ) (3 2 3) is : Q.49 (A) a rational (B) an irrational (C) both (A) and (B) (D) either (A) or (B) Which of the following is a rational number Q.51 Q.52 3 2 is close 2 3 2 1 1 Set of natural numbers is a subset of (A) set of even numbers (B) set of odd numbers (C) set of composite numbers (D) set of real numbers Q.50 The sum of t he a ddi ti ve i nver se a nd multiplicative inverse of 2 is 1 2 3 3 II. (A) I (B) IV (C) II (D) III Which of the following is not a rational number? (A) 1 4 1 .728 is 5 5 5 5 Q.47 1 2 3 III. Q.46 3 Q.43 Q.45 (A) 0 (B) 5 (C) can't be determined (D) none The greatest among the following is I. 0.16 as rational number in the simplest form is : 1 Q.42 The value of 126 495 (D) (A) a rational number (B) an irrational number (C) can't say (D) both (A) and (B) Q.39 Q.44 254 (B) 1000 5 (B) 6 (C) 8 (D) 9 The sum of two rational number is always (A) an irrational number (B) a rational number (C) a fraction (D) none of these The product of a rational and an irrational number is always : (A) a irrational number (B) a rational number (C) a fraction (D) none of these The sum of a rational number and an irrational number is always : (A) an irrational number (B) a rational number (C) an integer (D) a whole number Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) REAL NUMBERS Q.53 Page # 107 The product of two irrational number is : Q.61 In a morning walk three persons step off together. Their steps measures 80 cm, 85 cm and 90 cm respectively. The minimum distance each should walk so that they can cover the distance in complete step is. (A) 122 m 40 cm (B) 132 m 60 cm (C) 125 m 31 cm (D) 120 m 40 cm Q.62 The number (A) a rational number (B) an irrational number (C) either (A) or (B) (D) neither (A) nor (B) Q.54 1 is : 2 (A) a rational (C) both (A) and (B) (D) none of these If q is some integer, then any positive odd Q.63 integer is of the form : (A) q – 1 (B) 2q (C) 4q + 1 or 4q – 1 Q.64 (D) 4q + 1 or 4q + 3 Q.56 If p : All integers are rational number and q : Every rational is an integer, then which of the following statements is correct? 1 (iii) x > y (D) All (i), (ii), (iii) are correct Q.67 (A) A is false and R is the correct explanation of A (B) A is true and R is the correct explanation of A (C) A is true and R is false Q.68 (D) both A and R are true 8) , then the value of Q.60 The numbre 6 (A) rational (C) can't say (B) 25 (D) 34 2 6 x2 1 x2 (D) none of these 3 Q.69 2 (B) 2 3 is 3 2 (A) 2 (B) 3 (C) 5 (D) 11 The number 3 3 (A) rational (C) both is : 2 and (C) 1.5 (D) 1.8 The irrational number between 2 and 3 is 3 is 3 (B) irrational (D) can't say The rational number between (A) 2 5 (B) 1 5 (C) 3 5 (D) 4 5 2 is (B) irrational (D) none 1 1 (B) 34, 36 1 2 (C) only (ii) is correct (A) 24 (C) 30 1 Rational number between (A) If A : Every whole number is a natural number and R : 0 is not a natural number, then which of the following statement is true? y , x Q.66 (B) only (ii) and (iii) are correct If x = (3 y Two tankers contain 850 litres and 680 litres of petrol respectively. The maximum capacity of a container which can measure the petrol of either tanker in exact number of times is : (A) 160 litres (B) 168 litres (C) 170 litres (D) 180 litres For any two rational number x and y, which of the following properties are correct? (A) only (i) and (ii) are correct Q.59 is Q.65 (D) both p and q are false Q.58 2 where x, y > 0 is (A) rational (B) irational (C) both (D) none Two irrational numbers between 2 and 3 are : 1 (C) both p and q are true (ii) x = y x (C) 68, 34 (B) p is true and q is false (i) x < y The number (A) 22, 64 (A) p is false and q is true Q.57 3 (A) rational number (B) irrational number (C) can't say (D) none (B) an irrational Q.55 2 : 0744-2209671, 08003899588 | url : www.motioniitjee.com, 1 1 and is 2 3 : [email protected] REAL NUMBERS Page # 108 3 3 Q.70 2 2 3 3 2 2 (A) 15 (C) 10 Q.71 (B) 16 (D) 24 1008 is equal to : 4 63 Q.81 (A) 1 (C) 4 Q.72 Q.80 is equal to : 7 (B) 2 (D) 6 5 is : Q.74 Q.75 Q.76 Q.77 88 5 (C) 44 25 (D) none If p : Every fraction is a rational number and Which of the following is a rational number(s) ? (A) (C) Q.83 2 9 3 17 (B) 4 7 (D) All the three 3 is a ____ . 0 (A) positive rational number 121 is 23 32 75 (B) negative rational number (C) either positive or negative rational number (A) a terminating decimal number (B) a non-terminating repeating decimal (C) a rational number (D) both (B) and (C) The largest number of four digits exactly divisible by 12, 15, 18 and 27 is : (A) 9720 (B) 9820 (C) 9920 (D) 9930 (D) neither positive nor negative rational number If x, y, z be rational number such that x > y and z < y then ....... 1 3 1 8 8 1 7 7 1 6 6 4 9 (C) 17 (A) z > x (C) y < z Q.85 1 is 5 2 5 1 1 a b (B) 25 36 (D) 31 17 a is equal to : The domain of the function ƒ(x) = x 4 (A) R – {4} (C) [5, ) Q.84 (B) 1 (D) 5 If a = 2 and b = 3, then (A) Q.79 (B) (D) Both p and q are false Q.82 (A) a rational (B) an irrational (C) an integer (D) not real The greatest number of 6 digits exactly divisible by 24, 15 and 36 is : (A) 999998 (B) 999999 (C) 999720 (D) 999724 (A) 0 (C) 2 Q.78 53 3 (B) p is false and q is true (C) Both p and q are true 2) is : (6 (A) q : Every rational number is a fraction, then which of the following is correct? (A) p is true and q is false (A) an irrational (B) a rational (C) neither (A) nor (B) (D) all of the above Q.73 The equivalent rational form of 17 .6 is x 5 + |x| + x2 (B) R – {4, 5} (D) R Q.86 Q.87 (B) z < x (D) y > x If A : The quotient of two integers is always a 1 rational number and R : is not rational, then 0 which of the following statement is true (A) A is true and R is the correct explanation of A (B) A is false and R is the correct explanation of A (C) A is true and R is false (D) Both A and R are false For what least value of n, where n is a natural number, 5n is divisible by 3? (A) 1 (B) 0 (C) 2 (D) no value of n is possible Which one is the correct alternative of the decimal representation of an irrational number ? (A) non - terminating, non-repeating (B) terminating (C) termiating, repeating (D) non-terminating, repeating Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) REAL NUMBERS Q.88 (C) Q.90 133 990 (B) 5169 990 (D) 371 290 (A) 5411 990 1 3 3 1 3 3 (A) 6765207 (B) 6765201 (D) 23.10100100010000..... (C) 6765206 (D) 6765209 Two candles are of different lengths and thicknesses. The short and the long ones can burns respectively for 3.5 h and 5 h. After burning for 2 h, the lengths of the ca ndles become equal in length. What fraction of the long candle’s height was the short candle initially? [NTSE 2013] 5 (B) 7 3 ANSWER KEY 1. D 2. B 3. D 4. D 5. C 6. B 7. C 8. A 9. C 10. D 11. B 12. B 13. A 14. B 15. C 16. 17. C 18. C 19. B 20. A 22. D 23. A 24. C 25. C 26. A 27. C 28. B 29. C 30. A 31. C 32. C 33. B 34. A 35. C 36. A 37. B 38. B 39. B 40. C 41. C 42. B 43. A 44. B 45. D 46. A 47. D 48. B 49. D 50. B 51. A 52. A 53. C 54. B 55. D 56. B 57. D 58. A 59. D 60. A 61. A 62. B 63. A 64. C 65. C 66. C 67. C 68. B 69. C 70. C 71. B 72. A 73. B 74. C 75. D 76. A 77. D 78. B 79. C 80. A 81. A 82. D 83. D 84. B (B) 6n + 3 85. B 86. D 87. A 88. B (C) 8n + 3 89. B 90. B 91. D 92. C (D) 4n + 1 but may not be 8n + 1 93. D 94. D 3 5 (D) 21. 4 5 I left home for bringing milk between 7 am and 8 am. The angle between the hour hand and the minute hand was 90°. I returned home between 7 am and 8 am. Then, also the angle between the minute hand and hour hand was 90°. At what time (nearest to second) did I leave and return home? [NTSE 2013] (A) (B) (C) (D) 7 7 7 7 h h h h 18 19 20 21 min min min min 35 24 42 49 s s s s and and and and 7 7 7 7 h h h h 51 52 53 54 min min min min 24 14 11 33 s s s s The square of an odd integer must be of the form [NTSE 2013] (A) 6n + 1 Q.93 41616 (B) 23.232323 (C) (C) Q.92 Which of the following is an irrational number? [NTSE 2013] Which of the following numbers is the fourth power of a natural number? [NTSE 2013] 2 (A) 7 Q.91 Q.94 The value of 1.34 4 .12 is (A) Q.89 Page # 109 a b 2 b a 2 is [NTSE 2013] (A) always zero (B) never zero (C) positive if and only, if a > b (D) positivel only, if a b : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] Page # 110 WORK, LIFE AND LEISURE WORK, LIFE & LEISURE CHARACTERISTICS OF THE CITY 1. 2. Town and cities that first appeared along river valleys, such as Ur, Nippur and Mohenjodaro, were larger in scale than other human settlements. Ancient cities could develop only when an increase in food supplies made it possible to support a wide range of non-food producers. Cities were often the centres of political power, administrative network, trade and industry, religious institutions, and intellectual activity, and supported various social groups such a artisans, merchants and priests. Cities themselves can vary greatly in size and complexity. They can be densely settled modern-day metropolises, which combine political and economic functions for a entire region, and support very large populations. Or they can be smaller urban centres with limited functions. The industrialisation and the rise of the Modern city in England: The early industrial cities of Britain such as Leeds and Manchester attracted large number of migrants to the textile mills set up in the late eighteenth century. In 1851, more than three-quarters of the adults living Manchester were migrants from rural areas. Now let us look at London. By 1750, one out of every nine people of England and Wales lives in London. It was a colossal city with a population of about 675000. Over the nineteenth century. London continued to expand. Its population multiplied fourfold in the 70 years between 1810 and 1880, increasing 1 million to about 4 million. The city of London : The city of London was a powerful magnet for migrant populations, even though it did not have large factories. ‘Nineteenth century London’, says the historian Gareth Stedman Jones, ‘was a city of clerks and shopkeepers, of small masters and skilled artisans, of growing number of semi skilled and sweated outworkers, of soldiers and servants, of casual labourers, street sellers, and beggar’. Apart from the London dockyards, five major types of industries employed large numbers clothing and footwear, wood and furniture, metals and engineering, printing and stationary, and precision products such as surgical instruments, watches, and objects of precious metal. During the First World War The growth of London, (1914-18) London began manufacturing motor cars and electrical a map showing its population goods, and the number of large factories increased until they in four different years. accounted for nearly one-third of all jobs in the city. In the mid-nineteenth century. Henry Mayhew wrote several volumes on the land on labour and compiled long lists of those who made living from crime. Many of whom he listed as ‘criminals’ were in fact poor people who lived by stealing lead from roofs, food from shops, lumps of coal, and clothes drying on hedges. There were others who were more skilled at their trade, expert at their jobs. They were cheats and tricksters, pickpockets and petty thieves crowding the streets of London. In an attempt to discipline the population, the authorities imposed high penalties for crime and offered work to those who were considered the ‘deserving poor’. With technological developments, women gradually lost their industrial jobs, and were forced to work within household. The 1861 census recorded a quarter of million domestic servants in London of whom the vast majority were women, many of them recent migrants. A large number of women used their homes to increase family income by taking in lodgers or through such activities as tailoring, washing or matchbox making. However, there wa s a change once again in the twe nt ieth ce ntury. As women got employment in wartime industries and offices, they withdraw from domestic service. Large numbers of children were pushed into low-pad work, often by their parents. Andrew Means, a clergyman who wrote The Bitter Cry of outseast London in the 1880s, showed why crime was more profitable than labouring in small underpaid factories. A child seven years old is easily known to make 10 shillings 6 pence a week from thieving ... Before he can gain as much as the young thief (a boy) must make 56 gross of matchboxes a week, or 1,296 a day. It was only after the passage of the compulsory Elementary Education Act in 1870 and the factory acts beginning from 1902, that children were kept out of industrial work. Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) Page # 111 WORK, LIFE AND LEISURE 3. Housing : For a while the better-off city dwellers continued to demand that slums simply be cleared away. But gradually a larger and larger number of people began to recognise the need for housing for the poor. What were the reasons for this increasing concern ? A Stranger's Home, The Illustrated London New, 1870. First, the vast mass of one-room houses occupied by the poor were seen as a serious threat to public health; they were overcrowded, badly ventilated lacked sanitation. Second, there were worries about fire hazards created by poor housing. Third, there was a widespread fear of social disorder, especially after the Russian Revolution in 1917. Workers mass housing schemes were planned to prevent London poor from turning rebellious. Rat-trap seller, cartoon by Rowlandson, 1799 A London slum in 1889. For the poor, the street often was the only place for rest, leisure and fun. The Illustrated Lond News, 1856. : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] Page # 112 4. WORK, LIFE AND LEISURE Clearing London : The congestion in the nineteenth-century industrial city also led to a yearning for clean country air. Many wealthy resident of London were able to afford a holiday home in the countryside. Demands were made for new ‘lungs’ for the city, and some attempts were made to bridge the difference between city and countryside through such ideas as the Green Belt around London. Between two world wars (1919-39) the responsibility for housing the working classes was accepted by the British state, and a million houses, most of them single-family cottages, were built by local authorities. Meanwhile, the city had extended beyond the range where people could walk to work, and the development of suburbs made new forms of mass transport absolutely necessary. 5. Transport in the City : The very first section of the Underground in the world opened on 10 January 1863 between Paddington and Farrington Street in London. On that day 10,000 passengers were New Earswick, a garden suburb carried, with trains running every ten minutes. By 1880 the expanded train service was carrying 40 million passengers a year. At first people were afraid to travel underground. This is what one newspaper reader warned : To make approximately two miles of railway, 900 houses had to be destroyed. Thus the London tube railway led to a massive displacement of the London poor, especially between the two world wars. Yet the Underground eventually became huge success. By the twentieth century, most large metropolises such as New York, Tokyo and Chicago could not do without their well functioning transit system. As a result, the population in the city became more dispersed. Better planned suburbs and good railway network enabled large number to live outside central London and travel to work. Railway lines being laid in London, Illustrated Times, 1868. Cows on the streets of London, The Graphic, 1877 SOCIAL CHANGE IN THE CITY Ties between members of households loosened, and among the working class the institution of marriage tended to break down. Women of the upper and middle classes in Britain, on the other hand, faced increasingly higher levels of isolation, although their lives were made easier by domestic maids who cooked, cleaned and cared for young children on low wages. Women who worked for wages had some control over their lives, particularly among the lower social classes. However, many social reformers felt that the family as an institution had broken down, and needed to be saved or reconstructed pushing these women back into the home. Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) Page # 113 WORK, LIFE AND LEISURE 1. Men, Women and Family in the City : Men and women did not have equal access to this new urban space. As women lost their industrial jobs and conservative people railed against their presence in public spaces, women were forced to withdraw into their homes. The public space became increasingly a male preserve, and the domestic sphere was seen as the proper place for women. Most political movements of the nineteenth century, such as Chartism (a movement demanding the vote for all adult males) and the 10-hour movement (limiting hours of work in factories), mobilised large numbers of men. Only gradually did women come to participate in political movements for suffrage that demanded the right to vote for women, or for married women’s rights to property (from the 1870s). By the twentieth century, the urban family had been transformed yet again, partly by the experience of the valuable wartime work done by women, who were employed in large numbers to meet war demands. The family now consisted of much smaller units. 2. Leisure and Consumption : For wealthy Britishers, there had long been an annual ‘London Season’. Several cultural events, such as the open the theatre and classical music performances were organised for a elite group of 300-400 families in the late eighteenth century. Meanwhile, working classes met in pubs to have a drink, exchange news and sometimes also to organise for political action. Many new types of large-scale entertainment for the common people came into being, some made possible with money from the state. Libraries, art galleries and museums were established in the nineteenth century to provide people with a sense of history and pride in the achievements of the British. At first, visitors to the British Museum in London numbered just about 15,000 every year. A famous London resort, painting by T.E. Turner, 1923 POLITICS IN THE CITY In the severe winter of 1886, when outdoor work came to a standstill, the London poor exploded in a riot, demanding relief from the terrible conditions of poverty. Alarmed shopkeepers closed down their establishements, fearing the 10,000 strong crowd that was marching from Deptford to London. The marchers had to be dispersed by the police. A similar riot occurred in late 1887; this time, it was brutally suppressed by the police in what came to be known as the Bloody Sunday of November 1887. Two years later, thousands of London’s dockworkers went on strike and marched through the city. According to one writer, ‘thousands of the strikers had marched through the city without a pocket being picked or window being broken....’ The 12-day strike was called to gain recognition for the dockworkers’ union. : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] Page # 114 WORK, LIFE AND LEISURE THE CITY IN THE COLONIAL INDIA The pace of urbanisation in India was slow under colonial rule. In the early twentieth century, no more than 11 percent of Indians were living in cities. A large proportion of these urban dwellers were resident of the three Presidency cities. These were multi-functional cities, they had major ports, warehouses, homes and offices, army camps, as well as educational institutions, museums and libraries. Bombay was the premier city of India. It expanded rapidly from the late nineteenth century, its population going up from 644,405 in 1872 to nearly 1,500,000 in 1941. A bustling sreet in Null Bazaar, Bombay, photograph by Raja Deen Dayal, late nineteenth century. 1. Bombay the Prime city of India ? : Bombay was a group of seven islands under Portuguese control. In 1661, control of the islands passed into British hands after the marriage of Britain’s King Charles II to the Portuguese princess. The East India Company quickly shifted its base from Surat, its principal western port, to Bombay. Later in the nineteenth century, the city functioned a port through which large quantities of raw materials such as cotton and opium would pass. Gradually, it also became an important administrative centre in western India, and then, by the end of the nineteenth century, a major industrial centre. A view of Bombay, 1852. 2. Work in the City : The city quickly expanded. With the growth of trade in cotton and opium, large communities of traders and blankers as well as artisans and shopkeepers came to settle in Bombay. The establishment of textile mills led to fresh surge in migration. Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) Page # 115 WORK, LIFE AND LEISURE The first cotton textile mill in Bombay was establish in 1854. By 1921, there were 85 cotton mills with about 146,000 workers. Only about one-fourth of Bombay’s inhabitants between 1881 and 1931 were born in Bombay the rest came from outside. Large numbers flowed in from the nearby district of Ratnagiri to work in the Bombay mills. Women formed as much as 23 per cent of the mill workforce in the period between 1919 and 1926. After that, their numbers dropped steadily to less than 10 per cent of the total workforce, By the late 1930s, women’s jobs were increasingly taken over by machines or by men. 3. A map pf Bombay in the 1930s showing the seven islands and the reclamations. Housing and Neighbourings : Bombay was a crowded city. While every Londoner in the 1840s enjoyed an average space of 155 square yards, Bombay had a mere 9.5 square yards. By 1872, when London has a average of 8 persons per house, the density in Bombay was a high as 20. From its earliest days. Bombay did not grow according to any plan, and houses, especially in the Fort area, were interspersed with gardens. The Bombay First area which formed the heart of the city in the early 1800s was divided between a ‘native’ town, where most of the Indians lived, and European or ‘white’ section. Many families could reside at a time in a tenement. The Census of 1901 reported that the mass of the island’s population or 80 per cent of the total, resides in tenements of the one room; the average number of occupants lies between 4 and 5 ....’ High rent forced workers to share homes, either with relatives or caste fellows who were steaming into the city. People had to keep the windows of their rooms closed even in humid weather due to the ‘close proximity of filthy guttes, privies, buffalo stables etc.’ Yet though water was scarce, and people often quarrelled every morning for a turn at the tap, observers found that houses were kept quite clean. The homes being small, streets and neighbourhoods were used for a variety of activities such as cooking, washing and sleeping. Liquor shops and akbaras came up in any empty spot. Streets were also used for different types of leisure activities. Parvathibai Bhor recalled her childhood years in the early twentieth century this way. ‘There was an open space in the middle of our four charts. There the magicians, monkey players or players or acrobats used to regularly perform their acts. The Nandi bull used to come. I used to be especially afraid of the Kadaklakshmi. To see that they had to beat themselves on their naked bodies in order to fill their stomachs frigntened me’. Finally, chawls were also the place for the exchange of news about jobs-strikes riots or demonstrations. Caste and family groups in the mill neighbouring were headed by someone who was similar to a village headman. Somet imes, the jobber in t he mills could be the local neighbourhood leader. He settled disputes, organised food supplies or arranged informal credit. He also brought important information on political developments. : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] Page # 116 WORK, LIFE AND LEISURE Chawl on Kalbadevi Road built in the early twentieth century. 4. Land Reclamation in Bombay : The need for additional commercial space in the mid-nineteenth century led to the formulation of several plans, both by government and private companies, for the reclamation of more land from the sea. Private companies became more interested in taking financial risks. In 1864, the Back Bay Reclamation Company won the right to reclaim the western foreshore from the tip of Malabar Hill to the end of Colba. Reclamation often meant the levelling of the hills around Bombay. By the 1870s, although most of the private companies closed down due to the mounting cost, the city had expanded to about 22 square miles. As the population continued to increase rapidly in the early twentieth century, every bit of the available area was built over and new areas were reclaimed from the sea. 5. Bombay as the City of Drams : The world of Cinema and culture : Many Bombay films deal with the arrival in the city of new migrants, and their encounters with the real pressures of daily life. Some popular songs from the Bombay film industry speak of the contradictory aspects of the city. In the film CID (1956) the hero’s buddy sings, ‘Ai dil hai muskil jeena yahan : zara hatke zara bachke ye hai Bomaby meri Jaan’ (My heart, it is difficult to live here ! more over a little, take care of yourself this is Bombay my love). A slightly more disillusioned voice sings in Guest house (1959); Jiska juta usika sar, dil hai choota bada shahar, ye hai tumahri Bombay; (Bombay, you city what a place ! Here one gets beaten with one’s own shoes ! The city is big but people’s hearts are small). Most of the people in the film industry were themselves migrant who came from cities like Lahore, Calcutta, Madras and contributed to the national character of the industry. Those who came from Lahore, then in Punjab, were especially important for the development of the Hindi film industry. Many famous writers, like Ismat Chughtai and Saadat Hasan Manto, were associated with Hindi cinema. CITIES AND THE CHALLENGES OF THE ENVIRONMENT The widespread use of coal in homes and industries in nineteenth century. England raised serious problems. In industrial cities such as Leeds, Bradford and Manchester, hundreds of factory chimneys spewed black smoke into the skies. People joked that most inhabitants of these cities grew up believing that the skies were grey and all vegetation was black ! Shopkeepers, homeowner and other complained about the black fog that discended on their towns, causing bad tempers, smoke-related illnesses, and dirty clothes. Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) Page # 117 WORK, LIFE AND LEISURE When people first joined campaigns for cleaner air, the goal was to control the nuisance through legislation. This was not at all easy, since factory owners and stead engine owners did not want to spend on technologies that would improve their machines. By the 1840s, a few towns such as Derby, Leeds and Manchester had laws to control smoke in the city. But smoke was not easy to monitor or measure, and owners go away with small adjustments to their machinery that did nothing to stop the smoke. Moreover, the Somke Abatement Act of 1847 and 1853, as they were called, did not always work to clear the air. Calcutta had a long history of air pollution. Its inhabitants inhaled grey smoke, particularly in the winter. Since the city was built on marshy land, the resulting fog combined with smoke to generate thick black smog. High levels of pollution were a consequence of the huge population that depended on dung and wood as fuel in their daily life. But the main polluters were the industries and establishments that used steam engines run on coal. IMPORTANT TERMS 1. Many decades after the beginning of the industrial revolution, most western countries were largely rural till 1850. 2. More than three quarters of the adults living in Manchester were migrants from rurals areas till 1851. 3. One out of every nine people of England and Wales lived in London by 1750. 4. The population of London multiplied four fold between 1810-80. 5. The compulsory Elementary Education Act was passed in 1870. 6. The factory Acts beginning from 1902. 7. The responsibility for housing the working class was accepted by the British state in 1919-39. 8. ‘Charls Dickens wrote about the massive destruction in the process of construction in 1848. 9. The London poor exploded in riot demanding relief in 1886. 10. A similar riot occurred in late 1887. 11. One fifth of the streets of Paris were Haussmann’s creation by 1870. 12. Bankim Chandra Chattopadhyay wrote short sketches on urban life in Calcutta in 1962. 13. After the marriage of Britain’s King Charles II to the Portuguese princess the control of Bombay was transferred to Britishers in 1661. 14. Bombay became the capital of Bombay Presidency in 1819. 15. About 1/4 of Bombay’s inhabitants were born in Bombay, the rest came from outside between 1881 and 1931. 16. Bombay was built a dry dock between 1914-18. 17. The film industry employed 520,000 people by 1987. 18. Calcutta became the first city to get smoke nuisance legislation in 1863. 19. The smoke abatement Act of 1847 and 1853. : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] Page # 118 Exercise - I WORK, LIFE AND LEISURE UNSOLVED PROBLEMS A. VERY SHORT ANSWER TYPE QUESTIONS B. SHORT ANSWER TYPE QUESTIONS Q.1 What is metropolis ? Give an examples of Q.1 Examine the historical processes involved in metropolis in India. Q.2 Name two industrial cities in England in 19th the development of cities. Q.2 Mention the steps taken to clean up London. Q.3 Explain the evolution of Bombay as one of the century. Q.3 Mention two steps t aken by the London major cities of India. authorities to discipline its population. Q.4 Q.4 Describe the Bombay fort area. Q.5 What is referred to as Chawls in Bombay ? Why were the slams considered to be threat to public for London ? With which kind of London housing can these Q.5 Why were the slums considered to be threat be compared ? How are these similar ? to public health ? Q.6 Q.6 Examine the effects of air pollution on Calcutta. Q.7 By whom was the concept of a Garden city Name two Acts passed in England to keep the children out of industrial world. first developed ? What were the main features Q.7 When by whom was the first movie made in of the proposed Garden city ? Bombay ? What did the movie depict ? Q.8 Name the first proper Hindi movie. By whom & Q.8 construction of underground railways. when was this movie made ? Q.9 Mention the problems raised in England in 19th Q.9 Q.10 Q.11 Q.10 Q.11 Under what circumstances were the ancient Examine the ne w ty pes of large scale ent ert ainment fo r the common people When was the Rent Act passed in Bombay ? introduced in 19th century. What was its out come ? Q.12 What were the mode of entertainment in the 18th century England ? Which two stations of London were connected by the first underground railways ? How was the family life transformed in an industrial city of London ? century due to widespread use of coal in industrial cities. Examine the difficulties faced by people due to Q.12 Why was the expansion of the city of Bombay difficult ? Mention any one way adopted to cities developed ? develop the city. Q.13 Name four industries which employed largest member of people is London in early 20th Q.13 environment ? century ? Q.14 What is meant by temperance movement ? Q.14 When was the Bombay Improvement Trust est abli she d ? W hat was its imm ediat e When did Bombay film industry make its first appearance ? What was its main aim ? Q.15 How do es urba nisation pose a threat to Q.15 Why police was worried for the law and order of London ? achievement ? Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.) Page # 119 WORK, LIFE AND LEISURE Q.16 Q.17 Mention various measures which were taken Q.10 the cost of ecology and environment? Explain, centuries. giving examples of industrial cities of England [Delhi 2009] in the nineteenth century. How far was the underground railway able to solve trasnport problems as well as housing Q.11 crisis in London in the nineteenth century? Why is Mumbai (Bombay) known as the city of dreams? Give three reasons. [Delhi 2008] Explain any three reasons for which the population of the London City expanded over the nineteenth century. [O.I. 2008] Q.18 How is urban development directly related to to decongest London in the 19th and 20th Q.12 [O.I. 2009] Explain the social changes which led to the need for the underground railways in London. [Delhi 2010] [A.I. 2007] C. LONG ANSWER TYPE QUESTIONS Q.1 “London was powerful magnet for largest Q.13 What was the tradition of 'London Season'? Explain different forms of entertainment that came up in nineteenth century England to population”. Explain. Q.2 provide leisure activities for the people. How were women employed in London beyond [A.I. 2011] 19th century ? How did the situation change after 20th century. Q.3 Q.14 What were the reasons for concern behind Describe the means of entertainment available in England in the Nineteenth Century. providing housing for poor in London ? Q.4 [RBSE 2013] What were chartist movement and Ten Hour Movement ? Q.5 How do we distinguish between cities on the one hand and towns and villages on the other? Q.6 Explain the life style o f wo rkers of t he mid-nineteenth century in Britain. [A.I. 2010] Q.7 How did the development of cities influence the ecology and environment in late 19th century? Explain by giving an example of Calcutta. Q.8 [Delhi 2011] Explain any three reasons for the increasing concerns about the need for housing for the poor in London after the Industrial Revolution. [A.I. 2011] Q.9 Describe in brief the development of Bombay (Mumbai) as the 'Prime City' of India. [A.I. 2012] : 0744-2209671, 08003899588 | url : www.motioniitjee.com, : [email protected] Page # 120 WORK, LIFE AND LEISURE Exercise - II Q.1 NTSE/OLYMPIAD PROBLEMS What was not a reason for providing mass (A) Concern for the poor (A) 1996 (B) 1897 (B) Fear of Social disorder (C) 1898 (D) 1900 Q.11 passed in - Which movie did Dada Sahab Phalke make ? (A) 1860 (B) 1870 (A) CID (C) 1880 (D) 1890 Q.12 (D) Tezab Q.5 Bombay was first under whose control ? (A) Portuguese (B) English (C) French (D) Dutch Q.13 (B) Bombay (C) Calcutta (D) Lucknow Q.14 in a planned manner ? Q.6 Q.7 Q.8 (B) Madras (C) Signapore (D) Lucknow Q.15 (B) 1887 (C) 1888 (D) 1889 Q.16 When was the Rent Act passed in Bombay ? (A) 1910 (B) 1918 (C) 1920 (D) 1922 (C) Jaipur (D) Calcutta Bombay was built a ............... between (A) Harbour (B) Capital (C) Seaport (D) Dry dock The film industry employed .............. people (A) 500000 (B) 520,000 (C) 540,000 (D) 560,000 Bombay became the capi tal of Bo mbay Presidency in - When was the first movie made in India ? (A) 1886 (B) Bombay by 1987. Which of the following cities has developed (A) Delhi (A) Delhi 1914-18 Which of the following is not a Presidency city? (A) Madras ................ became the first city to get smoke nuisence legislation in 1863. (C) Raja Harishchandra Q.4 The compulsory Elementary Education Act was (D) All the above (B) Guest house Q.3 The city of Bombay improvement trust was established in - (C) Threat to public health Q.2 Q.10 housing schemes for the workers ? (A) 1817 (B) 1818 (C) 1819 (D) 1820 What is the meaning of urbanization? (A) Development of a city or town (B) People migrating from rural to urban (C) Expansion of city Who developed the concept of a Garden city? (D) All these (A) Ebenezer Howard (B) Clive ANSWER KEY (C) Pluto 1. A 2. C 3. A 4. D 5. C 6. A 7. B 8. A 9. B 10. C 11. B 12. D 13. D 14. B 15. C 16. D (D) John Mill Q.9 Name the Industrial city of England in 19th century (A) London (B) Leeds (C) Washington (D) None of these Corporate Head Office : Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5 (Raj.)