Download XI Science - DAV College

XI Science
(SUBJECT: PHYSICS (Day), TEACHER: R.P. SIR)
Short Questions
1. Why are convex mirrors used in cars for rear view?
2. Can a plane mirror ever form a real image? Explain.
-1
3. If you are bringing plane mirror towards your face at right angle to your face with speed of 10ms , at
what rate is the image approaching?
4. Spherical mirror may behave as a plane mirror as a special cases. Explain.
Long Questions
1. Prove mirror formula for a concave mirror when real image is formed?
2. Prove mirror formula for convex mirror?
3. Derive an expression for lateral shift?
Numerical problems
1. A 2 cm tall object is placed at 15 cm from a concave mirror of focal length 10 cm. Find the position,
size and nature of the image.
2. A concave mirror forms, on a screen, a real image of twice the linear dimension of the object. Object
and screen are the moved until the image is three times the size of object. If the shift of the screen is
25 cm, determine the shift of object and focal length of mirror.
(SUBJECT: PHYSICS, TEACHER: C.K. SIR)
Short Questions
1. How many number of electrons gained by the body when it is charged with -6μC?
2. Calculate the mass lost by the body on string +3.2μC charge.
3. Defien surface charge density and action of point.
4. Sharp corners are strictly probihited in the electrical machine. Explain why?
5. Define the term relative permitivity.
Long Questions
1. State and explain Coulumb's law of electrostatics.
2. Define electric field and electric field intensity. Derive an expression for it.
Numerical problems
1. Calculate electrostatice force between two charges +5μC and -10μC separated by 1cm in a medium.
(Er=7.5)
2. Two charges +6μC and -8μC are situated at two corners of an equilateral triangle (1cm side). Calcuate
resultant electric field intensity at third corner.
3. Two charges +2μC and +4μC are separated by 2cm. Find out hte point in between them at which
resultant electric field intensity is zero.
(SUBJECT: PHYSICS, TEACHER: C.M. SIR)
Short Question
1. Define precise and accurate measurement.
2. Taking force length and time to be fundamental quantities, find the dimensional formula for pressure
and density.
3. Convert 10 dynes to Newton.
4. What are the limitations of dimensional formula.
5. A physical quantity has magnitude and direction. Is it the necessary quality to be a vector?
6. if two vectors of unequal magnitude are combined, can they give zero resultant?
7. Can the resultant of three vectors be zero?
8. Is electric current a vector?
9. give the conditio nwhen two equal vectors 'P' and 'P' gives a resultant equal to '0'?
10. if 𝑖, 𝑗 𝑎𝑛𝑑 𝑘 are unit vectors along x, y and z-axis respectively, find 𝑖. 𝑘 × 𝑗 .
Long Question
1. A force (in Newton) expressed in vector notation as 𝐹 = 4𝑖 − 7𝑗 − 3𝑘 is applied on a body and
produces a displacement (in meter) 𝐷 = 3𝑖 − 2𝑗 − 5𝑘 in 4 seconds. Estimate the power.
2. State triangle law of vector additon. Obtain an expression for the resultant of two vectos 𝑃 𝑎𝑛𝑑 𝑄
inclined at angle θ.
3. State and explain the parallelogram law of vector addition.
Numerical
1. The displacement of an oscillator is given by 𝑥 = 𝑥0 + 𝐵1 cos 𝜔1 𝑡 +
𝐵2 2
𝐵1
cos 𝜔2 𝑡. Here x is measure in
metre and t is measure in seconds. Fidn the dimensional forumla of x 0, B2 and ω2.
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XI Science
(SUBJECT: PHYSICS, TEACHER: H.L. SIR)
Short Questions
1. Why water is not used as a thermometric substance?
2. What is absolute zero temperature?
3. Should a thermometer bulb have large heat capacity or small heat capacity?
4. Why are measuring scales generally made of wood or plastic but not of metals?
5. Does the coefficient of linear expansion of a body depends on its initial length? Explain.
6. Why a pendulum clock goes slow in summer and fast in winter?
7. Two bodies of same material have the same external diameters and appearance but one is hollow and
otehr is solid. When their temperature are raised equally, is the overall expansion same or different?
Long Questions
1. Define linear and suferpficial expansivity. Derive a relation between them.
2. What is differential expansion? Under what condition is its value zero?
3. Explain Pullinger's apparatus to determine the linear expansivity of a solid.
Numerical problems
1. Calculate the length of a brass rod which will show the same expansion as an iron rod 4m long, when
0
both are heated through the same range of temperature. (α for brass=0.000018/ C, α for
0
iron=0.000012/ C]
-5 0
2. The pendulum of a clock is made of brass whose linear expansivity is 1.9×10 / C. If the clock keeps
0
0
correct time at 15 C, how many seconds per day will it lose at 20 C?
(SUBJECT: PHYSICS (Morning), TEACHER: N.S. SIR)
1. Explain how a plane mirror can form a real image?
2. Can a plane mirror ever form a real image? Explain
3. Trace the position of an image formed by a concave mirror when real object is placed at a distance
less than its focal length?
4. A spherical mirror be immersed in water will its focal length change?
5. If light ray is normally incident on a plane mirror, what is the glancing angle and angle of deviation?
6. Distinguish between real and virtual images.
7. What should be the minimum height of a vertical plane mirror so that a person standing in front of it
can be his full image?
8. A Stick partially dipped in water seems to be bent why?
9. Define critical angle and total internal reflection.
10. What is lateral shift? Derive an expression for its value. How does the lateral shift change with the
increase in the angle of incidence?
11. What is the apparent position of an object below a rectangular block of glass 8cm thick if a layer of
water 6cm thick is on the top of the glass? (aμg=1.5 and aμw=1.33)
12. A microscope is focused on a scratch on the bottom of a breaker. Turpentine is poured into the beaker
to a depth of 4cm, and it is found necessary to raise the microscope through a vertical distance of
1.25m to bring the scratch again into focus. Find the refractive index of turpentine.
𝑟𝑒𝑎𝑙 𝑑𝑒𝑝𝑡 𝑕
13. Prove that 𝜇 =
.
𝑎𝑝𝑝𝑎𝑟𝑒𝑛𝑡 𝑑𝑒𝑝𝑡 𝑕
(SUBJECT: PHYSICS, TEACHER: R.D. SIR)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
Why bridges are declared unsafe after long time?
Which one is more elastic, air or iron? Explain
Explain why springs are made up of steel not of copper? Explain.
Differentiate between elasticity and plasticity.
Two wires A and B have equal lengths and are made of same material. If the diameter of wire A is
twice that of wire B, which wire has the greater extension for a given load?
What happens in the young’s modulus of elasticity of a material when the load hanging on it is
doubled?
Machine parts are jammed in cold day. Why?
Define viscosity. Does it depend on temperature?
Define coefficient of viscosity and express it’s unit and dimension.
Explain why a sphere falling through a viscous medium acquires a terminal velocity? Derive an
expression for it.
What is Poisson’s ratio? Derive an expression for the energy stored in a stretched wire?
State Hooke’s law. How would you verify it experimentally?
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XI Science
13. A uniform steel wire of density 7800kg/m… weights 16 gram and is 250cm. It lengthens by 1.2mm
when a load of 8kg is applied. Calculate the value young’s modulus for the steel and the energy stored
in the wire?
14. How much force is required to punch a hole 1cm in diameter in a steel 5mm thick whose shearing
8
-2
strength is 2.76×10 Nm .
-1
15. Two drops of same liquid of same radius are falling through air with steady velocity 2ms . If the two
drops coalesce what would be the terminal velocity?
0
-2
-3
16. Castor oil at 20 C has a coefficient of viscosity 2.42Nsm and density 940 kgm Calculate the terminal
velocity of a steel ball of radius 2mm falling under gravity in the oil.
(SUBJECT: CHEMISTRY)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Convert 0.1 mole CO2 at NTP into
a.
mass
b.
number
c.
volume
Atomic mass of Na is 23 amu. Calculate the mass of one sodium atom in gram.
What mass of Mg contains same no. of atoms present in 7 gram of nitrogen?
Calcuate the notal no. of oxygen atoms present in 18gram of C6H12O6.
How many grams of sulphur and how many gram atom of oxygen are required to prepare 0.2 mole
of SO2?
Define atomic weight? Why is it fractional?
Write short notes on quantum numbers.
Shat is atomic orbital? Write the shape of s and p orbitals.
Write the limitations of Rutherford's model of atom.
Draw well labeled diagram of spectral series of hydrogen. How do you explain hydrogen spectrum
on the basis of Bohr's model?
Write the electronic configuration of
a.
Cr
b.
Cu
Write modern periodic law.
Define the terms
a.
calcinations
b.
roasting
c.
flux
d.
slag
e.
pyrometallurgy
f.
froth flotation process
Write short notes on functional group.
Write short notes on advantages of modern periodic table.
(SUBJECT: MATHEMATICS, TEACHER: S.S. SIR)
1. Find a single H.M. between a and b.
2. The AM, GM, HM between two unequal and positive numbers will satisfy the relations.
2
a. AM×HM=(GM)
b. HM<GM<AM
3. If the three consecutive terms of a G.S. be increased by their middle term, then proe that the resulting
terms will be in H.s.
4. if one A.M. 'A' and two G.M.'s G1 and G2 are inserted between two given positive numbers. Prove that
𝐺1 1
𝐺2
+
𝐺2 2
𝐺1
= 2𝐴
𝑏𝑐
𝑐𝑎
𝑎𝑏
5. If a, b, c are in H.P. prove that
,
,
are in H.P.
𝑏+𝑐 𝑐+𝑎 𝑎+𝑏
6. The sume of an infinite numbers of terms in G.S. is 15, and the sum of their squares is 45; find the
series.
th
7. Find the n therm and then the sum of the first n terms of the series 1+3+6+10+....
8. Sum to n terms of the series 1+(1+2)+(1+2+3)+...
2
3
9. Sum to n terms of 1 + 2a + 3a + 4a + ....
10. Find the nth term and then sum of the first n terms of 3 + 7 + 13 + 21 + 31 + ...
11. Find the general term and then the sum of first n terms
1.n + 2.(n-1) + 3.(n-2) + ...
12. Sum to n terms of 0.4 + 0.44 + 0.444 + ...
3
7
15
13. Sum to infinity of 1 + + + + ⋯
4
16
64
3
XI Science
2
3
14. Sum to infinity of 1 - 5a + 9a - 13a + .... ∞ (-1 < a < 1)
15. If the AM of two positive nubmers a and b be twice their GM show that 𝑎: 𝑏 = 2 + 3 ∶ 2 − 3
4
7
10
16. Sum to n terms of 1 + + 2 + 3 + ⋯
5
17.
18.
19.
20.
5
1
5
2
3
4
Sum to n terms of the series + + + + ⋯
2
4
8
16
th
find the n term of 1 + 5 + 12 + 23 + ...
Find the sum of cubes of first n-natural nubmers.
if A be teh arithmetic mean and H be the harmonic mean between two quantities a and b show that
𝑎−𝐴
𝑏−𝐴
𝐴
×
=
𝑎−𝐻
𝑏−𝐻
𝐻
(SUBJECT: MATHEMATICS, TEACHER: S.K.S. SIR)
1. Define limit of a function at a point.
2. Evaluate
𝑙𝑖𝑚 𝑥 2 −16
a.
𝑥 → 4 3𝑥+4−4
𝑙𝑖𝑚 𝑥+𝑕− 𝑥
b.
𝑕
𝑕→0
𝑙𝑖𝑚
c.
𝑥 𝑥+1− 𝑥
𝑥→∞
𝑙𝑖𝑚
3. Prove that
sin 𝑥 = 0 geometrically
𝑥→0
4. Evaluate
𝑙𝑖𝑚 cos 𝑎𝑥 −cos 𝑏𝑥
a. i.
𝑥 → 0 sin 𝑎𝑥 −sin 𝑏𝑥
𝑙𝑖𝑚 𝑥 5 −𝑎 5
ii.
𝑥 → 𝑎 𝑥 4 −𝑎 4
𝑙𝑖𝑚 𝑥 tan 𝑥−𝜃 tan 𝜃
b. i
𝑥 −𝜃
𝑥→𝜃
𝑙𝑖𝑚 𝑥 cot 𝑥−𝜃 cot 𝜃
ii.
𝑥−𝜃
𝑥→𝜃
𝑙𝑖𝑚 1+cos 𝜋𝑥
c.
𝑥 → 1 tan 2 𝜋𝑥
𝑙𝑖𝑚 sec 2 𝑥 −2
d. 𝑥 → 𝜋
tan 𝑥−1
4
𝑙𝑖𝑚 𝑥
e.
𝑥→0 𝑥
𝑙𝑖𝑚 1+cos 2𝑥
f. 𝑥 → 𝜋
𝜋−2𝑥 2
2
5.
6.
7.
8.
𝑥2, 0 < 𝑥 < 1
A function f(x) is defined in (0.3) in the following way 𝑓 𝑥 = 𝑥, 1 ≤ 𝑥 < 2 . Show that f(x) is
1 3
𝑥 , 2≤𝑥<3
4
continuous at x=1 and x=2.
𝑎𝑥 + 5, 𝑖𝑓 𝑥 ≤ 2
Find the value for constant number 𝑔 𝑥 =
at x=2
𝑥 − 1, 𝑖𝑓 𝑥 < 2
Evaluate
𝑙𝑖𝑚 𝑥 2 +1
a.
𝑥 → ∞ 𝑥 +1
𝑙𝑖𝑚 𝑥 𝑛 −2𝑛
b.
= 80, find n
𝑥 → 2 𝑥−𝑛
𝑙𝑖𝑚
c.
𝑥 − 𝑥2 + 𝑥
𝑥→∞
𝑙𝑖𝑚 cos 𝜃 −sin 𝜃
d. 𝜃 → 𝜋
𝜋
𝜃−
4
4
𝑥− 𝑐
𝑙𝑖𝑚
e.
𝑥 → 𝑐 sin 𝑥−sin 𝑐
1
𝑙𝑖𝑚
f.
𝑥 sin
𝑥
𝑥→0
𝑙𝑖𝑚 𝑥+𝑦 sec (𝑥+𝑦)−𝑥 sec 𝑥
g.
𝑦
𝑦→0
Define the terms
a. LHL and RHL
b. continuity and discontinuity
4
XI Science
(SUBJECT: MATHEMATICS, TEACHER: P.N.G. SIR)
1. State and prove De-Morgan's law.
2. Prove the following.
a. A-(B∩C)=(A-B)U(A-C)
b. A ∆B=(A-B)U(B-A)
c. AU((B∩C)=(AUB)∩(AUC)
3. For any two real numbers x and y. Prove
a. |x+y|≤|x|+|y|
b. |x-y|≥|x|-|y|
(SUBJECT: MATHEMATICS, TEACHER: I.B. SIR)
1. Define
a. triangular matrix
b. symmetric matrix
c. skew symmetric matrix
with examples
2. Construct a 3×3 matrix whose elements are aij=i+2j
3. Construct a 3×2 matrix whose elements aij are given by aij=3j-i.
2 −3
6
0
4. If 𝐴 = 4
6 and 𝐵 = −2 3 , find a matrix X such that 2A+3X=5B
−5 1
1 −4
1 2 2
2
5. If 𝐴 = 2 1 2 , show that A -4A-5I=0 where I is 3×3 unit matrix
2 2 1
1 2
6. Let 𝐴 =
be a 2×2 matrix.
3 8
1 0
-1
-1
Show that AA =A A=
0 1
7. Express the following matrix in the sum of symmetric and skew symmetric matrix.
2
7 −1
−1 0 −5
9 −9 −9
8. Evaluate the following determinant by expanding
𝑎 𝑕 𝑔
a. 𝑕 𝑏 𝑓
𝑔 𝑓 𝑐
2
0 −2
b. −3 4
1
6 −1 3
9. Without expanding, prove that
1 𝑏𝑐 𝑏 + 𝑐
1 𝑎 𝑎2
a. 1 𝑐𝑎 𝑐 + 𝑎 = 1 𝑏 𝑏 2
1 𝑎𝑏 𝑎 + 𝑏
1 𝑐 𝑐2
2
1 𝑎 𝑎 − 𝑏𝑐
b. 1 𝑏 𝑏 2 − 𝑎𝑐 = 0
1 𝑐 𝑐 2 − 𝑎𝑏
1 1 1
10. Show that: 𝑎 𝑏
𝑐 = 𝑏−𝑐 𝑐−𝑎 𝑎−𝑏 𝑎+𝑏+𝑐
𝑎3 𝑏 3 𝑐 3
𝑎 𝑎2 𝑎3 + 1
11. If a, b, c are all different and 𝑏 𝑏 2 𝑏 3 + 1 = 0 prove that abc=-1
𝑐 𝑐2 𝑐3 + 1
𝑝+𝑥
𝑞
𝑟
𝑝
𝑞
𝑟
𝑞+𝑦
𝑟
12. Show that 𝑝
= 𝑥𝑦𝑧 1 + + +
𝑥
𝑦
𝑧
𝑝
𝑞
𝑟=𝑧
(SUBJECT: MATHEMATICS, TEACHER: K.G. SIR (DAY))
2,1
 1,3
1.
Define complex number. Find the value of x and y if x, y  
2.
3.
4.
If Z and W are two complex numbers, prove that |Z-W|≥|Z|-|W|
Define modules of complex number. Prove t hat: |ZW|=|Z|.|W|
Prove that
5
XI Science
Z W  Z W
Z
Z

if W  0.
W
W
a)
b)
5.
Express the following complex number into a+ib form:
1  i 2
1  2i
(SUBJECT: MATHEMATICS, TEACHER: B.R.S. SIR
(MORNING))
Short Questions
3  4i
3  4i
1.
Find the conjugate of the complex number
2.
Express the complex number  2  i 2 in polar form.
3.
4.
6.
7.
8.
9.
Simplify: 3 cos p u  i sin p u
Find the square roots of
a.
7+24i
5+12𝑖
b.
3−4𝑖
if 1,w,w2 be the cube roots of unity, prove:
2 3
3
a.
(1+w ) -(1+w) =0
2
2
4
b.
(2+w)(2+w )(2-w )(2-w )=21
Prove that the modulus of a complex number and its conjugate are equal.
0
Express the complex number in cartesian form whose modulus is 6 and amplitude is 60 .
Find the value of x and y if (x+2)+yi=(3+i)(1-2i)
2
If (x+iy)(3+2i)=1+i, show that 𝑥 2 + 𝑦 2 =
10.
If 𝑥 − 𝑖𝑦 =
11.
Prove that
5.

3−2𝑖
16
13
2
2
, prove that x +y =1
3+2𝑖
cos 8𝜃 +𝑖 sin 8𝜃
cos 𝜃 +𝑖 sin 𝜃 6
= cos 2𝜃 + 𝑖 sin 2𝜃
Long questions:
12.
State De-Moivre's theorem. Uding De Moivre's theorem. Find the square root of 2 + 2 3 𝑖
13.
Using De-Moivre's theorem, find the fourth roots of unity.
14.
Find the cube roots of unity. Write their properties.
6
15.
Using De-Moivre's theorem, solve z =1
16.
Define absolute value of a complex number. If z and w are compelx number, prove that
z+w|≤|z|+|w|
 THE END 
6