Download SRI SRI ACADEMY Hyderabad :: Ph. 23156744 IIT RAMAIAH

SRI SRI ACADEMY
Hyderabad :: Ph. 23156744
IIT RAMAIAH ENTRANCE TEST (SAT) - 2008
MATHEMATICS
Time : TWO HOURS
MAX Marks : 60
NOTE :
1.
Attempt all questions.
2.
Rough work must be enclosed with answer book
3.
While answering, refer to a question by its serial number as well as section
heading
(eg. Q2 / Sec.A)
4.
There is no negative marking.
5.
Answer each of sections A, B, C at one place.
6.
Elegant solutions will be rewarded.
7.
Use of calculators, slide rule, graph paper and logarithmic, trigonometric and
statistical
tables is not permitted.
Note: All answers to questions in Section-A, Section-B and Section-C must be
supported by mathematical arguments. In each of these sections order of the questions
must be maintained.
----------------------------------------------------------------------------------------------------------------------------SECTION – A
(6  2=
12Marks)
This section has six questions. Each question is provided with five alternative
answers. Only one of them is the correct answer. Indicate the correct answer by A, B,
C, D, E
1.
Let A = { 1, 2, 3, …., 2008} , B = { 1, 2, 3, ….., 1004}.
]
a) There can be infinitely many functions from A to B
b) There can not be an onto function from A to B
c) There can be at least one one-one function from A to B
d) There can be infinitely many onto functions from A to B
e) None of these
[
2.
The number of equiangular octagons fixing 6 consecutive sides is
]
a) infinitely many
b) exactly 8
c) at most 8 d) 0
[
e) none of
these
3.
All the numbers between 1947 and 2008 are written, including 1947 and 2008.
From the
list, all the multiples of 3 and 5 are struck off. The sum of the remaining
numbers is
[
]
a) 41517
b) 73137
c) 73138
d) 65247
e) 65248
4.
A square ABCD is inscribed in a quarter circle where B is on the circumference of
the
circle and D is the center of the circle. The length of diagonal AC of the square, if
the
circle’s radius is 5, is
[
]
a) 5  /4
b) 5  /2
c) 5
d) 5 2
e) the length cannot be determined
5.
50  50  50 ........ (where there are hundred 50s) is how many times
100  100  100  …
(where there are fifty 100s)?
[
]
a) 25  25  25  ….(where there are fifty 25s)
b) 4  4  4……(where there are
fifty 4s)
c) 2  2  2  ……(where there are fifty 2s) d) 1 time e) None of these
6.
a, b are positive integers. A is the set of all divisors of ‘a’ except for ‘a’. B is the set
of all divisors of ‘b’. If A = B then which of the following is a wrong statement? [
]
a) a  b
b) a is a multiple of b
c) b is not a multiple of a
d) a/b is a prime number
e) none of these
SECTION – B
This section six questions. In each question a blank is left. Fill in the blank.
12 M)
1.
2008
The domain of the real function f  x   
k 1
(6 x 2 =
1
is ______________
| xk |
2.
The number of points P strictly lying inside an equilateral triangle ABC such that
the
sum of the perpendicular distances from P to the three sides of the triangle is
minimum
is ___________________________
3.
Positive integers a, b are such that both are relatively prime and less than or
equal to
2008, a 2  b 2 is a perfect square and that b has the same digits as a in the
reverse order.
The number of such ordered pairs ( a, b) is____________
4.
5.
in
6.
the
Let ABCD be a square. E, F, G, H be the mid points of its sides AB , BC , CD , DA
respectively. Let P, Q, R, S be the points of intersection of the line segments
AF , BG , CH , DE inside the square. The ratio of the areas  PQRS :  ABCD is
____________
The number of elements in the set {(a, b, c) : a, b, c are three consecutive integers
some order, a + b+c = abc } is _______________
The sum of all positive integers for which the quotient and remainder are equal if
number is divided by 2008 is__________________
SECTION – C
(6 x 2 = 12
M)
1.
Is y a real function of x in the equation y  2008  x2  2?
2.
they
has
its
The people living on street ‘S’ of Y-City all decide to buy new house numbers so
line up at the only Hardware store in order of their address: 1, 2, 3 …. If the store
100 of each digit, what is the first address that won’t be able to buy the digits for
house number?
3.
Let ABCD be a quadrilateral such that AB is perpendicular to BC, AD is
perpendicular
to BD and AB = BC, BD = a, AD = c, CD = x . Find x in terms of a
and c.
4.
For what pair wise different positive integers is the value of
a
b
c
d



an
integer?
a 1 b 1 c 1 d 1
5.
Side AB of rectangle ABCD is 2 units long and side AD is 3 units. E is a point on
the line
AC such that C is the mid point of the line segment AE. What is the length
of line
segment BE?
6.
How many number of integers are there between 2008 and 2,00,82,008 including
2008 and 2,00,82,008 such that the sum of the digits in the square is 42 ?
1.
= S}
2.
the
SECTION – D
(6 x 4 = 24 Marks)
Let S = { 1, 2, 3, ……2008}. Find the number of elements in the set { (A, B) : A B
A square is drawn in side a triangle with sides 3, 4 and 5 such that one corner of
square touches the side 3 of the triangle, another corner touches the side 4 of the
triangle, and the base of the square rests on the longest
side of the triangle. What is the side of the square?
3.
State and prove the test of divisibility of a positive
integer ‘a’ by 11.
4.
A square cake 6” x 6” and 3” tall was cut into four
pieces of equal volume as
shown in the figure.
Determine how far in from the side of the cake the cuts
should be made? (i.e., x = ?)
5.
6.
Solve the following simultaneous equations for a and b:
a a  b b  183, a b  b a  182
f and g are two real variable real valued functions defined by
3x  7, if x  2
 x  2, if x  0

f  x  
,
g  x    x  1, if  2  x  2. Find gof
2 x  3, if x  0
 x  1, if x  2

SRI SRI ACADEMY
Hyderabad :: Ph. 23156744
IIT RAMAIAH ENTRANCE TEST (SAT) - 2008
CHEMISTRY
Time : ONE HOUR
: 60
MAX Marks
NOTE :
1.
Answer must be written either in English or the medium of instruction of the
candidate
in high school.
2.
There will be no negative marking
3.
Use of calculators or graph papers is not permitted
4.
Answer all the questions.
----------------------------------------------------------------------------------------------------------------------------I.
Explain the following
(5  3=
15Marks)
1.
with
2.
white
3.
4.
5.
The value of K (equilibrium constant, rate constant, solubility constant) changes
temperature. But radioactive decay constant is independent of temperature.
On expose to air, caustic soda becomes liquid and after some time it changes to
powder.
Aqueous solution of AlCl3 behaves acidic towards litmus while that of NaCl not.
Both coke and flux are used in smelting process of metallurgy.
Bottle containing NaOH solution should not be closed by glass lid.
II.
M)
Differentiate the following:
(5 x 3 = 15
1.
An equivalent in acid-base reaction and an equivalent in oxidation- reduction
reaction
2.
Acid strength and concentration
3.
Mixed salt and Double salt
4.
Complex salt and Simple salt
5.
Contrast the action of heat on the following (with equations)
a) Na2CO3 and CaCO3
b) MgCl2 .6H 2O and CaCl2 .6H 2O c)
Ca  NO3 2 and NaNO3
III.
Answer the following:
(10 x 3 = 30
M)
1.
A fuel gas contains carbon and hydrogen only. Burning a small sample of it in
oxygen
gives 3.38gm carbon dioxide, 0.69gm of water and no other products. A
volume of 10 lt
(measured at STP) of this gas is found to weigh 11.6gm.
a) Calculate (i) empirical formula
(ii) molecular mass of the gas
(iii) molecular formula
b) Write one single step preparation of the gas
c) Does it react with bromine? If so what colour change do you expect?
d) What do you expect the calorific value of the gas with reference to marsh gas?
2.
At a given temperature, the degree of ionization (fraction dissociated) of water is
found
to be 1.8 109 . Calculate the ionization constant and the ionic product of water at
this temperature.
3.
Suppose the gas-phase isomerisation reactions
K
K
K
3
1
2



A 
 B ; A 
 C ; B 
C
reach equilibrium at a fixed temperature. Express the equilibrium mole fractions
of A, B
and C in terms of equilibrium constants, K1 , K2 and K3 .
4.
Sample of P2O5 contains some impurity. 0.405gm sample is reacted with water
and the
resulting solution requires 42.5ml of 0.25M NaOH solution. The salt
resulted is monobasic acid salt. Calculate the percent impurity.
5.
What will be the resultant p H when 200 ml of an aqueous solution of HCl
( p H =2) is
mixed with 300ml of an aqueous solution of NaOH ( p H =12).
Kf

 CO  g   CF  g 
6.
2COF  g  

2
2
4
Kb
K = 2 for the reaction at 1000 0 C. If a 5L mixture contains 0.105 mole COF2 , 0.22
mol CO2
and 0.055 mol CF4 at 1000oC.
a) Will the mixture be at equilibrium ?
b) if the gases are not at equilibrium, in which direction will a net reaction occur?
c) What is the amount of each gas present when equilibrium is established.
d) What are the rate equations for the forward and backward reactions?
e) Compare the rate constants at (i) initial stage and (ii) equilibrium stage.
7.
For the reaction
(i)
A
B;
Kc = 2
(ii)
B
C;
Kc =4
(iii) C
D;
Kc =6
For the reaction A
D what is the Kc ?
8.
Four elements coded A, B, C and D form a series of substances e.g. AB,
B2 , CB3 , DB2 and DB3 . If the atomic number of these elements are not necessarily in the
order are 13, 19, 26 and 35. Write down extra nuclear electronic structures of these
elements. From
this information and the formula of the compounds, allocate A, B,
C and D with
appropriate atomic numbers. Mention the nature of bonding in
each of them.
9.
Calculate the molecular weight of hydrogen fluoride if density of this gas is 3.17
g/L at
300K and 1.0 atm pressure. What information can you deduce from the
result?
10.
Anhydrous copper sulphate turns to blue from colourless on expose to
atmosphere and
again make it colourless by some substance (X). When copper
sulphate is added to
water a blue colour solution is resulted with some turbidity.
The turbidity disappears by the addition of drop of HCl solution. On placing Iron rod
in it, a greenish solution is resulted. A chocolate like precipitate is resulted when a drop
of potassium ferrocyanide solution is added to the blue colour solution of copper
sulphate. Black precipitate is
resulted by passing H 2 S gas through copper sulphate
solution but the precipitate is
soluble in conc. HNO3.
a) What is X ?
b) Write the chemical reactions to explain the observations.
SRI SRI ACADEMY
Hyderabad :: Ph. 23156744
IIT RAMAIAH ENTRANCE TEST (SAT) - 2008
PHYSICS
Time : ONE HOUR
: 60
NOTE :
MAX Marks
1.
Answer must be written either in English or the medium of instruction of the
candidate
in high school.
2.
Answer all the questions in the booklets provided for the purpose
3.
There will be no negative marking
4.
The relevant working or the argument in arriving at an answer has to be include
in your
answer.
5.
Use of calculators or graph papers is not permitted
6.
Questions in Part A carry 6 marks each and questions in part B carry 3 marks
each.
----------------------------------------------------------------------------------------------------------------------------Part– A
1.
Two liquids of masses 600g and 500g and densities 0.6 gcm 3 and 1.5 gcm 3 are
combined to form a homogenous mixture. A solid block of mass 420g just floats
in this mixture. Find the density of the block material. If the equal volumes of the two
liquids
were mixed instead, would this block float in that mixture? If it floats find
the fraction of the block that is visible above the mixture.
2.
A lens of focal length f produces an image of an object located 30 cm on one side
of it at
a
distance of 60cm on the other side. If the lens is replaced by
another of 3f/4, where
would the image form? If the image has to form at the
earlier position by what distance should the object be shifted?
3.
The devices D1 and D2 shown (below left) are called diodes and have an
interesting property. When current flows in the direction of the arrow the resistance
is low and is called forward bias resistance. If the current were to flow in the opposite
direction the resistance is high and it is called reverse bias resistance . for D1 forward
bias resistance
is 20 Ohm and reverse bias resistance is 600 Ohm. For D2 forward
bias resistance is 30 ohm and reverse bias resistance is 200 Ohm. Find the equivalent
resistance between A
and B if (i) A is at a higher potential
(ii) B is at a higher
potential
4.
Rays of light are incident symmetrically on a sphere of radius R as shown (below
middle). Determine the refractive index of the sphere material if they meet at P
(you need to write the correct expression for refractive index). Can the rays be made to
meet at C, the center of the sphere. If not, how should the rays be incident to meet at C.
5.
If the measured potential difference between A and B is 5.4V, Find the rate of
heat production in the ring (above right). Also find the rate of heat production in
sections
ACB and ADB.
6.
Two identical rectangular tanks are connected by a
small tube at the bottom. In the left tank contains
liquid of density d1  800kg / m3 to a height
h1  30cm . The right tank contains liquid of density
d 2  1600kg / m3 , to a height h2  20cm . The two
liquids don’t mix. A) find the heights of the
respective columns, if a small tube connects them at
the bottom. B) Where should a horizontal tube be
connected, without causing any flow
between the tanks?
Part– B
7.
Two candles of identical lengths and different thicknesses were lit. Half of the
thin candle and one third of the thick candle could be seen to burn down in 15
minutes.
How long after the candles had been lit was the ratio of their lengths 4.
8.
The average daily loss of water of a human body is 0.8 kg, evaporated by the
body. How much food has to be consumed in order to compensate for the loss of
energy due to the evaporation if human body can use 70% of the energy provided by
the
decomposition of food. The heat of combustion of food is 6,000KJ/kg, the heat of
vaporization of water is 2440 kJ/kg.
9.
A train of length 300m passes through two tunnels with a gap of 400m between
them. The tunnels are of length 800m and 600m respectively. From the moment it just
emerges
from the first tunnel to the moment it just disappears in to the second
tunnel time elapsed is 60s. Find the time elapsed between the moments the train just
enters the first
tunnel to the moment it just leaves the second tunnel.
10.
Fiber optic cable of length L has an inner core surrounded by an outer jacket.
Light can
travel along the length of the cable through the inner and outer portions.
The refractive
indices of the material of the inner and outer portions are
1 and 2 . Find the time interval between the moments when a light pulse entering
one end of the cable arrives
at the other end traveling through the inner and outer
portions.
11.
A person’s heart does approximately a work of 1.6 J during a beat. How much
work does it do during a day? By how much does the temperature of 10kg of water
rise if it
absorbs this much of energy?
12.
Find the ratio Ei / E f where Ei and E f are the energies of a neutron before and
after interaction with the nuclei of the moderator in a nuclear reactor.
13.
A stone projected vertically upward on some planet reaches a maximum height
h. find
the ratio of times after projection when it is at a height of 5h/9.
14.
A horizontal conductor is oriented north south and carries some current. A
positively
charged particle located vertically above it and having a velocity directed
northward experiences an upward force. What is the direction of the force if this
charged particle
were located to the east of the conductor and had a velocity
directed towards the
conductor.