SECTOIN – 1
PHYSICS
1.
A uniform circular disc of radius r is placed on a rough horizontal surface
and given a linear velocity v0 and angular velocity 0 as shown. The disc
comes to rest after moving some distance to the right. It follows that
(a) 3v0 = 20 r
(b) 2v0 = 0r
(c) v0 = 0r
(d) 2v0 = 30r
2.
A uniform solid sphere of radius r is rolling on a smooth horizontal
surface with velocity V and angular velocity  = (V = r). The sphere
collides with a sharp edge on the wall as shown in figure. The
coefficient of friction between the sphere and the edge  = 1/5. Just
after the collision the angular velocity of the sphere becomes equal to
zero. The linear velocity of the sphere just after the collision is equal to
(a )V
(b) V/5
(c) 3V/5
(d) V/6
3.
A mass m is moving at speed v perpendicular to a rod of length d and mass
M = 6m which pivots around a frictionless axle running through its centre. It
strikes and sticks to the end of the rod. The moment of inertia of the rod about its
centre is Md2/12. Then the angular speed of the system just after the collision is
2v
2v
(a)
(b)
3d
d
v
3v
(c)
(d)
2d
d
A uniform solid sphere rolls up (without slipping) the rough fixed inclined
plane, and then back down. Which is the correct graph of acceleration a of
centre of mass of solid sphere as function of time t (for the duration sphere
is one the incline)? Assume that the sphere rolling up has a positive
velocity.
4.
(a)
5.
(b)
(c)
(d)
Two discs, each having moment of inertia 5kg m2 about its central axis, rotating with speeds 10rad s-1 and
20 rad s-1, are brought in contact face to face with their axes of rotation coincided. The loss of kinetic
energy in the process is
(a) 2J
(b) 5J
(c) 125J
(d) 0 J
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6.
A force F acts tangentially at the highest point of a disc of mass m kept on a
rough horizontal plane. If the disc rolls without slipping, the acceleration of
centre of the disc is:
2F
4F
10F
(a)
(b)
(c) zero
(d)
3m
3m
7m
Passage: (7 to 9)
A disc of radius 20cm is rolling with slipping on a flat horizontal surface. At a
certain instant the velocity of its centre is 4m/s and its angular velocity is 10
rad/s. The lowest contact point is O.
7.
8.
9.
10.
11.
12.
13.
Velocity of point O is
(a) 2m/s
(b) 4m/s
(c) 1m/s
(d) 3m/s
Instantaneous centre of the rotation of disc is located at
(a) 0.2m below O
(b) 0.2m above O
(c) 0.6m above O
(d) 0.4m below O
Velocity of point P is
(a) 10m / s
(b) 2 5m / s
(c) 5m / s
(d) 5m/s
A lamina is made by removing a small disc of diameter 2R from a bigger disc of
uniform mass density and radius 2R, as shown in the figure. The moment of inertia
of this lamina about axes passing through O and P is I0 and Ip, respectively. Both
these axes are perpendicular to the plane of the lamina. The ratio Ip/Io to the
nearest integer is
(a) 3
(b) 4
(c) 5
(d) 6
An iron rod of length 50cm is joined at an end to an aluminium rod of length 100cm. All measurements to
200C. The coefficients of linear expansion of iron and aluminium are 12x10-6/0C. and 24x10-6/0C,
respectively. The average coefficient of composite system is
(a) 36x10-6/0C
(b) 12x10-6/0C
(c) 20x10-6/0C
(d) 48x10-6/0C
The absolute coefficient of expansion of a liquid is 7times that the volume coefficient of expansion of the
vessel. Then the ratio of absolute and apparent expansion of the liquid is
1
6
7
(a)
(b)
(c)
(d) none of these
7
7
6
Two elastic rods are joined between fixed supports as shown in figure.
Condition for no change in the lengths of individual rods with the increase of
temperature (1, 2 = linear expansion coefficient, A1, A2 = area of rods, y1, y2 =
Young’s modulus) is
A
y
A
Ly
(a) 1  1 1
(b) 1  1 1 1
A 2 2 y2
A 2 L2 2 y 2
(c)
A1 L 2  2 y 2

A2
L11y1
(d)
A1  2 y 2

A 2 1y 2
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14.
A pendulum clock having copper rod keeps correct time at 200C. it gains 15s per day if cooled to 00C. The
coefficient of linear expansion of copper is
(a) 1.7x10-4/0C
(b) 1.7x10-5/0C
(c) 3.4x10-4/0C
(d) 3.4x10-5/0C
15.
5g of water at 300C and 5g of ice at -200C are mixed together in a calorimeter. Find the final temperature
of the mixture. Assume water equivalent of calorimeter to be negligible, sp. Heats of ice and water are 0.5
and 1cal/g C0, and latent heat of ice is 80cal/g.
(a) 00C
(b) 100C
(c) – 300C
(d) > 100C
16.
The gap between any two rails, each of length l laid on a railway
track equals x at 270C when the temperature rises to 400C, the
gap closes up. The coefficient of linear expansion of the material
of the rail is . The length of a rail at 270C will be
x
x
2x
(a)
(b)
(c)
(d) none of these
26
13
13
A tap supplies water at 150C and another tap connected to geyser supplies water at 950C. How much hot
water must be taken so as to get 60kg of water at 350C?
(a) 15kg
(b) 5kg
(c) 10kg
(d) 20kg
17.
18.
The remaining volume of a glass vessel is constant at all temperatures if 1/x of its volume is filled with
mercury. The coefficient of volume expansion of mercury is 7 times that of glass. The value of x should be
(a) 5
(b) 7
(c) 6
(d) 8
19.
2 kg of ice at -150C is mixed with 2.5kg of water at 250C in an insulating container. If the specific heat
capacities of ice and water are 0.5cal/g0C and 1 cal/g0C, find the amount of water present in the
container?(in kg nearest integer)
(a) 3
(b) 4
(c) 5
(d) 6
20.
2kg of ice at -200C is mixed with 5kg of water at 200C is an insulating vessel having a negligible heat
capacity. Calculate the final mass of water (in kg) remaining in the container.
(a) 5
(b) 6
(c) 7
(d) 8
21.
A modern 200W sodium street lamp emits yellow light of wavelength 0.6 m. Assuming it to be 25%
efficient in converting electrical energy to light, the number of photons of yellow light it emits per second is
(a) 62x1020
(b) 3x1019
(c) 1.5x1020
(d) 6x1018
22.
The work function of a metallic surface is 5.01 eV. The photoelectrons are emitted when light of
wavelength 2000A0 falls on it. The potential difference applied to stop the faster photoelectrons is [h =
4.14x10-15 eVs]
(a) 1.2V
(b) 2.24V
(c) 3.6V
(d) 4.8V
23.
What is the de Broglie wavelength of the wave associated with an electron that has been accelerated
through a potential difference of 50.0V?
(a) 2.7x10-10m
(b) 1.74x10-10m
(c) 3.6x10-9m
(d) 4.9x10-11m
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24.
Which one of the following statement is wrong in the context of X-rays generated from an X-ray tube?
(a) wavelength of characteristic X-rays decreases when the atomic number of the target increases.
(b) Cut-off wavelength of the continuous X-rays depends on the atomic number of the target.
(c) Intensity of the characteristic X-rays depends on the electric power given to the X-ray tube.
(d) Cut-off wavelength of the continuous X-rays depends on the energy of the electrons in the X-ray tube.
25.
The wavelength of the first spectral line in the Balmer series of hydrogen atom is 6561 A . The wavelength
of the second spectral line in the Balmer series of singly ionized helium atom is
0
0
26.
27.
28.
29.
30.
0
0
0
(a) 1215 A
(b) 1640 A
(c) 2430 A
(d) 4687 A
The electron in a hydrogen atom makes a transition n1 → n2, where n1 and n2 are the principal quantum
numbers of the two states. Assume the Bohr model to be valid. The time period of the electron in the
initial state is eight times that in the final state. The possible values of n1 and n2 are
(a) n1 = 4, n2 = 2
(b) n1 = 8, n2 = 2
(c) n1 = 8, n2 = 1
(d) n1 = 6, n2 = 3
A radioactive nucleus undergoes a series of decays according to the scheme




A 
 A1 
 A 2 
 A3 
 A 4 . If the mass number and atomic number of A are 180 and 72,
respectively, then what are these number for A4?
(a) 172 and 69
(b) 174 and 70
(c) 176 and 69
(d) 176 and 70
The activity of a radioactive element decreases to one third of the original activity I0 in a period of nine
years. After a further lapse of nine years, its activity will be
(a) I0
(b) (2/3)I0
(c) (I0/9)
(d) (I0/6)
In the nuclear reaction 1H2 1 H2 2 He3 0 n1 if the mass of the deuterium atom = 2.014741 amu, mass
of 2He3 atom = 3.016977 amu, and mass of neutron = 1.008987 amu, then the Q value of the reaction is
nearly
(a) 0.00352MeV
(b) 3.27 MeV
(c) 0.82MeV
(d) 2.45 MeV
Binding energy per nucleon vs. mass number curve for nuclei is shown in figure. W, X, Y and Z are four
nuclei indicated on the curve. The process that would release energy is
(a) Y → 2Z
(b) W → X+Z
(c) W → 2Y
(d) X →Y+Z
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SECTOIN – 2
CHEMISTRY
31.
A 0.1 molal aqueous solution of a weak acid is 30% ionized. If Kf for water is 1.860C/m, the freezing point
of the solution will be
(a) -0.240C
(b) -0.180C
(c) -0.540C
(d) -0.360C
32.
Acetic acid dimerises in benzene solution. The vant Hoff factor for dimerisation of acetic acid is 0.6. The
% of dimerisation of acetic acid is
(a) 20%
(b) 60%
(c) 80%
(d) 100%
33.
Consider the following solution
(i) 0.01 M Nacl (ii) 0.05 M urea
(iii) 0.01 MgCl2
(iv) 0.02M Nacl
The decreasing order of the boiling point of these solution is
(a) I > II > III > IV
(b) II > IV > III > I
(c) IV > III > II > I
(d) II > III > IV > I
34.
Equimolal solution will have the same boiling point, provided they do not show:
(a) Electrolysis
(b) dissociation
(c) association
(d) association or dissociation
35.
Solubility of deliquescent substances in water is generally?
(a) high
(b) low
(c) moderate
Select the correct statements:
1. The melting of ice becomes fast if salt is spreaded on it
2. The boiling occurs late in pressure cooker.
3. Osmosis is a bilateral (both direction) process.
4. Natural semipermeable membranes are perfectly semipermeable.
(a) 1, 2, 3, 4
(b) 1, 2, 3
(c) 1, 2, 4
36.
(d) cannot be said.
(d) 1, 2
37.
For [CrCl3 . x NH3], elevation in boiling point of one molal solution is double of one molal urea solution,
hence x is (complex is 100% ionized)
(a) 4
(b) 5
(c) 6
(d) none of these
38.
Each pairs forms ideal solution expect:
(a) C2H5Br and C2H5I (b) C6H6 and C6H5.CH3
(c) C6H5Cl and C6H5Br (d) C2H5I and C2H5OH
Which solution will have least vapour pressure.
(a) 0.01M BaCl2
(b) 0.1 urea
(c) 0.1M Na2So4
39.
40.
(d) 0.1M Na3Po4
The osmotic pressure of blood is 7.65 atm. at 310K. An aqueous solution of glucose which is isotonic with
blood has the percentage (wt/volume)
(a) 5.41
(b) 3.54
(c) 4.53
(d) 53.4
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41.
An ‘X’ molal solution of a compound in benzene has mole fraction of solute = 0.2. The value of ‘X’ is
(a) 14.0
(b) 3.2
(c) 1.4
(d) 2.0
42.
The exact Mathematical expression of Raoult’s law is (n = nsolute, N = nsolvent)
P0  PS n
P0  PS N
P0  PS n
(a)
(b)
(c)



0
0
N
n
PS
N
P
P
(d)
P0  PS
 nN
P0
43.
FeCl3 or rxn with K4[Fe(CN)6] in aqueous solution gives blue colour. These are separated by a semi
permeable membrane AB as shown due to osmosis there is
(a) blue colour formation in side x
(b) blue colour formation in side y
(c) blue colour formation in both side x and y
(d) no blue colour formation
44.
A mixture contains 1 mole of volatile liquid A (P0A = 100mm Hg) and 3 moles of volatile liquid B (P0B =
80mm Hg). If the solution behaves ideally, the total vapour pressure of the distillate is
(a) 85mm Hg
(b) 85.88mm HG
(c) 90mm Hg
(d) 92mm Hg
45.
15gm of a solute in 100gm water makes a solution freeze at – 10C. 30gm of a solute in 100gm of water
will give a depression in freezing point equal to
(a) -20C
(b) 0.50C
(c) 20C
(d) 10C
46.
For the given electrolyte AxBy, the degree of dissociation ‘’ can be given as
 i  I
i I
(a)  
(b)  
(c) i  (I  )  x  y
x  y I
I x  y
(d) all of these
47.
Consider equimolal aqueous solution of NaHSo4 and NaCl with Tb and T’b as their respective boiling
Tb
point elevations. The value of l t
will be.
m  0 T '
b
(a) 1
(b) 1.5
(c) 3.5
(d) 2/3
48.
A compound Z undergoes trimerization in organic solvent as 3Z
then Van’t Hoff factor is
(a) 1/3
(b) 0.5
(c) 2/3
Z3 . If degree of association is 0.5,
(d) none of these
49.
Of the following 0.10m aqueous solutions, which one will exhibit the largest freezing point depression?
(a) KCl
(b) C6H12O6
(c) Al2(So4)3
(d) K2So4
50.
An aqueous solution freezes at -0.1860C (Kf = 1.86 K Kg mol-1, Kb = 0.512K Kg mol-1). The elevation of
boiling point of the solution is
(a) 0.0186
(b) 0.512
(c) 0.512/1.86
(d) 0.0512
51.
Calucate the molal depression const of a solvent which has freezing point 16.60C and latent heat of fusion
180.75Jg-1
(a) 2.68
(b) 3.86
(c) 4.68
(d) 2.86
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52.
6gm urea is dissolved in 90g water at 373K. The vapour pressure of the solution is
(a) 745mm
(b) 735mm
(c) 755mm
(d) 725mm
53.
A solution weighing ‘a’ gm has molality ‘b’. The molecular mass of solute if the mass of solute is ‘c’ gm;
will be
c 1000
b 1000
b 1000
c 1000
(a) 
(b) 
(c) 
(d) 
b (a  c)
c (a  c)
a (a  b)
a (b  a)
54.
If liquid A and B form an ideal solution
(a) the free energy of mixing is zero
(c) enthalpy of mixing is zero
55.
(b) the free energy as well as entropy of mixing are each zero
(d) the entropy of mixing is zero
Isopiestic solution’s have
(a) same vapour pressure
(c) same freezing point
(b) same osmotic pressure
(d) same boiling point
56.
Total vapor pressure of mixture of 1 mole a (P0A = 1500 torr) and 2 mol B (P0B = 240 torr) is 200 torr. In
this case
(a) there is +ve deviation from Raoult’s law
(b) there is -ve deviation from Raoult’s law
(c) there is no deviation from Rault’s law
(d) molecular masses of A and B are also required for calculating the deviaton.
57.
Which of the following represents correctly the changes in thermodynamic properties during the formation
of 1 mole of an ideal binary solution?
(a)
(b)
(c)
(d)
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58.
Dry air is slowly passed through three solutions of different concentrations C1, C2 and C3, each containing
(non volatile) NaCl as solute and water as solvent, as shown in figure. If the vessel 2 gains weight and the
vessel 3 loses weight, then
(a) C1 > C2
(b) C1 = C2
(c) C1 < C3
(d) C2 > C3
59.
18gm of glucose and 4 gm of NaOH are dissolved in 1 liter aqueous solution at 300K. The osmotic
pressure of the solution is
(a) 0.3atm
(b) 0.92atm
(c) 4.926atm
(d) 7.389atm
60.
Which is incorrect about solution containing H2O and C2H5OH
(a) Hmix > 0
(b) Gmix > 0
(c) Smix > 0
(d) forms minimum boiling azeotrope
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SECTOIN – 3
MAHEMATICS
61.
Let |zi| = i, i = 1, 2, 3, 4 and | 16z1z2 z3  9z1z2 z4  4z1z3 z4  z2 z3 z4 | 48, then the value of
1

4
z1 z2
(a) 1
62.

9
z3

16
z4
is equal to
(b) 2
Let w be the complex number cos
z 1
w
w
z  w3 1
w
2
(a) 1
1
(c) 4
(d) 8
2
2
 isin
. Then the number of distinct complex numbers z satisfying
3
3
w2
 0 is equal to
zw
(b) 0
(c) 2
(d) 3
63.
The number of complex numbers z such that |z-1| = | z+1| = |z-i| equals
(a) 2
(b) 
(c) 0
(d) 1
64.
Let ,  be real and z be a complex number. If z2 + z +  = 0 has two distinct root on the line Re (z) = 1
then it is necessary that:
(a)   (0,1)
(b)   (-1, 0)
(c) || = 1
(d) (1, )
65.
 0 
70
If   1 is the complex cube root of unity and matrix H  
 , then H is equal to
0



(a) – H
(b) H2
(c) H
(d) O
66.
If z is any complex number satisfying |z-3-2i| 2, then the minimum value of |2z – 6 + 5i| is
(a) 3
(b) 4
(c) 5
(d) 5/2
67.
Let z be a complex number such that the imaginary part of z is non-zero and a = z2 + z + 1 is real. Then,
a cannot take the value.
(a) – 1
(b) 1/3
(c) 1/2
(d) ¾
68.
1
 2k 
 2k 
 isin 
;k  1,2,....,9. Then
Let zk  
| 1  z1 | | 1  z2 |...| 1  z9 | equals


10
 10 
 10 
(a) 0
(b) 1
(c) 2
(d) 3
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69.
70.
1
.
2
(a) is strictly greater than 5/2
(b) is strictly greater than 3/2 but less than 5/2
(c) is equal to 5/2
(d) lies in the interval (1, 2)
z(1  z)
If z is a complex number of unit modulus and argument , then the real part of
is
z(1  z)




(a) 2cos2
(b) 1  cos
(c) 1  sin
(d) 2sin2
2
2
2
2
If z is a complex number such that |z|2, then the minimum value of z 
71.
Let M be a 3x3 matrix satisfying
0   1
1  1 
1 0 








M 1   2  , M  1  1  and,M  1  0  then the sum of the diagonal entries of M is
0  3 
6   1
1 12
(a) 7
(b) 8
(c) 9
(d) 6
72.
If the trivial solution is the only solution of the system of equations
x-ky + z = 0
kx + 3y – kz = 0
3x + y – z = 0, then the set of values of k is
(a) R – {2}
(b) R-{-3}
(c) {2, -3}
73.
74.
The number of values of k for which the linear equations
4x + ky + 2z = 0
kx + 4y + z = 0
2x + 2y + z = 0
Posses a non-zero solution is
(a) 3
(b) 2
(c) 1
(d) 0
1 4 4 
If the adjoint of a 3x3 matrix P is  2 1 7  , then the possible values of the determinant of P are
 2 1 3 
(a) 2
75.
76.
(d) R – {2, -3}
(b) 1
(c) 3
(d) 4
Let M be a 3x3 non-singular matrix with det(M) = . If M-1 adj (adjM) = kI, then the value of k is
(a) 1
(b) 
(c) 2
(d) 3
0 0 a 
If AT denotes the transpose of the matrix A  0 b c  , where a, b, c, d, e and f are integers such that
d e f 
abd  0, then the number of such matrices for which A-1 = AT is:
(a) 2(3!)
(b) 32
(c) 3(2!)
(d) 23
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77.
78.
79.
80.
The number of values of k for which the system of equations: (k+1)x + 8y=4k, kx+(k+3)y=3k-1 has no
solution, is
(a) infinite
(b) 1
(c) 2
(d) 3
1  3 
If P  1 3 3  is the adjoint of a 3x3 matrix A and | A | = 4, then  is equal to
2 4 4 
(a) 4
(b) 11
(c) 5
(d) 10
If A is an 3x3 non-singular matrix such that AAT = ATA and B = A-1AT, then BBT equals
(a) B-1
(b) (B-1)T
(c) I+B
(d) I
1 k 
If Sk    ,k  N, where N is the set of all natural numbers, then (S2)n (Sk)-1, for n  N, is
0 1 
(a) S2n –k
(b) S2n+k-1
(c) S2n+k-1
(d) S2n+k+1
p
81.
If p  x
px
qy
q
qy
(a) 0
82.
(b) 1
(c) 2
sin x
The number of distinct real roots of cos x
cos x
(a) 0
83.
r z
p q r
r  z  0 , then the value of   is
x y z
r
(b) 2
cos x
sin x
cos x
(d) 4pqr
cos x
cos x  0 in the interval [-/4, /4] is
sin x
(c) 1
The number of values of k for which the system of equations
(k+1) x+ 8y = 4k
kx + (k+3)y = 3k-1
has infinitely many solutions, is
(a) 0
(b) 1
(c) 2
(d) 3
(d) infinite
x 2 x
84.
Let x 2 x 6  ax 4  bx 3  cx 2  dx  e
x x 6
Then, the value of 5a + 4b + 3c + 2d + e is equal to
(a) 0
(b) -16
(c) 16
(d) none of these
Space for Rough Work
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85.
a2
a
1
The value of determinant cosnx cos(n  1)x cos(n  2)x is independent of
sinnx sin(n  1)x sin(n  2)x
(a) n
86.
89.
90.
(d) none of these
(b) 6
(c) 8
(d) none of these
a
b
ax  b
c
bx  c , is
If a > 0 and discriminant of ax + 2bx + c is negative, then   b
ax  b bx  c
0
2
(a) positive
88.
(c) x
1
n
n
n
2
2
If Dk  2k n  n  2 n  n and  Dk  48 , then n equals
k 1
2k  1
n2
n2  n  2
(a) 4
87.
(b) a
(b) (ac – b2) (ax2 + 2bx + c)
If the system of linear equations
x + 2ay + az = 0
x + 3by + bz = 0
x + 4cy + cz = 0
Has a non zero solution, then a, b, c
(a) satisfy a + 2b + 3c = 0 (b) are in A.P.
(c) negative
(c) are in G.P.
(d) 0
(d) are in H.P.
Given 2x – y + 2z = 2
x - 2y + z = -4
x + y + z = 4
Then the value of  such that the given system of equations has no solution,is
(a) 3
(b) 1
(c) 0
(d) – 3
1a b
In a ABC, if 1 c a  0 , then sin2A + sin2B + sin2C is
1b c
(a)
3 3
2
(b)
9
4
(c)
5
4
(d) 2
Space for Rough Work
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