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PHYSICS
1. Water freezes inside a pipe, normally it expands by about 9% due to freezing. What would be the pressure
increase inside the pipe? The bulk modulus of ice is 2.00 × 109 N/m2. (a)1.80 × 108 N/m2 (b) 3.60 × 108 N/m2
(c) 9 × 107 N/m2 (d) 7.2 × 108 N/m2.
2. The temperature of end A of a rod is maintained at 0oC. The temperature of end B is changing slowly such that the
rod may be considered in steady state at all time and is given by TB =  t; where  is positive constant and t is
time. Temperature of point C, at a distance x from end A, at any time is
(a)
 xt 2
 xt
 ( L  x)
 x 2t
t.
(b)
(c)
(d)
L
L
2L
2L
3. A spring is kept pressed in between a block and a vertical wall. The block is pushed by a horizontal force on a
smooth level ground so that it is in equilibrium. St1: The force exerted by the spring on the wall is equal and
opposite to the force exerted by the spring on the block. St2: Every action has equal and opposite reaction.
(a) St1: is true, St2: is true and St2: is correct explanation for st1 (b) St2: is true, St2: is true and St2: is NOT the
correct explanation for St1. (c) St1: is true, St2: is false (d) St1: is false, St2: is true.
4. A rod of length l0, Young’s modulus Y and coefficient of thermal expansion  is heated by temperature difference
 . By means of an external force, it is constrained to maintain length l0. The compressive stress in the rod is
(a) Yl0 a (b) Yl0 2  2 (c) Y (d)
Yl0
.
2
5. A Sphere of mass m is kept between two inclined wall, as shown in the figure, If the coefficient of friction between
each wall and the sphere is zero, then the ratio of normal reaction (N1/N2) offered by the walls I and 2 on the
sphere will be (a) tan  (b) tan2  (c) 2 cos  (d) cos 2  .
6. In the figure shown, the acceleration of wedge is (Neglect friction) (a)
F
F
F
(b)
(c) zero (d) .
M
mM
m
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7. Three equal weights of mass 2kg each are hanging by a string passing over a fixed pulley. The tension in the
string (in N) connecting B and C is (a) 4g/3 (b) g/3 (c) 2g/3 (d) g/2.
8. An airplane flies from a town A to a town B when there is wind and takes a total time. T0 for a return trip. When
there is a wind blowing in a direction from town A to town B, the plane’s time for a similar return trip Tw, would
satisfy, (a) T0 < Tw (b) T0 > Tw (c) T0 = Tw (d) the result depends on the wind velocity between the towns.
9. A fuse wire made of lead has an area of cross – section A equal to 0.2 mm2. On short – circuiting, the current in the
fuse wire reaches 30 amp. Approximately how long after the short – circuiting, will fuse begin to melt? For lead
specific heat ‘S’ is 0.032 cal/gm/oC, melting point is 327oC, density ‘d’ is 11 g/cm3 and resistivity  is 22 ×10-8
ohm – m. The initial temperature of wire is 27oC. Heat losses may be neglected. (a) 0.1s (b) 0.2s (c) 0.3s (d) 0.4s.
10. Two bodies P and Q have to move equal distance starting from rest P is accelerated with 2a for first half distance
then its acceleration becomes a for last half, where as Q has acceleration a for first half and acceleration 2a for
last half, then for whole journey. (a) Average speed of P is more than that of Q (b) Average speed of both will be
same (c) Maximum speed during the journey is more for P (d) Maximum speed during the journey is more for Q.
11. A block of mass is kept on a rough inclined plane with coefficient of friction  . The force required to just move
the block up is
(a)  mg cos  (b) mg sin  (c) mg sin +  +  mg cos  (d) mg sin  -  mg cos  .
12. Three blocks are kept as shown in the figure. Acceleration of 20 kg. block with respect to ground. (a) 5 m/s2 (b) 2
m/s2 (c) 1 m/s2 (d) none.
13. The total energy of a black body radiation source is collected for five minutes and used to heat water. The
temperature of the water increases from 10.0o C to 11.0oC. The absolute temperature of the black body is doubled
and its surface area halved and the experiment repeated for the same time. Which of the following statements
would be most nearly correct (a) The temperature of the water would increase from 10.0oC to a final
temperature of 120C (b) the temperature of the water would increase from 10.0oC to a final temperature of 18oC.
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(c)The temperature of the water would increase from 10.0oC to a final temperature of 14oC (d) The temperature
of the water would increase from 10.0o to a final temperature of 11oC.
14. A projectile is fired with a velocity u making an angle  with the horizontal. What is the magnitude of change in
velocity when it is at the highest point? (a) u cos  (b) u (c) u sin  (d) u cos  - u.
15. Two similar cannon simultaneously fires two identical cannon balls at target 1 and 2 as shown in the figure. If the
cannon balls have identical initial speeds, which of the following statements is true? (a) Target 2 is hit before
target 1 (b) Target 1 is hit before target 2 (c) both are hit at the same time (d) information is insufficient.
16. The v – t graph for two particles P and Q are given in the figure. Consider the following statements. Then, which
of the following statements is true for time t > t0. (a) Their relative velocity is non – zero but constant (b) Their
relative velocity is continuously increasing (c) Their relative displacement is non – zero but constant (d) their
relative acceleration continuously increases.
17. A boy on skateboard is coming down on a smooth incline. He throws a ball such that he catches it back what
should be unit vector of the ball’s velocity relative to him (a) j (b)
i
j
i
j


(c) 
(d) none.
2
2
2
2
18. Copper and aluminium wires have equal resistances and masses. Which of the two wires is longer and how many
times? Densities of copper and Aluminium are 8.96 × 103 kg m-3 and 2.4 × 103 kg m-3. Their resistivities are 0.18
 and 0.028  m respectively. (a) Aluminium wire is nearly 8 times longer than copper (b) Copper wire is
nearly 5 times longer than aluminium (c) Aluminium wire is nearly 5 times longer than copper (d) Copper wire is
nearly 4 times longer than aluminium.
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19. In figure, infinite conducting rings each having current i in the direction shown are placed concentrically in the
same plane as shown in the figure. The radius of rings are r, 2r 22r, 23r…..  . The magnetic field at the centre of
rings will be (a) zero (b)
 0i
i
i
(c) 0 (d) 0 .
r
2r
3r
20. A current is flowing through the loop. The direction of the current and the shape of the loop are as shown in the
figure. The magnetic field at the centre of the loop is
(a) MA = R, MB = 2R, angle DMA = 90o) (a)
of the paper (c)
7 0i
5 0i
, but out of the plane of the paper (b)
, but out of the plane
16 R
16 R
7 0i
5 0i
, but into the plane of the paper (d)
, but into the plane of the paper.
16 R
16 R
21. The potential difference across AB is 5V. The voltage of ideal battery is
(a) 40 V (b) 15V (c) 30 V (d) 10 V.
22. A proton (mass m and charge +e) and an alpha particles (mass 4m and charge +2e) are projected with the same
kinetic energy at right angles to a uniform magnetic field. Which one of the following statements will be true?
(a) the alpha – particle will be bent in a circular path with a smaller radius than that of the proton. (b) the radius
of the path of the alpha particle will be greater than that of the proton (c) the alpha particle and the proton will
be bent in a circular path with the same radius (d) the alpha particle and the proton will go through the field a
straight line.
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23. Two identical bodies are made of a material for which the heat capacity increases with temperature. One of these
is at a temperature of 100oC while the other one is at 0oC. If the two are brought into contact, then assuming no
heat loss to the environment , the final temperature that they will reach is (a) 50oC (b) less than 50oC (c) more
than 50oC (d) 0oC.
24. A mass spectrometer is a device that selects particles of a fixed mass. An ion with electric charge q > 0 and mass
m starts at rest at a source S and is accelerated through a potential difference V. It passes through a hole into a
region with a constant magnetic field B perpendicular to the plane as in the figure. The particle is deflected by
the magnetic field and emerges through the hole in the bottom of the figure that is a distanced d from the hole at
the top. What is the mass of the particle?
(a) m 
8qV
qBd
q2 B
qB 2 d 2
m

(b)
(c)
(d)
.
m

m

B2
8V
3Vd 3
8V
25. A particular with charge ‘q’ is travelling with velocity ‘v’ parallel to a wire with a uniform linear charge
distribution  per unit length. The wire also carries a current I as shown in the fig. The velocity with which
particle travels in a straight line parallel to the wire at a distance ‘r’ away is
(a)



2
(b)
(c)
(d)
.
2
IC
2  I
I
I
26. For the following situation of (a) and (b), current is same. St1: In case of figure (a) and (b)
  .d
for two loops
shown will be different. St2: In case of figure (a) and (b) magnitude of magnetic field at similar points on
amperian loop may be different.
(a) St1: is true, St2: is true and St2: is correct explanation for St1 (b) St1: is true, St2: is true and St2: is NOT the
correct explanation for St1. (c) St1: is true, St2: is false (d) St1: is false, St2: is true.
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27. Figure shows a mater bridge. If there is no current through galvanometer then
1
is equal to
(a) 200/3 cm (b) 100/3 cm (c) 50 cm (d) 25 cm.
28. Find equivalent resistance of the network between A and B
(a)
216
225
726
385
 (b)
 (c)
 (d)
.
305
193
731
503
29. The wire of the potentiometer has resistance 4 ohms and length 80 cm. It is connected to a cell of e.m.f.2 volts and
internal resistance 1 ohm. If a cell of e.m.f. 1volts is balanced by it, the balancing length will be: (a) 40 cm
(b) 50 cm (c) 60 cm (d) 70 cm.
30. Figure, shows how the potential energy V for two neighbouring atoms varies with their separation r. Which
statement is correct?
(a) the atoms are in equilibrium at separation OX (b) the slope of the curve at Z is related to Hooke’s law
(c) the force between atoms is repulsive for separation less than OY (d) the force between atoms is repulsive for
separation greater than OY.
CHEMISTRY
31. From the graph given below, select the option which correctly matches the orbitals for which the radial
probability distribution is given
(a) A – 3p, B – 3d, C – 3s (b) A – 3s, B – 3d, C – 4p (c) A – 4p, B – 3d, C – 5f (d) A – 3p, B – 4d, C – 4p.
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1
32. The slope of ln K vs
was found to be – 40 if ‘T’ is in Kelvin. The value of ln 160k will be: ( T represents
T
temperature coefficient at T Kelvin) (a)
1
1
(b)
(c) 68 (d) 17.
17
68
33. For the reaction, 2SO2 + O2  2SO3 if rate of disappearance of O2 is 8 gm/sec., then rate of appearance of SO3 will
be (a) 16 gm/sec (b) 4 gm/sec (c) 40 gm/sec (d) 10 gm/sec.
34. The correct order of atomic orbitals in terms of energy between 8s and 8p orbital are (a) 7d 6f (b) 5g 6f 7d
(c) 6d 7f (d) 6h 5g 6f 7d.
35. Consider the following reaction 2A(g)  3B(g) + C(g). Starting with pure A having pressure 2atm initially, the
total pressure is exactly doubled in 2hrs. The possible order of reaction is (a) zero (b) first (c) second (d) third.
36. In the acid catalysed hydrolysis of methoxy ethanoate the rate law is found to be (a) Rate = K [CH3 COOCH3] [H+].
Calculate the value of “K” in M-1 min-1 from the following titration data.
[H+] = 0.1 M
Time (min)
Volume
of
T=0
NaOH required for 35 ml
T = 6.93 min
T= 
60ml
85ml
complete neutralization of small &
equal volume of reaction mixture
taken on out at different time
interval
(a)2 (b) 0.2 (c) 0.1 (d) 1.
37. If an electron at rest is accelerated by the potential different of 6 volts then the wavelength associated by the
electron is (a) 25 × 10-10 (b)25 Å (c) 5 × 10-8 (c) 0.5 × 10-10 meter.
38. Consider the reaction A
B. The concentration of both the reactants and the product varies exponentially with
time. Which of the following figure correctly describes the change in concentration of reactants and products
with time?
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Z2
39. According to Bohr’s atomic theory, which of the following is/are correct: (i) Kinetic energy of electron  2
n
(ii) The product of velocity of electron and principle quantum number ‘n’  Z 2 (iii) Frequency of revolution of
electron in an orbit 
Z3
Z2
(iv)
Coulombic
force
of
attraction
on
the
electron
(a) I, III, IV (b) I, IV (c) II (d) I.

n4
n3
40. A gaseous substance dissociates in a rigid vessel at constant temperature as shown P(g)  Q(g) + R(g) the pressure
at different is observed as shown. Calculate rate constant of the dissociation t = 0 min
t.5 atm 2 atm
7/3 atm (a)
t = 20 min t = 40 min
ln 2
1 3
0.5
5
min 1 (b)
ln min 1 (c)
atm min 1 (d)
atm min 1 .
20
20 2
2
120
41. Which of the following alkyl halides would be most likely to give a rearranged product under SNl conditions?
42. A compound that gives a positive iodoform test is (a) 1 – pentanol (b) 2 – pentanone (c) 3 – pentanone
(d) 3 – pentanol.
43. The halides which will not give ppt, with AgNO3?
44. Pick an ether which cannot be prepared by direct Williamson’s synthesis (a) CH3 CH2CH2-O-CH2CH2CH3
(b)Ph-O-CH2CH3 (c)(CH3)3C-O-C2H5 (d) CH3CH=CH-O-CH=CH2.
45. What will be the final product when Ethyl benzene is treated with reagent listed below? (i)NBS, peroxide, heat
(ii) alcoholic KOH,  (iii) B2H6 (iv)H2O2, HOΘ .
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46. Which is most reactive nucleophilic aromatic substitution?
47. Select the correct product from the following
P1 & P2 are respectively.
48.
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49.
50.
51. SO2 gas is passed through starch iodate solution in acidic medium and the resulting solution is (a) Salmon red
coloured precipitate (b) Red comound of unknown composition (c) Brown colour (d)Deep blue solution.
52. KI is add in excess into Hg(NO3)2 solution, the observation is (a) Yellow ppt. of HgI2 (b) Scarlet red ppt. of HgI2
(c) Colourless solution of (HgI4]2- (d) none.
53. Unknown solution of salt ‘A’ k3[ Fe(CN )6 ] green ppt is obtained. Which of the following radicals will be
confirmed (a) Ni2+ (b) Cu2+ (c) S2O32- (d) SO32-.
54. Compound ‘X’ is used in Bordeaux mixture. It has electrovalent, covalent, coordinate as well as ‘H’ – bond. In
compound ‘X’ based on the nature of bond & interaction, the number of types of water molecules is (a) 1 (b) 2
(c) 3 (d) 4.
55. Which of the following compounds liberates the same basic has only on heating which is produced by heating a
mixture of Zn and NaNO3 with NaOH? (a) (NH4)2CO3 (b) NH4NO3 (c) NH4NO2 (d) none.
56. Which of the following sulphides would dissolve in dilute HCI? (a) HgS (b) NiS (c) CoS (d)ZnS.
57. St1: Concentrated H2SO4 is not used during lab preparation HBr & HI. St2: Concentrated H2SO4 will oxidize Br- and
I- into Br2 & I2 respectively. (a)St1: is true, St2:is true and St2: is correct explanation for St1 (b) St1: is true, St2:is
true and St2:is NOT the correct explanation for st1 (c) St1: is true, St2: is false (d) St1: is false, St2: is true.
58. Which of the following would give yellow turbidity with dilute HCI? (a) S2- (b) S2O32- (c)CO32- (d) NO2-.
59. Borax bead test of salt (M) is performed, violet colour of the bead is obtained under oxidizing flame. What is the
oxidation state of the cation present in salt (M)? (a) +7 (b) + 4 (c) + 2 (d) can’t be predicted.
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60. Which of the following is incorrect option? CuI2 + KI → K3[CuI 4 ] (a)Oxidation state of central atom decreases
complex
during the formation of complex (b) Complex is tetrahedral (c)Hybridisation of the complex is sp3
(d) Hybridisation of the complex is dsp2.
MATHEMATICS
61. If log x = 2 log (x + k) where x  R+ and k is a positive real number then true set of values of k is


1


1


1


1
(a)  0,  (b)  0,  (c)  0,  (d)  0,  .
2
4
4
2

d 2x
62.
equals (a)
dy 2

1


1
3
 d2y 
 d 2 y   dy 
 d 2 y   dy 
 2  (b)   2    (c)  2  
 dx   dx 
 dx 
 dx   dx 
63. If the domain for the function f(x) =
2
3
 d 2 y   dy 
(d)   2   .
 dx   dx 
1
is (-  ,  ), then which of the following best describes all
x  2x  c
2
possible values of c? (a) c > 1 (b) c = 1 (c) c < 1 (d) c  1.
64. Number of words can be formed with the letters of the word ‘PATALIPUTRA’ without changing the relative
positions of vowels and consonents (a) 3000 (b) 3600 (c) 4200 (d) 4500.
 tan 1 x,
| x | 1

65. The domain of the derivative of the function f(x) =  1
is (a) R – {0} (b) R – {1} (c) R – {-1}
(|
x
|

1),
|
x
|

1

2
(d) R – {-1, 1}.
66. The domain of the function f(x) =
x2
is (a) (, 3)  [2, ) (b) [2, 3) (c) [-2, 3)  (3,  )
x2  9
(d)(-  , -3)  (3,  ).
 x3  1;
1 x  
 x  1;
  x  1
67. At the point x = 1, the given function f(x) = 
is (a) Continuous and differentiable
(b) Continuous and not differentiable (c) Discontinuous and differentiable (d) Discontinuous and not
differentiable.
68. The value of ‘a’ for which 3x2 – 2 (a + 1)x + (a2 – 1) is always positive for any real x, is (a) (, 1)  (2, )
(b) (, 1]  [2, ) (c) [-1, 2) (d) (-1, 2).
69. Consider the series r2 + r4 + r6 + r8 + r10 + …..  .The third term is 16 times the fifth term. The sum of the series
is (a)
1
1
1
4
(b) (c) (d) .
4
3
2
3
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70. If the domain of function g(x) is (0, 1) then the domain of function y = g(2x) + g(kn |x|)is (a) (-1, 0) (b) (-1, -e/2)
(c) (-e, -1) (d) (-e, 1).
71. If f’(x) = g(x) and g’(x) = -f(x) for all x and f(2) = 4 = f’(2) then f2(4) + g2(4) is (a) 8 (b) 16 (c) 32 (d) 64.
 2x 1 
  where [.] denote the greatest integer function, is discontinuous at
 2 
72. The function f(x) = [x] cos 
(a) All x (b) No x (c) All integer points (d) x which is not an integer.
73. Let c be a real number such that lim f(x) = 5 and lim (x + c) f(x) = 3, then the value of c is equal to
xc
xc
(a) 3/10 (b) 10/3 (c) 3/5 (d) 5/3.
74. If
3
    , then
4
2cot  
1
is equal to (a) 1 + cot  (b) -1 - cot  (c) 1 - cot  (d) – 1 + cot  .
sin 2 
75. If cot  + tan  = m and sec  - cos  = n, then which of the following is correct? (a) m(mn2)1/3 – n (nm2)1/3 = 1
(b) m((m2n)1/3 – n (mn2)1/3 = 1 (c) n(mn2)1/3 = m(nm2)1/3 = 1 (d) n(m2n)1/3 – m(mn2)1/3 = 1.


76. The value of sin-1  cos


4
5
19 
(b)
(c)
(d)
.
 is equal to (a)
3
6
3
3
6 
77. Let f(x) = [x3 – 3], [x] = G.I.F. Then the number of points in the interval (1, 2) where function is discontinuous is
(a) 5 (b) 4 (c) 6 (d) 3.
78. The value of tan 20o + 2 tan 50o – tan 70o is equal to (a) 1 (b) 0 (c) tan 50o (d) none.
79. If x = sin-1 (3t – 4t3) and y = cos-1
(1  t 2 ) then
dy
is equal to (a) 1/2 (b) 2/5 (c) 3/2 (d) 1/3.
dx
1  sin x  1  cos x  1  tan x 
80. If x > 0, then the value of expression
1  cos ec x  1  sec x  1  cot x 
2010
1
1
2010
1
1
2011
2011
1
1
2012
2012
, is (a) 1 (b) 2 (c) 3
(d) none.
81. The set of point where f(x) =
x
differentiable is (a) (, 0)  (0, ) (b) (, 1)  (1, ) (c) (, )
1 | x |
(d) (0, ) .
( x  c) 4  x 4
when x = 2 is (a) 16 (b) 32 (c) 8 (d) 64.
c 0
c
82. The value of lim
83. If the function f(x) =
x3
x
2
+ e and g(x) = f-1(x), then the value of g’(1) is (a)1/2 (b) 1 (c) 3/2 (d) 2.
MATHS4U
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Practice Question
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2.Complete test in stipulated time.
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 e(1/ x )  e( 1/ x )
x0
x
84. If f(x) =  e(1/ x )  e( 1/ x )
then which of the following is true? (a) f is continuous and differentiable at

0,
x0

every point (b) f is continuous at every point but is not (c) f is differentiable at every point (d) f is differentiable
only at the origin.
85. Let P(x) = x3 – 6x2 + Bx + C has 1 + 5i as a zero and B, C are real numbers, then value of (B + C) is (a) -70 (b) 70
(c) 24 (d) 138.
1
 2
x sin

86. Let f(x) =
x

 0
if x  0
and g(x) = sin x then which of the following is INCORRECT? (a)f(x) is
if x  0
differentiable at x = 0 (b) f(x) is continuous at x = 0 (c) lim
x 0
f ( x)
f '( x)
does not exist (d) lim
does not exist.
x 0 g '( x)
g ( x)
87. If 0 < x < 1, then 1  x 2 [{x cos(cot 1 x)  sin(cot 1 x)}2  1]1/2  (a)
x
1 x
2
(b) x (c) x 1  x 2 (d) 1  x 2 .
88. The function f(x) = (x2 – 1) |x2 – 3x + 2| + cos (|x|) is not differentiable at (a)-1 (b) 0 (c) 1 (d) 2.
89. The value of x satisfying the equation 2(eln(x+3)) (lne(2x-3))=
9  8 7
1 ln(-6x+20)
7
9
e
, is (a) 4 (b)
(c)
(d)
.
2
4
4
8
 4 x 2  16 x  16  m
  where m and are relatively prime natural numbers, then the sum of m and
2
2
 3x  9 x  12  n
90. Given that L im 
x 2
n is equal to (a) 10 (b) 11 (c) 12 (d) 13.
Answer
1.a 2.a 3.b 4.c 5.c 6.c 7.a 8.a 9.a 10.a 11.c 12.c 13.b 14.c 15.b 16.b 17.a 18.c 19.d 20.c 21.c 22.c
23.c 24.d 5.c 26.d 27.a 28.d 29.b 30.c
31.c
32.b 33.c
34.b
35.a
36.d 37.c
38.b 39.a 40.b 41.c
42.b 43.a 44.d 45.a 46.b 47.c 48.b 49.c 50.b 51.d 52.c 53.b 54.c 55.a 56.d 57.a 58.b 59.d 60.d 61.c
62.d 63.a 64.b 65.d 66.c 67.b 68.a 69.b 70.c 71.c 72.b 73.a 74.b 75.a 76.a 77.c 78.b 79.d 80.a
81.c 82.b 83.d 84.b 85.a 86.c 87.c 88.d 89.b 90.d