SECTOIN – 1
PHYSICS
1.
2.
3.
4.
On a rough circular track, the coefficient of friction varies with radial distance r from the centre of track as
r

  0  1   . Here, 0 and R are constants. At what distance from the centre, the safe speed for a
 R
vehicle is maximum?
R
R
R
(a) R
(b)
(c)
(d)
3
2
4
A particle in equilibrium displaces from (1, 1, 2) m to (2, 0, 3) m. If one of the forces acting on the particle
is (I – j + 3k) N, total work done by the remaining forces acting on the particle is
(a) 5J
(b) -5J
(c) zero
(d) 10 J
A particle is displaced from (1, 2) m to (0, 0) m along the path y = 2x3. Work done by a force
F  (x3 j  yi)N acting on the particle, during the displacement, is
(a) -1.5J
(b) 1.5J
(c) 2.5J
(d) -2.5J
2
2
The work done by the force F  x i  y j around the path shown in the figure is
2 3
a
3
(b) zero
(c) a3
4
(d) a3
3
A machine delivers constant power to a body which is proportional to velocity of the body. If the body
starts with a velocity which is almost negligible, then distance covered by the body is proportional to
(a)
5.
3/ 2
v
(b)  
(c) v3/5
(d) v2
2
 
A body is acted upon by a force which is inversely proportional to the distance covered. The work done
will be proportional to
(a) s
(b) s2
(c) s1/2
(d) None
a
b
In a molecule, the potential energy between two atoms is given by: U(x)  1/2  6 , where a and b are
x
x
positive constants and x is the distance between atoms. For equilibrium of atom, the value of x is
(a)
6.
7.
v
(a) zero
a
(b)  
 2b 
1/ 6
 2a 
(c)  
b 
1/ 6
11a 
(d) 

 5b 
1/ 6
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8.
In the given figure, a smooth parabolic wire track lies in the vertical
plane (x-y plane). The shape of track is defined by the equation
 x2 
y    (where a is constant). A ring of mass m which can slide freely
 a 
on the wire track, is placed at the position A (a, a). The track is rotated
with constant angular speed  such that there is no relative slipping
between the ring and the track then  is equal to
g
g
(a)
(b)
a
2a
1/ 2
2g
 g
(d) 21/ 4  
a
a
A car goes on a banked track with angle of banking 370. It comes across a turn of radius 100 m. If
1
coefficient of friction between the tyres and the surface is
, then the maximum velocity with which the
3
car can take the turn, assuming g = 10m/s2, is
(a) 48.38 m/s
(b) 55.76 m/s
(c) 27.38 m/s
(d) None
A heavy particle of weight w, attached to a fixed point by a light inextensible string describes a circle in a
vertical plane. The tension in the string has the values mw and nw respectively when the particle is at the
highest and lowest point in the path. Then
m
(a) m + n = 6
(b)
(c) m – n = - 6
(d) n - m = -6
2
n
Force F  yi  x j acts upon a particle of mass m.
(c)
9.
10.
11.
(a) potential energy is given by U  
xy
 C , where C is constant
2
(b) Force is conservative in nature and potential energy U = - xy + C, where C is constant
(c) Force is non conservative in nature
(d) Origin is the unstable equilibrium position
12.
A smooth track is shown in figure. A block of mass M is pushed against a spring of spring constant K
fixed at the left end and is then released. Find the initial compression of the spring so that the normal
reaction at point P is zero.
3MgR
2MgR
(a)
(b)
K
K
(c)
1 2MgR
2
K
(d)
MgR
K
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13.
14.
15.
16.
17.
18.
19.
The potential energy of a 4kg particle free to move along the x axis is given by U(x) 
x3 5x 2

 6x  3 .
3
2
Total mechanical energy of the particle is 17J. Then the maximum kinetic energy is
(a) 10J
(b) 2J
(c) 9.5J
(d) 0.5J
3


If the banking angle of curved road is given by tan1   and the radius of curvature of the road is 6m,
5
then the safe driving speed should not exceed: (g = 10m/s2)
(a) 86.4 km/h
(b) 43.2 km/h
(c) 21.6 km//h
(d) 30.4 km/h
A plank of mass 10kg and a block of mass 2kg are placed on a horizontal
plane as shown in the figure. There is no friction between plane and plank. The
coefficient of friction between block and plank is 0.5. a force of 60 N is applied
on plank horizontally. In first 2s the work done by the friction on the block is
(a) – 100J
(b) 100J
(c) zero
(d) 200J
A small block of mass m is kept on a rough inclined surface of inclination  fixed in an elevation. The
elevator goes up with a uniform velocity v and the block does not slide on the wedge. The work done by
the force of friction on the block in a time t will be
1
(a) zero
(b) mgvt cos2
(c) mgvt sin2
(d) mgvt sin2 
2
A particle of mass m begins to slide down a fixed smooth sphere from the top as
shown. What is its acceleration when it breaks off the sphere?
2g
g
(a)
(b) 5
3
3
g
(c) g
(d)
3
In the figure shown, a small block of mass m moves in fixed semi-circular
smooth track of radius R in vertical plane. It is released from the top. The
maximum centrifugal force on the block at the lowest point of track is
(a) 3mg
(b) 2mg
(c) mg
(d) zero
A weightless rod of length 2l carries two equal masses m, one tied at lower end A and the other at the
middle of the rod at B. The rod can rotate in vertical plane about a fixed
horizontal axis passing through C. The rod is released from rest in horizontal
position. The speed of the mass B at the instant rod becomes vertical is
3gl
4gl
(a)
(b)
5
5
(c)
6gl
5
(d)
7gl
5
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Two particles A and B are released simultaneously from two different inclined planes of inclination 300
and 600, respectively, with the horizontal. If KA and KB are their kinetic energies when they reach the foot
of the inclines after travelling the same distance l along the inclined plane then the ratio KA/KB is
(a) 1
(b) 3
(c) 1/ 3
(d) 1/3
21.
A force F = ( 3i + 4j) N acts on a particle moving along a line 4y + kx = 3. The work done by the force is
zero if the value of k is
(a) 1
(b) 2
(c) 3
(d) 4
Passage: (22 to 24)
A car is moving with speed v and is taking a turn on a circular road of radius 10m. The angle of banking is
370. The driver wants that car does not slip on the road. The coefficient of friction is 0.4 (g = 10 m/sec2)
22.
The speed of car for which no frictional force is produced, is
(a) 5 m/sec
(b) 5 3 m/sec
(c) 3 5 m/sec
(d) 10m/sec
23.
The friction force acting when v = 10 m/sec and mass of car is 50kg is
(a) 400N
(b) 100N
(c) 300N
(d) 200N
24.
If the car were moving on a flat road and distance between the from tyres is 2m and the height of the
centre of the mass of the car is 1m from the ground, then the minimum velocity for which car topples is
(a) 5m/sec.
(b) 5 3 m/sec
(c) 3 5 m/sec
(d) 10m/sec
20.
Passage: (25 to 27)
A small block of mass 200 gram is placed at the bottom of an inclined
plane which is 10m long and 3.2m high. Coefficient of friction between
the block and inclined plane is 0.1 [g = 10m/s2]
25.
Work required to lift the block from ground and put it at the top
(a) 3.2 J
(b) 6.4 J
(c) 9.6 J
(d) 1.6 J
26.
Work required to lift the block up the incline and taking it to top is
(a) 3.2 J
(b) 6.4 J
(c) 8.3 J
(d) 10 J
27.
If from the top it falls of the incline and drops vertically, with what speed it will hit the ground.
(a) 2 m/s
(b) 4 m/s
(c) 8 m/s
(d) 10 m/s
Passage: (28 to 30)
When the particle is acted upon by a conservative force, the potential
energy of a particle varies. The given figure shows the variation of
potential energy of a particle with displacement.
28.
The force acting on particle is maximum in magnitude at:
(a) B, C
(b) A, G
(c) B, F
(d) D
29.
Particle is in equilibrium at points:
(a) A, D, G
(b) C, E
(c) B, F
(d) A, G
30.
Body is in stable equilibrium at
(a) A and G
(b) D
(c) A, D, G
(d) C and E
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SECTOIN – 2
CHEMISTRY
31.
For reaction A → B, Ea = 10 kJ mol-1, H = 5kJ mol-1. Thus, potential energy profile for this reaction is:
(a)
32.
33.
34.
(b)
(d)
A decomposes as
The initial rate of appearance of B when 2M conc. of A is present is equal to
(a) 2 x 10-3 Ms-1 and independent on C(g)
(b) 4 x 10-3 Ms-1 and dependent on C(g)
-3
-1
(c) 8 x 10 Ms and independent on C(g)
(d) none of these
A G.M. counter is used to study the radioactive process of first-order. In absence of radioactive substance
A, it counts 3 disintegration per second (dps). When A is placed in the G.M. counter, it records 23 dps at
the start and 13 dps after 10 minutes. It records x dps after next 10 minutes and A has half-life period y
minutes. x and y are.
(a) 8dps, 10 min
(b) 5dps, 10min
(c) 5dps, 20min
(d) 5dps, 5min
A hypothetical reaction X2 + Y2 → 2XY follows the mechanism given below.
X2
X X
X  Y2 
 XY  Y
35.
(c)
[fast]
[slow]
[fast]
X  Y 
 XY
The order of overall reaction is
(a) 2
(b) 1
(c) 1.5
(d) zero
A reaction takes place in various steps. The rate constant for first, second, third and fifth steps are k 1, k2,
1/ 2
k3 and k5 respectively. The overall rate constant is given by k 
36.
k 2  k1 
 
k3  k5 
. If activation energy are 40, 60,
50 and 10kJ/mol respectively, the overall energy of activation (kJ/mol) is
(a) 10
(b) 20
(c) 25
(d) none of these
K3
K1
K2
 B 
C 
D ; K3 > K2 > K1, then the rate determining step
In the sequence of reaction A 
of the reaction is
(a) A → B
(b) C → D
(c) B → C
(d) A → D
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37.
38.
39.
40.
41.
For a general chemical change 2A + 3B → products,
The rate of disappearance of A is r1 and of B is r2. The rates r1 and r2 are related as
(a) 3r1 = 2r2
(b) r1 = r2
(c) 2r1 = 3r2
(d) r12 = 2r22
What is the half life of a radioactive substance if 87.5% of any given amount of the substance disintegrate
in 40 minutes?
(a) 160 min
(b) 10 min
(c) 20 min
(d) 13 min 20 sec.
A reaction of first order. After 100 minutes 75g of the reactant A are decomposed when 100g are taken
initially calculate the time required when 150g of the reactant A are decomposed, the initial weight taken
is 200g
(a) 100 minutes
(b) 200 minutes
(c) 150 minutes
(d) 175 minutes
Correct expression for the first order reaction is
C
C
(a) Ct  C0 ek1t
(b) Ct ek1t  C0
(c) n 0  k1t
(d) n t  k1t
Ct
C0
Given that K is the rate constant for some order of any reaction at temp T then the value of
lim logK ______
x 
A
(b) A
(c) 2.303 A
(d) log A
2.303
For a certain gaseous reaction a 100C rise of temp. from 250C to 350C doubles the rate of reaction. What
is the value of activation energy
10
2.303  10
0.693R  10
0.693R  298  308
(a)
(b)
(c)
(d)
2.303R  298  308
298  308R
290  308
10
According to collision theory of reaction rates –
(a) every collision between reactant leads to chemical reaction
(b) rate of reaction is proportional to velocity of molecules
(c) all reactions which occur in gaseous phase are zero order reaction
(d) rate of reaction is directly proportional to collision frequency
For producing the effective collisions, the colliding molecules must posses
(a) a certain minimum amount of energy
(b) energy equal to or greater than threshold energy
(c) proper orientation
(d) threshold energy as well as proper orientation of collision
What is false about N2O5
(a) it is anhydride of HNO3
(b) it is a powerful oxidizing agent
(c) solid N2O5 is called nitronium nitrate
(d) structure of N2O5 contains no [N→O] bond
The number of molecules of water needed to convert one molecules of P2O5 into orthophosphoric acid is
(a) 2
(b) 3
(c) 4
(d) 5
Which of the following is the correct statement for PH3
(a) it is less basis than NH3
(b) it is less poisonous tha NH3
(c) electronegativity of PH3 > NH3
(d) it does not show reducing properties
Which of the following does not leave any residue on heating
(a) Cu(NO3)2
(b) NaNO3
(c) Pb(NO3)2
(d) NH4NO3
(a)
42.
43.
44.
45.
46.
47.
48.
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49.
P  O  P bond is present in
(a) H4P2O6
(b) H4P2O5
(c) Both (A) and (B)
(d) H3PO4
50.
The least acidic oxide out of the following: N2O5(I), P2O5(II), As2O5(III) and Sb2O5(IV) is
(a) I
(b) II
(c) III
(d) IV
51.
When chlorine reacts with excess of ammonia, the ratio of volumes of chlorine used up and nitrogen
formed will be
(a) 1:3
(b) 3:1
(c) 8:3
(d) 3:8
52.
P4O10 has short and long P – O bonds. The number of short P – O bonds in this compound are
(a) 1
(b) 2
(c) 3
(d) 4
53.
1 mole each of H3PO2, H3PO3 and H3PO4 will neutralize respectively x mol of NaOH, y mole of Ca(OH)2
and z mole of Al(OH)3 (assuming all as strong electrolytes). x, y, z are in the ratio of
(a) 3 : 15 : 1
(b) 1 : 2 : 3
(c) 3 : 2 : 1
(d) 1 : 1 : 1
54.
The number of P  O  P bonds in the structure of phosphorus pentoxide and phosphorus trioxide are
respectively
(a) 5, 5
(b) 6, 6
(c) 5, 6
(d) 6, 5
55.
Which of the following pairs on heating give the same gas
(a) AgNO3, (NH4)2Cr2O7
(b) Pb(NO3)2, NH4NO3
(c) NH4NO2, NH4NO3
(d) NH4NO2, (NH4)2Cr2O7
56.
Nitrogen dioxide cannot be prepared by heating
(a) KNO3
(b) Pb(NO3)2
57.
(c) Cu(NO3)2
The percentage of -character in the orbitals forming P – P bonds in P4 is
(a) 25
(b) 33
(c) 50
(d) AgNO3
(d) 75
58.
The number of P  O  P and P  O  H bonds present respectively in pyrophosphoric acid molecule
are
(a) 1, 2
(b) 1, 4
(c) 2, 4
(d) 1, 3
59.
Nitric oxide is attracted towards magnetic field when it is in
(a) gaseous state
(b) liquid state
(c) solid state
(d) polymeric state
Which of the following oxides is a white crystalline solid at room temperature?
(a) NO
(b) N2O3
(c) N2O4
(d) N2O5
60.
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SECTOIN – 3
MAHEMATICS
61.
62.
63.
If y is a function of x and log (x+y)-2xy =0, then the value of y’ (0) is equal to
(a) 1
(b) -1
(c) 2
(d) 0
1
If f(x) =
, then the derivative of the composite function f f f(x) is equal to
1 x
(a) 0
(b) 1/2
(c) 1
(d) 2
 1  sin   


d
Let f = sin tan 
(f()) is
  , where     . Then the value of
4
4
d(tan )
 cos 2  

(a) 1
64.
65.
66.
dy
If y – x = 1, then the value of
at x = 1 is
dx
(a) 2(1-log2)
(b) 2 (1+log 2)
dy
-1
If y = sec (tan x), then
at x = 1 is equal to
dx
1
1
(a)
(b)
2
2
dy
If 1  x2  1  y2  a(x  y), then
equals
dx
(a)
67.
69.
70.
(c) 3
(d) 4
(c) 2 – log2
(d) 2+log2
(c) 1
(d)
y
(1  x2 )(1  y 2 )
1
If y  esin
(a)
68.
(b) 2
x
esin
1
x
(b)
1  y2
1  x2
and u = log x, then
x
1  x2
(a) x2
.....
xx
1
(b) x esin
, then x(1  ylog x)
(b) y2
(d) none of these
dy
is
du
x
(c)
 1  x2  1
 , then y’ (0) is
If y = tan1 


x


(a) 1/2
(b) 0
If f(x) = loga (logax), then f’(x) is
loga e
loge a
(a)
(b)
x loga x
x loge x
If y  x x
1  x2
1  y2
(c)
2
x esin
1
1  x2
(c) 1
(c)
loge a
x
1
x
(d)
esin
x
x
(d) -1
(d)
x
loge a
dy
dx
(c) xy2
(d) xy
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71.
(a) a constant
72.
73.
d2 y
, is equal to
dx 2
(c) a function of y
(d) a function of x and y both
If y2 = ax2 + bx + c where a, b, c are constants, then y 3
(b) a function of x
f(x)  1
If f(1) = 1 and f’(1) = 2 then lim
equals
x 1
x 1
(a) 2
(b) 4
(c) 1
1
x2
If f(x) = 3e , then f’(x) – 2x f(x) + f(0) – f’ (0) is equal to
3
(d) ½
2
74.
75.
76.
77.
78.
(a) 0
(b) 1
(c) (7 / 3)ex
The value of c in Rolle’s theorem when f(x) = 2x3 – 5x2 - 4x + 3, x  [1/2, 3] is
1
(a) 2
(b) 
(c) -2
3
In [0, 1] Lagrange’s mean value theorem is not applicable to
 1
1
x
 sin x
 2x
,
, x0


2
(a) f(x)  
(b) f(x)   x
(c) f (x) = x | x |
2
, x0
 1  x  , x  1
 1

 2
2

(d) e x
(d)
2
2
3
(d) f (x) = | x|
 2 3  1
If the function f(x) = x3–6x2+ax+b satisfies Rolle’s theorem in the interval [1, 3] and f’ 
  0 , then

3 

(a) a = -11
(b) b = - 6
(c) a = 6
(d) a = 11
The value of c for which the conclusion of mean value theorem-holds for the function f(x)=logex on the
interval [1,3], is
1
(a) 2log3e
(b) loge 3
(c) log3e
(d) loge3
2
If f(x) = (x – p) (x – q) (x – r, where p < q < r, are real numbers, then the application of Rolle’s theorem on
f leads to
(a) (p + q + r) (pq + qr + rp) = 3
(b) (p+q+r)2 = 3 (pq + qr + rp)
2
(c) (p+q+r) > 3 (pq + qr + rp)
(d) (p+q+r)2 < 3 (pq + qr + rp)
79.
Consider the polynomial f(x) = 1 + 2x + 3x2 + 4x3. Let s be the sum of all distinct real roots of f(x). Then s
lies in the interval
(a) (-1/4, 0)
(b) (-11, -3/4)
(c) (-3/4, -1/2)
(d) (0, 1/4)
80.
If f(x) = x3/2 (3x – 10), x  0, then f (x) is increasing in
(a)  , 1  1,  
(b) [2, )
81.
(c)  ,  1  [1, )
(d) (,0]  (2, )
  3 
Let f(x)  log(sin x  cos x),x  x   ,  , then f is strictly increasing in the interval
 4 4 
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82.
83.
84.
85.
86.
  3 
  
 3 
 
(a)   , 
(b)  0, 
(c)  , 
(d)  , 
2 4 
 4 4
 8 
4 2
f(x) = | x loge x | , x > 0, is monotonically decreasing in
(a) (e , )
(b) (0, 1/e)
(c) [1/e, 1]
(d) (1, e)
k

2x,
if
x


1

Let f : R → R be defined by f(x)  
2x  3,if x  1
If f has a local minimum at x = -1, then a possible value of k is
(a) – 1/2
(b) -1
(c) 1
(d) 0
x
 5 
For x   0,  , define f(x)   t sint dt . Then f has local maximum at  and 2
0
 2 
(a) local maximum at  and 2
(b) local minimum at  and 2
(c) local minimum at  and maximum at 2
(d) local maximum at  and minimum at 2
Let p(x) be a real polynomial of least degree which has a local maximum at x = 1 and a local minimum at
x = 3. If p(1) = 6 and p(3) = 2, then p’(0) is
(a) 8
(b) 9
(c) 3
(d) 6
Let f : R → R be defined as f(x) = | x | + | x2 – 1 |. The total number of points at which f attains either a
local maximum or a local minimum is
(a) 2
(b) 4
(c) 5
(d) 6
x
87.
If f(x)   e t (t  2)(t  3)dt for all x  (0, ), then which of the following is incorrect?
88.
(a) f has a local maximum at x = 2 and local minimum at x = 3
(b) f is decreasing on (2, 3)
(c) there exists c  (0, ) such that f’’ (c) = 0
(d) f is increasing on R+
The function f(x) = 2 | x | + | x + 2| - | | x + 2 | - 2 | x |} has a local minimum or a local maximum
respectively at x =
2
2
(a) – 2 and (b) – 2 and 0
(c)  and 2
(d) 2 and – 2
3
3
2
0
89.
90.
The number of points in the interval [ 13, 13] at which f(x) = sin x2 + cos x2 attains its maximum value
is
(a) 2
(b) 8
(c) 0
(d) 4
Let f(x) = | x – x1 | + | x – x2 |, where x1 and x2 are distinct real numbers. Then the number of points at
which f(x) is minimum, is
(a) More than 3
(b) 1
(c) 2
(d) 3
Space for Rough Work
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