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VM C/ JEE-2013 1 3. 0HRT - 3/ ACEG

Aggarw al Corporat e Height s, 3rd Floor, Plot No. A - 7, Net aj i Subhash Place,
Pit am Pura, Delhi - 110034 Phone: 011-45221190 - 93. Fax : 25222953
30/ 11/ 2011
3.0HRT - 3/ II TJEE - 2013
M . M . : 225
03:00 P. M . - 06:00 P. M . TEST CODE : ACEG TI M E : 3. 00 Hrs
1. The quest ion paper cont ains 75 quest ions and has 3 part s : (Part - I : Chemist ry, Part - I I : Physics,
Part - I I I : M at hemat ics) of 25 quest ions and 3 marks each.
2. Each quest i on has Only One choice correct . You w i l l be gi ven 3 marks cor r espondi ng t o t he cor r ect answ er and
minus one (1) marks (NEGATI VE M ARKI NG) f or ever y w r ong answ er .

PART - I CHEM ISTRY

1. Pure ammonia is placed in a vessel at a temperature where its dissociation constant is appreciable.
At equilibrium.
(A) K
p
does not change significantly with pressure
(B) o does not change with pressure
(C) Concentration of NH
3
does not change with pressure
(D) Concentration of H
2
is less than that of N
2

2. The equilibrium SO
2
Cl
2
(g)

SO
2
(g) + Cl
2
(g) is attained at 25 C in a closed container and an inert gas,
helium, is introduced. Which of the following statement is correct ?
(A) Concentrations of SO
2
, Cl
2
and SO
2
Cl
2
change
(B) More Cl
2
is formed
(C) Concentration of SO
2
is reduced
(D) None of these
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VM C/ JEE-2013 2 3. 0HRT - 3/ ACEG

3. The decomposition of N
2
O
4
into NO
2
is carried out at 280K in chloroform. When equilibrium has been
established 0.2 mole of N
2
O
4
and
3
2 10

mole of NO
2
are present in 2 litres of solution. The equilibrium
constant for the reaction
2 4 2
N O 2NO

is :
(A)
2
1 10

(B)
3
2 10

(C)
5
1 10

(D)
5
2 10

4. If pressure is applied to the equilibrium system of solid

liquid, the melting point of the solid

(A) will not change (B) may increase or decrease depending upon its nature
(C) will always increase (D) will always decrease

5. A buffer solution is prepared in which the concentration of NH
3
is 0.30 M and the concentration of
4
NH
+
is
0.20 M. What is the pH of this solution ? (The equilibrium constant K
b
for NH
3
equals
5
1.8 10

)
(A) 8.73 (B) 9.08 (C) 9.43 (D) 11.72

6. K
a
for hydrofluoric acid is
4
6.9 10

. What is K
C
for this reaction ?
( )
2
F (aq) H O( ) HF aq OH (aq)

+ +

(A)
11
6.9 10

(B)
11
1.4 10

(C)
9
2.6 10

(D)
6
8.3 10

7. The dissociation constant K
a
of a weak monobasic acid is
7
10

. What is the approximate pH of a 0.1 M solution

of the acid ?
(A) 1 (B) 2 (C) 3 (D) 4

8. For a certain temperature the chemical reaction represented by the following equation has an equilibrium
constant of 4.
2 2 2
CO(g) H O(g) CO (g) H (g) + +

A mixture initially containing one mole of each of CO and steam is allowed to reach equilibrium. How many
moles of CO are now present ?
(A) 1/4 (B) 1/3 (C) 1/2 (D) 2/3

9. One mole of a compound AB reacts with one mole of a compound CD according to the equation,
AB CD AD CB + +

. When equilibrium had been established, it was found that 3/4 mole each of reactant
AB and CD had been converted to AD and CB. There is no change in volume. The equilibrium constant for the
reaction is :
(A)
9
16
(B)
1
9
(C)
16
9
(D) 9
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Vidyamandir Classes

VM C/ JEE-2013 3 3. 0HRT - 3/ ACEG

10. When 25 g of MCO
3
(s) were enclosed in a 10 litre evacuated flask heated to 727 C 80% , of MCO
3
got
decomposed into solid MO (Molecular weight = 56) and CO
2
(g). K
p
for the decomposition of MCO
3
is :
(A) 1.642 atm (B) 3.91 atm (C) 0.631 atm (D) 4.261 atm


11. Which of the following solution cannot function as a buffer when mixed in equal volume ?
(A) 0.1 M HCl mixed with 0.2 M NH
4
OH. (B) 0.2 M CH
3
CO
2
H mixed with 0.1 M NaOH.
(C) 0.1 M NaOH mixed with 0.1 MH
2
CO
3
. (D) 0.1 M CH
3
CO
2
H mixed with 0.1 MNH
4
OH.


12. A 0.1 M solution of acetic acid is titrated with a 0.05M solution of NaOH. What is the pH when 60% of the
acid has been neutralized ? (pKa of CH
3
COOH = 4.74, log 2 = 0.3, log 3 = 0.48)
(A) 2.38 (B) 4.56 (C) 4.92 (D) 7

13. Ka for HCN is
10
5 10

at 25 C . For maintaining a constant pH = 9, the volume of 5 M KCN solution

required to be added to 10 ml of 2M HCN solution is :
(A) 4 ml (B) 7.95 ml (C) 2 ml (D) 9.3 ml

14. The oxidation state(s) of Cl in CaOCl
2
(bleaching powder) is/are :
(A) + 1 only (B) 1 only (C) 1 and 1 + (D) None of these

15.
3
6 10

mole K
2
Cr
2
O
7
reacts completely with
3
9 10

mole X
n+
to give
3
3
XO and Cr
+
. The value of n is :
(A) 1 (B) 2 (C) 3 (D) None of these

16. If m
A
gram of a metal A displaces m
B
gram of another metal B from its salt solution and if the equivalent
weights are E
A
and E
B
respectively then equivalent weight of A can be expressed as :
(A)
A
A B
B
m
E E
m
= (B)
A B
A
B
m m
E
E

= (C)
B
A B
A
m
E E
m
= (D)
A
A B
B
m
E E
m
=
17. In a chemical reaction, K
2
Cr
2
O
7
+ xH
2
SO
4
+ ySO
2
K
2
SO
4
+ Cr
2
(SO
4
)
3
+ zH
2
O ; the value of x, y and z
respectively are :
(A) x = 1, y = 3, z = 1 (B) x = 4, y = 1, z = 4
(C) x = 3, y = 2, z = 1 (D) x = 2, y = 2, z = 1
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VM C/ JEE-2013 4 3. 0HRT - 3/ ACEG

18. Hydrazine reacts with KIO
3
in presence of HCl as :
2 4 3 2 2
N H IO 2H Cl ICl N 3H O
+
+ + + + +
The equivalent masses of N
2
H
4
and KIO
3
respectively are :
(A) 8 and 53.5 (B) 16 and 53.5 (C) 8 and 35.6 (D) 8 and 87

19. The ratio of moles of Fe (II) oxidized by equal volumes of equimolar KMnO
4
and K
2
Cr
2
O
7
solutions in acidic
medium will be :
(A) 5 : 3 (B) 1: 1 (C) 1: 2 (D) 5 : 6

20. Dichromate ion in acidic medium oxidizes stannous ion as :
2 2 4 3
2 7 2
xSn yCr O zH aSn bCr cH O
+ + + +
+ + + +
The incorrect statement is :
(A) the value of x : y is 1: 3 (B) the value of x + y + z is 18
(C) a : b is 3: 2 (D) the value of z c is 7

21. pK
b
of NH
4
OH is 4.74 and pK
b
of A , B , C and D

are 3, 4, 5, 6 respectively. An aqueous solution of
0.01M has pH in given increasing order :
(A)
4 4 4 4
NH A NH B NH C NH D < < < (B)
4 4 4 4
NH D NH B NH C NH A < < <
(C)
4 4 4 4
NH D NH C NH B NH A < < < (D) None of these

22. Equilibrium constant of the reaction is
7
3.6 10

2
OCl (aq) H O( ) HOCl(aq) OH (aq)

+ +

. What is the K
a
for HOCl ?
(A)
8
2.8 10

(B)
7
3.6 10

(C)
4
6 10

(D)
6
2.8 10

23. The pH of 0.1M solution of the following salts increases in the order.
(A)
4
NaCl NH Cl NaCN HCl < < < (B)
4
HCl NH Cl NaCl NaCN < < <
(C)
4
NaCN NH Cl NaCl HCl < < < (D)
4
HCl NaCl NaCN NH Cl < < <

24. Which of the following will not show common ion effect on addition of HCl ?
(A) CH
3
COOH (B) H
2
S (C) C
6
H
5
COOH (D) H
2
SO
4

25. 10 ml of a strong acid solution of pH = 2.000 are mixed with 990 ml of another strong acid solution of
pH = 4.000 of. The pH of the resulting solution will be :
(A) 4.002 (B) 4.000 (C) 4.200 (D) 3.72
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VM C/ JEE-2013 5 3. 0HRT - 3/ ACEG

PART - II PHYSICS


26. An electron and a proton start moving towards each other under the action of mutual attraction. At a certain
instant their velocities are v
1
and v
2
respectively. The velocity of their centre of mass is :
(A) zero (B) v
1
(C) v
2
(D)
1 2
2
v v +


27. A particle of mass 4m which is at rest explodes into three fragments. Two of fragments, each of mass m are
found to move with a speed v each in mutually perpendicular directions. The total energy released in the
process is :
(A)
2
1
2
mv (B) mv
2
(C)
2
3
2
mv

(D)
2
5
2
m / v

28. Two persons A and B of weight 80 kg and 50 kg respectively
are standing at opposite ends of a boat of mass 70 kg and length
2m, at rest. When they interchange their positions then
displacement of the centre of mass of the boat will be :
(A) 60 cm towards left (B) 30 cm towards right
(C) 30 cm towards left (D) None of these

29. In a one-dimensional collision between two identical particles A and B, B is stationary and A has momentum P
before impact. During impact, B gives impulse J to A. Choose the incorrect statement :
(A) The total momentum of the A plus B system is P before and after the impact.
(B) During the impact, A gives impulse J to B
(C) The coefficient of restitution is
2
1
J
P

(D) The coefficient of restitution is 1
J
P

30. A ball of mass m is attached to one end of a light rod of length , the
other end of which is hinged. What minimum velocity v should be
imparted to the ball downwards, so that it can complete the circle?
(A) g (B) 5g

(C) 3g (D) 2g
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2m
A B
u

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VM C/ JEE-2013 6 3. 0HRT - 3/ ACEG

31. A particle is given an initial speed u inside a smooth spherical shell of radius R = 1m
that it is just able to complete the circle. Acceleration of the particle when its velocity
is vertical is :
(A) 10 g

(B) g (C) 2 g (D) 3g

32. A particle inside the rough surface of a rotating cone about its axis is at rest relative to it at a height of 1m above
its vertex. Friction coefficient is = 0.5. If half angle of cone is 45 , the maximum angular velocity of
revolution of cone can be :
(A) 10 rad / s (B) 30 rad / s (C) 40 rad / s (D) 50 rad / s

33. In the following figure, the velocities are in ground frame and the cylinder is
performing pure rolling on the plank, velocity of point A would be :
(A) 2
C
V (B) 2
C P
V V +
(C) 2
C P
V V (D) ( ) 2
C P
V V

34. In the following figure, the bar is uniform and weighing 500 N.
How large must W be if T
1
and T
2
are to be equal ?
(A) 500 N
(B) 300 N
(C) 750 N
(D) 1500 N

35. For the uniform T shaped structure, with mass 3M, moment of inertia
about an axis normal to the plane and passing through O would be :
(A)
2
2
M
3
(B)
2
M

(C)
2
M
3
(D) None of these
SPACE FOR ROUGH W ORK

R
u
V
C

A
C
V
P

2
O
T
1

0.3L
T
2

0.4L
0.3L
W
T
1

T
2

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VM C/ JEE-2013 7 3. 0HRT - 3/ ACEG

36. In the balance machine, shown in figure which arm will move downward ?
(A) left
(B) right
(C) None
(D) can not be said

37. A motorcycle is going on an over bridge of radius R. The driver maintains a constant speed. As the motorcycle
is ascending on the over bridge, the normal force on it :
(A) increases (B) decreases
(C) remains constant (D) first increases then decreases

38. A stone is attached to one end of a string and rotates in a vertical circle. If string
breaks at the position of maximum tension, it will break at :
(A) A (B) B
(C) C (D) D

39. For the system shown in figure, M
A
= m and M
B
= 2m. There is
no friction between B and ground while coefficient of friction
between A and B is . The block B is connected to the block C
by means of a string and pulley system. The system is released
from rest, then find the minimum value of mass of C so that
there is no relative motion between A and B.
(A)
m

(B)
2 1
1
m

+
+
(C)
3
1
m

(D)
6
1
m
+

40. A mass of 1 kg is acted upon by a single force

( )
4 4 F i j = +

N. Due to force, mass is displaced from (0, 0)

to (1m, 1m). If initially the speed of the particle was 2 m/s, its final speed should approximately be :
(A) 6 m/s (B) 4.5 m/s (C) 8 m/s (D) 7.2 m/s

41. The displacement x of a body of mass 1 kg on horizontal smooth surface as a function of time t is given by
4
4
t
x = . The work done in the first one second.
(A)
1
4
J (B)
1
2
J (C)
3
4
J (D)
5
4
J
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B
C
A
A
B
C
D
m
2m
L/2 L/2
3m
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VM C/ JEE-2013 8 3. 0HRT - 3/ ACEG

42. A ladder 2.5 m long and of weight 150 N has its center of gravity 1 m from its bottom. A weight of 40 N is
attached to the top end. The work required to raise the ladder from the horizontal position to the vertical
position is :
(A) 190 J (B) 250 J (C) 285 J (D) 475 J

Paragraph f or Q.43 - 45
A small body starts sliding from height h down an incline groove
passing into a half circle BCD of radius R. The centre of semi-
circle BCD is O and OC is horizontal.
43. Find the height h in terms of R so that it leaves the track at P where POD Z = .
(A) ( ) 1 R cos + (B) ( ) 2 1 R cos + (C) ( ) 2 3
2
R
cos + (D) ( ) 2 3 R cos +

44. The normal force exerted by block at B is :
(A) ( ) 3 1 mg cos + (B) ( ) 3 1 mg cos (C) ( ) 2 1 mg cos + (D) None of these

45. Find the total height it goes above the ground after leaving at P :
(A)
( )
3
1 2
2
R
cos cos + (B)
( )
3
1
2
R
cos cos + +
(C)
( )
3
1 2
2
R
cos cos + (D) None of these

For Q. 46 - 48
Each pulley in Figure has radius r = 5cm and moment of inertia
3 2
2 5 10

= I . kgm , 2 and 1 M kg m kg = = (g = 10m/s

2
) :
46. Find the acceleration of the blocks
(A)
2
1m/ s (B)
2
2m/ s (C)
2
3m/ s (D)
2
4m/ s
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A
h
D
P
C
O
R
B
m
M
Vidyamandir Classes

VM C/ JEE-2013 9 3. 0HRT - 3/ ACEG

47. Tension in the horizontal part of the string between the pulleys is :
(A) 7N (B) 9N (C) 14N (D) 16N

48. A solid sphere rolls down an incline plane of inclination 37 . What is the minimum coefficient of friction is
required ?
(A)
5
9
(B)
3
7
(C)
5
12
(D)
3
14


49. A solid sphere of radius r and mass m starts rolling without friction down a fixed horizontal surface of radius
R + r. It starts when the centers of the two are in the same horizontal level. Find the normal force exerted by the
sphere on the surface when the line joining the centers of the two makes an angle of 60 with vertical.
(A)
17
14
mg
(B)
3
2
mg
(C)
50
7
mgr
R
(D)
20
7
mgr
R


50. A particle of mass m is projected with velocity v
0
making an angle 30 with the horizontal. The magnitude of
the angular momentum of the particle about the point of projection when the particle comes back as same
horizontal level is :
(A)
3
0
4 2
mv
g
(B)
3
0
3
4
mv
g
(C)
3
0
2
mv
g
(D) Zero
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VM C/ JEE-2013 10 3. 0HRT - 3/ ACEG

PART - II I M ATHEM ATICS


51. If ( )
10
f x log x = then ( ) ( ) ( ) ( )
2
10
f x f f x log log x = =
The domain of the function f
3
(x) must be :
(A) ( ) 0 , (B) ( ) 1 , (C) ( ) 10 , (D)
( )
10
10 ,

52. If x satisfies 1 2 3 6 | x | | x | | x | + + > , then :
(A) 0 4 x s s (B) 1 s x or 3 > x
(C) 0 x s or 4 x > (D) None of these

53. If ( ) ( )
10
f x sin log x = and ( ) ( )
10
h x cos log x = , then ( ) ( ) ( )
1
2
x
f x f y h h xy
y
( | |

( |
\ .
equals :
(A) ( ) ( )
10
sin log xy (B) ( ) ( )
10
cos log xy
(C)
10
x
sin log
y
| | | |
|
|
\ . \ .
(D) Zero
54. The domain of definition of the function
( )
10
1
2
1
y x
log x
= + +

is :
(A) ( ) 3 2 , excluding 2 5 . (B) [0, 1] excluding 0.5
(C)
| ) 2 1 , excluding 0 (D) None of these

55. If K is any integer then the period of the function ( )
{ } 2 x |sin x| | sin x| . . . | sin K x|
f x e
+ + + +
= is :
(A) 1 (B) K (C)
2
K

(D) Does not exist

56. Suppose ( ) ( )
2
1 f x x = + for 1 x > . If g (x) is the function whose graph is the reflection of the graph of f (x)
with respect to the line y = x, then g (x) equals :
(A) 1 0 x , x > (B)
( )
2
1
1
1
, x
x
>
+

(C) 1 1 x , x + > (D) 1 0 > x , x
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VM C/ JEE-2013 11 3. 0HRT - 3/ ACEG

57. Let ( )
23 22
f x sin x cos x = and ( ) 2
x
g x e = + . Then, the number of values of x in interval | | 10 20 ,
satisfying the equation ( ) ( ) ( )
f x sgn g x = , is 5a. Then, a is equal to :
(A) 1 (B) 2 (C) 3 (D) 4

58. The domain of ( ) ( )
2
1 x
f x log x

= is :
(A)
( )
2, + (B) ( ) 0, + (C) ( ) 1, + (D) None of these

59. Consider the function g (x) defined as
( )
( )
( )
( ) ( )
( )
2008
2007 2 1
2 4 2
1 1 1 1 1 1 g x . x x x x . . . x
| |
= + + + + |
|
\ .

The value of g (2) equals to :
(A) 1 (B) 2 (C) 3 (D) 4

60. The number of real solutions of the equation 0 1
a
log x | x |, a = < < , is :
(A) 0 (B) 1 (C) 2 (D) None of these

61. The equation of the circle whose one diameter is PQ, where the ordinates of P, Q are the roots of the
equation
2
2 3 0 x x + = and the abscissae are the roots of the equation
2
4 12 0 y y + = , is :
(A)
2 2
2 4 15 0 x y x y + + + = (B)
2 2
4 2 15 0 x y x y + =
(C)
2 2
4 2 15 0 x y x y + + + = (D) None of these

62. The two circles
2 2
2 6 6 0 x y x y + + + = and
2 2
5 6 15 0 x y x y + + + = touch each other. The equation of
their common tangent is :
(A) x = 3 (B) y = 6
(C) 7 12 21 0 x y = (D) 7 12 21 0 x y + + =

63. The locus of the centre of a circle, which externally touches the circle
2 2
6 6 14 0 x y x y + + = and also
touches the y-axis, is given by the equation :
(A)
2
6 10 14 0 x x y + = (B)
2
10 6 14 0 x x y + =
(C)
2
6 10 14 0 y x y + = (D)
2
10 6 14 0 + = y x y
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VM C/ JEE-2013 12 3. 0HRT - 3/ ACEG

64. A circle with centre (h, k) [where k > 0] touches the x-axis and also touches the circle with centre at (0, 3) and
radius 2. The locus of (h, k) is :
(A) an ellipse (B) a circle (C) a hyperbola (D) a parabola

65. If the lines 2 3 1 0 x y + + = and 3 4 0 x y = lie along diameters of a circle of circumference 10 , then the
equation of the circle is :
(A)
2 2
2 2 23 0 x y x y + + = (B)
2 2
2 2 23 0 x y x y + =
(C)
2 2
2 2 23 0 x y x y + + + = (D)
2 2
2 2 23 0 x y x y + + =

66. If one of the diameters of the circle
2 2
2 6 6 0 x y x y + + = is a chord to a circle with centre (2, 1), then the
radius of that circle is :
(A) 3 (B) 2 (C) 3 (D) 2

67. Which of the following statements is true regarding the following two circles ?

2 2
4 8 0 x y x y + = and
2 2
8 6 20 0 x y x y + + =
(A) These circles do not touch each other (B) These circles touch each other internally
(C) These circles touch each other externally
(D) None of these

68. If the circles
2 2
9 x y + = and
2 2
2 2 1 0 x y x y + + + + = touch each other externally, then can be:
(A) 0 (B) 1 (C)
4
3
(D) No values
Paragraph f or Q.69 - 71
Tangents PA and PB are drawn from ( )
1 1
P x , y to the circle
2 2
2 2 0 S x y gx fy c + + + + = . Then answer the
following questions
( )
2 2 2 2
1 1 1 1 1
2 2 S x y g fy c, r g f c + + + + = + .
69. The angle between PA and PB :
(A)
2
1 1
1
2
S r
tan
r S

(B)
1 1
2
1
2r S
tan
S r

(C)
1 1
2 2
1
r S
tan
S r

(D)
2
1 1
S r
tan
S . r

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VM C/ JEE-2013 13 3. 0HRT - 3/ ACEG

70. The length of the chord AB is :
(A)
1
2
1
2r S
S r +
(B)
1
2 2
1
S
S r
(C)
1
2 2
1
2r S
S r
(D) None of these

71. The area of the triangle PAB is :
(A) S
1
(B)
1
2 2
1
r S
S r +
(C)
1
2
1
r S
S r
(D)
3 2
1
2
1
/
rS
S r +


72. True / False :
S
1
: f :
| | | |
3 3 9 9 , , defined as f (x) = x | x | is an odd function.
S
2
: For real values of x and y the relation
2 2
2 1 y x x = represents y as a function of x.
S
3
; If ( ) ( ) ( ) { }
2 3 = f x log x x and ( ) ( ) ( ) 2 3 g x log x log x = + , then f = g
S
4
: If ( ) 2 2 5 f x x + = , then ( ) 2 9 f x x =
(A) TTFF (B) TTFT (C) TFTF (D) FTTF

73. The function f ( ) 1
1 2
x
x x
x
e
= + +

is :
(A) an odd function (B) an even function
(C) neither an odd nor an even function (D) a periodic function

74. ( )
( )
2
10
1 f x log x x = + + is :
(A) an odd function (B) a periodic function
(C) an even function (D) None of these

75. True / False :
S
1
: If the point (0, g) lies inside the circle
2 2
2 0 x y gx c + + + = , then c cannot be positive.
S
2
: Length of tangent from origin to the circle
2 2
4 4 8 8 1 0 x y x y + + + + = is
1
2
.
S
3
; The equation
2 2
4 4 12 8 13 + + = x y x y k represents a point if k = 0.
S
4
: The point ( ) 1 , + lies inside the circle
2 2
1 x y + = if
1
2
= .
(A) FFTT (B) TTTF (C) TFFF (D) TTTT
SPACE FOR ROUGH W ORK



Vidyamandir Classes

VM C/ JEE-2013 14 3. 0HRT - 3/ ACEG

SPACE FOR ROUGH W ORK





Vidyamandir Classes

VM C/ JEE-2013 15 3. 0HRT - 3/ ACEG

SPACE FOR ROUGH W ORK







Vidyamandir Classes

VM C/ JEE-2013 16 3. 0HRT - 3/ ACEG

SPACE FOR ROUGH W ORK










































* * * * * * End of 3HRT-3/ ACEG/ JEE- 2013* * * * * *
Vidyamandir Classes

Answ ers - 3. 0HRT - 3(ACEG)/ II TJEE- 2013
CHEM I STRY
1 2 3 4 5 6 7 8 9 10
A D C B C B D B D A
11 12 13 14 15 16 17 18 19 20
D C C C A A A A D A
21 22 23 24 25
C A B D D


PHYSI CS
26 27 28 29 30 31 32 33 34 35
A C C D D A B C D B
36 37 38 39 40 41 42 43 44 45
B A A C B B B C A D
46 47 48 49 50
B C D B B


M ATHEM ATICS
51 52 53 54 55 56 57 58 59 60
C C D C A D C A B B
61 62 63 64 65 66 67 68 69 70
A A D D D C B D B A
71 72 73 74 75
D B C A D