3.0HRT-3-2013(ACEG)[1]

Vidyamandir Classes

VMC/JEE-2013 1 3.0HRT - 3/ACEG

Aggarwal Corporate Heights, 3rd Floor, Plot No. A - 7, Netaji Subhash Place,

Pitam Pura, Delhi - 110034 Phone: 011-45221190 - 93. Fax : 25222953

30/11/2011 3.0HRT - 3/IITJEE - 2013 M.M. : 225

03:00 P.M. - 06:00 P.M. TEST CODE : ACEG TIME : 3.00 Hrs

1. The question paper contains 75 questions and has 3 parts : (Part - I: Chemistry, Part - II: Physics,

Part - III: Mathematics) of 25 questions and 3 marks each.

2. Each question has Only One choice correct. You will be given 3 marks corresponding to the correct answer and

minus one (–1) marks (NEGATIVE MARKING) for every wrong answer.

PART - I CHEMISTRY

1. Pure ammonia is placed in a vessel at a temperature where its dissociation constant is appreciable. At equilibrium.

(A) Kp does not change significantly with pressure (B) does not change with pressure (C) Concentration of NH3 does not change with pressure (D) Concentration of H2 is less than that of N2

2. The equilibrium SO2Cl2(g) SO2(g) + Cl2(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 SO2, Cl2 and SO2Cl2 change (B) More Cl2 is formed (C) Concentration of SO2 is reduced (D) None of these

SPACE FOR ROUGH WORK

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3. The decomposition of N2O4 into NO2 is carried out at 280K in chloroform. When equilibrium has been established 0.2 mole of N2O4 and 32 10 mole of NO2 are present in 2 litres of solution. The equilibrium

constant for the reaction 2 4 2N O 2NO is :

(A) 21 10 (B) 32 10 (C) 51 10 (D) 52 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 NH3 is 0.30 M and the concentration of 4NH is 0.20 M. What is the pH of this solution ? (The equilibrium constant Kb for NH3 equals 51.8 10 )

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

6. Ka for hydrofluoric acid is 46.9 10 . What is KC for this reaction ?

2F (aq) H O( ) HF aq OH (aq)

(A) 116.9 10 (B) 111.4 10 (C) 92.6 10 (D) 68.3 10

7. The dissociation constant Ka of a weak monobasic acid is 710 . 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 2CO(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) 916

(B) 19

(C) 169

(D) 9


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10. When 25 g of MCO3(s) were enclosed in a 10 litre evacuated flask heated to 727 C 80% of MCO3 got decomposed into solid MO (Molecular weight = 56) and CO2(g). Kp for the decomposition of MCO3 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 NH4OH. (B) 0.2 M CH3CO2H mixed with 0.1 M NaOH. (C) 0.1 M NaOH mixed with 0.1 MH2CO3. (D) 0.1 M CH3CO2H mixed with 0.1 MNH4OH.

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 CH3COOH = 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 105 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 CaOCl2 (bleaching powder) is/are : (A) + 1 only (B) 1 only (C) 1 and 1 (D) None of these

15. 36 10 mole K2Cr2O7 reacts completely with 39 10 mole Xn+ to give 33XO and Cr . The value of n is :

(A) 1 (B) 2 (C) 3 (D) None of these

16. If mA gram of a metal A displaces mB gram of another metal B from its salt solution and if the equivalent weights are EA and EB respectively then equivalent weight of A can be expressed as :

(A) AA B

B

mE Em

(B) A BA

B

m mEE

(C) BA B

A

mE Em

(D) AA B

B

mE Em

17. In a chemical reaction, K2Cr2O7 + xH2SO4 + ySO2 K2SO4 + Cr2(SO4)3 + zH2O ; 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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18. Hydrazine reacts with KIO3 in presence of HCl as :

2 4 3 2 2N H IO 2H Cl ICl N 3H O The equivalent masses of N2H4 and KIO3 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 KMnO4 and K2Cr2O7 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 2xSn 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. pKb of NH4OH is 4.74 and pKb 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 4NH A NH B NH C NH D (B) 4 4 4 4NH D NH B NH C NH A

(C) 4 4 4 4NH D NH C NH B NH A (D) None of these

22. Equilibrium constant of the reaction is 73.6 10

2OCl (aq) H O( ) HOCl(aq) OH (aq) . What is the Ka for HOCl ?

(A) 82.8 10 (B) 73.6 10 (C) 46 10 (D) 62.8 10

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

(C) 4NaCN NH Cl NaCl HCl (D) 4HCl NaCl NaCN NH Cl

24. Which of the following will not show common ion effect on addition of HCl ? (A) CH3COOH (B) H2S (C) C6H5COOH (D) H2SO4

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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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 v1 and v2 respectively. The velocity of their centre of mass is :

(A) zero (B) v1 (C) v2 (D) 1 2

2v 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) 212

mv (B) mv2 (C) 232

mv (D) 252

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 1JP

(D) The coefficient of restitution is 1 JP

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


2m A B

u

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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) 10g (B) g (C) 2g (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 CV (B) 2 C PV V

(C) 2 C PV V (D) 2 C PV V

34. In the following figure, the bar is uniform and weighing 500 N. How large must W be if T1 and T2 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) 22 M3

(B) 2M

(C) 2M

3 (D) None of these


R u

VC

A

C

VP

2 O

T1

0.3L

T2

0.4L 0.3L W

T1

T2

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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, MA = m and MB = 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 11

m

(C) 31

m

(D) 61

m

40. A mass of 1 kg is acted upon by a single force 4 4F 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

4tx . The work done in the first one second.

(A) 14

J (B) 12

J (C) 34

J (D) 54

J


B

C

A A

B

C

D

m 2m

L/2 L/2

3m

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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 for 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 .

(A) 1R cos (B) 2 1R cos (C) 2 32

Rcos (D) 2 3R cos

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

45. Find the total height it goes above the ground after leaving at P :

(A) 31 22

Rcos cos (B) 31

2

Rcos cos

(C) 31 22

Rcos cos (D) None of these

For Q. 46 - 48

Each pulley in Figure has radius r = 5cm and moment of inertia 3 22 5 10 I . kgm , 2 and 1M kg m kg (g = 10m/s2) :

46. Find the acceleration of the blocks (A) 21m / s (B) 22m / s (C) 23m / s (D) 24m / s


A

h

D P

C O R

B

m

M

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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) 59

(B) 37

(C) 512

(D) 314

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) 1714mg (B) 3

2mg (C) 50

7mgrR

(D) 207mgrR

50. A particle of mass m is projected with velocity v0 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) 30

4 2mv

g (B)

303

4mvg

(C) 30

2mv

g (D) Zero


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PART - III MATHEMATICS

51. If 10f x log x then 210f x f f x log log x

The domain of the function f 3 (x) must be :

(A) 0 , (B) 1 , (C) 10 , (D) 1010 ,

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

53. If 10f x sin log x and 10h x cos log x , then 12

xf x f y h h xyy

equals :

(A) 10sin log xy (B) 10cos log xy

(C) 10xsin logy

(D) Zero

54. The domain of definition of the function 10

1 21

y xlog 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 2x |sin x| | sin x| . . . | sin K x|f x e is :

(A) 1 (B) K (C) 2K (D) Does not exist

56. Suppose 21f x x for 1x . 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 0x , x (B) 2

1 11

, xx

(C) 1 1x , x (D) 1 0 x , x


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57. Let 23 22f x sin x cos x and 2 xg 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 1xf x log x

is :

(A) 2 , (B) 0, (C) 1, (D) None of these

59. Consider the function g (x) defined as

2008 20072 1 2 4 21 1 1 1 1 1g 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 1alog 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 0x x and the abscissae are the roots of the equation 2 4 12 0y y , is :

(A) 2 2 2 4 15 0x y x y (B) 2 2 4 2 15 0x y x y

(C) 2 2 4 2 15 0x y x y (D) None of these

62. The two circles 2 2 2 6 6 0x y x y and 2 2 5 6 15 0x y x y touch each other. The equation of their common tangent is :

(A) x = 3 (B) y = 6 (C) 7 12 21 0x y (D) 7 12 21 0x y

63. The locus of the centre of a circle, which externally touches the circle 2 2 6 6 14 0x y x y and also touches the y-axis, is given by the equation :

(A) 2 6 10 14 0x x y (B) 2 10 6 14 0x x y

(C) 2 6 10 14 0y x y (D) 2 10 6 14 0 y x y


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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 0x y and 3 4 0x y lie along diameters of a circle of circumference 10 , then the equation of the circle is :

(A) 2 2 2 2 23 0x y x y (B) 2 2 2 2 23 0x y x y

(C) 2 2 2 2 23 0x y x y (D) 2 2 2 2 23 0x y x y

66. If one of the diameters of the circle 2 2 2 6 6 0x 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 0x y x y and 2 2 8 6 20 0x 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 9x y and 2 2 2 2 1 0x y x y touch each other externally, then can be:

(A) 0 (B) 1 (C) 4

3 (D) No values

Paragraph for Q.69 - 71

Tangents PA and PB are drawn from 1 1P x , y to the circle 2 2 2 2 0S x y gx fy c . Then answer the

following questions 2 2 2 21 1 1 1 12 2S x y g fy c, r g f c .

69. The angle between PA and PB :

(A) 2

11

12

S rtan

r S

(B) 112

1

2r Stan

S r

(C) 11

2 21

r Stan

S r

(D)

211 S r

tanS . r


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70. The length of the chord AB is :

(A) 1

21

2r S

S r (B) 1

2 21

SS r

(C) 1

2 21

2r S

S r (D) None of these

71. The area of the triangle PAB is :

(A) S1 (B) 12 2

1

r SS r

(C) 12

1

r SS r

(D) 3 21

21

/rSS r

72. True / False : S1 : f : 3 3 9 9 , , defined as f (x) = x | x | is an odd function.

S2 : For real values of x and y the relation 2 22 1y x x represents y as a function of x. S3 ; If 2 3 f x log x x and 2 3g x log x log x , then f = g

S4 : If 2 2 5f x x , then 2 9f x x (A) TTFF (B) TTFT (C) TFTF (D) FTTF

73. The function f 11 2x

x xx

e

is :

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

74. 210 1f x log x x is :

(A) an odd function (B) a periodic function (C) an even function (D) None of these

75. True / False : S1 : If the point (0, g) lies inside the circle 2 2 2 0x y gx c , then c cannot be positive.

S2 : Length of tangent from origin to the circle 2 24 4 8 8 1 0x y x y is 1

2.

S3 ; The equation 2 24 4 12 8 13 x y x y k represents a point if k = 0.

S4 : The point 1, lies inside the circle 2 2 1x y if 1

2 .

(A) FFTT (B) TTTF (C) TFFF (D) TTTT


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

3.0HRT-3-2013(ACEG)[1]

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