3.0HRT-2-2013(ACEG)

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

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

31/08/2011 3.0HRT - 2/IITJEE - 2013 M.M. : 195

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

1. The question paper contains 60 questions and has 3 parts : (Part - I : Chemistry, Part - II : Physics, Part - III : Mathematics) of 20 questions and 65 marks each.

2. In each part, first 15 questions are of Single Answer Type (Only One choice correct) of 3 marks each with a NEGATIVE MARKING of One mark (-1) and next 5 Question marked ‘*’ may have More Than One Correct option having 4 marks each and NO NEGATIVE MARKING.

PART - I CHEMISTRY

1. The transition of electron in H atom that will emit maximum energy is :

(A) (B) (C) (D)

2. The smallest and largest wave number in H spectrum of Lyman series is (R = Rydberg constant)

(A) (B) (C) (D)

3. The compressibility factor of a gas at its critical point is :(A) 1 (B) 3/8 (C) 9/8 (D) 8/3

SPACE FOR ROUGH WORK

VMC/JEE-2013 1 3.0HRT - 2/ACEG

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4. Which of the velocity distribution belongs to the gas with highest molecular mass if all the measurements were done at same temperature ?

5. According to Bohr’s theory, the angular momentum of an electron in 5th orbit is :

(A) (B) (C) (D)

6. Which of the following statements in relation to the hydrogen atom is correct ?(A) 3s, 3p and 3d orbitals all have the same energy(B) 3s and 3p orbitals are of lower energy than 3d orbital(C) 3p orbital is lower in energy than 3d orbital (D) 3s orbital is lower in energy than 3p orbital

7. A vessel containing 1 gm of oxygen at a pressure of 10 atm and a temperature of 47ºC. The pressure drops to

of its original value and temperature falls to 27ºC due to leakage of gas. The mass of oxygen leaked out

will be :

(A) 0.22 g (B) 0.82 g (C) 0.66 g (D) 0.33 g

8. If velocity of an electron in 1st orbit of H atom is V, what will be the velocity in 3rd orbit of Li2+ ?(A) V (B) V/3 (C) 3V (D) 9V

9. In the emission of photo-electrons, the number of photo-electrons emitted per unit time depends upon the (A) Energy of incident radiations (B) Frequency of incident radiations(C) Intensity of incident radiations (D) None of the above facts

10. An electron of a velocity ‘v’ is found to have a certain value of de-Broglie wavelength. The velocity to be possessed by the neutron to have the same de-Broglie wavelength is :

(A) v (B) (C) 1840 v (D)



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11. At low pressure, the van der Waals equation is written as :

The compressibility factor is equal to :

(A) (B) (C) (D)

12. Which of the following is (are) true (T) or false (F) ?I. Kinetic energy of a molecule is zero at

II. A gas in a closed container will exert much higher pressure due to gravity at the bottom than at the top.

III. In the van der Waals’ equation , the term ‘nb’ reflects the actual

volume of the gas molecules.

(A) FTT (B) FFF (C) FFT (D) None of these

13. Statement 1 : Spectral line are not be seen for a transition.

Statement 2 : p-orbitals are degenerate orbitals. (A) Statement-1 is True, Statement-2 is True and Statement-2 is a correct explanation for Statement-1(B) Statement-1 is True, Statement-2 is True and Statement-2 is NOT a correct explanation for Statement-1(C) Statement-1 is True, Statement-2 is False(D) Statement-1 is False, Statement-2 is True

14. Atoms may be regarded as comprising of protons, electrons and neutrons. If the mass attributed to the neutrons were halved and that attributed to electrons were doubled then atomic mass of 6C12 would :(A) remain approximately the same (B) be doubled(C) approximately be halved (D) be reduced by approximately 25%

15. The work function of a metal is 4.2 eV. If radiations of fall on the metal then the kinetic energy of the

fastest photo electron is :

(A) (B) (C) (D)



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*16. Which of the following is(are) the limitation(s) of Bohr’s model ? (A) It could not explain the intensities of the five spectrums of the spectral lines (B) No justification was given the principle of quantization of angular momentum (C) It could not explain why atoms should combine to form bond (D) It could not be successfully applied to single electron atoms

*17. Which of the following is(are) correct statements ?(A) The S.I. unit of Boltzman’s constant (R = Universal Gas Constant and NAV = Avogadro’s Number)

is J/K

(B) The units of van der waal’s constants a and b are and respectively

(C) The S.I units of van der waal’s constants a and b are and respectively

(D) The atm-Lt is a unit of energy

*18. Which of the following statements is(are) true ?(A) If the value of l = 0, the electron distribution is spherical(B) The shape of the orbital is given by azimuthal quantum number(C) The orbital angular momentum of 1s, 2s and 3s electrons are equal(D) In an atom, all electrons travel with the same velocity



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*19. Which of the following graphs is inconsistent with ideal gas behaviour ?

(A) (B) (C) (D)

*20. Maxwell Distribution for an ideal gas corresponds to the plot of fraction of molecules having velocity “c” as a function of velocity “c” at a particular temperature “T” is shown below :

Which of the following is(are) true ?

(A) (B)

(C) T1 > T2 > T3 (D) T1 < T2 < T3



T1

T2

P

V

T2 > T1 T2

T1

PV

V

T2 > T1

p2

p1

V

T(K)

p2 > p1

T2

T1

PV

n

T2 > T1

C1C2C3 Velocity (c) (ms1)

Fraction of moleculeshaving velocity “c”

T1

T2

T3

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PART - II PHYSICS

21. Two particle A and B are projected from the same point and at the same time and with same velocity 2 m/s with

different angles of projection , then the ratio of maximum height, hA/hB will be :

(A) 1 : 3 (B) 3 : 1 (C) 1 : 1 (D) 2 : 1

22. A particle is projected vertically upwards with a velocity of 20m/sec. Find the time at which the distance traveled is twice the magnitude of displacement

(A) (B) (C) (D)

23. If time taken by the projectile to reach Q is T, than PQ =

(A)

(B)

(C)

(D)

24. A particle moves in a circle of radius 25 cm at two revolutions per second. The average acceleration of the particle in half cycle in meters per sec2 is

(A) (B) (C) (D)

25. A particle starts from rest with constant acceleration on a straight line. It covers a distance x in first 2 seconds and a displacement y in next 4 seconds. x and y are related as :(A) 2x = y (B) y = 2x (C) y = 4x (D) None of the above

26. A particle is moving in a circular path of radius 1m with tangential acceleration 1 m/sec2. The total acceleration of particle, after one sec of its starting from rest, is (A) 1 m/s2 (B) 2 m/s2 (C) 3 m/s2 (D) None of these

27. A particle is projected with v0 at angle of with vertical. Its average velocity for its time of flight is :

(A) (B) (C) (D) None of the above



90

P

v

Q

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28. A ball is projected horizontally from the top of a tower of height H with a velocity v0. It will be moving at an

angle of with the horizontal after time

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

29. A boy is running over a circular track with uniform speed of 10 m/s. Find the average acceleration for movement of boy from A to B.

(A) (B)

(C) (D) Cannot find

30. Initial velocity of a particle moving along a straight line is 10 m/s and retardation is 2m/s2. The distance covered by it in 5th second of the motion is :(A) 1 m (B) 50 m (C) 19 m (D) 85 m

31. The displacement x of a body and the time ‘t’ are related by x = 4 3t + 2t2. The average velocity in a time interval of 1 to 4 sec is :(A) 7 m/s (B) 10 m/s (C) 15 m/s (D) None of these

32. A body moving with a uniform acceleration has velocities of u and v when passing through points A and B in its path. The velocity of the body midway between A and B is :


33. A body is projected with velocity v0 at an angle of projection . The radius of curvature of trajectory at the

point of projection is :

(A) (B) (C) (D)

34. A lift is moving upwards with an acceleration of 2 m/sec2. When the upward velocity of the lift is 5m/sec, a particle is projected vertically upwards with a velocity of 3 m/sec with respect to the floor of the lift by a passenger. Find the time after which it reaches the passenger again :

(A) (B) (C) (D) 1 sec



20m

B

A

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35. The displacement – time graph of a particle at time t makes an angle of with time axis. After two seconds it

makes an angle with time axis. The average acceleration of particle is :

(A) units (B) units (C) units (D) unit

*36. Two cars A and B are initially 400 m apart, A is behind B. The car A is moving with uniform velocity of 10 m/s towards B. And, the car B starts moving away from A with constant acceleration of 0.2 m/s2. (A) The time at which minimum distance between the two occurs is 40 sec(B) The time at which the minimum distance between the two occurs is 50 sec(C) The minimum distance between them is 150 m(D) The minimum distance between them is 160 m

*37. A man sitting in the rear end of a long compartment of a train running at constant horizontal velocity, tosses a ball to his friend sitting opposite to him near the front end of the compartment. The trajectory of the ball is drawn by a physics student sitting in the compartment and by a classmate of his, standing on the ground. The two trajectories will have

(A) different vertical ranges, but equal horizontal ranges

(B) equal Time of flight and equal vertical ranges

(C) equal vertical ranges but different horizontal ranges

(D) different vertical and different horizontal ranges

*38. The vertical height of point P above the ground is twice that of Q. A particle is projected downward with a speed of 5 m/s from P and at the same time another particle is projected upward with the same speed from Q. Both particles reach the ground simultaneously then.(A) PQ = 30m (B) PQ = 60m(C) time of flight of the stones = 3s (D) time of flight of the stones = 1/3s



A

VA = 10 m/s

BaB = 0.2

VB = 0

400 m

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*39. Two particles are projected simultaneously from the same point with the same speed but at different angles of

projection . Then which of the following statements (is/are true?)

(A) The line joining the positions of the particle at any subsequent time makes a constant angle

with the horizontal

(B) The line joining the position of the particle at any subsequent time makes a constant angle

with the horizontal

(C) The magnitude of the relative velocity of the first particle with respect to the second is 2u sin

(D) The magnitude of the relative velocity of the first particle with respect to the second is 2u sin

*40. A particle moving in X-Y plane has vy = 8t m/s and ax = 4t m/s2. At t = 0, y = 2m, x = 0 and vx = 0. Then (A) velocity at x = 18 m is 15 m/sec (B) path of the particle is x2 2 = y3

(C) velocity at x = 18 m is 30 m/s (D) path of the particle is (y 2)3 =144 x2

PART - III MATHEMATICS

41. Let , then :

(A) (B) (C) (D) or

42. If , then :




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43. If and the equation has at least one real solution, then a + b =


44. Which of the following statements is true ?

(A) , if n is even

(B)

(C) , if n is even

(D) , if n is even

45. The equation has real solutions, then k belongs to :

(A) (B)

(C) (D)

46. The number of integral values of k for which the equation has a solution is :

(A) 4 (B) 8 (C) 10 (D) 12

47. The value of is :

(A) (B) (C) (D)



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48. The value of k for which the distinct points and are collinear is(are) :

(A) or (B) only (C) only (D) can not be found

49. A line meets the coordinate axes at A and B respectively, such that the centroid of the is (1, 2).

The equation of the line AB is :(A) x + y = 6 (B) 2x + y = 6 (C) x + 2y = 6 (D) None of these

50. Consider the lines and point . Then :

(A) A lies between the lines

(B) Sum of perpendicular distance from A to the lines

(C) Distance between lines is

(D) None of these

51. Image of the point P(1, 5) with respect to the line 4x + 3y + 6 = 0 is :

(A) (B) (C) (D)

52. Equation of the straight line whose slope is 3 and which bisects the line joining and (3, 4) is :


53. The point P divides the line joining and B(3, 5) in the ratio internally. Points Q and R are (1, 5)

and respectively. Area of is 2, for

(A) 6 (B) (C) (D) both (A) and (B)

54. The centroid of a triangle is (1, 4) and the coordinates of its two vertices are and . Then the

area of the triangle is (in sq. units) :

(A) 183 (B) 366 (C) (D) None of these



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55. If a line is perpendicular to the line and forms a triangle with coordinate axes of area 5 sq. unit,

then its equation is :

(A) (B)

(C) (D) None of these

*56. If and , then is :

(A) (B) (C) (D)

*57. if is :

(A) (B) (C) (D)

*58. If P is a point (x, y) on the line such that P and the point (3, 4) are on the opposite sides of the line

, then :

(A) (B) (C) (D)

*59. Let . P be a moving point such that the area of triangle POA is two times the area

of the triangle POB. Locus of P will be straight line whose equation can be :

(A) (B) (C) (D)

*60. Given three straight lines and . Then,

(A) They form a triangle (B) They are concurrent(C) One line bisects the angle between the other two(D) Two of them are parallel



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* * * * * *End of 3HRT-2/ACEG/JEE-2013* * * * * *


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3.0HRT-2-2013(ACEG)