JEE MAIN_CPT - I

PHYSICS

1) A proton, a deuteron and an particle are accelerated through same potential

difference and then they enter a normal uniform magnetic field, the ratio of their

kinetic energies will be

A) B) C) D)

2) A conducting rod of length and mass is moving down a smooth inclined plane of

inclination with constant velocity V. A current i is flowing in the conductor in a

direction perpendicular to paper inwards. The magnitude of field is

A) B) C) D)

3) A copper wire of cross sectional area carrying a current of has free

.If this wire is now placed in a field of induction perpendicular to wire.

The force on each electron is

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A) B) C) D)4) is a uniform rod of length and mass carrying current i and is suspended in

uniform magnetic field of induction acting inward as shown in figure. The tension in each string is

A) B) C) D)

5) A wire (with each side of length ) bent as shown in figure and carrying a current I is placed in a magnetic field. Force on the wire is

A)BiL along B)BiL along

C)BiL along D) BiL along

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6) A wire of length is shaped into a circle and then bent in such a way that the two semi-circles are perpendicular. The magnetic moment of the system when current I flows through the system is

A) B) C) D)

7) A proton accelerated by a potential difference moves through a transverse magnetic field T as shown in figure. Then the angle through which the proton deviates from the initial direction of its motion is (approximately) (mass of proton )

A) B) C) D)

8) Two particles of different masses and , different charges and , are accelerated through the same potential difference and then enter a uniform magnetic field in a direction perpendicular to the field. If they trace circular paths of same

radius, then the ratio of their masses must be

A) B) C) D)


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9) A circular coil of 100 turns and effective diameter 20cm carries a current of 0.5A. It is

to be turned in a magnetic field of B=2T from a position in which the normal to the

plane of the coil makes an angle equals to zero to one in which equals to . The

work required in this process is (in joule)

A) B) C) D)

10) A wire bent in the form a right angled triangle PQR, carries a current . It is placed in

a region of a uniform magnetic field . If , the net force on the wire is

A) B) C) D)

11) An electron whose e/m is enter a region where there is a uniform

magnetic field of induction tesla with a velocity of in a direction

making an angle of 45º with the field. The pitch of its helical path in the region is

A) B) C) D)


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12) Electrons emitted with negligible speed from an electron gun are accelerated through a

potential difference along the axis. These electrons emerge from a narrow hole

into a uniform magnetic field of strength directed along axis, some electrons

emerging at slightly divergent angles as shown in the figure. These paraxial electrons

are refocused on the axis at a distance

A) B) C) D)

13) Two long conductors, separated by a distance d carry currents and in the same

direction. They exert a force on each other. Now the current in one of them is

increased to two times and its direction is reversed. The distance is also increased to 3

times. The new value of the force between them is


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A) B) C) D)

14) A charged particle is moving with a velocity at a point in a magnetic field

and experiences a force If the same charge moves with velocity

from the same point in that magnetic field and experiences a force

the magnetic induction at that point will be

A) B) C) D)

15) A particle having a charge of and mass moves in a circle of radius

under the influence of a magnetic field of induction . When the particle is at a

point p, a uniform electric field is switched on so that the particle starts moving along

the tangent with a uniform velocity the electric field is

A) B) C) D)

16) An electron in a circular orbit of radius makes revolutions in each second.

This electron orbit is equivalent to a magnetic shell of moment (in Am)

A) B) C) D)


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17) A proton is projected with a velocity , at right angles to a uniform magnetic

field of induction 100mT.The time (in seconds ) taken by the proton to travels arc

is : (Mass of proton = and charge of proton )

A) B) C) D)

18) A nucleus at rest undergoes a decay emitting an particle of de-Broglie wave-length If the mass of the daughter nucleus is and that of

particle is determine the total kinetic energy in the final state. A) 4.7 MeV B) 6.25 MeVC) 10.2 MeV D) 2.77 eV

19) A current carrying wire AB of finite length is placed near another long current

carrying conductor CD. If CD is fixed and AB is free to move. Then it will have

A) Translational motion


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B) Rotational motion

C) Neither Translational nor Rotational motions

D) Translational motion as well as Rotational motions

20) Two long parallel wires are placed on a smooth horizontal table. They have equal and

opposite currents. Work done to increase the separation between wires from a to 2a if

magnitude of current in each wire is I, is

A) B) C) D)

21) A particle of specific charge enters a uniform magnetic field velocity

from the origin. Then the position of particle at time where

A) B)

C) D)

22. A square of side 2.0 m is placed in a uniform magnetic field in a direction

perpendicular to the plane of the square inwards. Equal current I =3.0 A is flowing in

the directions shown in fig. The magnitude of magnetic force on the loop.


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A) B)

C) D) Zero

23. Deuterons in a cyclotron describes a circle of radius 32.0 cm. Just before emerging

from the D’s. the frequency of the applied alternating voltage is 10 MHz. The energy

of the deuterons upon emergence.

A) 4.22 GeV B) 4.22 MeV

C) 4.22 KeV D) None of these

24. Each of two long parallel wires carries a constant current I along the same direction.

The wires are separated by a distance 2L. The maximum force experienced by unit

length of a third wire carrying the same current along the same direction if third wire

is parallel to and in the symmetry plane of other two wires.

A) B) C) D)

25. Assume that the de-Broglie wave associated with an electron can form a standing wave between the atoms arranged in a one dimensional array with nodes at the each of the atomic sites. It is found that one such standing wave is formed if the distance d between the atoms of array is . similar standing wave is again formed if d is


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increased to 2.5 A but not for any intermediate values of d for which the standing wave of the type described above can form.The kinetic energy of electron is approxA) 105 eV B) 15 eV

C) 150 eV D) 1.5 KeV

26. System shown in fig. consists of two large parallel metallic plates carrying current in

opposite directions. Current density in each plate is j per unit width. Assuming that

uniform magnetic field is developed parallel to plane of plates by each plate given by

. Then force acting per unit area on each plate.

A) B)

C) D)

27. A positively charged particle having charge coulomb and mass , is

revolving along a circle of radius R = 40 cm with velocity in a uniform

magnetic field with centre of circle at origin O of a three dimensional system. At t = 0,

the particle was at ( 0, 0.4, 0) meter and velocity was directed along positive x-


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direction. Another particle having charge coulomb and mass moving

uniformly parallel to positive z-direction with velocity collides with the

revolving particle at t = 0 and gets stuck to it. Neglecting gravitational force and

coulomb force, calculate x, y and z co-ordinates of the combined particle at

second.

A) (0.6,0.2,0) B) (0.2,0.2,0.2)

C)(0.2,0.2,0) D) (0.4,0,0.2)

28. An electron accelerated by a potential difference V = 3 volt first enters into a uniform

electric field of a parallel-plate capacitor whose plates extend over a length l = 6 cm in

the direction of initial velocity. The electric field is normal to the direction of initial

velocity and its strength varies with time as . t where . Then the

electron enters into a uniform magnetic field of induction T. Direction of

magnetic field is same as that of the electric field. Calculate pitch of helical path

traced by the electron in the magnetic field.

A) 0.6 cm B) 1.22 cm

C) 0.8 cm D) 2.06 cm


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29. Suppose potential energy between electron and proton separation r is given by

where K is a constant. For such a hypothetical hydrogen atom, The energy

of electron in Bohr’s orbit.

A) B)

C) D)

30. Atoms of a hydrogen like gas are in a particular excited energy level. When these

atoms de-excite, the emit photons of different energies. Maximum and minimum

energies of emitted photons are and respectively. The

principle quantum number of initially excited energy level.

A) n = 2 B) n = 3

C) n = 4 D) n = 5

CHEMISTRY

31. To carry out the following , the correct sequence of reagent to be used is


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A) B) m – CPBA,

C) D)

32.

Which of the following statements is/are correct regarding the product

A) Product will not be a six membered compound

B) A migrating group determines the product

C) It is a Benzilic acid rearrangement

D)All of them

33.

Which of the following statements is/are correct regarding the product

A) It is an example of intramolecular bezoin condensation space for rough work Page 13

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B) One more four membend ring will be formed in product

C) Reaction talles places due to nucleophilic nature of carbonyl carbon

D) All of them

34. Which of the following is not correctly matched

Column – I Column – II

A) P) Backman regrrangement

B) Q) Balz - Reduction

C) R) Bouveault -Blane reduction

D) S) Benzillic acid rearrangene


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35.

X may be

A) Paraconic acid B) Cinnamic acid

C) Crotonic acid D) Salicylic acid

36. Predict the product,

A) B)

C) D)

37.


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1. 2.

3. 4.

5. 6.

7. 8.

Out of above which of the following are A,B,C,D respectively

A) 5,3,7,1 B) 2,3,4,1

C) 5,3,2,1 D) None of these

38. Predict the product,


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A) B)

C) D)

39. Predict the product

A) B)

C) D)


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40. Which of the following pair would yield the given product in Reformatsky reaction

followed by dehydration?

A)

B)

C)

D)


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41. Which of the following is not a preferred path for synthesis of alkene by Witting

reaction?

A) B)

C) D)

42. The following cyclisation can be classified as

A ) 5-exo-dig B) 5-endo-dig

C) 6-endo-trig D) 6-endo-dig

43. Identify the last product.


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B and C are

A)

B)

C)

D)

44.


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What is true about the above reactions?

A) In both the reactions, a group or atom migrates with an electron pair

B) Reactions start with nucleophilic attack

C) Both are intramolecular

D) All the above

45. Predict the product

A) B)

C) D)

46.


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Where X is

A) - Cl B) –OH

C) D)

47. The probable products are enlisted for the given reaction

Identify the products likely to be formed

A) I and III B) I, II and III

C) II and III D) I and II


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48. Watch the following two benzidine rearrangements and choose the right answer

I.

II

A) I- true , II - false B) I- false , II – true

C) Both true D) both false

49. Which of the following substrate would give Ph in Favorskii

rearrangement

A) Only I B) Only II C) Both I & II D) None of these space for rough work Page 23

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50. which of the statement is true for given conversion

A) This reaction give two isomeric productB) Product will contain groupC) It is a sterospecific reactionD) All of them

51. Which of the following compound cannot used in Knoevenagel condensation reaction as a source of nucleophile

A) Diethyl malonate B) PropandinitrileC) Ethylene Glucol D) Acetylacetone

52. You are to prepare by Michael Condensation. Select the pair of Michael acceptor and donor for this purpose.

A) and

B) and

C) and

D) and


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53. The following is a product of Knoevenagel condensation :

Select the pair of starting material for this

A) and

B) and

C) and

D) and 54. Which of the following cannot give deuterium incorporated product upon treatment

with

A) B)

C) D)


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55. Given , What is false about this?A) This involves keto-enol tautomerisationB) Only hydrogens - to the carbonyl group are substitutedC) Protonation and deprotonation are the basicsD) It is the benzylic hydrogens which are substituted

56. Which of the following statement is not correct for oppenauer oxidation A) It is a method of converting secondary alcohol to Ketone by using aluminium t-butoxide.B) this reaction can also be extended to oxidize Primary alcohol in Presence of benzoquinone.C) This reaction has been replaced by oxidation methods using PCC or dimethy sulphoxideD) None of these

57. Mercury is transported in the containers made of A) Ag B) PbC) Al D) Fe

58. The higher oxidation states of transition elements are found to be in the combination with A and B, which are A) F, O B) O, NC) O, S D) F, Cl

59. The iron salt used in blue prints isA) B) C) D)

60. ZnO shows yellow colour on heating due to A) d-d transition B) C-T spectraC) Higher polarization caused by D) F-centre


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MATHEMATICS

61. If m is the slope of a tangent to the curve , then

A) B) C) D)

62. The equation of the tangent to the curve at the point where it crosses the y-

axis is

A) B) C) D)

63. If the length of sub-normal is equal to the length of sub. Tangent at any point (3,4) on

the curve and the tangent at (3,4) to meets the coordinate axes at A

and B, then the maximum area of the triangle OAB, where O is origin, is

A) 45/2 B) 49/2 C) 25/2 D) 81/2

64. The two curves cut orthogonally at a point, then is equal to

A) B) 3 C) 2 D)

65. The radius of a right circular cylinder increases at the rate of 0.1 cm/min, and the

height decreases at the rate of 0.2 cm/min. The rate of change of the volume of the

cyclinder, in , when the radius is 2 cm and the height in 3 cm is

A) -2 B) C) D)


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66. A cube of ice melts without changing its shape at the uniform rate of . The

rate of change of the surface area of the cube, in , when the volume of the

cube is , is

A) -4 B) – 16/5 C) -16/6 D) -8/15

67. The tangent to the curve at a point (0,1) meets the x-axis at (a,0) where

, then

A) B) C) [0,1] D) [1/2,1]

68. The triangle formed by the tangent to the curve at the point (1,1) and

the co-ordinate axes lies in the first quadrant . If its area is 2, then the value of b is

A) -1 B) 3 C) -3 D) 1

69. If and , then the value of for which Rolle’s theorem can be

applied in [0,1]

A) -2 B) -1 C) 0 D) ½

70. The tangent to the curve drawn at the point intersects the line joining the

points ( and

A) On the left of x = c B) On the right of x = c

C) At no point D) At all point


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71. Let and Then increases in

A) B) C) D)

72. The function is an increasing function in

A) B) C) D)

73. The function decreases in the interval

A) B) C) D) None of these

74. Function is monotonically increasing whenA) B) C) D)

75. The number of solutions of the equation in isA) One B) Two C) Three D) Zero

76. If has local maximum and minimum at and respectively, then A) B) C) D) None of these

77. The maximum value of is A) 1 B) C) D)

78. The maximum value of is

A) B) C) D)

79. The set of value(s) of for which the function

possesses a negative point of inflection is


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A) B) C) D) empty set

80. then the range of so that has maxima at

isA) B) C) D)

81. A factory is to be connected by a road with a straight railway line on which a town A is situated. The distance DB of the factory to the railway line is km. Length AB of the railway line is 20 km. Freight charges on the road are twice the charges on the railway. The point on the railway line should the road be connected so as to ensure minimum freight charges from the factory to the town isA) B) C) D) None of these

82. The volume of the greatest cylinder which can be inscribed in a cone of height 30cm and semi vertical angle isA) B) C) D) None of these

83. A rectangle is inscribed in an equilateral triangle of side length units. The maximum area of this rectangle can be

A) B) C) D)

84. The length of the longest interval in which the function is increasing is

A) B) C) D)


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85. Let then at x = 0, f has

A) A local maximum B) No local maximumC) A local minimum D) No extremism

86. The function increases if a) B) C) D)

87. If , then maximum value of is

A) –10 B) C) D) 10

88. If t1, t2, t3, t4, t5 be in A.P. of common difference d then the value of

is A) 4d4 B) 2d4 C) 8d4 D) none of these

89. If x = -9 is a root of then the other roots are

A) 7, -2 B) -7,2 C) 7,2 D) -7,-2

90. If are the cube roots of 8 then

A) 0 B) 1 C) 8 D) 2


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JEE MAIN_CPT - I