Aieee

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FIITJEELtd., ICES House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi-110016, Ph: 26515949, 26569493, Fax: 011-26513942.

PAPER -2003

1. A particle of mass M and charge Q moving with velocity v describes a circular path of radius R when subjected to a uniform transverse magnetic field of induction B. The work done by the field when the particle completes one full circle is

(A) 2 Mv 2 R R   _     (B) zero (C) BQ2R (D) BQv2R 1. B.

Since the particle completes one full circle, therefore displacement of particle = 0 Work done = force displacement = 0

2. A particle of charge 16  1018_{coulomb moving with velocity 10 ms}1_{along the x-axis}

enters a region where a magnetic field of induction B is along the y –axis, and an electric field of induction B is along the y-axis, and an electric field of magnitude 104 V/m is along the negative z-axis. If the charged particle continues moving along the x-axis, the magnitude of B is

(A) 103 Wb/m2 (B) 105 Wb/m2

(C) 1016 Wb/m2 (D) 103 Wb/m2

2. A.

F q(E v B)  …(1)

The solution of this problem can be obtained by resolving the motion along the three coordinate axes namely

x x x y z z y F q a (E v B v B ) m m     y y y z x x z F q a (E v B v B ) m m     z z z x y y z F q a (E v B v B ) m m    

For the given problem,

x y

E E 0, v_y v_z 0 and B_x B_z 0 Substituting in equation (2), we get

x z

a a 0 and a_y E_y v B_x _z

If the particle passes through the region undeflected ay is also zero, then

y x z E v B  y 4 3 2 z z E 10 B 10 Wb / m v 10   

3. A thin rectangular magnet suspended freely has a period of oscillation equal to T. Now it is broken into two equal halves (each having half of the original length) and one piece is made to oscillate freely in the same field. If its period of oscillation is T’, the ratio T/T is

(A) 1

2 2 (B) 1/2

(C) 2 (D) 1/4

3. B.

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AIEEE-PAPER-03-PH-2

M = pole strength length M 2

 and moment of inertia 2 1 I' mass (length) 12    = 2 1 m 12 2 2    _{ }     I' I 8  Time period 2 I' M'B   2 I / 8 M B 2   T T ' 2   T ' 1 T 2

4. A magnetic needle lying parallel to a magnetic field requires W units of work to turn it through 60. The torque needed to maintain the needle in this position will be

(A)3 W (B) W

(C) (3/2) W (D) 2W

4. A.

W =MB(cos2 cos1)

Initially magnetic needle is parallel to a magnet field, therefore 1 0,   2 60     W MB(cos 60 cos 0 ) MB  eMB sin 60 ZW 3 / 2 3W

5. The magnetic lines of force inside a bar magnet (A) are from north-pole to south-pole of the magnet (B) do not exist

(C) depend upon the area of cross-section of the bar magnet (D) are from south-pole to north-pole of the magnet.

5. D.

The magnetic lines of force inside a bar magnet are from south pole to north pole of the magnet.

6. Curie temperature is the temperature above which (A) a ferromagnetic material becomes paramagnetic (B) a paramagnetic material becomes diamagnetic (C) a ferromagnetic material becomes diamagnetic (D) a paramagnetic material becomes ferromagnetic.

6. A.

Curie temperature is the temperature above which a ferromagnetic material becomes paramagnetic.

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AIEEE PAPER-03-PH-3

7. A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads 49 N, when the lift is stationary. If the lift moves downward with an acceleration of 5 m/s2, the reading of the spring balance will be

(A) 24 N (B) 74 N

(C) 15 N (D) 49 N

7. A.

Reading of spring balance = m(g a) = 5 4.8 = 24 N

8. The length of a wire of a potentiometer is 100 cm, and the e.m.f. of its stand and cell is E volt. It is employed to measure the e.m.f. of a battery whose internal resistance is 0.5. If the balance point is obtained at =30 cm from the positive end, the e.m.f. of the battery is (A) 30 E 100.5 (B) 30 E 1000.5 (C) 30(E 0.5i) 100 

, where I is the current in the potentiometer wire. (D) 30 E 100 8. A. E E 30 30E V . L 100 100    

9. A strip of copper and another germanium are cooled from room temperature to 80 K. The resistance of

(A) each of these decreases

(B) copper strip increases and that of germanium decreases (C) copper strip decreases and that of germanium increases (D) each of these increases.

9. C.

The temperature coefficient of resistance of copper is positive and that of germanium is negative, therefore when copper and germanium are cooled, resistance of copper strip decreases and that of germanium increases.

10. Consider telecommunication through optical fibres. Which of the following statements is not true?

(A) Optical fibres can be of graded refractive index.

(B) Optical fibres are subject to electromagnetic interference from outside. (C) Optical fibres have extremely low transmission loss.

(D) Optical fibres may have homogeneous core with a suitable cladding

10. B.

Optical fibres are subject to electromagnetic interference from outside.

11. The thermo e.m.f. of a thermo-couple is 25 V/C at room temperature. A galvanometer of 40 ohm resistance, capable of detecting current as low as 105 A, is connected with the thermocouple. The smallest temperature difference that can be detected by this system is

(A) 16C (B) 12C

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11. A. E = 25  106 V IR = 105 40 = 4 104 V 4 6 4 10 16 C 25 10        

12. The negative Zn pole of a Daniell cell, sending a constant current through a circuit, decreases in mass by 0.13 g in 30 minutes. If the electrochemical equivalent of Zn and Cu are 32.5 and 31.5 respectively, the increase in the mass of the positive Cu pole in this time is

(A) 0.180 g (B) 0.141 g (C) 0.126 g (D) 0.242 g 12. C. Zn zx Cu Cx m Z m Z

I and t are same for both Cu and Zn electrodes

Cu 0.13 31.5 m  32.5 Cu 0.13 32.5 m 0.126 g. 32.5    13. Dimensions of 0 0 1

  , where symbols have their usual meaning, are

(A) [L1T] (B) [L2T2]

(C) [L2T2] (D) [LT1]

13. C.

14. A circular disc X of radius R is made from an iron pole of thickness t, and another disc Y of radius 4R is made from an iron plate of thickness t/4. then the relation between the moment of inertia IX and IY is

(A)I_Y32I_X (B)I_Y16I_X

(C)I_Y 32 I_X (D)I_Y 64 I_X

14. D.

If t is the thickness and R is the radius of the disc, then mass =R2t

 = density of the material of the disc. Moment of inertia of disc X,

4 x 1 I R t 2    …(i)

Moment of inertia of disc Y, 4

y

I 32 R t  …(ii)

From equation (i) and (ii)

y x

I 64 I

15. The time period of a satellite of earth is 5 hours. If the separation between the earth and the satellite is increased to 4 times the previous value, the new time period will become

(A) 10 hours (B) 80 hours

(C) 40 hours (D) 20 hours

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Time period of a satellite T =

3 e 2 r

R g



r = distance between satellite and the earth. 3 / 2 Tr  3 / 2 1 1 2 2 T r T r        2 1 T 8T   8 5 40 hours

16. A particle performing uniform circular motion has angular momentum L. If its angular frequency is doubled and its kinetic energy halved, then the new angular momentum is

(A) L/4 (B) 2L

(C) 4L (D) L/2

16. A.

Angular momentum of a particle performing uniform circular motion L = I Kinetic energy, 1 2 K I 2   Therefore, L2K₂  2K   1 1 2 2 2 1 L K L K    1 2 L 2 2 4 L    2 L L 4  .

17. Which of the following radiations has the least wavelength?

(A)-rays (B)-rays

(C)-rays (D) X-rays

17. D.

18. When U238 nucleus originally at rest, decays by emitting an alpha particle having a speed u, the recoil speed of the residual nucleus is

(A) 4u 238 (B) 4u 234  (C) 4u 234 (D) 4u 238  18. B.

According to principle of conservation of linear momentum the momentum of the system remains the same before and after the decay.

Atomic mass of uranium = 238 and after emitting an alpha particle. = 238 4 = 234

 238 0 = 4u + 234 v

 v 4u

234

  .

19. Two spherical bodies of mass M and 5M and radii R and 2R respectively are released in free space with initial separation between their centres equal to 12R. If they attract each other

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due to gravitational force only, then the distance covered by the smaller body just before collision is

(A) 2.5R (B) 4.5R

(C) 7.5R (D) 1.5R

19. C.

The two spheres collide when the smaller sphere covered the distance of 7.5 R.

20. The difference in the variation of resistance with temperature in a metal and a semiconductor arises essentially due to the difference in the

(A) crystal structure

(B) variation of the number of charge carries with temperature (C) type of bonding

(D) variation for scattering mechanism with temperature.

20. B.

Variation of the number charge carriers with temperature.

21. A car moving with a speed of 50 km/hr, can be stopped by brakes after at least 6 m. If the same car is moving at a speed of 100 km/hr, the minimum stopping distance is

(A) 12 m (B) 18 m

(C) 24 m (D) 6 m

21. C.

22. A boy playing on the roof of a 10 m high building throws a ball with a speed of 10 m/s at an angle of 30 with the horizontal. How far from the throwing point will the ball be at the height of 10 m from the ground?

[g = 10 m/s2, sin 30 = ½, cos 30 =3/2]

(A) 5.20 m (B) 4.33 m

(C) 2.60 m (d) 8.66 m.

22. D.

The ball will be at the height of 10 m from the ground when it cover its maximum horizontal range.

Maximum horizontal range 2 u sin 2 R g   2 3 1 (10) 2 2 2 R 8.66 10      m.

23. An ammeter reads upto 1 ampere. Its internal resistance is 0.81 ohm. To increase the range to 10 A the value of the required shunt is

(A) 0.03 (B) 0.3 (C) 0.9 (D) 0.09 23. D. S = g g I G 1 0.81 0.09 I I 10 1      

24. The physical quantities not having same dimensions are

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(C) stress and Young’s modulus (D) speed and (00)1/2

24. B.

Dimensions of momentum = kg m/sec = [MLT2] Dimensions of Planck’s constant = joule sec = [ML2T1]

 Dimensions of momentum dimensions of Planck’s constant.

25. Three forces start acting simultaneously on a particle moving with velocity v. These forces are represented in magnitude and direction by the three sides of a triangle ABC(as shown). The particle will now move with velocity

(A) less than v (B) greater than v

(C) v in the direction of the largest force BC (D) v, remaining unchanged.

A

B C

25. D.

According to triangle law of vector addition if three vectors addition if three vectors are represented by three sides of a triangle taken in same order, then their resultant is zero. Therefore resultant of the forces acting on the particle is zero, so the particles velocity remains unchanged.

26. If the electric flux entering and leaving an enclosed surface respectively is 1 and 2, the electric charge inside the surface will be

(A) (   ₂ ₁) ₀ (B) 2 1 0 (  )  (C) 2 1 0 (  )  (D) (   2 1) 0 26. A.

According to Gauss’s theorem, charge in flux =

0

ch arg e enclosed by the surface

  q    ( ₂ ₁) ₀.

27. A horizontal force of 10 N is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is 0.2. The weight of the block is

(A) 20 N (B) 50 N

(C) 100 N (D) 2 N

10 N

27. D.

Weight of the block =R = 0.2 10 = 2N.

28. A marble block of mass 2 kg lying on ice when given a velocity of 6 m/s is stopped by friction in 10 s. then the coefficient of friction is

(A) 002 (B) 0.03 (C) 0.04 (D) 0.01 28. C. Retardation u 6 0.6 t 10    m/sec2 Frictional force = mg = ma  a 0.6 0.06. g 10    

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(1) Linear momentum of a system of particles is zero. (2) Kinetic energy of system of particles is zero. (A) A does not imply B and B does not imply A. (B) A implies B but B does not imply A

(C) A does not imply B but b implies A’ (D) A implies B and B implies A.

29. C.

30. Two coils are placed close to each other. The mutual inductance of the pair of coils depends upon

(A) the rates at which current are changing in the two coils (B) relative position and orientation of the two coils

(C) the materials of the wires of the coils (D) the currents in the two coils

30. C.

The mutual inductance of the pair of coils depends on geometry of two coils, distance between two coils, distance between two coils, relative placement of two coils etc.

31. A block of mass M is pulled along a horizontal friction surface by a rope of mass m. If a force P is applied at the free end of the rope, the force exerted by the rope on the block is

(A) Pm M m (B) Pm M m (C) P (D) Pm M m 31. D.

Force on block = mass acceleration = PM M m

32. A light spring balance hangs from the hook of the other light spring balance and a block of mass M kg hangs from the former one. Then the true statement about scale reading is (A) both the scales read M kg each

(B) the scale of the lower one reads M kg and of upper one zero

(C) the reading of the two scales can be anything but sum of the reading will be M kg (D) both the scales read M/2 kg.

32. A.

Both the scales read M kg each.

33. A wire suspended vertically from one of its ends stretched by attaching weight of 200 N to the lower end. The weight stretches the wire by 1 mm. Then the elastic energy stored in the wire is

(A) 0.2 J (B) 10 J

(C) 20 J (D) 0.1 J

33. D.

The elastic potential energy stored in the wire, 1

U stress strain volume 2     1 F A 2 A        = 1 F 2  = 3 1 200 10 0.1 J 2    

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34. The escape velocity for a body projected vertically upwards from the surface of earth is 11 km/s. If the body is projected at an angle of 45 with the vertical, the escape velocity will be

(A) 112 km/s (B) 22 km/s

(C) 11 km/s (D) 11/2 m/s

34. C.

The escape velocity of a body is independent of the angle of projection.

35. A mass M is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes SHM of time period T. If the mass is increased by m, the time period becomes 5T/3. then the ratio of m/M is

(A) 3/5 (B) 25/9 (C) 16/9 (D) 5/3 35. C. T M T ' M m  9 25 M M m    9M + 9m = 25 M  m 16 M 9

36. “Heat cannot by itself flow from a body at lower temperature to a body at higher temperature” is a statement of consequence of

(A) second law of thermodynamics (B) conservation of momentum (C) conservation of mass (D) first law of thermodynamics.

36. A.

Second law of thermodynamics.

37. Two particles A and B of equal masses are suspended from two massless springs of spring constants k1 and k2 respectively. If the maximum velocities, during oscillations, are equal, the

ratio of amplitudes of A and B is (A) 1 2 k k (B) 2 1 k k (C) 2 1 k k (D) 1 2 k k 37. C. 1 2 2 1 a k a  k .

38. The length of a simple pendulum executing simple harmonic motion is increased by 21%. The percentage increase in the time period of the pendulum of increased length is

(A) 11% (B) 21%

(C) 42% (D) 10%

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Time period of simple pendulum is given by. T 2 g    New length ' 21 121 100 199         T ' ' 21 T   100   T ' 11 T 10  T ' T 1 T 10   T 10% of T.

39. The displacement y of wave travelling in the x-direction is given by y = 104sin 600t 2x 3   _ _      metres,

where x is expressed in metres and t in seconds. The speed of the wave-motion, in ms1 is

(A) 300 (B) 600 (C) 1200 (D) 200 39. A. Velocity of wave = n= 600 2 2 2    = 300 m/sec.

40. When the current changes from +2 A to2 A in 0.05 second, an e.m.f. of 8 V is induced in a coil. The coefficient of self-induction of the coil is

(A) 0.2 H (B) 0.4 H

(C) 0.8 H (D) 0.1 H

40. D.

If e is the induced e.m.f. in the coil, then e Ldi dt

 

Therefore, L e di / dt

 

Substituting values, we get L 8 0.05 0.1 H 4

 

 



41. In an oscillating LC circuit the maximum charge on the capacitor is Q. The charge on the capacitor when the energy is stored equally between the electric and magnetic field is

(A) Q/2 (B) Q/3

(C) Q/2 (D) Q

41. C.

energy stored in capacitor =

2 1 Q E 2 C   1 1 Q2 1 q2 22 C  2 C  q = Q 2.

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(A) reduce the energy loss due to eddy currents (B) make it light weight

(C) make it robust and strong (D) increase the secondary voltage.

42. A.

43. Let F be the force acting on a particle having position vector r and T be the torque of this force about the origin. Then

(A) r T  0 and F T 0 (B) r T  0 and F T 0

(C) r T  0 and F T 0 (D) r T  0 and F T 0

43. D.

Torque = Force Position vector T  F r 

r T    r (F r ) 0

  

F T    F (F r )   0

44. A radioactive sample at any instant has its disintegration rate 5000 disintegrations per minute. After 5 minutes, the rate is 1250 disintegrations per minute.

Then, the decay constant (per minute) is

(A) 0.4 In 2 (B) 0.2 In 2 (C) 0.1 In 2 (D) 0.8 In 2. 44. A. 2In2 0.4 In 2. 5   

45. A nucleus with Z = 92 emits the following in a sequence;,,,,,,,,,,, +,

+

,. The Z of the resulting nucleus is

(A) 76 (B) 78

(C) 82 (D) 74

45. B.

The Z of resultant nucleus = 92 16 + 4 2 = 78

46. Two identical photo cathodes receive light of frequencies f1 and f2. if the velocities of the

photoelectrons (of mass m) coming out are respectively v1 and v2, then

(A) 2 2 1 2 1 2 2h v v (f f ) m    (B) 1/ 2 1 2 1 2 2h v v (f f ) m    _  _   (C) 2 2 1 2 1 2 2h v v (f f ) m    (D) 1/ 2 1 2 1 2 2h v v (f f ) m    _  _   46. A. 2 2 1 2 1 2 1 m(v v ) h(f f ) 2     2 2 1 2 1 2 2h v v (f f ) m    .

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(A) protons (B) neutrinos

(C) helium nuclei (D) electrons

47. A.

48. A 3 volt battery with negligible internal resistance is connected in a circuit as shown in the figure. The current I, in the circuit will be

(A) 1 A (B) 1.5 A (C) 2 A (D) 1/3 A 3V 3 3 3 i 48. B.

The current through the circuit,I V 3 1.5 A

R 2

  

49. A sheet of aluminium foil of negligible thickness is introduced between the plates of a capacitor. The capacitance of the capacitor

(A) decreases (B) remains unchanged

(C) becomes infinite (D) increases.

49. B.

When a sheet of aluminium foil of negligible thickness is introduced between the plates of a capacitor, the capacitance of capacitor remains unchanged.

50. The displacement of a particle varies according to the relation x = 4(cos t + sin t). the amplitude of the particle is

(A)4 (B) 4

(C) 42 (D) 8

50. C.

The amplitude of given wave equation = 4 2 .

51. A thin spherical conduction shell of radius R has a charge q. another charge Q is placed at the centre of the shell. The electrostatic potential at a point P at a distance R/2 from the centre of the shell is

(A) 0 2Q 4R (B) ₀ 2Q 4R  ₀ 2q 4R (C) 0 0 2Q q 4R4R (D) ₀ (q Q) 2 4 R   51. C.

The total potential at P = 0

1 1

(q 2Q) 4 R 

52. The work done in placing a charge of 8  1018 coulomb on a condenser of capacity 100 micro-farad is

(A) 16 1032 joule (B) 3.2 1026 joule (C) 4 1010 joule (D) 32 1032 joule

52. D.

Required work done is

2 2 1 Q w 2 C  = 18 2 32 4 1 (8 10 ) 32 10 J 2 10       

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53. The co-ordinates of a moving particle at any time t are given by x = t3 and y = t3. The speed to the particle at time t is given by

(A) 2 2 3t    (B) 2 2 2 3t    (C) _t2   2 2 _(D)   2 2 53. B. Speed = _v  _{(3 t )}2 2 _{(3 t )}2 2 _3t2   2 2 _.

54. During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio p

v C

C for the gas is

(A) 4/3 (B) 2 (C) 5/3 (D) 3/2 54. A. P V C 4 C 3.

55. Which of the following parameters does not characterize the thermodynamic state of matter?

(A) temperature (B) pressure

(C) work (D) volume

55. C.

The work done does not characterize a thermodynamic state of matter. It gives only a relationship between two different thermodynamic state.

56. A carnot engine takes 3 106 cal of heat from a reservoir at 627C, and gives it to a sink at 27C. The work done by the engine is

(A) 4.2 106 J (B) 8.4 106 J

(C) 16.8 106 J (D) zero.

56. B.

Work done by the engine while taking heat

Q = 3 106 cal is W = 2 106 4.2 = 8.4 106 J.

57. A spring of spring constant 5  103 N/m is stretched initially by 5 cm from the unstretched position. Then the work required to stretch is further by another 5 cm is

(A) 12.50 N-m (B) 18.75 N-m

(C) 25.00 N-m (D) 6.25 N-m

57. B.

Required work done = 25 6.25 = 18.75 N–m.

58. A metal wire of linear mass density of 9.8 gm is stretched with a tension of 10 kg-wt between two rigid supports 1 metre apart. The wire passes at its middle point between the poles of a per magnet and it vibrates in resonance when carrying an alternating current of frequency n. The frequency n of the alternating source is

(A) 50 Hz (B) 100 Hz (C) 200 Hz (D) 25 Hz 58. A. Frequency of oscillation n 1 T 2L m  2 2 3 1 10 9.8 1 1 10 10 50Hz 2L 9.8 10 2L 2 1         

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59. A tuning fork of known frequency 256 Hz makes 5 beats per second with the vibrating string of a piano. The beat frequency decreases to 2 beats per second when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was

(A) (256 + 2) Hz (B) (2562) Hz

(C) (256 5) Hz (D) (256 + 5) Hz

59. C.

60. A body executes simple harmonic motion. The potential energy (P.E.), the kinetic energy (K.E.) and total energy (T.E.) are measured as function of displacement x. Which of the following statement is true?

(A) K.E. is maximum when x = 0 (B) T.E. is zero when x = 0 (C) K.E. is maximum when x is maximum (D) P.E. is maximum when x = 0.

60. A.

Since at x = 0, the potential energy is minimum, the kinetic energy is maximum. 61. In the nuclear fusion reaction,

2 3 4

1H1H2Hen given that the repulsive potential energy between the two nuclei is7.7 1014 J, the temperature at which the gases must be heated to initiate the reaction is nearly [Boltzmann’s constant k = 1.38 1023 J/K] (A) 107K (B) 105 K (C) 103 K (D) 109 K 61. D. 14 9 23 7.7 10 2 T 3.7 10 K. 3 1.38 10          

62. Which of the following atoms has the lowest ionization potential? (A) 14 7N (B) 133 55 Cs (C) 40 18Ar (D) 16 8 O 62. B. Since 133

55 Cs has larger size among the four atoms given, thus the electrons present in the outermost orbit will be away from the nucleus and the electrostatic force experienced by electrons due to nucleus will be minimum. Therefore the energy required to liberate electron from outer orbit will be minimum in the case of 133

55 Cs. 63. The wavelengths involved in the spectrum of deuterium 2

1

( D) are slightly different from that of hydrogen spectrum, because

(A) size of the two nuclei are different

(B) nuclear forces are different in the two cases (C) masses of the two nuclei are different

(D) attraction between the electron and the nucleus is different in the two cases.

63. C.

64. In the middle of the depletion layer of a reverse-biased p-n junction, the (A) electric field is zero (B) potential is maximum (C) electric field is maximum (D) potential is zero

64. A.

65. If the binding energy of the electron in a hydrogen atom is 13.6 eV, the energy required to remove the electron from the first excited state of Li++ is

(A) 30.6 eV (B) 13.6 eV

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65. A.

The energy of the first excited state of Li is

2 2 0 2 2 2 Z E 3 13.6 E 30.6 eV. n 2      

66. A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time t is proportional to

(A) t3/4 (B) t3/2

(C) t1/4 (D) t1/2

66. B.

Distance goes as t3/2

67. A rocket with a lift-off mass 3.5 104 kg is blasted upwards with an initial acceleration of 10 m/s2. Then the initial thrust of the blast is

(A) 3.5 105 N (B) 7.0 105 N (C) 14.0 105 N (D) 1.75 105 N

67. A.

68. To demonstrate the phenomenon of interference we require two soruces which emit radiation of

(A) nearly the same frequency (B) the same frequency (C) different wavelength

(D) the same frequency and having a definite phase relationship.

68. A.

Initial thrust of the blast = m a = 3.5 104 10 = 3.5 105 N

69. Three charges q1, +q2 and q3 are placed as shown in the figure.

The x-component of the force onq1 is proportional to

(A) 2 3 2 2 q q cos b a  (B) 2 3 2 2 q q sin b a  (C) q₂2 q3₂cos b a  (D) 2 3 2 2 q q sin b a  q3 q1 _q2 x b a  y 69. B. 2 3 x 2 2 q q F sin b a   

70. A 220 volt, 1000 watt bulb is connected across a 110 volt mains supply. The power consumed will be

(A) 750 watt (B) 500 watt

(C) 250 watt (D) 1000 watt 70. C. 2 2 consumed 2 V (110) P 250 watt. R (220) / 1000   

71. The image formed by an objective of a compound microscope is (A) virtual and diminished (B) real and diminished (C) real and enlarged (D) virtual and enlarged

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71. C.

The objective of compound microscope is a convex lens. We know that a convex lens forms real and enlarged image when an object is placed between its focus and lens.

72. The earth radiates in the infra-red region of the spectrum. The spectrum is correctly given by (A) Rayleigh Jeans law (B) Planck’s law of radiation

(C) Stefan’s law of radiation (D) Wien’s law

72. D.

73. To get three images of a single object, one should have two plane mirrors at an angle of

(A) 60 (B) 90

(C) 120 (D) 30

73. B.

The number of images formed of two plane mirrors are placed at an angle is n = 3601

 Here n = 3  33601   360 90 4     

74. According to Newton’s law of cooling, the rate of cooling of a body is proportional to ()n, where   is the difference of the temperature of the body and the surroundings, and n is equal to

(A) two (B) three

(C) four (D) one

74. D.

According to Newton’s law of cooling. Rate of cooling d

dt

_{ }

Therefore n = 1.

75. The length of a given cylindrical wire is increased by 100%. Due to the consequent decrease in diameter the change in the resistance of the wire will be

(A) 200% (B) 100%

(C) 50% (D) 300%

75. D.

%change = 3R 100% 300%

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PAPER -2004

1. Which one of the following represents the correct dimensions of the coefficient of viscosity?

(A) ML1T2 (B) MLT1

(C) ML1T1 (D) ML2T2

1. C.

Dimensions of (coefficient of viscosity)

2 0 0 0 1 MLT M L M LT     = ML 1 T1

2. A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement x is proportional to

(A) x2 (B) ex (C) x (D) logex 2. A. 2 f i mk K K x 2   2 f i K  k x .

3. A ball is released from the top of a tower of height h metres. It takes T seconds to reach the ground. What is the position of the ball in T/3 seconds?

(A) h/9 metres from the ground (B) 7h/9 metres from the ground (C) 8h/9 metres from the ground (D) 17h/18 metres from the ground.

3. C.

4. If A B   B A,  then the angle between A and B is

(A) (B)/3

(C)/2 (D)/4

4. A.

5. A projectile can have the same range R for two angles of projection. If T1 and T2 be the time

of flights in the two cases, then the product of the two time of flights is directly proportional to

(A) 1/R2 (B) 1/R

(C) R (D) R2

5. C.

Range is same for complimentary angles.

1 2u sin T g   and T₂ 2u sin (90 ) g    and 2 u sin 2 R g    T T₁ ₂ 2u sin 2u cos 2R. g g g     

6. Which of the following statements is false for a particle moving in a circle with a constant angular speed?

(A) The velocity vector is tangent to the circle. (B) The acceleration vector is tangent to the circle.

(C) The acceleration vector points to the centre of the circle.

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6. B.

The acceleration vector is along the radius of circle.

7. An automobile travelling with speed of 60 km/h, can brake to stop within a distance of 20 cm. If the car is going twice as fast, i.e 120 km/h, the stopping distance will be

(A) 20 m (B) 40 m

(C) 60 m (D) 80 m

7. D.

If the initial speed is doubled, the stopping distance becomes four times, i.e. 80 m.

8. A machine gun fires a bullet of mass 40 g with a velocity 1200 ms1. The man holding it can exert a maximum force of 144 N on the gun. How many bullets can he fire per second at the most?

(A) one (B) four

(C) two (D) three

8. D.

Change in momentum for each bullet fired is

40

1200 48 N 1000

  

If a bullet fired exerts a force of 48 N on man’s hand so man can exert maximum force of 144 N, number of bullets that can be fired = 144/48 = 3 bullets.

9. Two masses m1 = 5 kg and m2 = 4.8 kg tied to a string are hanging

over a light frictionless pulley. What is the acceleration of the masses when lift free to move?

(g = 9.8 m/s2) (A) 0.2 m/s2 (B) 9.8 m/s2 (C) 5 m/s2 (D) 4.8 m/s2 9. A. 2 1 2 1 2 m m a g 0.2 m / s m m    _ _     m1 m2

10. A uniform chain of length 2 m is kept on a table such that a length of 60 cm hangs freely from the edge of the table. The total mass of the chain is 4 kg. What is the work done in pulling the entire chain on the table?

(A) 7.2 J (B) 3.6 J

(C) 120 J (D) 1200 J

10. B.

Work done = mgh = 1.2 0.3 10 = 3.6 J.

11. A block rests on a rough inclined plane making an angle of 30 with the horizontal. The coefficient of static friction between the block and the plane is 0.8. If the frictional force on the block is 10 N, the mass of the block (in kg) is (take g = 10 m/s2)

(A) 2.0 (B) 4.0

(C) 1.6 (D) 2.5

11. A.

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12. A force F(5iˆ3 jˆ2k)Nˆ is applied over a particle which displaces it from its origin to the point r(2iˆˆj)m. The work done on the particle in joules is

(A)7 (B) +7 (C) +10 (D) +13 12. B. Work done, W = F s  Here s  r_f r_i (2iˆˆj) ˆ ˆ ˆ ˆ ˆ W(5i3 j2k)(2ij) = 10 3 = 7 J.

13. A body of mass m, accelerates uniformly from rest to v1 in time t1. The instantaneous power

delivered to the body as a function of time t is (A) 1 1 mv t t (B) 2 1 2 1 mv t t (C) 2 1 1 mv t t (D) 2 1 1 mv t t 13. B. Power 2 1 1 1 2 1 1 1 v v mv t P F v mav m t t t t        _ _ _     

14. A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle, the motion of the particle takes place in a plane. It follows that (A) its velocity is constant (B) its acceleration is constant

(C) its kinetic energy is constant (D) it moves in a straight line.

14. C.

When a force of constant magnitude which is always perpendicular to the velocity of the particle acts on a particle, the work done and hence change in kinetic energy is zero.

15. A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same which one of the following will not be affected?

(A) moment of inertia (B) angular momentum (C) angular velocity (D) rotational kinetic energy.

15. B.

Let it be assume that in “free space” not only the acceleration due to gravity it acting but also there are no external torque acting but also there are no external torque acting on the sphere. If due to internal changes in the system, the radius has increased, then the law of the conservation of angular momentum holds good.

16. A ball is thrown from a point with a speed0 at an angle of projection. From the same point and at the same instant person starts running with a constant speed 0/2 to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection?

(A) yes, 60 (B) yes, 30

(C) no (D) yes, 45

16. A.

For the person to be able to catch the ball, the horizontal component of the velocity of the ball should be same as the speed of the person.

0 0 v v cos 2     = 60.

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17. One solid sphere A and another hollow sphere B are of same mass and same outer radii. Their moment of inertia about their diameters are respectively IA and IB such that

(A) IA = IB (B) IA > IB

(C) IA < IB (D) IA/IB = dA/dB

Where dA and dB are their densities.

17. C.

Moment of inertia of a uniform density solid sphere, A = 2 2 MR 5 And of hollow sphere B = 2 2

MR 3 Since M and R are same, IA < IB.

18. A satellite of mass m revolves around the earth of radius R at a height x from its surface. If g is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is (A) gx (B) gR Rx (C) 2 gR Rx (D) 1/ 2 2 gR R x    _    18. D.

For the satellite, the gravitational force provides the necessary centripetal force i.e. 2 e 0 2 GM m Mv (RX) (RX) and e 2 GM g R   1/ 2 2 0 gR v R X     _   

19. The time period of an earth satellite in circular orbit is independent of (A) the mass of the satellite

(B) radius of its orbit

(C) both the mass and radius of the orbit

(D) neither the mass of the satellite nor the radius of its orbit.

19. A.

The time period of satellite is given by 3 (R h) T 2 GM   

where, R + h = radius of orbit satellite, M = mass of earth.

20. If g is the acceleration due to gravity on the earth’s surface, the gain in the potential energy of object of mass m raised from the surface of the earth to a height equal to the radius R of the earth is (A) 2 mgR (B) 1mgR 2 (C) 1mgR 4 (D) mgR 20. B.

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21. Suppose the gravitational force varies inversely as the nth power of distance. Then the time period planet in circular orbit of radius R around the sun will be proportional to

(A) n 1 2 R        _(B) n 1 2 R        (C) Rn (D) n 2 2 R        21. A. (n 1) / 2 TR 

22. A wire fixed at the upper end stretches by length by applying a force F. The work done in stretching is

(A) F/2 (B) F

(C) 2F (D) F/2

22. D.

Work done = 1_kx2 1_k 2

2 2  where  is the total extensions.

1 1

(k ) F

2 2

   

23. Spherical balls of radius R are falling in a viscous fluid of viscosity  with a velocity v. The retarding viscous force acting on the spherical ball is

(A) directly proportional to R but inversely proportional to v. (B) directly proportional to both radius R and velocity v. (C) inversely proportional to both radius R and velocity v.

(D) inversely proportional to R but directly proportional to velocity v.

23. B.

Retarding viscous force = 6Rv

24. If two soap bubbles of different radii are connected by a tube,

(A) air flows from the bigger bubble to the smaller bubble till the sizes are interchanged. (B) air flows from bigger bubble to the smaller bubble till the sizes are interchanged (C) air flows from the smaller bubble to the bigger.

(D) there is no flow of air.

24. C.

The pressure inside the smaller bubble will be more P_i P₀ 4T r

 _ _ 

 

 

Therefore, if the bubbles are connected by a tube, the air will flow from smaller bubble to the bigger.

25. The bob of a simple pendulum executes simple harmonic motion in water with a period t, while the period of oscillation of the bob is t0 in air. Neglecting frictional force of water and

given that the density of the bob is 4 1000 3

    

  kg/m

3

. What relationship between t and t0 is

true?

(A) t = t0 (B) t = t0/2

(C) t = 2t0 (D) t = 4t0

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FIITJEELtd., ICES House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi-110016, Ph: 26515949, 26569493, Fax: 011-26513942. 0 T 1 1 1 T ' 1 1 3    _  _  _    0 T 2 T  or, T = 2T0

26. A particle at the end of a spring executes simple harmonic motion with a period t1, while the

corresponding period for another spring is t2. If the period of oscillation with the two springs

in series is t, then (A) T = t1 + t2 (B) T2 t12 t22 (C) 1 1 1 1 2 T t t (D) 2 2 2 1 2 T t t 26. B. 2 2 2 1 2 t t T

27. The total energy of particle, executing simple harmonic motion is

(A)x (B)x2

(C) independent of x (D)x1/2

27. C.

In simple harmonic motion, as a particle is displaced from its mean position, its kinetic energy is converted to potential energy and vice versa and total energy remains constant. The total energy of simple harmonic motion is independent of x.

28. The displacement y of a particle in a medium can be expressed as

y = 106sin(110t + 20 x + /4) m, where t is in seconds and x in meter. The speed of the wave is (A) 2000 m/s (B) 5 m/s (C) 20 m/s (D) 5 m/s. 28. B. 1 v 5 ms k    

29. A particle of mass m is attached to a spring (of spring constant k) and has a natural angular frequency0. An external force F(t) proportional to cost (0) is applied to the oscillator. The time displacement of the oscillator will be proportional to

(A) ₂ ₂ 0 m    (B) 2 2 0 1 m(   ) (C) ₂ ₂ 0 1 m(   ) (D) 2 2 0 m    29. B.

For forced oscillations, the displacement is given by xA sin( t  ) with 0 2 2 0 F / m A   

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30. In forced oscillation of a particle the amplitude is maximum for a frequency1 of the force, while the energy is maximum for a frequency2 of the force, then

(A)1 =2 (B)1 >2

(C)1 <2 when damping is small and1 >2 when damping is large (D)1 <2

30. A.

Both amplitude and energy get maximised when the frequency is equal to the natural frequency. This is the condition of resonance.

1 =2

31. One mole of ideal monoatomic gas ( = 5/30) is mixed with one mole of diatomic gas ( = 7/5). What is for the mixture? denotes the ratio of specific heat at constant pressure, to that at constant volume.

(A) 3/2 (B) 23/15 (C) 35/23 (D) 4/3 31. A. Q = Q1+ Q2 1 2 1 2 m 1 2 n n n n 1 1 1  _ _       m 3 2  

32. If the temperature of the sun were to increase from T to 2T and its radius from R to 2R, then the ratio of the radiant energy received on earth to what it was previously will be

(A) 4 (B) 16

(C) 32 (D) 64.

32. D.

According to Stefan’s law, P AT4 and A r2 P r2T4

33. Which of the following statements is correct for any thermodynamic system? (A) The internal energy changes in all processes.

(B) Internal energy and entropy are state functions. (C) The change in entropy can never be zero.

(D) The work done in an adiabatic process is always zero.

33. B.

34. Two thermally insulated vessels 1 and 2 are filled with air at temperatures (T1, T2), volume

(V1, V2) and pressure (P1, P2) respectively. If the valve joining two vessels is opened, the

temperature inside the vessel at equilibrium will be

(A) T1 + T2 (B) (T1 + T2)/2 (C) 1 2 1 1 2 2 1 1 2 2 2 1 T T (P V P V ) P V T P V T   (D) 1 2 1 1 2 2 1 1 1 2 2 2 T T (P V P V ) P V T P T T   34. C.

The number of moles of system remains same According to Boyle’s law,

P1V1 + P2V2 = P(V1 + V2)  1 2 1 1 2 2 1 1 2 2 2 1 T T (P V P V ) T P V T P V T   

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35. A radiation of energy E falls normally on a perfectly reflecting surface. The momentum transferred to the surface is

(A) E/c (B) 2E/c

(C) Ec (D) E/c2 35. B. surface 2E P P . c    

36. The temperature of two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity K and 2K and thickness x and 4x, respectively are T2 and T1 (T2 > T1). The rate of heat transfer through the slab,

in a steady state is A(T2 T )K1 _f, x        with f equal to (A) 1 (B) ½ (C) 2/3 (D) 1/3 x 4x 2K K _T1 T2 36. D. 2 1 2 2T T kA q T x 3      _  _   = kA



T₂ T₁



3x 

37. A light ray is incident perpendicular to one face of a 90 prism and is totally internally reflected at the glass-air interface. If the angle of reflection is 45, we conclude that the refractive index n

(A) n 1 2  (B) n 2 (C) n 1 2  (D) n 2 45 45 37. B.

Angle of incidence i > C for total internal reflection. Here i = 45 inside the medium.

 45 > sin1(1/n)

 n >2.

38. A plane convex lens of refractive index 1.5 and radius of curvature 30 cm is silvered at the curved surface. Now this lens has been used to form the image of an object. At what distance from this lens an object be placed in order to have a real image of the size of the object? (A) 20 cm (B) 30 cm (C) 60 cm (D) 80 cm 38. A. 1 m 1 2 1 F f f and 1 1 1 1 1 (1.5 1) f 30 60     _  _     and f_m15 cm.  F = 10 cm.

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39. The angle of incidence at which reflected light totally polarized for reflection from air to glass (refractive index n), is

(A) sin1(n) (B) sin1(1/n)

(C) tan1(1/n) (D) tan1(n)

39. D.

Brewster’s law: According to this law the ordinary light is completely polarised in the plane of incidence when it gets reflected from transparent medium at a particular angle known as the angle of polarisation.

n = tan ip.

40. The maximum number of possible interference maxima for slit-separation equal to twice the wavelength in Young’s double-slit experiment is

(A) infinite (B) five

(C) three (D) zero

40. B.

For interference maxima, d sin = n Here d = 2

 sin  = n/2 and is satisfied by 5 integral values of n (2, 1, 0, 1, 2), as the maximum value of sin can only be 1.

41. An electromagnetic wave of frequency  = 3.0 MHz passes from vacuum into a dielectric medium with permittivity = 4.0. Then

(A) wavelength is doubled and the frequency remains unchanged (B) wavelength is doubled and frequency becomes half

(C) wavelength is halved and frequency remains unchanged (D) wavelength and frequency both remain unchanged.

41. C. Refractive index, 0 2     

Speed and wavelength of wave will becomes half, the frequency remaining unchanged (frequency of a wave depends on the source as due to refraction, it is assumed that the energy is conserved. h remains the same)

42. Two spherical conductor B and C having equal radii and carrying equal charges in them repel each other with a force F when kept apart at some distance. A third spherical conductor having same radius as that of B but uncharged brought in contact with B, then brought in contact with C and finally removed away from both. The new force of repulsion, between B and C is (A) F/4 (B) 3F/4 (C) F/8 (D) 3F/8. 42. D. 2 0 1 (q / 2)(3q / 4) 3F F ' . 4 d 8   

43. A charged particle q is shot towards another charged particle Q which is fixed, with a speed v it approaches Q upto a closest distance r and then returns. If q were given a speed 2v, the closest distances of approach would be

(A) r (B) 2r

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43. D.

By principle of conservation of energy 2 1 KqQ mv 2  r …(i) Finally, 2 2 1 KqQ m(2v) 2  r …(ii)

Equation (i) (ii), 1 r '

4 r

 r ' r

4

 .

44. Four charges equal toQ are placed at the four corners of a square and a charge q is at its centre. If the system is in equilibrium the value of q is

(A) Q(1 2 2) 4   (B) Q(1 2 2) 4  (C) Q(1 2 2) 2   (D) Q(1 2 2) 2  44. B. q = Q(1 2 2) 4  

45. Alternating current can not be measured by D.C. ammeter because (A) A.C. cannot pass through D.C.

(B) A.C. changes direction

(C) average value of current for complete cycle is zero (D) D.C. ammeter will get damaged.

45. C.

46. The total current supplied to the circuit by the battery is

(A) 1 A (B) 2 A

(C) 4 A (D) 6 A

46. C.

The given circuit can be written as 6 V I 4A 1.5    . 6 V 2 3 1.5 6

47. The resistance of the series combination of two resistances is S. When they are joined in parallel through total resistance is P. If S = nP, then the minimum possible value of n is

(A) 4 (B) 3

(C) 2 (D) 1

47. A.

Let resistances be R1 and R2

So, S = R1 + R2; 1 2 1 2 R R P R R   S = nP 1 2 1 2 1 2 nR R R R R R    2 1 2 1 2 (R R ) nR R If R1 = R2, so minimum value of n = 4.

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48. An electric current is passed through a circuit containing two wires of the same material, connected in parallel. If the length and radii of the wires are in the ratio of 4/3 and 2/3, then the ratio of the currents passing through the wire will be

(A) 3 (B) 1/3 (C) 8/9 (D) 2. 48. B. 1 2 2 1 I R I  R

[current divider rule since voltage is same in parallel] 2 1 2 1 2 2 1 2 I L r I  L r  2 1 2 I 3 2 1 I 4 3 3    _{ }    .

49. In a metre bridge experiment null point is obtained at 20 cm from one end of the wire when resistance X is balanced against another resistance Y. If X < Y, then where will be the new position of the null point from the same end, if one decides to balance a resistance of 4X against Y?

(A) 50 cm (B) 80 cm

(C) 40 cm (D) 70 cm

49. A.

We have from meter bridge experiment,

1 1 2 2 R R    , where2 = (1001) cm In the first case, X/Y = 20/80 In the second case 4X

Y 100 

  = 50 cm.

50. The thermistors are usually made of

(A) metals with low temperature coefficient of resistivity (B) metals with high temperature coefficient of resistivity (C) metal oxides with high temperature coefficient of resistivity ‘

(D) semiconducting materials having low temperature coefficient of resistivity.

50. C.

These are devices whose resistance varies quite markedly with temperature mean having high temperature coefficient of resistivity. [Their name are derived from thermal resistors]. Depending on their composition they can have either negative temperature coefficient or positive temperature coefficient or positive temperature coefficient or positive temperature coefficient characteristics.

The negative temperature coefficient types consists of a mixture of oxides of iorn, nickel and cobalt with small amounts of other substance. The positive temperature coefficient types are based on barium titanate.

51. Time taken by a 836 W heater to heat one litre of water from 10C to 40C is

(A) 50 s (B) 100 s

(C) 150 s (D) 200 s

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Let t be the time taken, then 836 t 1000 1 (40 10) 4.2  _ _{ } _ [using Q = mst]  t = 150 sec.

52. The thermo emf of a thermocouple varies with the temperature  of the hot junction as E = a + b2 in volts where the ratio a/b is 700C. If the cold junction is kept at 0C, then the neutral temperature is

(A) 700C (B) 350C (C) 1400C

(D) no neutral temperature is possible for this thermocouple.

52. D.

E = a + b2

At neutral temperature dE/d = 0

 dE a 2b _n 0 d     ; n a 2b    Now a 700 C b  (given) n =700/2 =350C Now   _c 0 C. So,   _n 0 C But mathematically   _n 0 C.

53. The electrochemical equivalent of a metal is 3.3  107 kg per coulomb. The mass of the metal liberated at the cathode when a 3 A current is passed for 2 seconds will be

(A) 19.8 107 kg (B) 9.9 107 kg (C) 6.6 107 kg (D) 1.1 107 kg

53. A.

m = Zit,

m = 3.3 107 3 2 = 19.8 107 kg.

54. A current I ampere flows along an infinitely long straight thin walled tube, then the magnetic induction at any point inside the tube is

(A) infinite (B) zero

(C) 0 2i 4 r   tesla (D) 2i r tesla 54. B.

Considering Ampere’s loop (shown by dotted line), no current is enclosed by this loop. Therefore, the magnetic field will be zero inside the tube.

55. A long wire carries a steady current. It is bent into a circle of one turn and the magnetic field at the centre of the coil is B. It is then bent into a circular loop of n turns. The magnetic field at the centre of the coil will be

(A) nB (B) n2 B (C) 2nB (D) 2n2B 55. B. 0 n i B ' 2r '   = _n2 0i _{n B}2  .

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56. The magnetic field due to a current carrying circular loop of radius 3 cm at a point on the axis at a distance of 4 cm from the centre is 54 T. What will be its value at the centre of the loop? (A) 250T (B) 150T (C) 125T (D) 75T 56. A. Using formula 2 0 2 2 3 / 2 iR B 2(R X )    , we get 2 0 2 2 3 / 2 i(3) 54 2[(3) (4) ]    …(i)

At the centre of the coil, X = 0 and B = 0i 2(3)



Using equation (i) 3 2 54 5 B (3) 3     B = 250T.

57. Two long conductors, separated by a distance d carry current I1 and I2 in the same direction.

They exert a force F on each other. Now the current in one of them increased to two times and its direction reversed. The distance is also increased to 3d. The new value of the force between them is

(A)2F (B) F/3

(C)2F/3 (D)F/3

57. C.

Force between two long conductor carrying current 0 I I1 2 F 2 d     According to question 0 ( 2I )(I )1 2 F ' 2 d     

From equation (i) and (ii),F ' 3F. 2

 

58. The length of a magnet is large compared to its width and breadth. The time period of its width and breadth. The time period of its oscillation in a vibration magnetometer is 2 s. The magnet is cut along its length into three equal parts and three parts are then placed on each other with their like poles together. The time period of this combination will be

(A) 2 s (B) 2/3 s

(C) 23 s (D) 2/3 s .

58. B.

Time period of vibration, T 2 T MB

 

Where = moment of inertia of magnet, M = magnetic moment 2

m I

12

  and M = pole strength  2 1 m I I' 3 12 3 3 9     _{  }      

and M’ = pole strength (will remain the same) (/3) 3 = M.

T 2

T ' s.

9 9

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59. The materials suitable for making electromagnets should have

(A) high retentivity and high coercivity (B) low retentivity and low coercivity (C) high retentivity and low coercivity (D) low retentivity and high coercivity

59. B.

60. In an LCR series a.c. circuit, the voltage across each of the components, L, C and R is 50 V. The voltage across the LC combination will be

(A) 50 V (B) 502 V

(C) 100 V (D) 0 V(zero)

60. D.

In series LCR circuit, the voltage across the inductor (L) and the capacitor (C) are in opposite phase.

61. A coil having n turns and resistance 4R. This combination is moved in time t seconds from a magnetic field W1 weber to W2 weber. The induced current in the circuit is

(A) W2 W1 5Rnt   (B) (W2 W )1 5Rt   (C) W2 W1 Rnt   (D) n(W2 W )1 Rt   61. B. n d I R ' dt    or, 2 1 2 1 W W 1 I n R ' t t      _ _   

(W1 and W2 are not the magnetic field, but the values of flux associated with one turn of coil)

2 1 n(W W ) 1 I (R 4R) t     or, _I n(W2 W )1 5Rt   

62. In a uniform magnetic field of induction B a wire in the form of semicircle of radius r rotates about the diameter of the circle with angular frequency . The axis of rotation is perpendicular to the field. If the total resistance of the circuit is R the mean power generated per period of rotation is

(A) 2 B r 2R   (B) 2 2 (B r ) 2R   (C) 2 (B r ) 2R   (D) 2 2 (B r ) 8R   62. B.

Magnetic flux = BA cos = B 2 r cos t 2     2 ind d 1 B r dt 2        sint  _P 2ind B2 2 4r 2 sin2 t R 4R      

Now, <sin2t> = ½ (mean value)

 P (B r2 )2.

8R

    

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63. In a LCR circuit capacitance is changed from C to 2C. For the resonant frequency to remain unchanged, the inductance should be changed from L to

(A) 4L (B) 2L (C) L/2 (D) L/4 63. C. res 1 LC  

ifres is to remain same, the product LC should also not change.

 LC = LC

 LC = L2C

 L = L/2

64. A metal conductor of length 1 m rotates vertically about one of its ends at angular velocity 5 radians per second. If the horizontal component of earth’s magnetic field is 0.3 104 T, then the e.m.f. developed between the two ends of the conductor is

(A) depends on the nature of the metal used (B) depends on the intensity of the radiation

(C) depends both on the intensity of the radiation and the metal used

(D) is the same for all metals and independent of the intensity of the radiation.

64. B.

emf. developed is given by 2 ind 1 B R 50 V. 2     

65. According to Einstein’s photoelectric equation, the plot of the kinetic energy of the emitted photo electrons from a metal Vs the frequency, of the incident radiation gives straight line

whose slope

(A) depends on the nature of the metal used (B) depends on the intensity of the radiation

(C) depends both on the intensity of the radiation and the metal used

(D) is the same for all metals and independent of the intensity of the radiation.

65. D.

max

KE   h W {y = mx + C}

Slope of the line in the graph is h, the Planck’s constant.

K.E.

 = h

W 

66. The work function of a substance is 4.0 eV. Then longest wavelength of light that can cause photoelectron emission from this substance approximately

(A) 540 nm (B) 400 nm (C) 310 nm (D) 220 nm 66. C. hc W   34 8 longest 19 hc 6.6 10 3 10 W 4.0 1.6 10            _longest 310 nm.

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67. A charged oil drop is suspended in a uniform field of 3 104 V/m so that it neither falls nor rises. The charge on the drop will be (take the mass of the charge = 9.9 1015 kg and g = 10 m/s2)

(A) 3.3 1018 C (B) 3.2 1018 C (C) 1.6 1018 C (D) 4.8 1018 C.

67. A.

Since ball is hanging in equilibrium, force by gravity is balanced by electric force. qE = mg  q m g E    9.9 1015₄ 10 3 10      q = 3.3 1018 C

68. A nucleus disintegrates into two nuclear parts which have their velocities in the ratio 2 : 1. The ratio of their nuclear sizes will be

(A) 21/3 : 1 (B) 1 : 31/2 (C) 31/2 : 1 (D) 1 : 21/3 68. B. 1/ 3 1 2 2 2 R m R 2m         1 1/ 3 2 R 1: 2 R  .

69. The binding energy per nucleon of deuteron 2 1

( H) and helium nucleus 4 2

( He) is 1.1 MeV and 7 MeV respectively. If two deuteron nuclei react to form a single helium nucleus, then the energy released is

(A) 13.9 MeV (B) 26.9 MeV

(C) 23.6 MeV (D) 19.2 MeV

69. C.

Energy released = total binding energy of product total binding energy of reactants

 28 (2 2.2) = 28 4.4 = 236 MeV.

70. An -particle of energy 5 MeV is scattered through 180 by a fixed uranium nucleus. The distance of the closest approach is of the order of

(A) 1 Å (B) 1010 cm

(C) 1012 cm (D) 1015 cm

70. C.

At closest approach, all the kinetic energy of the -particle will converted into the potential energy of the system, K.E. = P.E.

1 2 0 q q 1 5 MeV 4 r   5 106 e = 9 109 2 1 2 Z Z e r  9 19 6 9 10 92 2 1.6 10 r 5 10          r = 5.3 1014 m = 5.3 1012 cm.

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71. When npn transistor is used as amplifier

(A) electrons move from base to collector (B) holes move from emitter to base (C) electrons move from collector to base (D) holes move from base to emitter.

71. A.

When npn transistor is used, majority charge carrier electrons of n type emitter move from emitter to base and then base to collector.

72. For a transistor amplifier in common emitter configuration having load impedance of 1 k (hfe

= 50 and hoe = 25) the current gain is

(A)5.2 (B)15.7 (C)24.8 (D)48.78 72. D. In CE configuration, fe i 0e L h A 1 h R    = 6 3 50 48.78 1 25 10 1 10  _{ }    

73. A piece of copper and another of germanium are cooled from room temperature to 77 K, the resistance of

(A) each of them increases (B) each of them decreases

(C) copper decreases and germanium increases (D) copper increases and germanium decreases.

73. D.

Copper is metallic conductor and germanium is semiconductor therefore as temperature decreases resistance of good conductor decreases while for semiconductor it increases. 74. The manifestation of band structure in solids is due to

(A) Heisenberg’s uncertainty principle (B) Pauli’s exclusion principle (C) Bohr’s correspondence principle (D) Boltzmann’s law

74. B.

75. When p-n junction diode is forward biased

(A) the depletion region is reduced and barrier height is increased (B) the depletion region is widened and barrier height is reduced. (C) both the depletion region and barrier height reduced

(D) both the depletion region and barrier height increased.

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-1-FIITJEE

SOLUTION TO AIEEE-2005

PHYSICS

1. A projectile can have the same range R for two angles of projection. If t1 and t2 be the

times of flights in the two cases, then the product of the two time of flights is proportional to (1) R2₍₂₎_1/R2 (3) 1/R (4) R 1. (4) 2 1 2 2 2u sin 2 2R t t g g θ = =

2. An annular ring with inner and outer radii R1 and R2 is rolling without slipping with a

uniform angular speed. The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring, F1/F2 is

(1) 2 1 R R (2) 2 1 2 R R       (3) 1 (4) 1 2 R R 2. (4) 2 1 1 1 2 2 2 2 F R R F R R ω = = ω

3. A smooth block is released at rest on a 45° incline and then slides a distance d. The time taken to slide is n times as much to slide on rough incline than on a smooth incline. The coefficient of friction is

(1) k 2 1 1 n µ = − (2) k 2 1 1 n µ = − (3) s 2 1 1 n µ = − (4) s 2 1 1 n µ = − 3. (1) 2 1 1 g d t 2 2 =

(

)

2 k 2 1 g d 1 t 2 2 = − µ 2 2 2 2 1 k t 1 n t = =1− µ

4. The upper half of an inclined plane with inclination φ is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half is given by

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(1) 2sinφ (2) 2cosφ (3) 2tanφ (4) tanφ 4. (3) mg s sin φ = mgcos .s 2 µ φ S/2 S/2 φ

5. A bullet fired into a fixed target loses half of its velocity after penetrating 3 cm. How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion? (1) 3.0 cm (2) 2.0 cm (3) 1.5 cm (4) 1.0 cm 5. (4) F.3 2 2 1 1 v mv m 2 2 4 = − F(3+x) 1_mv2 2 = x = 1 cm

6. Out of the following pair, which one does NOT have identical dimensions is (1) angular momentum and Planck’s constant

(2) impulse and momentum

(3) moment of inertia and moment of a force (4) work and torque

6. (3)

Using dimension

7. The relation between time t and distance x is t=ax2_{+bx where a and b are constants.}

The acceleration is

(1) −2abv2₍₂₎_2bv3

(3) −2av3 _{(4) 2av}2

7. (3)

t = ax2_{+ bx}

by differentiating acceleration = - 2av3

8. A car starting from rest accelerates at the rate f through a distance S, then continues at constant speed for time t and then decelerates at the rate f/2 to come to rest. If the total distance traversed is 15 S, then

(1) S=ft (2) S = 1/6 ft2 (3) S = 1/2 ft2 _{(4) S = 1/4 ft}2 8. (none) 2 1 ft S 2 = 0 v = 2Sf During retardation t1 t2 t V0 V S2 = 2S