SCRA Set B Solved Question Paper

Will you please provide the Solved Question Paper of SCRA Set B exam ?

[Raman Vij]

Here is the list of few questions of Solved Question Paper of SCRA Set B exam which you are looking for .

1. What is the ratio of minimum wavelength of radiation emitted in Balmer series of hydrogen atom to maximum wavelength of the series ?

(a) 5 : 9

(b) 9 : 5

(c ) 1 : 4

(d) 4 : 1

Ans: a

2. An object X of mass m moving forward with velocity v along x-axis collides elastically with a stationary object Y of mass 2 m at the origin. After collision, the object X moves backward along x-axis. Given that the kinetic energy of the system is conserved, the speed of the object Y after collision is

(a) 2v/3

(b) v/3

(c ) v/2

(d) 3v/4

ANs: a

3. There is a linear current I going around a circular wire of radius (a) with centre at origin in the xy-plane. The magnetic field B at (0,0,z) in Cartesian coordinates is given by

(a) B=(μ_0 Ia^2)/(2(z^2+a^2 )^(3/2) )

(b) B=(μ_0 Iza)/(2(z^2+a^2 )^(3/2) )

(c ) B=(μ_0 Iz^2)/(2(z^2+a^2 )^(3/2) )

(d) B=(μ_0 Ia^2)/(2(z^2+a^2 )^(1/2) )

ANs: a

4. There are two long wires each parallel to z-axis, each carrying current I, are at (0 , 0) and the other at (a,b). The force on unit length of each wire is

(a) (μ_0 I^2)/2π(a^2+b^2 )

(b) (μ_0 I^2 (a+b))/2π(a^2+b^2 )

(c ) (μ_0 I^2)/(2π(a^2+b^2 )^(3/2) )

(d) (μ_0 I^2)/(2π(a^2+b^2 )^(1/2) )

Ans: d

5. In a fusion process, effectively 4 protons each of mass m_p each combine to form an alpha particle of mass M, two positrons each of mass m_e, some gamma rays and neutrinos. With c being speed of light, the energy released in the formation of one alpha particle is

(a) (4m_p-M+2m_e ) c^2

(b) (M-4m_p+2m_e ) c^2

(c ) (M-4m_p-2m_e ) c^2

(d) (4m_p-M-2m_e ) c^2

Ans: d

6. A piece of bar magnet of length L having pole strength m is held at an angle θ with a uniform magnetic field of strength H. The piece is then transversely cut into two equal pieces; one of the pieces is held in the same field in similar manner. The ratio of torque of the former to the latter piece of the bar magnet is

(a) 1 : 2

(b) 2 : 1

(c ) 1 : 4

(d) 4 : 1

Ans: b

7. The critical angle of incidence of a ray of light going from a medium A to another medium B is 〖30〗^0. If the velocity of light in the medium A is half the velocity of light in vacuum, then velocity of light in B is

(a) c/4

(b) c

(c ) (√3 c)/2

(d) c/(2√3)

Where c is the speed of light in vacuum.

Ans: b

8. A particle of mass m and charge q is thrown at velocity u in the x-direcion against uniform electric field E in the negative x-direction. The distance it will travel before coming to momentary rest is

(a) (mu^2)/qE

(b) (2mu^2)/qE

(c ) (mu^2)/2qE

(d) (mu^2)/4qE

Ans: c

9. The optical path of a monochromatic light is the same if it passes through 0.665 cm of glass or 0.750 cm of a liquid of refractive index 1.5. The refractive index of glass is

(a) 1.5

(b) 1.7

(c ) 1.2

(d) 1.6

Ans: b

10. The lateral displacement of light passing through a parallel plate of glass of thickness t with angle of incidence 〖60〗^0 and angle of refraction 〖45〗^0 is

(a) (√3-1)t (b)

(√3-1)t/2

(c ) (√3+1)t/2

(d) None of the above

Ans: b

11. A small bar starts sliding down on inclined plane making an angle α with the horizontal. The coefficient of friction μ depends on the distance x as μ=ax where a is a constant. The distance covered by the bar till it stops is

(a) ((tan⁡α ))/a

(b) 2(tan⁡α )/a

(c ) 2a tan⁡α

(d) tan⁡α/((2a) )

Ans: b

12. Which one of the following waves does not involve oscillations of particles of a medium ?

(a) Waves in a hanging spring

(b) Ripples on a water surface

(c ) A light wave

(d) Ultrasonic waves

Ans: c

13. A certain mass of a given gas of specific heat ratio 1 .5 is compressed such that its volume becomes one –fourth of original volume, first adiabatically and then isothermally. In both the cases the initial state of gas is the same. The ratio of the respective works in each compression respectively is approximately (ln⁡〖2=0.3) 〗

(a) 4

(b) 3

(c ) 2

(d) 1

Ans: b

14. Two plane mirrors form an angle of 〖120〗^0. The distance between the two images of a point source formed in them is 20 cm and the point source lies on the bisector of the angle formed by the mirrors. What would be the least distance of the point source form the line along which the mirrors would touch each other ?

(a) 10 cm

(b) 20/√3 cm

(c ) 10√2 cm

(d) None of the above

Ans: b

15. An astronomical telescope consists of an objective lens that forms at or very near to its principal focus an image of the object which is

(a) real, inverted and reduced

(b) real, inverted and magnified

(c ) virtual, erect and reduced

(d) real, erect and reduced

Ans: A

16. A particle in uniform circular motion can possess

(a) radial acceleration only

(b) tangential acceleration only

(c ) both radial and tangential acceleration

(d) neither radial nor tangential acceleration

Ans: a

17. A particle motion on a apace curve is governed by x=2sin⁡〖t ,y=3 cos⁡t 〗 and z=√5 sin⁡〖t.〗 The speed of the particle at any instant is

(a) 3√2 sin⁡t

(b) 3 √(cos⁡2t )

(c) 3√(sin⁡2t )

(d) independent of time

Ans: d

18. The frictional force on a rolling cylinder is proportional to

(a) the tangential force and directed perpendicular to the surfaces in contact

(b) the tangential force and directed parallel to the surfaces in contact

(c ) the normal force and directed parallel to the surfaces in contact

(d) the normal force and directed perpendicular to the surfaces in contact

Ans: b

19. The kinetic energy (T) of a particle moving along a circle of radius R depends on the distance covered (s) as T=cs^2 where c is a constant. The force acting on the particle as a function of s is

(a) ks√(1+s/R)

(b) ks√(1+(s/R)^2 )

(c ) ks√(1+(s/R)^3 )

(d) ks√(1+(s/R)^4 )

Where k is a constant.

Ans: b

20. A point mass moves along x-axis according to the law x=A cos^2 (ωt-π/4) . The amplitude of the oscillation is

(a) A

(b) A/2

(c ) 2A

(d) A/3

Ans: b

21. A pendulum consisting of a small sphere of mass m, suspended by an inextensible and massless string of length L is made to swing in a vertical plane. If the breaking strength of the string is 2 mg where g is the acceleration due to gravity, then the maximum angular amplitude of the displacement from the vertical can be

(a) 〖15〗^0

(b) 〖30〗^0

(c ) 〖60〗^0

(d) 〖75〗^0

Ans: c

For the next 02 (two ) items that follow:

A body of mass m is thrown up with velocity v_0. The air drag is equal to kv^2 where v is the velocity at any instant and k is a positive constant (proportionally constant) .

22. The maximum height to which the body can go is

(a) m/2k (1+(kv_0^2)/mg)

(b) m/k ln⁡〖 (1+(kv_0^2)/mg)〗

(c ) m/2k ln⁡(1+(kv_0^2)/mg)

(d) None of the above

Ans: c

23. What is the velocity with which the body comes down ?

(a) v_0/((1+(kv_0^2)/mg) )

(b) v_0/(1+(kv_0^2)/mg)^(1/2)

(c ) v_0/(1+(kv_0^2)/mg)^(1/3)

(d) None of the above

Ans: b

24. The velocity of a particle moving in the positive direction of x-axis is given by v=α√x where α is a positive constant. The acceleration of the particle will be

(a) α^2

(b) α^2/2

(c ) 2α^2

(d) α^(3/2)

Ans: b

25. a planet moves round the Sun in a circular orbit. The angular velocity of planet will be proportional to

(a) velocity of planet

(b) square of velocity of planet

(c ) cube of velocity of planet

(d) None of the above

Ans: c

26. A wave is represented by y(x,t)=y_m sin⁡〖(kx-ωt-φ).〗 The phase of the wave is

(a) φ

(b) kx-ωt

(c ) ωt+φ

(d) kx-ωt-φ

Ans: d

27. Consider the following statements in respect of a plane progressive wave :

1. All the particles of the medium vibrate in same phase at any instant of time.

2. All the particles of the medium execute simple harmonic motion.

3. The wave velocity depends upon the nature of the medium.

Which of the above statements are correct ?

(a) 1 and 2 only

(b) 2 and 3 only

(c ) 1 and 3 only

(d) 1, 2 and 3

Ans: b

28. Electric charges A and B attract each other. Electric charges B and C also attract each other. But electric charges C and D repel each other. If A and D are held close together then which one of the following is correct ?

(a) They cannot affect each other

(b) They attract each other

(c ) They repel each other

(d) Cannot be predicted due to insufficient data

Ans: c

29. Two small charged spheres contain charges +q and +Q. Some charge is removed from the sphere carrying charge q and is transferred to the other. The charge on each sphere which will result in maximum force between them is

(a) √qQ

(b) ((q+Q))/2

(c ) ((q-Q))/2

(d) None of the above

Ans: b

30. Permanent magnets are those substances that

(a) retain their ferromagnetic property for a long time at room temperature

(b) retain their ferromagnetic property for a long time at all temperatures

(c ) have high permeability and low retentivity at room temperature

(d) high coercivity and low retentivity at room temperature

For the next 03 (three) items at follow:

A non –conducting disc of radius r and uniform positive surface charge density σ is palced on the ground, with its axis vertical. A particle of mass m and charge q is dropped along the axis of the disc from a height h with zero initial velocity. The ratio of charge to mass of the particle is given by q/m=(4∈_0 g)/σ .

Ans: a

31. What is the value of h if the particle just reaches the disc ?

(a) 4r/3

(b) 2r

(c ) 3r/2

(d) None of the above

Ans: a

32. At what position z (from the ground) will the particle attain equilibrium position ?

(a) z=r/2

(b) z=r/√3

(c ) z=r/√2

(d) None of the above

Ans: b

33. What is the minimum potential energy of the particle ?

(a) mgr

(b) √2 mgr

(c ) √3 mgr

(d) None of the above

Ans; c

For the next 02 (two ) items that follow :

A prism of refractive index n and another prism of refractive index m are stuck together without a gap as shown in the figure. The angles of the prisms are as shown. Refractive indices n and m depend on wavelength λ as follows :

n=1.20 +(10.8×〖10〗^4)/λ^2 and

m=1.45 +(1.80×〖10〗^4)/λ^2

Where λ is in nanometer.

34. What is the wavelength λ_0 for which rays incident at an angle on the interface BC pass through without bending at the interface ?

(a) 500 nm

(b) 600 nm

(c ) 650 nm

(d) None of the above

Ans: b

35. For light of wavelength λ_0 what is the angle of incidence on the face AC such that the deviation produced by the combination of the prisms is minimum ?

(a) 〖30〗^0

(b) 〖45〗^0

(c ) sin^(-1)⁡〖 (3/4)〗

(d) None of the above

Ans: c

For the next 02 (two) items that follow:

A disc of mass m and radius R is connected to springs each with spring constant k as shown in the figure. The disc is rolling on a rough surface.

36. If v is the velocity at any instant, then what is the kinetic energy of disk at that instant ?

(a) (mv^2)/2

(b) (2mv^2)/3

(c ) (3mv^2)/4

(d) None of the above

Ans: c

37. What is the time period of oscillation of disc ?

(a) T=2π √(m/k)

(b) T=2π √(3m/10k)

(c ) T=2π √(7m/10k)

(d) None of the above

Ans: b

For the next 02 (two ) items that follow:

12 wires, each having resistance R are joined to form a skeleton cube as shown in the figure.

38. What is the current through wire BE ?

(a) 0

(b) i/3

(c ) i-i_1

(d) None of the above

Ans: a

39. What is the equivalent resistance between A and C ?

(a) R/6

(b) 2R/3

(c ) 3R/4

(d) None of the above

Ans: c

40. A resistor is in the shape of a truncated right circular cone as shown in the figure. The end radii are a and b, and the length is L. The specific resistance of the material is ρ. What is the resistance of the object ? [Assume that the taper is small, so that the current density is uniform across any cross-section ]

(a) ρL/ab

(b) ρL/πab

(c ) ρL/π(b^2-a^2 )

(d) ρL/2π(b^2-a^2 )

Ans: b

41. A battery of emf 3V and internal resistance 0.2Ω is being charged with a current of 5 A. What is the potential difference between the terminals of the battery ?

(a) 2V

(b) 3V

(c ) 3.5 V

(d) 4V

Ans: d

42. An equilateral triangle is made of wires each having a resistance of 1 Ω . Any two corners are connected to a cell of emf 2 V. The current drawn from the cell is equal to

(a) 0.66 A

(b) 2 A

(c ) 3 A

(d) 3.5 A

Ans: c

43. A ray of light incident at an angle θ on the first refracting surface of a prism having small angle A gets refracted out normally from the second surface. If n is the refractive index of the material of the prism, then

(a) θ=A/n

(b) θ=nA

(c ) θ=A/((2n) )

(d) θ=(n-1)A

Ans: b

44. Light travels from air to water, from water to glass and then again from glass to air. If x represents refractive index of water with respect to air , y represents refractive index of glass with respect to water and z represents refractive index of air with respect to glass, then which one of the following is correct ?

(a) xy=z

(b) yz=x

(c ) zx=y

(d) xyz=1

Ans: d

45. A fusion reactor when achieved will have which of the following advantages over fission reactor ?

1. Elimination of nuclear waste disposal and nuclear pollution problems

2. Relative ease of procurement of nuclear fuel

Select the correct answer using the code given below :

(a) 1 only

(b) 2 only

(c) Both 1 and 2

(d) Neither 1 nor 2

Ans: c

46. A Particle with a positive charge travelling in the x-direction enters a region with a uniform magnetic field □(□(→┬B=Bj))

1. The particle will move in circular path.

2. The kinetic energy of the particle will increase.

3. The particle path will be confined to x= constant plane.

Which of the above statements is/are correct ?

(a) 1 and 3

(b) 2 and 3

(c ) 1 only

(d) 2 only

Ans: c

47. To increase the range of an ammeter of resistance (r)n times, a shunt of resistance (s) is connected in parallel with the ammeter coil. What would be the appropriate value of s ?

(a) nr

(b) r/((n-1) )

(c ) r/n

(d) r/((n+1) )

Ans: b

48. Consider the following statements :

When no current flows through a conductor,

1. the average velocity of free electrons over a large period of time is zero.

2. the average of the velocities of all the free electrons at any instant is zero.

Which of the above statements is/are correct ?

(a) 1 only

(b) 2 only

(c ) Both 1 and 2

(d) Neither 1 nor 2

Ans: c

49. Given that the ground state energy (n=1) of the hydrogen atom is -13.6 eV. The energy difference between n=1 and n=2 states of He^+ is

(a) 13.6 eV

(b) 27.2 eV

(c ) 40.8 eV

(d) 54.4 eV

Ans: c

50. Consider the following statements in respect of stationary waves :

1. The energy flux per unit area is zero.

2. The energy density is same throughout.

Which of the above statements is/are correct ?

(a) 1 only

(b) 2 only

(c ) Both 1 and 2

(d) Neither 1 nor 2

Ans: c
Here is the list of few questions of Solved Question Paper of SCRA Set B exam which you are looking for .

1. What is the ratio of minimum wavelength of radiation emitted in Balmer series of hydrogen atom to maximum wavelength of the series ?

(a) 5 : 9

(b) 9 : 5

(c ) 1 : 4

(d) 4 : 1

Ans: a

2. An object X of mass m moving forward with velocity v along x-axis collides elastically with a stationary object Y of mass 2 m at the origin. After collision, the object X moves backward along x-axis. Given that the kinetic energy of the system is conserved, the speed of the object Y after collision is

(a) 2v/3

(b) v/3

(c ) v/2

(d) 3v/4

ANs: a

3. There is a linear current I going around a circular wire of radius (a) with centre at origin in the xy-plane. The magnetic field B at (0,0,z) in Cartesian coordinates is given by

(a) B=(μ_0 Ia^2)/(2(z^2+a^2 )^(3/2) )

(b) B=(μ_0 Iza)/(2(z^2+a^2 )^(3/2) )

(c ) B=(μ_0 Iz^2)/(2(z^2+a^2 )^(3/2) )

(d) B=(μ_0 Ia^2)/(2(z^2+a^2 )^(1/2) )

ANs: a

4. There are two long wires each parallel to z-axis, each carrying current I, are at (0 , 0) and the other at (a,b). The force on unit length of each wire is

(a) (μ_0 I^2)/2π(a^2+b^2 )

(b) (μ_0 I^2 (a+b))/2π(a^2+b^2 )

(c ) (μ_0 I^2)/(2π(a^2+b^2 )^(3/2) )

(d) (μ_0 I^2)/(2π(a^2+b^2 )^(1/2) )

Ans: d

5. In a fusion process, effectively 4 protons each of mass m_p each combine to form an alpha particle of mass M, two positrons each of mass m_e, some gamma rays and neutrinos. With c being speed of light, the energy released in the formation of one alpha particle is

(a) (4m_p-M+2m_e ) c^2

(b) (M-4m_p+2m_e ) c^2

(c ) (M-4m_p-2m_e ) c^2

(d) (4m_p-M-2m_e ) c^2

Ans: d

6. A piece of bar magnet of length L having pole strength m is held at an angle θ with a uniform magnetic field of strength H. The piece is then transversely cut into two equal pieces; one of the pieces is held in the same field in similar manner. The ratio of torque of the former to the latter piece of the bar magnet is

(a) 1 : 2

(b) 2 : 1

(c ) 1 : 4

(d) 4 : 1

Ans: b

7. The critical angle of incidence of a ray of light going from a medium A to another medium B is 〖30〗^0. If the velocity of light in the medium A is half the velocity of light in vacuum, then velocity of light in B is

(a) c/4

(b) c

(c ) (√3 c)/2

(d) c/(2√3)

Where c is the speed of light in vacuum.

Ans: b

8. A particle of mass m and charge q is thrown at velocity u in the x-direcion against uniform electric field E in the negative x-direction. The distance it will travel before coming to momentary rest is

(a) (mu^2)/qE

(b) (2mu^2)/qE

(c ) (mu^2)/2qE

(d) (mu^2)/4qE

Ans: c

9. The optical path of a monochromatic light is the same if it passes through 0.665 cm of glass or 0.750 cm of a liquid of refractive index 1.5. The refractive index of glass is

(a) 1.5

(b) 1.7

(c ) 1.2

(d) 1.6

Ans: b

10. The lateral displacement of light passing through a parallel plate of glass of thickness t with angle of incidence 〖60〗^0 and angle of refraction 〖45〗^0 is

(a) (√3-1)t (b)

(√3-1)t/2

(c ) (√3+1)t/2

(d) None of the above

Ans: b

11. A small bar starts sliding down on inclined plane making an angle α with the horizontal. The coefficient of friction μ depends on the distance x as μ=ax where a is a constant. The distance covered by the bar till it stops is

(a) ((tan⁡α ))/a

(b) 2(tan⁡α )/a

(c ) 2a tan⁡α

(d) tan⁡α/((2a) )

Ans: b

12. Which one of the following waves does not involve oscillations of particles of a medium ?

(a) Waves in a hanging spring

(b) Ripples on a water surface

(c ) A light wave

(d) Ultrasonic waves

Ans: c

13. A certain mass of a given gas of specific heat ratio 1 .5 is compressed such that its volume becomes one –fourth of original volume, first adiabatically and then isothermally. In both the cases the initial state of gas is the same. The ratio of the respective works in each compression respectively is approximately (ln⁡〖2=0.3) 〗

(a) 4

(b) 3

(c ) 2

(d) 1

Ans: b

14. Two plane mirrors form an angle of 〖120〗^0. The distance between the two images of a point source formed in them is 20 cm and the point source lies on the bisector of the angle formed by the mirrors. What would be the least distance of the point source form the line along which the mirrors would touch each other ?

(a) 10 cm

(b) 20/√3 cm

(c ) 10√2 cm

(d) None of the above

Ans: b

15. An astronomical telescope consists of an objective lens that forms at or very near to its principal focus an image of the object which is

(a) real, inverted and reduced

(b) real, inverted and magnified

(c ) virtual, erect and reduced

(d) real, erect and reduced

Ans: A

16. A particle in uniform circular motion can possess

(a) radial acceleration only

(b) tangential acceleration only

(c ) both radial and tangential acceleration

(d) neither radial nor tangential acceleration

Ans: a

17. A particle motion on a apace curve is governed by x=2sin⁡〖t ,y=3 cos⁡t 〗 and z=√5 sin⁡〖t.〗 The speed of the particle at any instant is

(a) 3√2 sin⁡t

(b) 3 √(cos⁡2t )

(c) 3√(sin⁡2t )

(d) independent of time

Ans: d

18. The frictional force on a rolling cylinder is proportional to

(a) the tangential force and directed perpendicular to the surfaces in contact

(b) the tangential force and directed parallel to the surfaces in contact

(c ) the normal force and directed parallel to the surfaces in contact

(d) the normal force and directed perpendicular to the surfaces in contact

Ans: b

19. The kinetic energy (T) of a particle moving along a circle of radius R depends on the distance covered (s) as T=cs^2 where c is a constant. The force acting on the particle as a function of s is

(a) ks√(1+s/R)

(b) ks√(1+(s/R)^2 )

(c ) ks√(1+(s/R)^3 )

(d) ks√(1+(s/R)^4 )

Where k is a constant.

Ans: b

20. A point mass moves along x-axis according to the law x=A cos^2 (ωt-π/4) . The amplitude of the oscillation is

(a) A

(b) A/2

(c ) 2A

(d) A/3

Ans: b

21. A pendulum consisting of a small sphere of mass m, suspended by an inextensible and massless string of length L is made to swing in a vertical plane. If the breaking strength of the string is 2 mg where g is the acceleration due to gravity, then the maximum angular amplitude of the displacement from the vertical can be

(a) 〖15〗^0

(b) 〖30〗^0

(c ) 〖60〗^0

(d) 〖75〗^0

Ans: c

For the next 02 (two ) items that follow:

A body of mass m is thrown up with velocity v_0. The air drag is equal to kv^2 where v is the velocity at any instant and k is a positive constant (proportionally constant) .

22. The maximum height to which the body can go is

(a) m/2k (1+(kv_0^2)/mg)

(b) m/k ln⁡〖 (1+(kv_0^2)/mg)〗

(c ) m/2k ln⁡(1+(kv_0^2)/mg)

(d) None of the above

Ans: c

23. What is the velocity with which the body comes down ?

(a) v_0/((1+(kv_0^2)/mg) )

(b) v_0/(1+(kv_0^2)/mg)^(1/2)

(c ) v_0/(1+(kv_0^2)/mg)^(1/3)

(d) None of the above

Ans: b

24. The velocity of a particle moving in the positive direction of x-axis is given by v=α√x where α is a positive constant. The acceleration of the particle will be

(a) α^2

(b) α^2/2

(c ) 2α^2

(d) α^(3/2)

Ans: b

25. a planet moves round the Sun in a circular orbit. The angular velocity of planet will be proportional to

(a) velocity of planet

(b) square of velocity of planet

(c ) cube of velocity of planet

(d) None of the above

Ans: c

26. A wave is represented by y(x,t)=y_m sin⁡〖(kx-ωt-φ).〗 The phase of the wave is

(a) φ

(b) kx-ωt

(c ) ωt+φ

(d) kx-ωt-φ

Ans: d

27. Consider the following statements in respect of a plane progressive wave :

1. All the particles of the medium vibrate in same phase at any instant of time.

2. All the particles of the medium execute simple harmonic motion.

3. The wave velocity depends upon the nature of the medium.

Which of the above statements are correct ?

(a) 1 and 2 only

(b) 2 and 3 only

(c ) 1 and 3 only

(d) 1, 2 and 3

Ans: b

28. Electric charges A and B attract each other. Electric charges B and C also attract each other. But electric charges C and D repel each other. If A and D are held close together then which one of the following is correct ?

(a) They cannot affect each other

(b) They attract each other

(c ) They repel each other

(d) Cannot be predicted due to insufficient data

Ans: c

29. Two small charged spheres contain charges +q and +Q. Some charge is removed from the sphere carrying charge q and is transferred to the other. The charge on each sphere which will result in maximum force between them is

(a) √qQ

(b) ((q+Q))/2

(c ) ((q-Q))/2

(d) None of the above

Ans: b

30. Permanent magnets are those substances that

(a) retain their ferromagnetic property for a long time at room temperature

(b) retain their ferromagnetic property for a long time at all temperatures

(c ) have high permeability and low retentivity at room temperature

(d) high coercivity and low retentivity at room temperature

For the next 03 (three) items at follow:

A non –conducting disc of radius r and uniform positive surface charge density σ is palced on the ground, with its axis vertical. A particle of mass m and charge q is dropped along the axis of the disc from a height h with zero initial velocity. The ratio of charge to mass of the particle is given by q/m=(4∈_0 g)/σ .

Ans: a

31. What is the value of h if the particle just reaches the disc ?

(a) 4r/3

(b) 2r

(c ) 3r/2

(d) None of the above

Ans: a

32. At what position z (from the ground) will the particle attain equilibrium position ?

(a) z=r/2

(b) z=r/√3

(c ) z=r/√2

(d) None of the above

Ans: b

33. What is the minimum potential energy of the particle ?

(a) mgr

(b) √2 mgr

(c ) √3 mgr

(d) None of the above

Ans; c

For the next 02 (two ) items that follow :

A prism of refractive index n and another prism of refractive index m are stuck together without a gap as shown in the figure. The angles of the prisms are as shown. Refractive indices n and m depend on wavelength λ as follows :

n=1.20 +(10.8×〖10〗^4)/λ^2 and

m=1.45 +(1.80×〖10〗^4)/λ^2

Where λ is in nanometer.

34. What is the wavelength λ_0 for which rays incident at an angle on the interface BC pass through without bending at the interface ?

(a) 500 nm

(b) 600 nm

(c ) 650 nm

(d) None of the above

Ans: b

35. For light of wavelength λ_0 what is the angle of incidence on the face AC such that the deviation produced by the combination of the prisms is minimum ?

(a) 〖30〗^0

(b) 〖45〗^0

(c ) sin^(-1)⁡〖 (3/4)〗

(d) None of the above

Ans: c

For the next 02 (two) items that follow:

A disc of mass m and radius R is connected to springs each with spring constant k as shown in the figure. The disc is rolling on a rough surface.

36. If v is the velocity at any instant, then what is the kinetic energy of disk at that instant ?

(a) (mv^2)/2

(b) (2mv^2)/3

(c ) (3mv^2)/4

(d) None of the above

Ans: c

37. What is the time period of oscillation of disc ?

(a) T=2π √(m/k)

(b) T=2π √(3m/10k)

(c ) T=2π √(7m/10k)

(d) None of the above

Ans: b

For the next 02 (two ) items that follow:

12 wires, each having resistance R are joined to form a skeleton cube as shown in the figure.

38. What is the current through wire BE ?

(a) 0

(b) i/3

(c ) i-i_1

(d) None of the above

Ans: a

39. What is the equivalent resistance between A and C ?

(a) R/6

(b) 2R/3

(c ) 3R/4

(d) None of the above

Ans: c

40. A resistor is in the shape of a truncated right circular cone as shown in the figure. The end radii are a and b, and the length is L. The specific resistance of the material is ρ. What is the resistance of the object ? [Assume that the taper is small, so that the current density is uniform across any cross-section ]

(a) ρL/ab

(b) ρL/πab

(c ) ρL/π(b^2-a^2 )

(d) ρL/2π(b^2-a^2 )

Ans: b

41. A battery of emf 3V and internal resistance 0.2Ω is being charged with a current of 5 A. What is the potential difference between the terminals of the battery ?

(a) 2V

(b) 3V

(c ) 3.5 V

(d) 4V

Ans: d

42. An equilateral triangle is made of wires each having a resistance of 1 Ω . Any two corners are connected to a cell of emf 2 V. The current drawn from the cell is equal to

(a) 0.66 A

(b) 2 A

(c ) 3 A

(d) 3.5 A

Ans: c

43. A ray of light incident at an angle θ on the first refracting surface of a prism having small angle A gets refracted out normally from the second surface. If n is the refractive index of the material of the prism, then

(a) θ=A/n

(b) θ=nA

(c ) θ=A/((2n) )

(d) θ=(n-1)A

Ans: b

44. Light travels from air to water, from water to glass and then again from glass to air. If x represents refractive index of water with respect to air , y represents refractive index of glass with respect to water and z represents refractive index of air with respect to glass, then which one of the following is correct ?

(a) xy=z

(b) yz=x

(c ) zx=y

(d) xyz=1

Ans: d

45. A fusion reactor when achieved will have which of the following advantages over fission reactor ?

1. Elimination of nuclear waste disposal and nuclear pollution problems

2. Relative ease of procurement of nuclear fuel

Select the correct answer using the code given below :

(a) 1 only

(b) 2 only

(c) Both 1 and 2

(d) Neither 1 nor 2

Ans: c

46. A Particle with a positive charge travelling in the x-direction enters a region with a uniform magnetic field □(□(→┬B=Bj))

1. The particle will move in circular path.

2. The kinetic energy of the particle will increase.

3. The particle path will be confined to x= constant plane.

Which of the above statements is/are correct ?

(a) 1 and 3

(b) 2 and 3

(c ) 1 only

(d) 2 only

Ans: c

47. To increase the range of an ammeter of resistance (r)n times, a shunt of resistance (s) is connected in parallel with the ammeter coil. What would be the appropriate value of s ?

(a) nr

(b) r/((n-1) )

(c ) r/n

(d) r/((n+1) )

Ans: b

48. Consider the following statements :

When no current flows through a conductor,

1. the average velocity of free electrons over a large period of time is zero.

2. the average of the velocities of all the free electrons at any instant is zero.

Which of the above statements is/are correct ?

(a) 1 only

(b) 2 only

(c ) Both 1 and 2

(d) Neither 1 nor 2

Ans: c

49. Given that the ground state energy (n=1) of the hydrogen atom is -13.6 eV. The energy difference between n=1 and n=2 states of He^+ is

(a) 13.6 eV

(b) 27.2 eV

(c ) 40.8 eV

(d) 54.4 eV

Ans: c

50. Consider the following statements in respect of stationary waves :

1. The energy flux per unit area is zero.

2. The energy density is same throughout.

Which of the above statements is/are correct ?

(a) 1 only

(b) 2 only

(c ) Both 1 and 2

(d) Neither 1 nor 2

Ans: c