Q1. A ray is incident at an angle of incidence i on one surface of a small angle prism (with angle of prism A) and emerges normally from the opposite surface. If the refractive index of the material of the prism is μ, then the angle of incidence is nearly equal to:
(1) A/2μ
(2) 2A/μ
(3) μA
(4) μA/2
Answer: (3)
Explanation: The angle of incidence is μA.
Q2. Two cylinders A and B of equal capacity are connected to each other via a stopcock. A contains an ideal gas at standard temperature and pressure. B is completely evacuated. The entire system is thermally insulated. The stopcock is suddenly opened. The process is:
(1) Isothermal
(2) Adiabatic
(3) Isochoric
(4) Isobaric
Answer: (2)
Explanation: The process is adiabatic.
Q3. The energy equivalent of 0.5 g of a substance is:
(1) 4.5 × 10¹⁶ J
(2) 4.5 × 10¹³ J
(3) 1.5 × 10¹³ J
(4) 0.5 × 10¹³ J
Answer: (2)
Explanation: The energy equivalent is 4.5 × 10¹³ J.
Q4. A body weighs 72 N on the surface of the earth. What is the gravitational force on it, at a height equal to half the radius of the earth?
(1) 48 N
(2) 32 N
(3) 30 N
(4) 24 N
Answer: (2)
Explanation: The gravitational force is 32 N.
Q5. The solids which have the negative temperature coefficient of resistance are:
(1) Metals
(2) Insulators only
(3) Semiconductors only
(4) Insulators and semiconductors
Answer: (4)
Explanation: Insulators and semiconductors have a negative temperature coefficient of resistance.
Q6. The phase difference between displacement and acceleration of a particle in a simple harmonic motion is:
(1) π rad
(2) 3π/2 rad
(3) π/2 rad
(4) Zero
Answer: (1)
Explanation: The phase difference is π radians.
Q7. A screw gauge has a least count of 0.01 mm and there are 50 divisions in its circular scale. The pitch of the screw gauge is:
(1) 0.01 mm
(2) 0.25 mm
(3) 0.5 mm
(4) 1.0 mm
Answer: (3)
Explanation: The pitch is 0.5 mm.
Q8. In a guitar, two strings A and B made of the same material are slightly out of tune and produce beats of frequency 6 Hz. When tension in B is slightly decreased, the beat frequency increases to 7 Hz. If the frequency of A is 530 Hz, the original frequency of B will be:
(1) 523 Hz
(2) 524 Hz
(3) 536 Hz
(4) 537 Hz
Answer: (2)
Explanation: The original frequency of B is 524 Hz.
Q9. Two particles of mass 5 kg and 10 kg respectively are attached to the two ends of a rigid rod of length 1 m with negligible mass. The centre of mass of the system from the 5 kg particle is nearly at a distance of:
(1) 33 cm
(2) 50 cm
(3) 67 cm
(4) 80 cm
Answer: (3)
Explanation: The center of mass is at 67 cm from the 5 kg particle.
Q10. Find the torque about the origin when a force of 3j N acts on a particle whose position vector is 2k m:
(1) 6i Nm
(2) 6j Nm
(3) -6i Nm
(4) 6k Nm
Answer: (3)
Explanation: The torque is -6i Nm.
Q11. Light with an average flux of 20 W/cm² falls on a non-reflecting surface at normal incidence having a surface area of 20 cm². The energy received by the surface during a time span of 1 minute is:
(1) 10 × 10³ J
(2) 12 × 10³ J
(3) 24 × 10³ J
(4) 48 × 10³ J
Answer: (3)
Explanation: The energy received is 24 × 10³ J.
Q12. A spherical conductor of radius 10 cm has a charge of 3.2 × 10⁻⁷ C distributed uniformly. What is the magnitude of the electric field at a point 15 cm from the centre of the sphere?
(1) 1.28 × 10⁴ N/C
(2) 1.28 × 10⁵ N/C
(3) 1.28 × 10⁶ N/C
(4) 1.28 × 10⁷ N/C
Answer: (2)
Explanation: The electric field is 1.28 × 10⁵ N/C.
Q13. In a certain region of space with volume 0.2 m³, the electric potential is found to be 5 V throughout. The magnitude of the electric field in this region is:
(1) Zero
(2) 0.5 N/C
(3) 1 N/C
(4) 5 N/C
Answer: (1)
Explanation: The electric field is zero.
Q14. The increase in the width of the depletion region in a p-n junction diode is due to:
(1) Forward bias only
(2) Reverse bias only
(3) Both forward bias and reverse bias
(4) Increase in forward current
Answer: (2)
Explanation: The width increases due to reverse bias.
Q15. A 40 μF capacitor is connected to a 200 V, 50 Hz AC supply. The rms value of the current in the circuit is, nearly:
(1) 1.7 A
(2) 2.05 A
(3) 2.5 A
(4) 25.1 A
Answer: (3)
Explanation: The rms current is 2.5 A.
Q16. The mean free path for a gas, with molecular diameter d and number density n can be expressed as:
(1) 1/√2 nπd
(2) 1/√2 nπd²
(3) 1/√2 n²πd²
(4) 1/√2 n²π²d²
Answer: (2)
Explanation: The mean free path is 1/√2 nπd².
Q17. For transistor action, which of the following statements is correct?
(1) Base, emitter, and collector regions should have the same doping concentrations.
(2) Base, emitter, and collector regions should have the same size.
(3) Both emitter junction as well as the collector junction are forward biased.
(4) The base region must be very thin and lightly doped.
Answer: (4)
Explanation: The base region must be very thin and lightly doped.
Q18. Light of frequency 1.5 times the threshold frequency is incident on a photosensitive material. What will be the photoelectric current if the frequency is halved and intensity is doubled?
(1) Doubled
(2) Four times
(3) One-fourth
(4) Zero
Answer: (4)
Explanation: No photoelectric current will be produced.
Q19. When a uranium isotope ²³⁵U is bombarded with a neutron, it generates ⁸⁹Kr, three neutrons, and:
(1) ¹⁴⁴Ba
(2) ⁹¹Zr
(3) ¹⁰¹Kr
(4) ¹⁰³Kr
Answer: (1)
Explanation: The product is ¹⁴⁴Ba.
Q20. The energy required to break one bond in DNA is 10⁻²⁰ J. This value in eV is nearly:
(1) 6
(2) 0.6
(3) 0.06
(4) 0.006
Answer: (3)
Explanation: The energy is 0.06 eV.
Q21. Two bodies of mass 4 kg and 6 kg are tied to the ends of a massless string. The string passes over a pulley which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity (g) is:
(1) g
(2) g/2
(3) g/5
(4) g/10
Answer: (3)
Explanation: The acceleration is g/5.
Q22. A wire of length L, area of cross-section A is hanging from a fixed support. The length of the wire changes to L₁ when mass M is suspended from its free end. The expression for Young’s modulus is:
(1) MgL₁/AL
(2) Mg(L₁ - L)/AL
(3) MgL/AL₁
(4) MgL/A(L₁ - L)
Answer: (4)
Explanation: Young’s modulus is MgL/A(L₁ - L).
Q23. The average thermal energy for a mono-atomic gas is:
(k_B is Boltzmann constant and T, absolute temperature)
(1) 1/2 k_B T
(2) 3/2 k_B T
(3) 5/2 k_B T
(4) 7/2 k_B T
Answer: (2)
Explanation: The average thermal energy is 3/2 k_B T.
Q24. The values of resistance and tolerance, respectively, are:
(1) 470 kΩ, 5%
(2) 47 kΩ, 10%
(3) 4.7 kΩ, 5%
(4) 470 Ω, 5%
Answer: (4)
Explanation: The resistance is 470 Ω with a tolerance of 5%.
Q25. In Young’s double slit experiment, if the separation between coherent sources is halved and the distance of the screen from the coherent sources is doubled, then the fringe width becomes:
(1) Double
(2) Half
(3) Four times
(4) One-fourth
Answer: (3)
Explanation: The fringe width becomes four times.
Q26. The capacitance of a parallel plate capacitor with air as medium is 6 μF. With the introduction of a dielectric medium, the capacitance becomes 30 μF. The permittivity of the medium is:
(ε₀ = 8.85 × 10⁻¹² C² N⁻¹ m⁻²)
(1) 0.44 × 10⁻¹³ C² N⁻¹ m⁻²
(2) 1.77 × 10⁻¹² C² N⁻¹ m⁻²
(3) 0.44 × 10⁻¹⁰ C² N⁻¹ m⁻²
(4) 5.00 C² N⁻¹ m⁻²
Answer: (3)
Explanation: The permittivity is 0.44 × 10⁻¹⁰ C² N⁻¹ m⁻².
Q27. Dimensions of stress are:
(1) [MLT⁻²]
(2) [ML²T⁻²]
(3) [ML⁰T⁻²]
(4) [ML⁻¹T⁻²]
Answer: (4)
Explanation: The dimensions of stress are [ML⁻¹T⁻²].
Q28. Assume that light of wavelength 600 nm is coming from a star. The limit of resolution of a telescope whose objective has a diameter of 2 m is:
(1) 3.66 × 10⁻⁷ rad
(2) 1.83 × 10⁻⁷ rad
(3) 7.32 × 10⁻⁷ rad
(4) 6.00 × 10⁻⁷ rad
Answer: (1)
Explanation: The limit of resolution is 3.66 × 10⁻⁷ rad.
Q29. A series LCR circuit is connected to an AC voltage source. When L is removed from the circuit, the phase difference between current and voltage is π/3. If instead C is removed from the circuit, the phase difference is again π/3 between current and voltage. The power factor of the circuit is:
(1) Zero
(2) 0.5
(3) 1.0
(4) -1.0
Answer: (3)
Explanation: The power factor is 1.0.
Q30. A short electric dipole has a dipole moment of 16 × 10⁻⁹ C m. The electric potential due to the dipole at a point at a distance of 0.6 m from the centre of the dipole, situated on a line making an angle of 60° with the dipole axis is:
(1) 50 V
(2) 200 V
(3) 400 V
(4) Zero
Answer: (2)
Explanation: The electric potential is 200 V.
Q31. An iron rod of susceptibility 599 is subjected to a magnetising field of 1200 A m⁻¹. The permeability of the material of the rod is:
(μ₀ = 4π × 10⁻⁷ T m A⁻¹)
(1) 2.4π × 10⁻⁴ T m A⁻¹
(2) 8.0 × 10⁻⁵ T m A⁻¹
(3) 2.4π × 10⁻⁵ T m A⁻¹
(4) 2.4π × 10⁻⁷ T m A⁻¹
Answer: (1)
Explanation: The permeability is 2.4π × 10⁻⁴ T m A⁻¹.
Q32. A long solenoid of 50 cm length having 100 turns carries a current of 2.5 A. The magnetic field at the centre of the solenoid is:
(μ₀ = 4π × 10⁻⁷ T m A⁻¹)
(1) 6.28 × 10⁻⁴ T
(2) 3.14 × 10⁻⁴ T
(3) 6.28 × 10⁻⁵ T
(4) 3.14 × 10⁻⁵ T
Answer: (1)
Explanation: The magnetic field is 6.28 × 10⁻⁴ T.
Q33. A charged particle having a drift velocity of 7.5 × 10⁻⁴ m s⁻¹ in an electric field of 3 × 10⁻¹⁰ V m⁻¹, has a mobility in m² V⁻¹ s⁻¹ of:
(1) 2.25 × 10¹⁵
(2) 2.5 × 10⁶
(3) 2.5 × 10⁻⁶
(4) 2.25 × 10⁻¹⁵
Answer: (2)
Explanation: The mobility is 2.5 × 10⁶ m² V⁻¹ s⁻¹.
Q34. The quantities of heat required to raise the temperature of two solid copper spheres of radii r₁ and r₂ (r₁ = 1.5 r₂) through 1 K are in the ratio:
(1) 27/8
(2) 9/4
(3) 3/2
(4) 5/3
Answer: (1)
Explanation: The ratio is 27/8.
Q35.An electron is accelerated from rest through a potential difference of V volt. If the de Broglie wavelength of the electron is 1.227 × 10⁻² nm, the potential difference is:
(1) 10 V
(2) 10² V
(3) 10³ V
(4) 10⁴ V
Answer: (4)
Explanation: The potential difference is 10⁴ V.
Q38. Taking into account of the significant figures, what is the value of 9.99 m - 0.0099 m?
(1) 9.9801 m
(2) 9.98 m
(3) 9.980 m
(4) 9.9 m
Answer: (2)
Explanation: The value is 9.98 m.
Q39. A ball is thrown vertically downward with a velocity of 20 m/s from the top of a tower. It hits the ground after some time with a velocity of 80 m/s. The height of the tower is:
(g = 10 m/s²)
(1) 360 m
(2) 340 m
(3) 320 m
(4) 300 m
Answer: (4)
Explanation: The height of the tower is 300 m.
Q40. A capillary tube of radius r is immersed in water and water rises in it to a height h. The mass of the water in the capillary is 5 g. Another capillary tube of radius 2r is immersed in water. The mass of water that will rise in this tube is:
(1) 2.5 g
(2) 5.0 g
(3) 10.0 g
(4) 20.0 g
Answer: (3)
Explanation: The mass of water is 10.0 g.
Q41. A resistance wire connected in the left gap of a metre bridge balances a 10 Ω resistance in the right gap at a point which divides the bridge wire in the ratio 3:2. If the length of the resistance wire is 1.5 m, then the length of 1 Ω of the resistance wire is:
(1) 1.0 × 10⁻² m
(2) 1.0 × 10⁻¹ m
(3) 1.5 × 10⁻¹ m
(4) 1.5 × 10⁻² m
Answer: (2)
Explanation: The length is 1.0 × 10⁻¹ m.
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