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/(4πε₀) = 9 × 10⁹ N m²/C²)
a.
(1) 400 V
b.
(2) zero
c.
(3) 50 V
d.
(4) 200 V
Correct Answer
Step-by-Step AI Explanation
Verified Method
The formula for electric potential due to a dipole is V = (kp cosθ) / r². Using k = 9 × 10⁹, p = 16 × 10⁻⁹, cos(60°) = 0.5, and r = 0.6: V = (9 × 10⁹ × 16 × 10⁻⁹ × 0.5) / (0.6 × 0.6) = 72 / 0.36 = 200 V.
Q92mcq
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:
a.
(1) 1.0
Correct Answer
b.
(2) -1.0
c.
(3) zero
d.
(4) 0.5
Step-by-Step AI Explanation
Verified Method
When L is removed, tan(π/3) = Xc/R = √3. When C is removed, tan(π/3) = XL/R = √3. Thus XL = Xc. The circuit is at resonance, so phase difference is 0 and power factor cos(0) = 1.0.
Q93mcq
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?
a.
(1) one-fourth
b.
(2) zero
Correct Answer
c.
(3) doubled
d.
(4) four times
Step-by-Step AI Explanation
Verified Method
Threshold frequency (ν₀) is 1.5ν₀. If the new frequency is halved, the new frequency is 0.75ν₀, which is less than the threshold frequency. No emission occurs, so the current is zero.
Q94mcq
Dimensions of stress are:
a.
(1) [ML⁰T⁻²]
b.
(2) [ML⁻¹T⁻²]
Correct Answer
c.
(3) [MLT⁻²]
d.
(4) [ML²T⁻²]
Step-by-Step AI Explanation
Verified Method
Stress = Force / Area. Force is [MLT⁻²] and Area is [L²]. Thus, stress = [MLT⁻²] / [L²] = [ML⁻¹T⁻²].
Q95mcq
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:
a.
(1) 10³ V
b.
(2) 10⁴ V
Correct Answer
c.
(3) 10 V
d.
(4) 10² V
Step-by-Step AI Explanation
Verified Method
The formula for de Broglie wavelength is λ = 1.227/√V nm. Given λ = 1.227 × 10⁻² nm, then 10⁻² = 1/√V, which means √V = 100, so V = 10⁴ V.
Q96mcq
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)
The solids which have the negative temperature coefficient of resistance are:
a.
(1) semiconductors only
b.
(2) insulators and semiconductors
Correct Answer
c.
(3) metals
d.
(4) insulators only
Step-by-Step AI Explanation
Verified Method
Materials that show a decrease in resistivity with an increase in temperature, such as semiconductors and insulators, have a negative temperature coefficient of resistance.
Q98mcq
For transistor action, which of the following statements is correct?
a.
(1) Both emitter junction as well as the collector junction are forward biased.
b.
(2) The base region must be very thin and lightly doped.
Correct Answer
c.
(3) Base, emitter and collector regions should have same doping concentrations.
d.
(4) Base, emitter and collector regions should have same size.
Step-by-Step AI Explanation
Verified Method
For effective transistor action, the base is designed to be very thin and lightly doped so that most of the charge carriers from the emitter pass through it to the collector.
Q99mcq
A screw gauge has least count of 0.01 mm and there are 50 divisions in its circular scale. The pitch of the screw gauge is :
a.
0.5 mm
Correct Answer
b.
1.0 mm
c.
0.01 mm
d.
0.25 mm
Step-by-Step AI Explanation
Verified Method
Pitch = Least Count × Total circular scale divisions = 0.01 mm × 50 = 0.5 mm.
Q99mcq
A screw gauge has least count of 0.01 mm and there are 50 divisions in its circular scale. The pitch of the screw gauge is:
a.
(1) 0.5 mm
Correct Answer
b.
(2) 1.0 mm
c.
(3) 0.01 mm
d.
(4) 0.25 mm
Step-by-Step AI Explanation
Verified Method
Least Count = Pitch / Number of circular scale divisions. Pitch = Least Count × Circular scale divisions = 0.01 mm × 50 = 0.5 mm.
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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)
a.
6.28 × 10⁻⁵ T
b.
3.14 × 10⁻⁵ T
c.
6.28 × 10⁻⁴ T
d.
3.14 × 10⁻⁴ T
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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)
a.
(1) 6.28 × 10⁻⁵ T
b.
(2) 3.14 × 10⁻⁵ T
c.
(3) 6.28 × 10⁻⁴ T
d.
(4) 3.14 × 10⁻⁴ T
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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)
a.
(1) 320 m
b.
(2) 300 m
c.
(3) 360 m
d.
(4) 340 m
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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)
a.
320 m
b.
300 m
c.
360 m
d.
340 m
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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 :
a.
μA
b.
A/2μ
c.
A/2μ
d.
2A/μ
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Two cylinders A and B of equal capacity are connected to each other via a stop cock. A contains an ideal gas at standard temperature and pressure. B is completely evacuated. The entire system is thermally insulated. The stop cock is suddenly opened. The process is :
a.
isochoric
b.
isobaric
c.
isothermal
d.
adiabatic
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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. The acceleration of the system in terms of acceleration due to gravity (g) is :
a.
g/5
b.
g/10
c.
g
d.
g/2
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In a certain region of space with volume 0.2 m³, the electric potential is found to be 5 V throughout. The magnitude of electric field in this region is :
a.
1 N/C
b.
5 N/C
c.
zero
d.
0.5 N/C
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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 :
a.
MgL/AL1
b.
MgL / (A(L1-L))
c.
MgL/AL1
d.
Mg(L1-L)/AL
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A spherical conductor of radius 10 cm has a charge of 3.2 × 10⁻⁷ C distributed uniformly. What is the magnitude of electric field at a point 15 cm from the centre of the sphere?
a.
1.28 × 10⁶ N/C
b.
1.28 × 10⁷ N/C
c.
1.28 × 10⁴ N/C
d.
1.28 × 10⁵ N/C
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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 :
a.
four times
b.
one-fourth
c.
double
d.
half
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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 :
a.
four times
b.
one-fourth
c.
double
d.
half
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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 :
a.
10.0 g
b.
20.0 g
c.
2.5 g
d.
5.0 g
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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 :
a.
10.0 g
b.
20.0 g
c.
2.5 g
d.
5.0 g
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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 x 10^-7 T m A^-1)
a.
2.4π x 10^-5 T m A^-1
b.
2.4π x 10^-7 T m A^-1
c.
2.4π x 10^-4 T m A^-1
d.
8.0 x 10^-5 T m A^-1
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Light with an average flux of 20 W/cm^2 falls on a non-reflecting surface at normal incidence having surface area 20 cm^2. The energy received by the surface during time span of 1 minute is :
a.
24 x 10^3 J
b.
48 x 10^3 J
c.
10 x 10^3 J
d.
12 x 10^3 J
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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 :
a.
1.5 x 10^-1 m
b.
1.5 x 10^-2 m
c.
1.0 x 10^-2 m
d.
1.0 x 10^-1 m
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In a guitar, two strings A and B made of 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:
a.
536 Hz
b.
537 Hz
c.
523 Hz
d.
524 Hz
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In a guitar, two strings A and B made of 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:
a.
536 Hz
b.
537 Hz
c.
523 Hz
d.
524 Hz
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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 :
a.
67 cm
b.
80 cm
c.
33 cm
d.
50 cm
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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 :
a.
67 cm
b.
80 cm
c.
33 cm
d.
50 cm
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