A short electric dipole has a dipole moment of 16 x 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 degrees with the dipole axis is (Given: 1/(4πε₀) = 9 x 10^9 N m²/C²):
a.
400 V
b.
zero
c.
50 V
d.
200 V
Correct Answer
Step-by-Step AI Explanation
Verified Method
Potential V = (kp cosθ) / r². Substituting values: V = (9x10^9 * 16x10^-9 * cos 60) / (0.6)^2 = (9 * 16 * 0.5) / 0.36 = 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.
1.0
b.
-1.0
c.
zero
d.
0.5
Correct Answer
Step-by-Step AI Explanation
Verified Method
Given tan(π/3) = (Xc/R) and tan(π/3) = (Xl/R). At resonance, the circuit is purely resistive, so cos(0) = 1. However, since the phase shift is π/3 in both cases, the circuit at resonance has a power factor of cos(0) = 1, but for the given conditions the power factor at resonance is 1.
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.
one-fourth
b.
zero
Correct Answer
c.
doubled
d.
four times
Step-by-Step AI Explanation
Verified Method
Threshold frequency is f₀. Initial frequency is 1.5f₀. If frequency is halved, f_new = 0.75f₀. Since f_new < f₀, no photoelectric emission occurs.
Q94mcq
Dimensions of stress are :
a.
[ M L^0 T^-2 ]
b.
[ M L^-1 T^-2 ]
Correct Answer
c.
[ M L T^-2 ]
d.
[ M L^2 T^-2 ]
Step-by-Step AI Explanation
Verified Method
Stress = Force / Area = [MLT^-2] / [L^2] = [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 x 10^-2 nm, the potential difference is :
a.
10^3 V
b.
10^4 V
Correct Answer
c.
10 V
d.
10^2 V
Step-by-Step AI Explanation
Verified Method
λ = 1.227 / sqrt(V) nm. 1.227 x 10^-2 = 1.227 / sqrt(V). sqrt(V) = 100, so V = 10^4 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 x 10^-12 C² N^-1 m^-2):
a.
0.44 x 10^-10 C² N^-1 m^-2
Correct Answer
b.
5.00 C² N^-1 m^-2
c.
0.44 x 10^-13 C² N^-1 m^-2
d.
1.77 x 10^-12 C² N^-1 m^-2
Step-by-Step AI Explanation
Verified Method
Dielectric constant K = C_medium / C_air = 30 / 6 = 5. ε_medium = K * ε₀ = 5 * 8.85 x 10^-12 = 44.25 x 10^-12 = 0.44 x 10^-10 C² N^-1 m^-2.
Q97mcq
The solids which have the negative temperature coefficient of resistance are :
a.
semiconductors only
b.
insulators and semiconductors
Correct Answer
c.
metals
d.
insulators only
Step-by-Step AI Explanation
Verified Method
Materials with a negative temperature coefficient of resistance exhibit decreased resistance as temperature increases; this applies to both semiconductors and insulators.
Q98mcq
For transistor action, which of the following statements is correct?
a.
Both emitter junction as well as the collector junction are forward biased.
b.
The base region must be very thin and lightly doped.
Correct Answer
c.
Base, emitter and collector regions should have same doping concentrations.
d.
Base, emitter and collector regions should have same size.
Step-by-Step AI Explanation
Verified Method
For effective transistor operation, the base must be very thin and lightly doped to allow most charge carriers from the emitter to reach 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
Least Count = Pitch / Number of circular scale divisions. Pitch = Least Count * Number of divisions = 0.01 * 50 = 0.5 mm.
Q100mcq
The phase difference between displacement and acceleration of a particle in a simple harmonic motion is :
a.
π/2 rad
b.
zero
c.
π rad
Correct Answer
d.
3π/2 rad
Step-by-Step AI Explanation
Verified Method
Displacement x = A sin(ωt). Acceleration a = -ω² A sin(ωt) = ω² A sin(ωt + π). The phase difference is π.
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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 x 10^-7 T m A^-1):
a.
6.28 x 10^-5 T
b.
3.14 x 10^-5 T
c.
6.28 x 10^-4 T
d.
3.14 x 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.
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 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 / AL
d.
Mg(L1 - L) / AL
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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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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)
a.
2.4π×10^-5 T m A^-1
b.
2.4π×10^-7 T m A^-1
c.
2.4π×10^-4 T m A^-1
d.
8.0×10^-5 T m A^-1
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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 × 10^-7 T m A^-1)
a.
2.4π × 10^-5 T m A^-1
b.
2.4π × 10^-7 T m A^-1
c.
2.4π × 10^-4 T m A^-1
d.
8.0 × 10^-5 T m A^-1
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Light with an average flux of 20 W/cm2 falls on a non-reflecting surface at normal incidence having surface area 20 cm2. The energy received by the surface during time span of 1 minute is:
a.
24×10^3 J
b.
48×10^3 J
c.
10×10^3 J
d.
12×10^3 J
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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 × 10^3 J
b.
48 × 10^3 J
c.
10 × 10^3 J
d.
12 × 10^3 J
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The ratio of contributions made by the electric field and magnetic field components to the intensity of an electromagnetic wave is: (c = speed of electromagnetic waves)
a.
1 : c
b.
1 : c^2
c.
c : 1
d.
1 : 1
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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 × 10^-1 m
b.
1.5 × 10^-2 m
c.
1.0 × 10^-2 m
d.
1.0 × 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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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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