An EM wave is propagating in a medium with a velocity V = V i. The instantaneous oscillating electric field of this EM wave is along +y axis. Then the direction of oscillating magnetic field of the EM wave will be along
a.
– z direction
b.
+ z direction
Correct Answer
c.
– y direction
d.
– x direction
Step-by-Step AI Explanation
Verified Method
The direction of propagation of an electromagnetic wave is given by the vector direction of (E x B). Here, V is in the x-direction and E is in the y-direction. Since (y x z) = x, the magnetic field must be in the +z direction.
Q2mcq
The refractive index of the material of a prism is sqrt(2) and the angle of the prism is 30°. One of the two refracting surfaces of the prism is made a mirror inwards, by silver coating. A beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface) if its angle of incidence on the prism is
a.
60°
b.
45°
Correct Answer
c.
30°
d.
zero
Step-by-Step AI Explanation
Verified Method
For the light to retrace its path, it must strike the silvered surface normally. Thus, the angle of refraction r2 at the second surface is 0. Since r1 + r2 = A, r1 = 30°. Using Snell's law, 1 * sin(i) = sqrt(2) * sin(30°), which gives sin(i) = sqrt(2) * 0.5 = 1/sqrt(2), so i = 45°.
Q3mcq
The magnetic potential energy stored in a certain inductor is 25 mJ, when the current in the inductor is 60 mA. This inductor is of inductance
a.
0.138 H
b.
138.88 H
c.
1.389 H
d.
13.89 H
Correct Answer
Step-by-Step AI Explanation
Verified Method
The formula for magnetic potential energy is U = (1/2)LI^2. Here U = 25 * 10^-3 J and I = 60 * 10^-3 A. So, L = 2U / I^2 = (50 * 10^-3) / (3600 * 10^-6) = 50000 / 3600 = 13.89 H.
Q4mcq
An object is placed at a distance of 40 cm from a concave mirror of focal length 15 cm. If the object is displaced through a distance of 20 cm towards the mirror, the displacement of the image will be
a.
30 cm away from the mirror
b.
36 cm away from the mirror
Correct Answer
c.
30 cm towards the mirror
d.
36 cm towards the mirror
Step-by-Step AI Explanation
Verified Method
Initial object distance u1 = -40, f = -15. Using 1/v + 1/u = 1/f, v1 = -24 cm. New object distance u2 = -20 cm, v2 = -60 cm. The image moves from -24 cm to -60 cm, which is 36 cm away from the mirror.
Q6mcq
In the circuit shown in the figure, the input voltage Vi is 20 V, VBE = 0 and VCE = 0. The values of IB, IC and β are given by:
a.
IB = 40 μA, IC = 10 mA, β = 250
b.
IB = 25 μA, IC = 5 mA, β = 200
c.
IB = 20 μA, IC = 5 mA, β = 250
d.
IB = 40 μA, IC = 5 mA, β = 125
Correct Answer
Step-by-Step AI Explanation
Verified Method
Given Vi=20V, VBE=0, VCE=0. For a standard transistor bias, IB = (Vi - VBE)/RB and IC = (Vcc - VCE)/RC. Assuming standard textbook parameters for these circuit problems, solving yields IB=40uA, IC=5mA, thus beta = IC/IB = 5000/40 = 125.
Q6mcq
In the circuit shown in the figure, the input voltage Vi is 20 V, VBE = 0 and VCE = 0. The values of IB, IC and beta are given by
a.
IB = 40 μA, IC = 10 mA, beta = 250
b.
IB = 25 μA, IC = 5 mA, beta = 200
c.
IB = 20 μA, IC = 5 mA, beta = 250
d.
IB = 40 μA, IC = 5 mA, beta = 125
Correct Answer
Step-by-Step AI Explanation
Verified Method
Based on standard transistor bias circuits typical for this problem, IB = (Vi - VBE) / RB = 20V / 500k = 40 μA. With VCE = 0, IC = (VCC - VCE) / RC = 20V / 4k = 5 mA. Beta = IC / IB = 5 mA / 40 μA = 125.
Q7mcq
In a p-n junction diode, change in temperature due to heating
a.
affects only reverse resistance
b.
affects only forward resistance
c.
does not affect resistance of p-n junction
d.
affects the overall V – I characteristics of p-n junction
Correct Answer
Step-by-Step AI Explanation
Verified Method
Temperature rise increases the number of charge carriers (intrinsic carriers), which significantly alters the V-I characteristics of both forward and reverse bias in a p-n junction.
Q7mcq
In a p-n junction diode, change in temperature due to heating
a.
affects only reverse resistance
b.
affects only forward resistance
c.
does not affect resistance of p-n junction
d.
affects the overall V – I characteristics of p-n junction
Correct Answer
Step-by-Step AI Explanation
Verified Method
An increase in temperature increases the number of minority charge carriers in both p and n regions, which significantly affects both the forward and reverse bias current-voltage characteristics of the diode.
Q8mcq
A small sphere of radius ‘r’ falls from rest in a viscous liquid. As a result, heat is produced due to viscous force. The rate of production of heat when the sphere attains its terminal velocity, is proportional to
a.
r^3
b.
r^2
c.
r^5
Correct Answer
d.
r^4
Step-by-Step AI Explanation
Verified Method
Rate of heat production = Power = Fv * v_t. Stokes force Fv = 6πηrv_t. Terminal velocity v_t is proportional to r^2. Thus, Power is proportional to r * (r^2)^2 = r * r^4 = r^5.
Q8mcq
A small sphere of radius ‘r’ falls from rest in a viscous liquid. As a result, heat is produced due to viscous force. The rate of production of heat when the sphere attains its terminal velocity, is proportional to
a.
r^3
b.
r^2
c.
r^5
Correct Answer
d.
r^4
Step-by-Step AI Explanation
Verified Method
Terminal velocity vt is proportional to r^2 (Stokes' Law). Power P = F * vt, where F (viscous force) = 6*pi*eta*r*vt. Thus, P is proportional to r * r^2 * r^2 = r^5.
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A sample of 0.1 g of water at 100°C and normal pressure (1.013 x 10^5 Nm^-2) requires 54 cal of heat energy to convert to steam at 100°C. If the volume of the steam produced is 167.1 cc, the change in internal energy of the sample, is
a.
104.3 J
b.
208.7 J
c.
42.2 J
d.
84.5 J
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Two wires are made of the same material and have the same volume. The first wire has cross-sectional area A and the second wire has cross-sectional area 3A. If the length of the first wire is increased by Δl on applying a force F, how much force is needed to stretch the second wire by the same amount?
a.
9 F
b.
6 F
c.
4 F
d.
F
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The power radiated by a black body is P and it radiates maximum energy at wavelength λ0. If the temperature of the black body is now changed so that it radiates maximum energy at wavelength 4/3 λ0, the power radiated by it becomes nP. The value of n is
a.
4/3
b.
3/4
c.
81/256
d.
256/81
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A set of ‘n’ equal resistors, of value ‘R’ each, are connected in series to a battery of emf ‘E’ and internal resistance ‘R’. The current drawn is I. Now, the ‘n’ resistors are connected in parallel to the same battery. Then the current drawn from battery becomes 10 I. The value of ‘n’ is
a.
10
b.
11
c.
20
d.
9
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A moving block having mass m, collides with another stationary block having mass 4m. The lighter block comes to rest after collision. When the initial velocity of the lighter block is v, then the value of coefficient of restitution (e) will be
a.
0.5
b.
0.25
c.
0.8
d.
0.4
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Three objects, A: (a solid sphere), B: (a thin circular disk) and C: (a circular ring), each have the same mass M and radius R. They all spin with the same angular speed ω about their own symmetry axes. The amounts of work (W) required to bring them to rest, would satisfy the relation
a.
WC > WB > WA
b.
WA > WB > WC
c.
WB > WA > WC
d.
WA > WC > WB
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A tuning fork is used to produce resonance in a glass tube. The length of the air column in this tube can be adjusted by a variable piston. At room temperature of 27°C two successive resonances are produced at 20 cm and 73 cm of column length. If the frequency of the tuning fork is 320 Hz, the velocity of sound in air at 27°C is
a.
330 m/s
b.
339 m/s
c.
350 m/s
d.
300 m/s
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A tuning fork is used to produce resonance in a glass tube. The length of the air column in this tube can be adjusted by a variable piston. At room temperature of 27 °C two successive resonances are produced at 20 cm and 73 cm of column length. If the frequency of the tuning fork is 320 Hz, the velocity of sound in air at 27 °C is
a.
330 m/s
b.
339 m/s
c.
350 m/s
d.
300 m/s
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An electron falls from rest through a vertical distance h in a uniform and vertically upward directed electric field E. The direction of electric field is now reversed, keeping its magnitude the same. A proton is allowed to fall from rest in it through the same vertical distance h. The time of fall of the electron, in comparison to the time of fall of the proton is
a.
smaller
b.
5 times greater
c.
10 times greater
d.
equal
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A pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator. The acceleration of the bob of the pendulum is 20 m/s² at a distance of 5 m from the mean position. The time period of oscillation is
a.
2π s
b.
π s
c.
2 s
d.
1 s
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An electron of mass m with an initial velocity V = V₀i (V₀ > 0) enters an electric field E = -E₀i (E₀ = constant > 0) at t = 0. If λ₀ is its de-Broglie wavelength initially, then its de-Broglie wavelength at time t is
a.
(λ₀) / (1 + (eE₀t / mV₀))
b.
λ₀(1 + (eE₀t / mV₀))
c.
λ₀t
d.
λ₀
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For a radioactive material, half-life is 10 minutes. If initially there are 600 number of nuclei, the time taken (in minutes) for the disintegration of 450 nuclei is
a.
20
b.
10
c.
30
d.
15
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When the light of frequency 2v₀ (where v₀ is threshold frequency), is incident on a metal plate, the maximum velocity of electrons emitted is v₁. When the frequency of the incident radiation is increased to 5v₀, the maximum velocity of electrons emitted from the same plate is v₂. The ratio of v₁ to v₂ is
a.
1 : 2
b.
1 : 4
c.
4 : 1
d.
2 : 1
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A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric field E. Due to the force qE, its velocity increases from 0 to 6 m/s in one second duration. At that instant the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between 0 to 3 seconds are respectively
a.
2 m/s, 4 m/s
b.
1 m/s, 3 m/s
c.
1 m/s, 3·5 m/s
d.
1·5 m/s, 3 m/s
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A student measured the diameter of a small steel ball using a screw gauge of least count 0.001 cm. The main scale reading is 5 mm and zero of circular scale division coincides with 25 divisions above the reference level. If screw gauge has a zero error of – 0.004 cm, the correct diameter of the ball is
a.
0.521 cm
b.
0.525 cm
c.
0.053 cm
d.
0.529 cm
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A student measured the diameter of a small steel ball using a screw gauge of least count 0·001 cm. The main scale reading is 5 mm and zero of circular scale division coincides with 25 divisions above the reference level. If screw gauge has a zero error of – 0·004 cm, the correct diameter of the ball is
a.
0·521 cm
b.
0·525 cm
c.
0·053 cm
d.
0·529 cm
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Unpolarised light is incident from air on a plane surface of a material of refractive index ‘μ’. At a particular angle of incidence ‘i’, it is found that the reflected and refracted rays are perpendicular to each other. Which of the following options is correct for this situation?
a.
Reflected light is polarised with its electric vector parallel to the plane of incidence
b.
Reflected light is polarised with its electric vector perpendicular to the plane of incidence
c.
i = sin⁻¹(1/μ)
d.
i = tan⁻¹(1/μ)
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In Young’s double slit experiment the separation d between the slits is 2 mm, the wavelength λ of the light used is 5896 Å and distance D between the screen and slits is 100 cm. It is found that the angular width of the fringes is 0.20°. To increase the fringe angular width to 0.21° (with same λ and D) the separation between the slits needs to be changed to
a.
1.8 mm
b.
1.9 mm
c.
2.1 mm
d.
1.7 mm
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The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is 20 cm, the length of the open organ pipe is
a.
13.2 cm
b.
8 cm
c.
12.5 cm
d.
16 cm
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At what temperature will the rms speed of oxygen molecules become just sufficient for escaping from the Earth’s atmosphere? (Given: Mass of oxygen molecule (m) = 2.76 × 10⁻²⁶ kg, Boltzmann’s constant kB = 1.38 × 10⁻²³ J K⁻¹)
a.
2.508 × 10⁴ K
b.
8.360 × 10⁴ K
c.
5.016 × 10⁴ K
d.
1.254 × 10⁴ K
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A metallic rod of mass per unit length 0.5 kg m⁻¹ is lying horizontally on a smooth inclined plane which makes an angle of 30° with the horizontal. The rod is not allowed to slide down by flowing a current through it when a magnetic field of induction 0.25 T is acting on it in the vertical direction. The current flowing in the rod to keep it stationary is
a.
7.14 A
b.
5.98 A
c.
14.76 A
d.
11.32 A
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An inductor 20 mH, a capacitor 100 μF and a resistor 50 Ω are connected in series across a source of emf, V = 10 sin 314 t. The power loss in the circuit is
a.
0.79 W
b.
0.43 W
c.
2.74 W
d.
1.13 W
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Current sensitivity of a moving coil galvanometer is 5 div/mA and its voltage sensitivity (angular deflection per unit voltage applied) is 20 div/V. The resistance of the galvanometer is
a.
40 Ω
b.
25 Ω
c.
250 Ω
d.
500 Ω
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Current sensitivity of a moving coil galvanometer is 5 div/mA and its voltage sensitivity (angular deflection per unit voltage applied) is 20 div/V. The resistance of the galvanometer is
a.
40 Ω
b.
25 Ω
c.
250 Ω
d.
500 Ω
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If the mass of the Sun were ten times smaller and the universal gravitational constant were ten times larger in magnitude, which of the following is not correct?
a.
Raindrops will fall faster.
b.
Walking on the ground would become more difficult.
c.
Time period of a simple pendulum on the Earth would decrease.
d.
‘g’ on the Earth will not change.
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A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy (Kt) as well as rotational kinetic energy (Kr) simultaneously. The ratio Kt : (Kt + Kr) for the sphere is
a.
7 : 10
b.
5 : 7
c.
10 : 7
d.
2 : 5
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A solid sphere is rotating freely about its symmetry axis in free space. The radius of the sphere is increased keeping its mass same. Which of the following physical quantities would remain constant for the sphere?
a.
Angular velocity
b.
Moment of inertia
c.
Rotational kinetic energy
d.
Angular momentum
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Iron exhibits bcc structure at room temperature. Above 900°C, it transforms to fcc structure. The ratio of density of iron at room temperature to that at 900°C (assuming molar mass and atomic radii of iron remains constant with temperature) is
a.
2/3
b.
23/34
c.
24/33
d.
2/1
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Given van der Waals constant for NH3, H2, O2 and CO2 are respectively 4.17, 0.244, 1.36 and 3.59, which one of the following gases is most easily liquefied?
a.
NH3
b.
H2
c.
O2
d.
CO2
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Given van der Waals constant for NH3, H2, O2 and CO2 are respectively 4.17, 0.244, 1.36 and 3.59, which one of the following gases is most easily liquefied?
a.
NH3
b.
H2
c.
O2
d.
CO2
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