An inductor of inductance L, a capacitor of capacitance C and a resistor of resistance R are connected in series to an ac source of potential difference V volts. Potential difference across L, C and R is 40 V, 10 V and 40 V, respectively. The amplitude of current flowing through LCR series circuit is 10√2 A. The impedance of the circuit is:
a.
4√2 Ω
b.
5√2 Ω
c.
4 Ω
d.
5 Ω
Correct Answer
Step-by-Step AI Explanation
Verified Method
In an LCR series circuit, V_L = 40V, V_C = 10V, V_R = 40V. The resultant voltage V = sqrt(V_R^2 + (V_L - V_C)^2) = sqrt(40^2 + (40-10)^2) = sqrt(1600 + 900) = 50V. The peak current I_0 = 10√2 A. Impedance Z = V_0 / I_0 = (V_rms * √2) / I_0 = 50 / 10 = 5 Ω.
Q1mcq
An inductor of inductance L, a capacitor of capacitance C and a resistor of resistance R are connected in series to an ac source of potential difference V volts. Potential difference across L, C and R is 40 V, 10 V and 40 V, respectively. The amplitude of current flowing through LCR series circuit is 10√2 A. The impedance of the circuit is:
a.
4√2 Ω
b.
5√2 Ω
c.
4 Ω
d.
5 Ω
Correct Answer
Step-by-Step AI Explanation
Verified Method
Net voltage V = sqrt(V_R^2 + (V_L - V_C)^2) = sqrt(40^2 + (40-10)^2) = sqrt(1600 + 900) = 50 V. Current I_rms = I_0 / sqrt(2) = (10√2) / sqrt(2) = 10 A. Impedance Z = V/I_rms = 50 / 10 = 5 Ω.
Q3mcq
A dipole is placed in an electric field as shown. In which direction will it move?
a.
towards the left as its potential energy will increase.
b.
towards the right as its potential energy will decrease.
Correct Answer
c.
towards the left as its potential energy will decrease.
d.
towards the right as its potential energy will increase.
Step-by-Step AI Explanation
Verified Method
In a non-uniform electric field, a dipole experiences a force directed towards the region of stronger field. For a dipole, the potential energy U = -pE cosθ. Movement toward a region of increasing field intensity corresponds to a decrease in potential energy as the system seeks a state of stability.
Q4mcq
A capacitor of capacitance C, is connected across an ac source of voltage V, given by V = V_0 sinωt. The displacement current between the plates of the capacitor, would then be given by:
a.
I_d = V_0 ωC cosωt
Correct Answer
b.
I_d = (V_0 / ωC) cosωt
c.
I_d = (V_0 / ωC) sinωt
d.
I_d = V_0 ωC sinωt
Step-by-Step AI Explanation
Verified Method
Displacement current I_d is equal to conduction current I = dQ/dt. Since Q = CV, Q = C V_0 sinωt. Thus, I = d/dt (C V_0 sinωt) = C V_0 ω cosωt.
Q4mcq
A capacitor of capacitance C is connected across an ac source of voltage V, given by V = V_0 sin(ωt). The displacement current between the plates of the capacitor would then be given by:
a.
I_d = V_0 ωC cos(ωt)
Correct Answer
b.
I_d = (V_0 / ωC) cos(ωt)
c.
I_d = (V_0 / ωC) sin(ωt)
d.
I_d = V_0 ωC sin(ωt)
Step-by-Step AI Explanation
Verified Method
Displacement current I_d = dq/dt = d(CV)/dt = C(dV/dt). Since V = V_0 sin(ωt), dV/dt = V_0 ω cos(ωt). Thus, I_d = V_0 ωC cos(ωt).
Q6mcq
A convex lens A of focal length 20 cm and a concave lens B of focal length 5 cm are kept along the same axis with a distance d between them. If a parallel beam of light falling on A leaves B as a parallel beam, then the distance d in cm will be:
a.
25
b.
15
Correct Answer
c.
50
d.
30
Step-by-Step AI Explanation
Verified Method
For parallel light to emerge parallel from the combination, the focal point of the convex lens must coincide with the focal point of the concave lens. Thus d = f_convex - |f_concave| = 20 - 5 = 15 cm.
Q8mcq
Match Column I with Column II based on flow of current through a metallic conductor: Column I (A) Drift Velocity (B) Electrical Resistivity (C) Relaxation Period (D) Current Density; Column II (P) m / (ne^2τ) (Q) nev_d (R) eEτ/m (S) E/J
The effective resistance of a parallel connection that consists of four wires of equal length, equal area of cross-section and same material is 0.25 Ω. What will be the effective resistance if they are connected in series?
a.
0.25 Ω
b.
0.5 Ω
c.
1 Ω
d.
4 Ω
Correct Answer
Step-by-Step AI Explanation
Verified Method
Let resistance of one wire be R. Parallel: R/4 = 0.25 => R = 1 Ω. Series: 4R = 4(1) = 4 Ω.
Q12mcq
The half-life of a radioactive nuclide is 100 hours. The fraction of original activity that will remain after 150 hours would be:
a.
1/2
b.
1/(2√2)
Correct Answer
c.
2/3
d.
2/(3√2)
Step-by-Step AI Explanation
Verified Method
Number of half-lives n = t/T = 150/100 = 1.5. Fraction remaining = (1/2)^n = (1/2)^1.5 = (1/2)^3/2 = 1 / (2 * √2).
Q14mcq
The number of photons per second on an average emitted by the source of monochromatic light of wavelength 600 nm, when it delivers the power of 3.3×10^-3 watt will be : (h=6.6×10^-34 Js)
a.
10^18
b.
10^17
c.
10^16
Correct Answer
d.
10^15
Step-by-Step AI Explanation
Verified Method
Power P = n(hc/λ). So n = Pλ / hc = (3.3×10^-3 * 600×10^-9) / (6.6×10^-34 * 3×10^8) = 10^16.
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The number of photons per second on an average emitted by a source of monochromatic light of wavelength 600 nm, when it delivers the power of 3.3×10⁻³ watt will be: (h=6.6×10⁻³⁴ Js)
a.
10¹⁸
b.
10¹⁷
c.
10¹⁶
d.
10¹⁵
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An infinitely long straight conductor carries a current of 5 A. An electron is moving with a speed of 10⁵ m/s parallel to the conductor. The perpendicular distance is 20 cm. Calculate the magnitude of the force experienced by the electron.
a.
4×10⁻²⁰ N
b.
8π×10⁻²⁰ N
c.
4π×10⁻²⁰ N
d.
8×10⁻²⁰ N
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A nucleus with mass number 240 breaks into two fragments each of mass number 120, the binding energy per nucleon of unfragmented nuclei is 7.6 MeV while that of fragments is 8.5 MeV. The total gain in the Binding Energy in the process is :
a.
0.9 MeV
b.
9.4 MeV
c.
804 MeV
d.
216 MeV
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A screw gauge gives the following readings when used to measure the diameter of a wire. Main scale reading: 0 mm, Circular scale reading: 52 divisions. Given that 1 mm on main scale corresponds to 100 divisions on the circular scale. The diameter of the wire from the above data is :
a.
0.52 cm
b.
0.026 cm
c.
0.26 cm
d.
0.052 cm
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The escape velocity from the Earth’s surface is v. The escape velocity from the surface of another planet having a radius, four times that of Earth and same mass density is :
a.
v
b.
2v
c.
3v
d.
4v
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In a potentiometer circuit a cell of EMF 1.5 V gives balance point at 36 cm length of wire. If another cell of EMF 2.5 V replaces the first cell, then at what length of the wire, the balance point occurs ?
a.
60 cm
b.
21.6 cm
c.
64 cm
d.
62 cm
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The velocity of a small ball of mass M and density d, when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is d/2, then the viscous force acting on the ball will be :
a.
Mg/2
b.
Mg
c.
3Mg/2
d.
2Mg
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The velocity of a small ball of mass M and density d, when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is d/2, then the viscous force acting on the ball will be :
a.
Mg/2
b.
Mg
c.
3Mg/2
d.
2Mg
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A parallel plate capacitor has a uniform electric field E in the space between the plates. If the distance between the plates is d and the area of each plate is A, the energy stored in the capacitor is : (ε0 = permittivity of free space)
a.
1/2 ε0 E^2
b.
ε0 EAd
c.
1/2 ε0 E^2 Ad
d.
ε0 E Ad / 2
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A parallel plate capacitor has a uniform electric field ‘E’ in the space between the plates. If the distance between the plates is ‘d’ and the area of each plate is ‘A’, the energy stored in the capacitor is : (ε0=permittivity of free space)
a.
1/2 * ε0 * E^2
b.
ε0 * E * A * d
c.
1/2 * ε0 * E^2 * A * d
d.
ε0 * E^2 * A * d
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The electron concentration in an n-type semiconductor is the same as hole concentration in a p-type semiconductor. An external field (electric) is applied across each of them. Compare the currents in them.
a.
current in n-type = current in p-type.
b.
current in p-type > current in n-type.
c.
current in n-type > current in p-type.
d.
No current will flow in p-type, current will only flow in n-type.
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Consider the following statements (A) and (B) and identify the correct answer. (A) A zener diode is connected in reverse bias, when used as a voltage regulator. (B) The potential barrier of p-n junction lies between 0.1 V to 0.3 V.
a.
(A) and (B) both are correct.
b.
(A) and (B) both are incorrect.
c.
(A) is correct and (B) is incorrect.
d.
(A) is incorrect but (B) is correct.
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Water falls from a height of 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional force are 10% of the input energy. How much power is generated by the turbine ? (g=10 m/s^2)
a.
10.2 kW
b.
8.1 kW
c.
12.3 kW
d.
7.0 kW
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A car starts from rest and accelerates at 5 m/s^2. At t=4 s, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at t=6 s ? (Take g=10 m/s^2)
a.
20 m/s, 5 m/s^2
b.
20 m/s, 0
c.
20√2 m/s, 0
d.
20√2 m/s, 10 m/s^2
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A ball of mass 0.15 kg is dropped from a height 10 m, strikes the ground and rebounds to the same height. The magnitude of impulse imparted to the ball is (g=10 m/s^2) nearly :
a.
0 kg m/s
b.
4.2 kg m/s
c.
2.1 kg m/s
d.
1.4 kg m/s
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A point object is placed at a distance of 60 cm from a convex lens of focal length 30 cm. If a plane mirror were put perpendicular to the principal axis of the lens and at a distance of 40 cm from it, the final image would be formed at a distance of :
a.
20 cm from the lens, it would be a real image.
b.
30 cm from the lens, it would be a real image.
c.
30 cm from the plane mirror, it would be a virtual image.
d.
20 cm from the plane mirror, it would be a virtual image.
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A step down transformer connected to an ac mains supply of 220 V is made to operate at 11 V, 44 W lamp. Ignoring power losses in the transformer, what is the current in the primary circuit ?
a.
0.2 A
b.
0.4 A
c.
2 A
d.
4 A
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A step down transformer connected to an ac mains supply of 220 V is made to operate at 11 V, 44 W lamp. Ignoring power losses in the transformer, what is the current in the primary circuit?
a.
0.2 A
b.
0.4 A
c.
2 A
d.
4 A
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A particle of mass 'm' is projected with a velocity v = k Ve (k < 1) from the surface of the earth (Ve = escape velocity). The maximum height above the surface reached by the particle is:
a.
R * k^2 / (1 - k^2)
b.
R * k^2 / (1 + k^2)
c.
R * k / (1 + k)
d.
R * k^2 / (1 - k)
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A particle of mass ‘m’ is projected with a velocity v=kVe (k < 1) from the surface of the earth. (Ve=escape velocity) The maximum height above the surface reached by the particle is :
a.
(k^2 / (1-k^2)) * R
b.
(k^2 / (1+k^2)) * R
c.
(R * k) / (1+k)
d.
(R*k^2) / (1-k^2)
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A series LCR circuit containing 5.0 H inductor, 80 µF capacitor and 40 Ω resistor is connected to 230 V variable frequency ac source. The angular frequencies of the source at which power transferred to the circuit is half the power at the resonant angular frequency are likely to be:
a.
25 rad/s and 75 rad/s
b.
50 rad/s and 25 rad/s
c.
46 rad/s and 54 rad/s
d.
42 rad/s and 58 rad/s
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A particular station of All India Radio, New Delhi, broadcasts on a frequency of 1,368 kHz (kilohertz). The wavelength of the electromagnetic radiation emitted by the transmitter is : [speed of light, c=3.0×10^8 ms^−1]
a.
219.3 m
b.
219.2 m
c.
2192 m
d.
21.92 cm
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Choose the correct option for the total pressure (in atm.) in a mixture of 4 g O2 and 2 g H2 confined in a total volume of one litre at 273 K is : [Given R=0.082 L atm mol^−1 K^−1, T=273 K]
a.
2.518
b.
2.602
c.
25.18
d.
26.02
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