If E and G respectively denote energy and gravitational constant, then E/G has the dimensions of:
a.
[M^2][L^-2][T^-1]
b.
[M^2][L^-1][T^0]
Correct Answer
c.
[M][L^-1][T^-1]
d.
[M][L^0][T^0]
Step-by-Step AI Explanation
Verified Method
Energy E = [ML^2T^-2]. Gravitational constant G = [M^-1L^3T^-2]. Therefore, E/G = [ML^2T^-2] / [M^-1L^3T^-2] = [M^2L^-1T^0].
Q1mcq
If E and G respectively denote energy and gravitational constant, then E/G has the dimensions of:
a.
[M^2][L^-2][T^-1]
b.
[M^2][L^-1][T^0]
Correct Answer
c.
[M][L^-1][T^-1]
d.
[M][L^0][T^0]
Step-by-Step AI Explanation
Verified Method
Energy E = [ML^2T^-2]. Gravitational constant G = [M^-1L^3T^-2]. Therefore, E/G = [ML^2T^-2] / [M^-1L^3T^-2] = [M^2L^-1T^0].
Q2mcq
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. 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.
5 Ω
Correct Answer
b.
4√2 Ω
c.
5√2 Ω
d.
4 Ω
Step-by-Step AI Explanation
Verified Method
VR = 40 V, VL = 40 V, VC = 10 V. Net voltage V = sqrt(VR^2 + (VL - VC)^2) = sqrt(40^2 + (40-10)^2) = sqrt(1600 + 900) = 50 V. Impedance Z = V_rms / I_rms. Given current amplitude I0 = 10√2, so I_rms = 10 A. Z = 50/10 = 5 Ω.
Q2mcq
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.
5 Ω
Correct Answer
b.
4√2 Ω
c.
5√2 Ω
d.
4 Ω
Step-by-Step AI Explanation
Verified Method
V_R = 40 V, V_L = 40 V, V_C = 10 V. Net voltage V = sqrt(V_R^2 + (V_L - V_C)^2) = sqrt(40^2 + (30)^2) = 50 V. Peak current I = 10√2 A. Impedance Z = V_rms / I_rms = V_peak / I_peak = 50 / 10 = 5 Ω.
Q3mcq
A body is executing simple harmonic motion with frequency n, the frequency of its potential energy is:
a.
4n
b.
n
c.
2n
Correct Answer
d.
3n
Step-by-Step AI Explanation
Verified Method
Potential energy U = (1/2)k(x_0 sin ωt)^2 = (1/2)k x_0^2 sin^2(ωt) = (1/4)k x_0^2 (1 - cos 2ωt). The frequency of potential energy oscillation is 2ω, which corresponds to 2n.
Q3mcq
A body is executing simple harmonic motion with frequency 'n', the frequency of its potential energy is:
a.
4n
b.
n
c.
2n
Correct Answer
d.
3n
Step-by-Step AI Explanation
Verified Method
In SHM, displacement is x = A sin(ωt). Potential energy U = 1/2 k x^2 = 1/2 k A^2 sin^2(ωt) = 1/4 k A^2 (1 - cos(2ωt)). The frequency of oscillation for potential energy is 2ω, which corresponds to 2n.
Q5mcq
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 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 Ad
Correct Answer
b.
1/2 ε0 E^2
c.
ε0 EAd
d.
1/2 ε0 E Ad
Step-by-Step AI Explanation
Verified Method
Energy density = 1/2 ε0 E^2. Total energy = Energy density × Volume = 1/2 ε0 E^2 × (Ad).
Q7mcq
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 capacitor of capacitance C, is connected across an ac source of voltage V, given by V=V0 sinωt. The displacement current between the plates of the capacitor, would then be given by:
a.
I_d = V0 ωC sin ωt
b.
I_d = V0 ωC cos ωt
c.
I_d = (V0/ωC) cos ωt
d.
I_d = (V0/ωC) sin ωt
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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.
0.052 cm
b.
0.52 cm
c.
0.026 cm
d.
0.26 cm
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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.
62 cm
b.
60 cm
c.
21.6 cm
d.
64 cm
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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.
4 Ω
b.
0.25 Ω
c.
0.5 Ω
d.
1 Ω
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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.
7.0 kW
b.
10.2 kW
c.
8.1 kW
d.
12.3 kW
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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.
7.0 kW
b.
10.2 kW
c.
8.1 kW
d.
12.3 kW
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An infinitely long straight conductor carries a current of 5 A. An electron is moving with a speed of 10^5 m/s parallel to the conductor. The perpendicular distance between the electron and the conductor is 20 cm. Calculate the magnitude of the force experienced by the electron.
a.
8×10^-20 N
b.
4×10^-20 N
c.
8π×10^-20 N
d.
4π×10^-20 N
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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) is incorrect but (B) is correct.
b.
(A) and (B) both are correct.
c.
(A) and (B) both are incorrect.
d.
(A) is correct and (B) is incorrect.
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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) is incorrect but (B) is correct.
b.
(A) and (B) both are correct.
c.
(A) and (B) both are incorrect.
d.
(A) is correct and (B) is incorrect.
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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 electric field is applied across each of them. Compare the currents in them.
a.
No current will flow in p-type, current will only flow in n-type.
b.
current in n-type = current in p-type.
c.
current in p-type > current in n-type.
d.
current in n-type > current in p-type.
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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.
30
b.
25
c.
15
d.
50
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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.
4 v
b.
v
c.
2 v
d.
3 v
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A small block slides down on a smooth inclined plane, starting from rest at time t=0. Let Sn be the distance travelled by the block in the interval t=n-1 to t=n. Then, the ratio Sn / Sn+1 is:
a.
(2n)/(2n-1)
b.
(2n-1)/(2n)
c.
(2n-1)/(2n+1)
d.
(2n+1)/(2n-1)
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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.
2 Mg
b.
Mg/2
c.
Mg
d.
3 Mg/2
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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.
2 Mg
b.
Mg/2
c.
Mg
d.
3 Mg/2
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A radioactive nucleus undergoes spontaneous decay in the sequence: A/Z X -> A-4/Z-2 B -> A-4/Z-3 C -> A-4/Z-2 D. The possible decay particles in the sequence are:
a.
beta-, alpha, beta+
b.
alpha, beta-, beta+
c.
alpha, beta+, beta-
d.
beta+, alpha, beta-
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From a circular ring of mass M and radius R an arc corresponding to a 90-degree sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the centre and perpendicular to the plane is K times MR^2. Value of K is:
a.
1/8
b.
3/4
c.
7/8
d.
1/4
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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.
1.4 kg m/s
b.
0 kg m/s
c.
4.2 kg m/s
d.
2.1 kg m/s
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A step down transformer connected to 220 V ac mains is made to operate at 11 V, 44 W lamp. Ignoring power losses, what is the current in the primary circuit?
a.
4 A
b.
0.2 A
c.
0.4 A
d.
2 A
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A uniform conducting wire of length 12a and resistance R is wound as a coil: (i) equilateral triangle of side a, (ii) square of side a. Magnetic dipole moments in each case respectively are:
a.
4 Ia^2 and 3 Ia^2
b.
3 Ia^2 and 3 Ia^2
c.
3 Ia^2 and Ia^2
d.
3 Ia^2 and 4 Ia^2
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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.
(Rk^2) / (1 - k^2)
b.
R * (k^2 / (1 - k))
c.
R * (k^2 / (1 + k))
d.
(R * k) / (1 + k)
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A particle of mass m is projected with velocity v = k Ve (k < 1) from the surface of the earth. The maximum height above the surface reached by the particle is:
a.
Rk^2 / (1-k^2)
b.
R(k^2 / (1-k^2))
c.
R(k^2 / (1+k^2))
d.
R(k / 1+k)
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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 ac source. The angular frequencies at which power is half the resonant power are:
a.
42 rad/s and 58 rad/s
b.
25 rad/s and 75 rad/s
c.
50 rad/s and 25 rad/s
d.
46 rad/s and 54 rad/s
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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.
42 rad/s and 58 rad/s
b.
25 rad/s and 75 rad/s
c.
50 rad/s and 25 rad/s
d.
46 rad/s and 54 rad/s
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A particle moving in a circle of radius R with a uniform speed takes a time T to complete one revolution. If this particle were projected with the same speed at an angle θ to the horizontal, the maximum height attained by it equals 4R. The angle of projection, θ, is then given by:
a.
θ = sin^-1 [ (2gT^2 / (π^2 R)) - 1 / 2 ]
b.
θ = cos^-1 [ (gT^2 / (π^2 R)) - 1 / 2 ]
c.
θ = cos^-1 [ (R / (2 * g * T^2)) - π^2 ]
d.
θ = sin^-1 [ (R / (2 * g * T^2)) - π^2 ]
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Two conducting circular loops of radii R1 and R2 are placed in the same plane with their centres coinciding. If R1 >> R2, the mutual inductance M between them will be directly proportional to:
a.
R1^2 / R2
b.
R2 / R1
c.
R2^2 / R1
d.
R1^2 / R2^2
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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 plane mirror, it would be a virtual image.
b.
20 cm from the lens, it would be a real image.
c.
30 cm from the lens, it would be a real image.
d.
30 cm from the plane mirror, it would be a virtual image.
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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.
21.92 cm
b.
219.3 m
c.
219.2 m
d.
2192 m
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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 0°C is: [Given R=0.082 L atm mol^-1 K^-1, T=273 K]
a.
26.02
b.
2.518
c.
2.602
d.
25.18
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