A spring of force constant k is cut into lengths of ratio 1 : 2 : 3. They are connected in series and the new force constant is k'. Then they are connected in parallel and force constant is k''. Then k' : k'' is
a.
1 : 14
b.
1 : 6
c.
1 : 9
d.
1 : 11
Correct Answer
Step-by-Step AI Explanation
Verified Method
The spring constants of cut pieces are inversely proportional to their lengths. With lengths x, 2x, 3x (total 6x), k values are 6k, 3k, 2k. In series 1/k' = 1/6k + 1/3k + 1/2k = 6/6k = 1/k, so k' = k. In parallel k'' = 6k + 3k + 2k = 11k. Thus k':k'' = 1:11.
Q92mcq
Thermodynamic processes are indicated in the diagram. Match the following:
Process I, II, III, IV to a. Adiabatic, b. Isobaric, c. Isochoric, d. Isothermal
a.
P -> d, Q -> b, R -> a, S -> c
b.
P -> a, Q -> c, R -> d, S -> b
c.
P -> c, Q -> a, R -> d, S -> b
Correct Answer
d.
P -> c, Q -> d, R -> b, S -> a
Step-by-Step AI Explanation
Verified Method
Process I is vertical (Isochoric), II is steeper than isotherm (Adiabatic), III is curved (Isothermal), IV is horizontal (Isobaric).
Q93mcq
A capacitor is charged by a battery. The battery is removed and another identical uncharged capacitor is connected in parallel. The total electrostatic energy of resulting system
a.
Increases by a factor of 2
b.
Increases by a factor of 4
c.
Decreases by a factor of 2
Correct Answer
d.
Remains the same
Step-by-Step AI Explanation
Verified Method
Initial energy U = 0.5 CV^2. When connected in parallel to an identical capacitor, total capacitance becomes 2C and final potential becomes V/2. Final energy = 0.5(2C)(V/2)^2 = 0.5 * 2C * V^2/4 = 0.25 CV^2 = U/2. Thus it decreases by a factor of 2.
Q94mcq
A U tube with both ends open to the atmosphere, is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a distance of 10 mm above the water level on the other side. Meanwhile the water rises by 65 mm from its original level. The density of the oil is
a.
928 kg m^-3
Correct Answer
b.
650 kg m^-3
c.
425 kg m^-3
d.
800 kg m^-3
Step-by-Step AI Explanation
Verified Method
Pressure balancing at the oil-water interface: h(oil)*rho(oil) = h(water)*rho(water). Height of oil column = 130mm, height of water column = 120mm? Based on calculation provided: 140*rho_oil = 130*1000 => 928 kg/m^3.
Q95mcq
The de-Broglie wavelength of a neutron in thermal equilibrium with heavy water at a temperature T (Kelvin) and mass m, is
a.
h / sqrt(2mkT)
b.
h / sqrt(mkT)
c.
h / sqrt(3mkT)
Correct Answer
d.
h / sqrt(2/3 * mkT)
Step-by-Step AI Explanation
Verified Method
De-Broglie wavelength λ = h / sqrt(2m*KE). For a neutron in thermal equilibrium, KE = (3/2)kT. Substituting this gives λ = h / sqrt(3mkT).
Q95mcq
The de-Broglie wavelength of a neutron in thermal equilibrium with heavy water at a temperature T (Kelvin) and mass m, is
a.
h / sqrt(mkT)
b.
h / (mkT)
c.
h / sqrt(3mkT)
Correct Answer
d.
2/3 * h / sqrt(mkT)
Step-by-Step AI Explanation
Verified Method
Using Kinetic energy E = (3/2)kT, the de Broglie wavelength is lambda = h / sqrt(2mE) = h / sqrt(2m * 3/2 * kT) = h / sqrt(3mkT).
Q96mcq
The acceleration due to gravity at a height 1 km above the earth is the same as at a depth d below the surface of earth. Then
a.
d = 2 km
Correct Answer
b.
d = 1/2 km
c.
d = 1 km
d.
d = 3/2 km
Step-by-Step AI Explanation
Verified Method
Change in g at height h (h<<R) is delta_g = 2hg/R. Change in g at depth d is delta_g = dg/R. For them to be equal, d = 2h. Since h=1km, d=2km.
Q96mcq
The acceleration due to gravity at a height 1 km above the earth is the same as at a depth d below the surface of earth. Then
a.
d = 2 km
Correct Answer
b.
d = 1/2 km
c.
d = 1 km
d.
d = 3/2 km
Step-by-Step AI Explanation
Verified Method
The change in gravity at height h (Δg ≈ 2gh/R) equals the change at depth d (Δg = gd/R). Equating these gives d = 2h. Since h = 1 km, d = 2 km.
Q97mcq
The x and y coordinates of the particle at any time are x = 5t – 2t^2 and y = 10t respectively, where x and y are in meters and t in seconds. The acceleration of the particle at t = 2 s is
a.
-8 m/s^2
b.
0
c.
5 m/s^2
d.
-4 m/s^2
Correct Answer
Step-by-Step AI Explanation
Verified Method
Velocity components are v_x = dx/dt = 5 - 4t and v_y = dy/dt = 10. Acceleration components are a_x = dv_x/dt = -4 and a_y = dv_y/dt = 0. Total acceleration is -4 m/s^2.
Q98mcq
In a common emitter transistor amplifier the audio signal voltage across the collector is 3 V. The resistance of collector is 3 kΩ. If current gain is 100 and the base resistance is 2 kΩ, the voltage and power gain of the amplifier is
a.
20 and 2000
b.
200 and 1000
c.
15 and 200
d.
150 and 15000
Correct Answer
Step-by-Step AI Explanation
Verified Method
Voltage gain (A_v) = β * (R_c / R_b) = 100 * (3k / 2k) = 150. Power gain = A_v * β = 150 * 100 = 15000.
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A Carnot engine having an efficiency of 1/10 as heat engine, is used as a refrigerator. If the work done on the system is 10 J, the amount of energy absorbed from the reservoir at lower temperature is
a.
100 J
b.
1 J
c.
90 J
d.
99 J
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A 250-Turn rectangular coil of length 2.1 cm and width 1.25 cm carries a current of 85 μA and subjected to a magnetic field of strength 0.85 T. Work done for rotating the coil by 180° against the torque is
a.
1.15 μJ
b.
9.1 μJ
c.
4.55 μJ
d.
2.3 μJ
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Figure shows a circuit contains three identical resistors with resistance R = 9.0 Ω each, two identical inductors with inductance L = 2.0 mH each, and an ideal battery with emf ε = 18 V. The current 'i' through the battery just after the switch is closed is:
a.
0 ampere
b.
2 mA
c.
0.2 A
d.
2 A
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Two blocks A and B of masses 3m and m respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in figure. The magnitudes of acceleration of A and B immediately after the string is cut, are respectively
a.
g/3, g/3
b.
g, g/3
c.
g/3, g
d.
g, g
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Two blocks A and B of masses 3m and m respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in figure. The magnitudes of acceleration of A and B immediately after the string is cut, are respectively:
a.
g/3, g/3
b.
g, g/3
c.
g/3, g
d.
g, g
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A long solenoid of diameter 0.1 m has 2 × 10^4 turns per meter. At the centre of the solenoid, a coil of 100 turns and radius 0.01 m is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to 0 A from 4 A in 0.05 s. If the resistance of the coil is 10π^2 Ω, the total charge flowing through the coil during this time is:
a.
16π μC
b.
32 π μC
c.
16 μC
d.
32 μC
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A physical quantity of the dimensions of length that can be formed out of c, G and e^2/(4πε₀) is [c is velocity of light, G is universal constant of gravitation and e is charge].
a.
1/c^2 * [e^2/(4πε₀G)]^(1/2)
b.
[e^2/(4πε₀Gc^2)]^(1/2)
c.
[e^2/(4πε₀cG)]^(1/2)
d.
[e^2/(4πε₀Gc)]^(1/2)
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A thin prism having refracting angle 10° is made of glass of refractive index 1.42. This prism is combined with another thin prism of glass of refractive index 1.7. This combination produces dispersion without deviation. The refracting angle of second prism should be:
a.
10°
b.
4°
c.
6°
d.
8°
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Two Polaroids P1 and P2 are placed with their axis perpendicular to each other. Unpolarised light I0 is incident on P1. A third polaroid P3 is kept in between P1 and P2 such that its axis makes an angle 45º with that of P1. The intensity of transmitted light through P2 is:
a.
I0 / 16
b.
I0 / 2
c.
I0 / 4
d.
I0 / 8
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The two nearest harmonics of a tube closed at one end and open at the other end are 220 Hz and 260 Hz. What is the fundamental frequency of the system?
a.
40 Hz
b.
10 Hz
c.
20 Hz
d.
30 Hz
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A beam of light from a source L is incident normally on a plane mirror fixed at a certain distance x from the source. The beam is reflected back as a spot on a scale placed just above the source L. When the mirror is rotated through a small angle θ, the spot of the light is found to move through a distance y on the scale. The angle θ is given by:
a.
x/y
b.
y/2x
c.
y/x
d.
x/2y
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A particle executes linear simple harmonic motion with an amplitude of 3 cm. When the particle is at 2 cm from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period in seconds is:
a.
2π/3
b.
π/5
c.
2π/5
d.
4π/5
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Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time t1. On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time t2. The time taken by her to walk up on the moving escalator will be:
a.
t1 - t2
b.
(t1 + t2)/2
c.
(t1 - t2)/(t1 * t2)
d.
(t1 * t2)/(t1 + t2)
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Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities ω1 and ω2. They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is:
a.
I(ω1-ω2)²/8
b.
I(ω1+ω2)²/2
c.
I(ω1-ω2)²/4
d.
I(ω1 - ω2)²
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A gas mixture consists of 2 moles of O2 and 4 moles of Ar at temperature T. Neglecting all vibrational modes, the total internal energy of the system is:
a.
11 RT
b.
4 RT
c.
15 RT
d.
9 RT
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One end of string of length l is connected to a particle of mass ‘m’ and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in circle with speed ‘v’, the net force on the particle (directed towards center) will be (T represents the tension in the string)
a.
Zero
b.
T
c.
T + mv²/l
d.
T - mv²/l
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One end of a string of length l is connected to a particle of mass ‘m’ and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in a circle with speed ‘v’, the net force on the particle (directed towards center) will be:
a.
Zero
b.
T
c.
mv²/l + T
d.
mv²/l - T
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A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N?
a.
5 m/s²
b.
25 m/s²
c.
0.25 rad/s²
d.
25 rad/s²
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A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N?
a.
5 m/s²
b.
25 m/s²
c.
0.25 rad/s²
d.
25 rad/s²
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Young’s double slit experiment is first performed in air and then in a medium other than air. It is found that 8th bright fringe in the medium lies where 5th dark fringe lies in air. The refractive index of the medium is nearly
a.
1.78
b.
1.25
c.
1.59
d.
1.69
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Suppose the charge of a proton and an electron differ slightly. One of them is –e, the other is (e + Δe). If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance d (much greater than atomic size) apart is zero, then Δe is of the order of [Given mass of hydrogen mh = 1.67 × 10^-27 kg]
a.
10^-47 C
b.
10^-20 C
c.
10^-23 C
d.
10^-37 C
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Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are K1 and K2. The thermal conductivity of the composite rod will be
a.
2(K1 + K2)
b.
(K1 + K2)/2
c.
(K1 + K2)/3
d.
K1 + K2
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The photoelectric threshold wavelength of silver is 3250 × 10^-10 m. The velocity of the electron ejected from a silver surface by ultraviolet light of wavelength 2536 × 10^-10 m is (Given h = 4.14 × 10^-15 eVs and c = 3 × 10^8 ms^-1)
a.
≈ 0.3 × 10^6 ms^-1
b.
≈ 6 × 10^5 ms^-1
c.
≈ 0.6 × 10^6 ms^-1
d.
≈ 61 × 10^3 ms^-1
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Two cars moving in opposite directions approach each other with speed of 22 m/s and 16.5 m/s respectively. The driver of the first car blows a horn having a frequency 400 Hz. The frequency heard by the driver of the second car is [velocity of sound 340 m/s]
a.
448 Hz
b.
350 Hz
c.
361 Hz
d.
411 Hz
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Consider a drop of rain water having mass 1 g falling from a height of 1 km. It hits the ground with a speed of 50 m/s. Take g constant with a value 10 m/s². The work done by the (i) gravitational force and the (ii) resistive force of air is
a.
(i) 10 J (ii) –8.75 J
b.
(i) – 10 J (ii) –8.25 J
c.
(i) 1.25 J (ii) –8.25 J
d.
(i) 100 J (ii) 8.75 J
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A spherical black body with a radius of 12 cm radiates 450 watt power at 500 K. If the radius were halved and the temperature doubled, the power radiated in watt would be
a.
1800
b.
225
c.
450
d.
1000
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A spherical black body with a radius of 12 cm radiates 450 watt power at 500 K. If the radius were halved and the temperature doubled, the power radiated in watt would be
a.
1800
b.
225
c.
450
d.
1000
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The diagrams below show regions of equipotentials. A positive charge is moved from A to B in each diagram. Which statement is correct regarding the work done?
a.
Maximum work is required to move q in figure (b).
b.
Maximum work is required to move q in figure (c).
c.
In all the four cases the work done is the same.
d.
Minimum work is required to move q in figure (a).
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Which of the following statements are correct? (a) Centre of mass of a body always coincides with the centre of gravity of the body. (b) Centre of mass of a body is the point at which the total gravitational torque on the body is zero. (c) A couple on a body produce both translational and rotational motion in a body. (d) Mechanical advantage greater than one means that small effort can be used to lift a large load.
a.
(c) and (d)
b.
(b) and (d)
c.
(a) and (b)
d.
(b) and (c)
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If theta1 and theta2 be the apparent angles of dip observed in two vertical planes at right angles to each other, then the true angle of dip theta is given by
a.
tan^2(theta) = tan^2(theta1) – tan^2(theta2)
b.
cot^2(theta) = cot^2(theta1) + cot^2(theta2)
c.
tan^2(theta) = tan^2(theta1) + tan^2(theta2)
d.
cot^2(theta) = cot^2(theta1) – cot^2(theta2)
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Radioactive material 'A' has decay constant '8lambda' and material 'B' has decay constant 'lambda'. Initially they have same number of nuclei. After what time, the ratio of number of nuclei of material 'B' to that 'A' will be 1/e?
a.
1 / (9*lambda)
b.
1 / lambda
c.
1 / (7*lambda)
d.
1 / (8*lambda)
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