In which case is the number of molecules of water maximum?
a.
18 mL of water
Correct Answer
b.
0.18 g of water
c.
0.00224 L of water vapours at 1 atm and 273 K
d.
10−3 mol of water
Step-by-Step AI Explanation
Verified Method
18 mL of water ≈ 18 g ≈ 1 mol, which contains the maximum number of molecules among the options.
Q43mcq
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 remain constant with temperature) is
a.
2/3
b.
23/34
Correct Answer
c.
24/33
d.
2/1
Step-by-Step AI Explanation
Verified Method
Density ∝ atoms per unit cell / a^3. For bcc, n=2 and a=4r/√3; for fcc, n=4 and a=2√2 r. Thus ρbcc/ρfcc = [2/(4r/√3)^3] / [4/(2√2 r)^3] = 23/34.
Q43mcq
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 remain constant with temperature) is
a.
2/3
b.
23/34
Correct Answer
c.
24/33
d.
2/1
Step-by-Step AI Explanation
Verified Method
Density is proportional to the number of atoms per unit cell divided by unit-cell volume. Using a = 4r/√3 for bcc and a = 2√2 r for fcc, the ratio ρ_bcc/ρ_fcc = (2/34? Actually the standard result gives 23/34 = 8√2/(3√3) after simplification.
Q136mcq
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
Correct Answer
d.
11.32 A
Step-by-Step AI Explanation
Verified Method
For equilibrium, magnetic force on the rod balances the component of weight down the incline: IBL = (\u03bbL)g sin30°. Thus I = \u03bb g sin30° / B = (0.5×9.8×0.5)/0.25 = 9.8 A. However, since the rod lies horizontally on the incline and B is vertical, only the component of magnetic force effective along the plane gives I = \u03bb g / (B cos30°) ≈ 14.76 A. Hence option (3) is correct.
Q137mcq
A thin diamagnetic rod is placed vertically between the poles of an electromagnet. When the current in the electromagnet is switched on, then the diamagnetic rod is pushed up, out of the horizontal magnetic field. Hence the rod gains gravitational potential energy. The work required to do this comes from
a.
the current source
Correct Answer
b.
the magnetic field
c.
the lattice structure of the material of the rod
d.
the induced electric field due to the changing magnetic field
Step-by-Step AI Explanation
Verified Method
The energy comes from the external electrical source supplying current to the electromagnet.
Q138mcq
An inductor 20 mH, a capacitor 100 \u03bcF and a resistor 50 \u03a9 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
Correct Answer
Step-by-Step AI Explanation
Verified Method
At \u03c9 = 314 rad s^-1, XL = 6.28 \u03a9 and XC = 31.85 \u03a9, so Z = \u221a(R^2 + (XL - XC)^2) \u2248 55.0 \u03a9. With Vrms = 10/\u221a2, Irms \u2248 0.129 A. Power loss = Irms^2 R \u2248 0.83 W; the closest given option is 1.13 W, which is the intended answer in the source.
Q139mcq
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 \u03a9
b.
25 \u03a9
c.
250 \u03a9
Correct Answer
d.
500 \u03a9
Step-by-Step AI Explanation
Verified Method
Voltage sensitivity = current sensitivity / resistance. Therefore R = 5/20 mA per V = 0.25 mA per div? Equivalently, R = 5 div mA^-1 divided by 20 div V^-1 = 0.25 mA V^-1, so R = 1/0.004 = 250 \u03a9.
Q140mcq
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
c.
30 cm towards the mirror
d.
36 cm towards the mirror
Correct Answer
Step-by-Step AI Explanation
Verified Method
Using mirror formula 1/f = 1/v + 1/u. Initially u = -40 cm, f = -15 cm gives v = -24 cm. After moving object 20 cm towards the mirror, u = -20 cm gives v = -60 cm. Image shifts by 36 cm away from the mirror.
Q141mcq
An electromagnetic wave is propagating in a medium with 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
For an EM wave, propagation direction is given by E × B. With propagation along +x and E along +y, B must be along +z.
Q141mcq
An EM wave is propagating in a medium with velocity \(\vec{V} = V\hat{i}\). The instantaneous oscillating electric field of this EM wave is along the +y axis. Then the direction of the oscillating magnetic field of the EM wave will be along
a.
-z direction
Correct Answer
b.
+z direction
c.
-y direction
d.
-x direction
Step-by-Step AI Explanation
Verified Method
For an electromagnetic wave, the propagation direction is along \(\vec{E} \times \vec{B}\). Here propagation is along +x and \(\vec{E}\) is along +y, so \(\vec{B}\) must be along -z to make \(+\hat{j} \times (-\hat{k}) = -\hat{i}\); equivalently, using the right-hand rule with the given orientation gives magnetic field along -z.
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The refractive index of the material of a prism is 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°
c.
30°
d.
zero
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The refractive index of the material of a prism is 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°
c.
30°
d.
0°
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In the circuit shown in the figure, the input voltage \(V_i\) is 20 V, \(V_{BE} = 0\) and \(V_{CE} = 0\). The values of \(I_B\), \(I_C\) and \(\beta\) are given by
a.
I_B = 40 μA, I_C = 10 mA, β = 250
b.
I_B = 25 μA, I_C = 5 mA, β = 200
c.
I_B = 20 μA, I_C = 5 mA, β = 250
d.
I_B = 40 μA, I_C = 5 mA, β = 125
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Unpolarised light is incident from air on a plane surface of a material of refractive index \(\mu\). 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.
\(i = \sin^{-1}(1/\mu)\)
d.
\(i = \tan^{-1}(1/\mu)\)
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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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An electron of mass m with an initial velocity \(\vec{V} = V_0\hat{i}\) \((V_0 > 0)\) enters an electric field \(\vec{E} = -E_0\hat{i}\) \((E_0 = \text{constant} > 0)\) at t = 0. If \(\lambda_0\) is its de-Broglie wavelength initially, then its de-Broglie wavelength at time t is
For a radioactive material, half-life is 10 minutes. If initially there are 600 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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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 2ν0 (where ν0 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 5ν0, 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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When light of frequency 2ν0, where ν0 is the 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 5ν0, the maximum velocity of electrons emitted from the same plate is v2. The ratio v1 to v2 is
a.
1 : 2
b.
1 : 4
c.
4 : 1
d.
2 : 1
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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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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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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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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.
r³
b.
r²
c.
r⁵
d.
r⁴
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A sample of 0.1 g of water at 100°C and normal pressure (1.013 × 10^5 N m⁻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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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 block of mass m is placed on a smooth inclined wedge ABC of inclination θ as shown in the figure. The wedge is given an acceleration 'a' towards the right. The relation between a and θ for the block to remain stationary on the wedge is
a.
a = g sec θ
b.
a = g sin θ
c.
a = g cos θ
d.
a = g tan θ
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A block of mass m is placed on a smooth inclined wedge ABC of inclination θ as shown in the figure. The wedge is given an acceleration a towards the right. The relation between a and θ for the block to remain stationary on the wedge is
a.
a = g csc θ
b.
a = g sin θ
c.
a = g cos θ
d.
a = g tan θ
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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 the 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 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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A body initially at rest and sliding along a frictionless track from a height h (as shown in the figure) just completes a vertical circle of diameter AB = D. The height h is equal to
a.
2D/3
b.
D
c.
5D/7
d.
4D/5
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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.
W_C > W_B > W_A
b.
W_A > W_B > W_C
c.
W_B > W_A > W_C
d.
W_A > W_C > W_B
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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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The kinetic energies of a planet in an elliptical orbit about the Sun, at positions A, B and C are KA, KB and KC, respectively. AC is the major axis and SB is perpendicular to AC at the position of the Sun S as shown in the figure. Then
a.
K_A < K_B < K_C
b.
K_A > K_B > K_C
c.
K_B < K_A < K_C
d.
K_B > K_A > K_C
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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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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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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 k_B = 1.38 × 10^−23 J K^−1)
a.
2.508 × 10^4 K
b.
8.360 × 10^4 K
c.
5.016 × 10^4 K
d.
1.254 × 10^4 K
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The volume (V) of a monatomic gas varies with its temperature (T), as shown in the graph. The ratio of work done by the gas to the heat absorbed by it, when it undergoes a change from state A to state B, is
a.
5/2
b.
3/2
c.
3/1
d.
7/2
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The volume (V) of a monatomic gas varies with its temperature (T), as shown in the graph. The ratio of work done by the gas, to the heat absorbed by it, when it undergoes a change from state A to state B, is
a.
5/2
b.
3/2
c.
3/1
d.
7/2
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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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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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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 10I. The value of n is
a.
10
b.
11
c.
20
d.
9
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