A mixture of N₂ and Ar gases in a cylinder contains 7 g of N₂ and 8 g of Ar. If the total pressure of the mixture of the gases in the cylinder is 27 bar, the partial pressure of N₂ is:
[Use atomic masses (in g mol⁻¹): N = 14, Ar = 40]
a.
15 bar
Correct Answer
b.
18 bar
c.
9 bar
d.
12 bar
Step-by-Step AI Explanation
Verified Method
Moles of N₂ = 7/28 = 0.25 mol; Moles of Ar = 8/40 = 0.2 mol. Total moles = 0.25 + 0.2 = 0.45 mol. Mole fraction of N₂ = 0.25/0.45 = 5/9. Partial pressure of N₂ = (5/9) × 27 = 15 bar.
Q136mcq
In a guitar, two strings A and B made of same material are slightly out of tune and produce beats of frequency 6 Hz. When tension in B is slightly decreased, the beat frequency increases to 7 Hz. If the frequency of A is 530 Hz, the original frequency of B will be:
a.
536 Hz
b.
537 Hz
c.
523 Hz
d.
524 Hz
Correct Answer
Step-by-Step AI Explanation
Verified Method
Beat frequency = |f_A – f_B| = 6 Hz, so f_B = 524 Hz or 536 Hz. Decreasing tension in B lowers its frequency. If f_B were 536 Hz, lowering it would bring it closer to 530 Hz (beats decrease). Since beats increased to 7 Hz upon lowering tension, f_B must have been below f_A, i.e., f_B = 524 Hz. Lowering it further increases the difference from 530 Hz to 7 Hz, consistent with the observation.
Q136mcq
In a guitar, two strings A and B made of same material are slightly out of tune and produce beats of frequency 6 Hz. When tension in B is slightly decreased, the beat frequency increases to 7 Hz. If the frequency of A is 530 Hz, the original frequency of B will be:
a.
536 Hz
b.
537 Hz
c.
523 Hz
d.
524 Hz
Correct Answer
Step-by-Step AI Explanation
Verified Method
Beat frequency = |f_A – f_B| = 6 Hz, so f_B = 536 Hz or 524 Hz. Decreasing tension decreases frequency of B. If f_B were 536 Hz (> f_A), decreasing f_B would bring it closer to f_A = 530 Hz, reducing beat frequency — but beats increased to 7 Hz. If f_B = 524 Hz (< f_A), decreasing f_B moves it further from 530 Hz, increasing the beat frequency to 7 Hz. This is consistent. Therefore original frequency of B = 524 Hz.
Q137mcq
The increase in the width of the depletion region in a p-n junction diode is due to:
a.
Both forward bias and reverse bias
b.
Increase in forward current
c.
Forward bias only
d.
Reverse bias only
Correct Answer
Step-by-Step AI Explanation
Verified Method
When a p-n junction is reverse biased, the external voltage aids the built-in potential, pulling majority carriers away from the junction and widening the depletion region. Forward bias does the opposite — it narrows the depletion region. Hence, the increase in width of the depletion region is due to reverse bias only.
Q138mcq
The quantities of heat required to raise the temperature of two solid copper spheres of radii r₁ and r₂ (r₁ = 1.5 r₂) through 1 K are in the ratio:
a.
3/2
b.
5/3
c.
27/8
Correct Answer
d.
9/4
Step-by-Step AI Explanation
Verified Method
Heat required Q = mcΔT. Mass m = ρ·(4/3)πr³. Since both spheres are of the same material (same ρ and same specific heat c) and ΔT = 1 K, Q ∝ r³. Therefore Q₁/Q₂ = (r₁/r₂)³ = (1.5)³ = (3/2)³ = 27/8.
Q139mcq
A series LCR circuit is connected to an ac voltage source. When L is removed from the circuit, the phase difference between current and voltage is π/3. If instead C is removed from the circuit, the phase difference is again π/3 between current and voltage. The power factor of the circuit is
a.
1.0
Correct Answer
b.
–1.0
c.
zero
d.
0.5
Step-by-Step AI Explanation
Verified Method
When L is removed: RC circuit with tan(π/3) = X_C/R, so X_C = R√3. When C is removed: RL circuit with tan(π/3) = X_L/R, so X_L = R√3. In the full LCR circuit, X_L = X_C, so the circuit is at resonance. At resonance, impedance Z = R and power factor = cos(0°) = 1.0.
Q140mcq
A ball is thrown vertically downward with a velocity of 20 m/s from the top of a tower. It hits the ground after some time with a velocity of 80 m/s. The height of the tower is: (g = 10 m/s²)
a.
320 m
b.
300 m
Correct Answer
c.
360 m
d.
340 m
Step-by-Step AI Explanation
Verified Method
Using v² = u² + 2gh: (80)² = (20)² + 2×10×h → 6400 = 400 + 20h → 20h = 6000 → h = 300 m.
Q141mcq
In Young's double slit experiment, if the separation between coherent sources is halved and the distance of the screen from the coherent sources is doubled, then the fringe width becomes:
a.
Four times
Correct Answer
b.
One-fourth
c.
Double
d.
Half
Step-by-Step AI Explanation
Verified Method
Fringe width β = λD/d. If d becomes d/2 and D becomes 2D, then new β' = λ(2D)/(d/2) = 4λD/d = 4β. So the fringe width becomes four times the original.
Q143mcq
A long solenoid of 50 cm length having 100 turns carries a current of 2.5 A. The magnetic field at the centre of the solenoid is: (μ₀ = 4π × 10⁻⁷ T m A⁻¹)
a.
6.28 × 10⁻⁵ T
b.
3.14 × 10⁻⁵ T
c.
6.28 × 10⁻⁴ T
Correct Answer
d.
3.14 × 10⁻⁴ T
Step-by-Step AI Explanation
Verified Method
B = μ₀nI where n = N/L = 100/0.5 = 200 turns/m. B = 4π × 10⁻⁷ × 200 × 2.5 = 4π × 10⁻⁷ × 500 = 2000π × 10⁻⁷ = 2π × 10⁻⁴ ≈ 6.28 × 10⁻⁴ T.
Q144mcq
Light of frequency 1.5 times the threshold frequency is incident on a photosensitive material. What will be the photoelectric current if the frequency is halved and intensity is doubled?
a.
One-fourth
b.
Zero
Correct Answer
c.
Doubled
d.
Four times
Step-by-Step AI Explanation
Verified Method
Original frequency f = 1.5f₀ (where f₀ is threshold frequency). If frequency is halved: new frequency = 0.75f₀, which is below the threshold frequency f₀. Since the incident frequency is less than the threshold frequency, no photoelectric effect occurs regardless of intensity. Hence photoelectric current = zero.
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Two bodies of mass 4 kg and 6 kg are tied to the ends of a massless string. The string passes over a frictionless pulley. The acceleration of the system in terms of acceleration due to gravity (g) is:
a.
g/5
b.
g/10
c.
g
d.
g/2
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A capillary tube of radius r is immersed in water and water rises in it to a height h. The mass of the water in the capillary is 5 g. Another capillary tube of radius 2r is immersed in water. The mass of water that will rise in this tube is:
a.
10.0 g
b.
20.0 g
c.
2.5 g
d.
5.0 g
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A capillary tube of radius r is immersed in water and water rises in it to a height h. The mass of the water in the capillary is 5 g. Another capillary tube of radius 2r is immersed in water. The mass of water that will rise in this tube is:
a.
10.0 g
b.
20.0 g
c.
2.5 g
d.
5.0 g
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The ratio of contributions made by the electric field and magnetic field components to the intensity of an electromagnetic wave is: (c = speed of electromagnetic waves)
a.
1 : c
b.
1 : c²
c.
c : 1
d.
1 : 1
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The ratio of contributions made by the electric field and magnetic field components to the intensity of an electromagnetic wave is: (c = speed of electromagnetic waves)
a.
1 : c
b.
1 : c²
c.
c : 1
d.
1 : 1
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An iron rod of susceptibility 599 is subjected to a magnetising field of 1200 A m⁻¹. The permeability of the material of the rod is: (μ₀ = 4π × 10⁻⁷ T m A⁻¹)
a.
2.4 × 10⁻⁵ T m A⁻¹
b.
2.4 × 10⁻⁷ T m A⁻¹
c.
2.4 × 10⁻⁴ T m A⁻¹
d.
8.0 × 10⁻⁵ T m A⁻¹
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An iron rod of susceptibility 599 is subjected to a magnetising field of 1200 A m⁻¹. The permeability of the material of the rod is: (μ₀ = 4π × 10⁻⁷ T m A⁻¹)
a.
2.4 × 10⁻⁵ T m A⁻¹
b.
2.4 × 10⁻⁷ T m A⁻¹
c.
2.4 × 10⁻⁴ T m A⁻¹
d.
8.0 × 10⁻⁵ T m A⁻¹
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Two particles of mass 5 kg and 10 kg respectively are attached to the two ends of a rigid rod of length 1 m with negligible mass. The centre of mass of the system from the 5 kg particle is nearly at a distance of:
a.
67 cm
b.
80 cm
c.
33 cm
d.
50 cm
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A spherical conductor of radius 10 cm has a charge of 3.2 × 10⁻⁷ C distributed uniformly. What is the magnitude of electric field at a point 15 cm from the centre of the sphere? (1/4πε₀ = 9 × 10⁹ N m² C⁻²)
a.
1.28 × 10⁶ N/C
b.
1.28 × 10⁷ N/C
c.
1.28 × 10⁴ N/C
d.
1.28 × 10⁵ N/C
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A short electric dipole has a dipole moment of 16 × 10⁻⁹ C m. The electric potential due to the dipole at a point at a distance of 0.6 m from the centre of the dipole, situated on a line making an angle of 60° with the dipole axis is: (1/4πε₀ = 9 × 10⁹ N m²/C²)
a.
400 V
b.
zero
c.
50 V
d.
200 V
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A resistance wire connected in the left gap of a metre bridge balances a 10 Ω resistance in the right gap at a point which divides the bridge wire in the ratio 3:2. If the length of the resistance wire is 1.5 m, then the length of 1 Ω of the resistance wire is:
a.
1.5 × 10⁻¹ m
b.
1.5 × 10⁻² m
c.
1.0 × 10⁻² m
d.
1.0 × 10⁻¹ m
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A resistance wire connected in the left gap of a metre bridge balances a 10 Ω resistance in the right gap at a point which divides the bridge wire in the ratio 3 : 2. If the length of the resistance wire is 1.5 m, then the length of 1 Ω of the resistance wire is:
a.
1.5 × 10⁻¹ m
b.
1.5 × 10⁻² m
c.
1.0 × 10⁻² m
d.
1.0 × 10⁻¹ m
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A wire of length L, area of cross section A is hanging from a fixed support. The length of the wire changes to L₁ when mass M is suspended from its free end. The expression for Young's modulus is:
a.
MgL / (AL₁)
b.
MgL / (A(L₁ − L))
c.
MgL₁ / (AL)
d.
Mg(L₁ − L) / (AL)
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A wire of length L, area of cross section A is hanging from a fixed support. The length of the wire changes to L₁ when mass M is suspended from its free end. The expression for Young's modulus is:
a.
MgL / (AL₁)
b.
MgL / (A(L₁ − L))
c.
MgL₁ / (AL)
d.
Mg(L₁ − L) / (AL)
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An electron is accelerated from rest through a potential difference of V volt. If the de Broglie wavelength of the electron is 1.227 × 10⁻² nm, the potential difference is:
a.
10³ V
b.
10⁴ V
c.
10 V
d.
10² V
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A ray is incident at an angle of incidence i on one surface of a small angle prism (with angle of prism A) and emerges normally from the opposite surface. If the refractive index of the material of the prism is μ, then the angle of incidence is nearly equal to:
a.
μA
b.
A / (2μ)
c.
A / 2
d.
2A / μ
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In a certain region of space with volume 0.2 m³, the electric potential is found to be 5 V throughout. The magnitude of electric field in this region is:
a.
1 N/C
b.
5 N/C
c.
Zero
d.
0.5 N/C
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Light with an average flux of 20 W/cm² falls on a non-reflecting surface at normal incidence having surface area 20 cm². The energy received by the surface during time span of 1 minute is:
a.
24 × 10³ J
b.
48 × 10³ J
c.
10 × 10³ J
d.
12 × 10³ J
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The capacitance of a parallel plate capacitor with air as medium is 6 μF. With the introduction of a dielectric medium, the capacitance becomes 30 μF. The permittivity of the medium is: (ε₀ = 8.85 × 10⁻¹² C² N⁻¹ m⁻²)
a.
0.44 × 10⁻¹⁰ C² N⁻¹ m⁻²
b.
5.00 C² N⁻¹ m⁻²
c.
0.44 × 10⁻¹³ C² N⁻¹ m⁻²
d.
1.77 × 10⁻¹² C² N⁻¹ m⁻²
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Two cylinders A and B of equal capacity are connected to each other via a stop cock. A contains an ideal gas at standard temperature and pressure. B is completely evacuated. The entire system is thermally insulated. The stop cock is suddenly opened. The process is:
a.
Isochoric
b.
Isobaric
c.
Isothermal
d.
Adiabatic
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