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 cylinder contains hydrogen gas at pressure of 249 kPa and temperature 27°C. Its density is : (R = 8.3 J mol–1 K–1)
a.
0.2 kg/m3
Correct Answer
b.
0.1 kg/m3
c.
0.02 kg/m3
d.
0.5 kg/m3
Step-by-Step AI Explanation
Verified Method
Using PV = (m/M)RT => P = (ρ/M)RT => ρ = PM/RT. For H2, M = 2x10^-3 kg/mol. P = 2.49x10^5 Pa, T = 300K. ρ = (2.49x10^5 * 2x10^-3) / (8.3 * 300) = 0.2 kg/m3.
Q3mcq
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.
12 × 10^3 J
b.
24 × 10^3 J
Correct Answer
c.
48 × 10^3 J
d.
10 × 10^3 J
Step-by-Step AI Explanation
Verified Method
Energy = Power x Time. Power = Flux x Area = 20 W/cm^2 x 20 cm^2 = 400 W. Time = 60s. Energy = 400 x 60 = 24000 J = 24 x 10^3 J.
Q4mcq
Two bodies of mass 4 kg and 6 kg are tied to the ends of a massless string. The string passes over a pulley which is frictionless. The acceleration of the system in terms of acceleration due to gravity (g) is :
a.
g/2
b.
g/5
Correct Answer
c.
g/10
d.
g
Step-by-Step AI Explanation
Verified Method
For an Atwood machine, acceleration a = |m1-m2|g / (m1+m2) = |6-4|g / (6+4) = 2g / 10 = g/5.
Q5mcq
The mean free path for a gas, with molecular diameter d and number density n can be expressed as :
a.
1 / (√2 * n * π * d^2)
Correct Answer
b.
1 / (2 * n^2 * π * d^2)
c.
1 / (√2 * n^2 * π * d^2)
d.
1 / (n * π * d^2)
Step-by-Step AI Explanation
Verified Method
The formula for mean free path is λ = 1 / (√2 * n * σ) where σ is the collision cross-section πd^2. Thus, λ = 1 / (√2 * n * π * d^2).
Q6mcq
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.
340 m
b.
320 m
c.
300 m
Correct Answer
d.
360 m
Step-by-Step AI Explanation
Verified Method
Using v^2 - u^2 = 2gh. v = 80, u = 20, g = 10. 80^2 - 20^2 = 2 * 10 * h => 6400 - 400 = 20h => 6000 = 20h => h = 300 m.
Q7mcq
The color code of a resistance is given below. The values of resistance and tolerance, respectively, are:
a.
47 kΩ, 10%
b.
4.7 kΩ, 5%
c.
470 Ω, 5%
Correct Answer
d.
470 kΩ, 5%
Step-by-Step AI Explanation
Verified Method
Standard color code for 470 Ω, 5%: Yellow (4), Violet (7), Brown (10^1), Gold (5%).
Q8mcq
When a uranium isotope 235/92 U is bombarded with a neutron, it generates 89/36 Kr, three neutrons and :
a.
91/40 Zr
b.
101/36 Kr
c.
103/36 Kr
d.
144/56 Ba
Correct Answer
Step-by-Step AI Explanation
Verified Method
Nuclear fission equation balance: 235 + 1 = 89 + 3(1) + X => 236 = 92 + A => A = 144. 92 = 36 + 0 + Z => Z = 56. Element is 144/56 Ba.
Q9mcq
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?
a.
1.28 × 10^5 N/C
Correct Answer
b.
1.28 × 10^6 N/C
c.
1.28 × 10^7 N/C
d.
1.28 × 10^4 N/C
Step-by-Step AI Explanation
Verified Method
Electric field E = kQ/r^2. E = (9x10^9 * 3.2x10^-7) / (0.15)^2 = 2880 / 0.0225 = 1.28 x 10^5 N/C.
Q10mcq
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.
2A/μ
b.
μA
Correct Answer
c.
A/2μ
d.
A/2μ
Step-by-Step AI Explanation
Verified Method
Snell's Law at first face: sin i = μ sin r1. For small angles, i ≈ μ r1. Since ray emerges normally, r2 = 0. We know A = r1 + r2, so A = r1. Therefore i = μA.
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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.
2A/μ
b.
μA
c.
A/2μ
d.
A/2μ
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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.
adiabatic
b.
isochoric
c.
isobaric
d.
isothermal
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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.
adiabatic
b.
isochoric
c.
isobaric
d.
isothermal
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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.
8.0 × 10⁻⁵ T m A⁻¹
b.
2.4π × 10⁻⁵ T m A⁻¹
c.
2.4π × 10⁻⁷ T m A⁻¹
d.
2.4π × 10⁻⁴ 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.
8.0 × 10–5 T m A–1
b.
2.4π × 10–5 T m A–1
c.
2.4π × 10–7 T m A–1
d.
2.4π × 10–4 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.
50 cm
b.
67 cm
c.
80 cm
d.
33 cm
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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.
1.0 × 10⁻¹ m
b.
1.5 × 10⁻¹ m
c.
1.5 × 10⁻² m
d.
1.0 × 10⁻² m
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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.
half
b.
four times
c.
one-fourth
d.
double
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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.
0.5
b.
1.0
c.
-1.0
d.
zero
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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.
5.0 g
b.
10.0 g
c.
20.0 g
d.
2.5 g
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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.
1.77 × 10⁻¹² C² N⁻¹ m⁻²
b.
0.44 × 10⁻¹⁰ C² N⁻¹ m⁻²
c.
5.00 C² N⁻¹ m⁻²
d.
0.44 × 10⁻¹³ C² N⁻¹ m⁻²
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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.
1.77 × 10⁻¹² C² N⁻¹ m⁻²
b.
0.44 × 10⁻¹⁰ C² N⁻¹ m⁻²
c.
5.00 C² N⁻¹ m⁻²
d.
0.44 × 10⁻¹³ C² N⁻¹ m⁻²
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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.
524 Hz
b.
536 Hz
c.
537 Hz
d.
523 Hz
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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.
200 V
b.
400 V
c.
zero
d.
50 V
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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.
0.5 N/C
b.
1 N/C
c.
5 N/C
d.
zero
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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.
four times
b.
one-fourth
c.
zero
d.
doubled
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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.
3.14 × 10⁻⁴ T
b.
6.28 × 10⁻⁵ T
c.
3.14 × 10⁻⁵ T
d.
6.28 × 10⁻⁴ T
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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.
10² V
b.
10³ V
c.
10⁴ V
d.
10 V
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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.
10^2 V
b.
10^3 V
c.
10^4 V
d.
10 V
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