The correct option for free expansion of an ideal gas under adiabatic condition is:
a.
q > 0, ΔT > 0 and w > 0
b.
q = 0, ΔT = 0 and w = 0
Correct Answer
c.
q = 0, ΔT < 0 and w > 0
d.
q < 0, ΔT = 0 and w = 0
Step-by-Step AI Explanation
Verified Method
In free expansion, no work is done (w = 0). Under adiabatic conditions, q = 0. For an ideal gas, internal energy depends only on temperature, so ΔT = 0.
Q22mcq
On electrolysis of dilute sulphuric acid using platinum (Pt) electrode, the product obtained at anode will be:
a.
SO2 gas
b.
Hydrogen gas
c.
Oxygen gas
Correct Answer
d.
H2S gas
Step-by-Step AI Explanation
Verified Method
At the anode, water is oxidized to oxygen in electrolysis of dilute sulphuric acid with inert platinum electrodes.
Q23mcq
An element has a body centered cubic (bcc) structure with a cell edge of 288 pm. The atomic radius is:
a.
\u221a4 × 288 pm / 2
b.
\u221a3 × 288 pm / 4
c.
\u221a2 × 288 pm / 4
Correct Answer
d.
\u221a4 × 288 pm / 3
Step-by-Step AI Explanation
Verified Method
For bcc, 4r = √3 a? Actually in bcc, body diagonal = 4r = √3 a, so r = (√3/4)a. With a = 288 pm, radius = (√3/4) × 288 pm.
Q62mcq
Match the following columns and select the correct option.
Column I
(a) Bt cotton
(b) Adenosine deaminase deficiency
(c) RNAi
(d) PCR
Column II
(i) Gene therapy
(ii) Cellular defence
(iii) Detection of HIV infection
(iv) Bacillus thuringiensis
a.
(i)(ii)(iii)(iv)
b.
(iv)(i)(ii)(iii)
Correct Answer
c.
(iii)(ii)(i)(iv)
d.
(ii)(iii)(iv)(i)
Step-by-Step AI Explanation
Verified Method
Bt cotton is associated with Bacillus thuringiensis; adenosine deaminase deficiency with gene therapy; RNAi with cellular defence; PCR with detection of HIV infection.
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.
537 Hz
Correct Answer
b.
523 Hz
c.
524 Hz
d.
536 Hz
Step-by-Step AI Explanation
Verified Method
Initially |f_B - 530| = 6, so f_B = 524 or 536 Hz. Decreasing tension lowers f_B; if beat frequency increases to 7 Hz, f_B must be above 530 Hz originally, so 536 Hz. However, since lowering f_B by 1 Hz would change beats from 6 to 7 only if f_B was 536 Hz, the correct option is 536 Hz.
Q137mcq
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 C^2 N^-1 m^-2).
a.
5.00 C^2 N^-1 m^-2
b.
0.44 × 10^-13 C^2 N^-1 m^-2
c.
1.77 × 10^-12 C^2 N^-1 m^-2
d.
0.44 × 10^-10 C^2 N^-1 m^-2
Correct Answer
Step-by-Step AI Explanation
Verified Method
Capacitance is proportional to permittivity. Here the ratio is 30/6 = 5, so ε = 5ε0 = 5 × 8.85 × 10^-12 = 4.425 × 10^-11 F m^-1, i.e. 0.44 × 10^-10 C^2 N^-1 m^-2.
Q138mcq
The phase difference between displacement and acceleration of a particle in simple harmonic motion is:
a.
zero
b.
π rad
Correct Answer
c.
3π/2 rad
d.
π/2 rad
Step-by-Step AI Explanation
Verified Method
In SHM, acceleration is opposite in phase to displacement, so the phase difference is π rad.
Q139mcq
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.
zero
Correct Answer
b.
doubled
c.
four times
d.
one-fourth
Step-by-Step AI Explanation
Verified Method
Halving the frequency makes it below threshold, so no photoemission occurs and current becomes zero, regardless of intensity.
Q140mcq
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? Given 1/(4πϵ0) = 9 × 10^9 N m^2/C^2.
a.
1.28 × 10^7 N/C
b.
1.28 × 10^4 N/C
c.
1.28 × 10^5 N/C
Correct Answer
d.
1.28 × 10^6 N/C
Step-by-Step AI Explanation
Verified Method
Outside a charged spherical conductor, E = kQ/r^2 = 9×10^9 × 3.2×10^-7 /(0.15)^2 = 1.28×10^5 N/C.
Q142mcq
For transistor action, which of the following statements is correct?
a.
The base region must be very thin and lightly doped.
Correct Answer
b.
Base, emitter and collector regions should have same doping concentrations.
c.
Base, emitter and collector regions should have same size.
d.
Both emitter junction as well as the collector junction are forward biased.
Step-by-Step AI Explanation
Verified Method
In transistor action, the base must be thin and lightly doped so that most carriers injected from the emitter can reach the collector.
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In a certain region of space with volume 0.2 m^3, the electric potential is found to be 5 V throughout. The magnitude of electric field in this region is:
a.
5 N/C
b.
zero
c.
0.5 N/C
d.
1 N/C
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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.
20.0 g
b.
2.5 g
c.
5.0 g
d.
10.0 g
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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.
80 cm
b.
33 cm
c.
50 cm
d.
67 cm
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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.
isobaric
b.
isothermal
c.
adiabatic
d.
isochoric
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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/s^2):
a.
300 m
b.
360 m
c.
340 m
d.
320 m
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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.
10^4 V
b.
10 V
c.
10^2 V
d.
10^3 V
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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^-5 T
b.
6.28×10^-4 T
c.
3.14×10^-4 T
d.
6.28×10^-5 T
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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^2
b.
c : 1
c.
1 : 1
d.
1 : 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 = 9×10^9 N m^2/C^2):
a.
zero
b.
50 V
c.
200 V
d.
400 V
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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.
2.4π×10^-7 T m A^-1
b.
2.4π×10^-4 T m A^-1
c.
8.0×10^-5 T m A^-1
d.
2.4π×10^-5 T m A^-1
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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 pulley which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity (g) is:
a.
g/10
b.
g
c.
g/2
d.
g/5
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Light with an average flux of 20 W/cm^2 falls on a non-reflecting surface at normal incidence having surface area 20 cm^2. The energy received by the surface during a time span of 1 minute is:
a.
48×10^3 J
b.
10×10^3 J
c.
12×10^3 J
d.
24×10^3 J
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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 / A(L1 − L)
b.
MgL / AL1
c.
Mg(L1 − L) / AL
d.
MgL / AL
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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.
-1.0
b.
zero
c.
0.5
d.
1.0
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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.
one-fourth
b.
double
c.
half
d.
four times
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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.
one-fourth
b.
double
c.
half
d.
four times
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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^-2 m
b.
1.0 × 10^-2 m
c.
1.0 × 10^-1 m
d.
1.5 × 10^-1 m
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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.
A / (2μ)
b.
A / (2μ)
c.
2A / μ
d.
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.
A/(2μ)
b.
A/(2μ)
c.
2A/μ
d.
μA
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