An increase in the concentration of the reactants of a reaction leads to change in:
a.
heat of reaction
b.
threshold energy
c.
collision frequency
Correct Answer
d.
activation energy
Step-by-Step AI Explanation
Verified Method
According to collision theory, increasing concentration increases the number of molecules per unit volume, which increases the frequency of collisions.
Q1mcq
A wire of length L, area of cross section A is hanging from a fixed support. The length of the wire changes to L_1 when mass M is suspended from its free end. The expression for Young's modulus is:
a.
Mg(L_1-L) / AL
b.
MgL / A(L_1-L)
Correct Answer
c.
MgL_1 / AL
d.
MgL / AL_1
Step-by-Step AI Explanation
Verified Method
Young's Modulus Y = (Stress) / (Strain) = (F/A) / (ΔL/L). Here F = Mg, ΔL = (L_1 - L). Thus, Y = (Mg/A) / ((L_1 - L)/L) = MgL / A(L_1 - L).
Q2mcq
A cylinder contains hydrogen gas at a 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 = nRT = (m/M)RT, then P = (ρ/M)RT where ρ is density and M is molar mass of H₂ (2x10⁻³ kg/mol). ρ = PM/RT = (249x10³ * 2x10⁻³) / (8.3 * 300) = 498 / 2490 = 0.2 kg/m³.
Q5mcq
The mean free path for a gas, with molecular diameter d and number density n can be expressed as:
a.
1 / (√2 nπd²)
Correct Answer
b.
1 / (√2 n²πd²)
c.
1 / (√2 n²π²d²)
d.
1 / (√2 nπd)
Step-by-Step AI Explanation
Verified Method
The standard kinetic theory expression for mean free path λ is 1 / (√2 nσ), where σ = πd² is the collision cross-section.
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 v² = u² + 2gh, where v=80, u=20, g=10. 80² = 20² + 2(10)h => 6400 = 400 + 20h => 6000 = 20h => h = 300 m.
Q7mcq
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 a time span of 1 minute is:
a.
12 x 10³ J
b.
24 x 10³ J
Correct Answer
c.
48 x 10³ J
d.
10 x 10³ J
Step-by-Step AI Explanation
Verified Method
Power = Intensity * Area = 20 W/cm² * 20 cm² = 400 W. Energy = Power * Time = 400 W * 60 s = 24,000 J = 24 x 10³ J.
Q8mcq
When a uranium isotope 235U is bombarded with a neutron, it generates 92Kr, three neutrons and:
a.
141Ba
Correct Answer
b.
142Zr
c.
141Kr
d.
142Kr
Step-by-Step AI Explanation
Verified Method
In nuclear fission of 235U, the sum of atomic numbers and mass numbers must be conserved. 235 + 1 = 92 + X + 3(1). For 92Kr (Z=36), the remaining mass is 236 - 92 - 3 = 141. The balanced product is 141Ba (Z=56).
Q9mcq
A spherical conductor of radius 10 cm has a charge of 3.2 x 10⁻⁷ C distributed uniformly. What is the magnitude of the electric field at a point 15 cm from the centre of the sphere? (1/4πε₀ = 9 x 10⁹ N m²/C²)
a.
1.28 x 10⁵ N/C
Correct Answer
b.
1.28 x 10⁶ N/C
c.
1.28 x 10⁷ N/C
d.
1.28 x 10⁴ N/C
Step-by-Step AI Explanation
Verified Method
E = kQ / r². r = 0.15 m. E = (9 x 10⁹ * 3.2 x 10⁻⁷) / (0.15 * 0.15) = (28.8 * 10²) / 0.0225 = 128000 = 1.28 x 10⁵ 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
b.
μA
Correct Answer
c.
A/2μ
d.
2μA
Step-by-Step AI Explanation
Verified Method
For a small angle prism, Snell's law at the first surface is sin(i) ≈ i = μr1. At the second surface, if it emerges normally, r2 = 0. Since A = r1 + r2, then r1 = A. Thus, i = μA.
Q11mcq
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
Correct Answer
b.
isochoric
c.
isobaric
d.
isothermal
Step-by-Step AI Explanation
Verified Method
The system is thermally insulated, so no heat exchange with the surroundings occurs (Q=0). The gas expands into a vacuum, meaning work done W=0. This process is a free expansion, which is adiabatic.
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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 x 10^-1 m
b.
1.5 x 10^-1 m
c.
1.5 x 10^-2 m
d.
1.0 x 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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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:
a.
200 V
b.
400 V
c.
zero
d.
50 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 x 10⁻⁷ T m A⁻¹):
a.
3.14 x 10⁻⁴ T
b.
6.28 x 10⁻⁵ T
c.
3.14 x 10⁻⁵ T
d.
6.28 x 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 x 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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