Major Competitive Exams
Q. What is the relationship between the intensity of light and the energy of individual photons in the photoelectric effect?
A.
Directly proportional
B.
Inversely proportional
C.
Independent
D.
Depends on frequency
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Solution
The energy of individual photons is dependent on frequency (E = hν) and not on intensity.
Correct Answer: C — Independent
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Q. What is the relationship between the magnetic field and the distance from a long straight wire carrying current?
A.
Directly proportional
B.
Inversely proportional
C.
Independent
D.
Exponential
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Solution
The magnetic field around a long straight wire is inversely proportional to the distance from the wire, as given by B = μ₀I/2πr.
Correct Answer: B — Inversely proportional
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Q. What is the relationship between the magnetic field and the enclosed current according to Ampere's Law?
A.
B is proportional to the square of the current
B.
B is inversely proportional to the current
C.
B is directly proportional to the current
D.
B is independent of the current
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Solution
According to Ampere's Law, the magnetic field B is directly proportional to the enclosed current.
Correct Answer: C — B is directly proportional to the current
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Q. What is the relationship between the mean free path (λ) and the diameter (d) of gas molecules?
A.
λ ∝ d^2
B.
λ ∝ 1/d
C.
λ ∝ d
D.
λ ∝ d^3
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Solution
The mean free path (λ) is inversely proportional to the diameter (d) of the gas molecules, meaning λ ∝ 1/d.
Correct Answer: B — λ ∝ 1/d
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Q. What is the relationship between the mean free path and the density of gas molecules?
A.
Mean free path increases with density
B.
Mean free path decreases with density
C.
Mean free path is independent of density
D.
Mean free path is proportional to the square of density
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Solution
The mean free path is inversely proportional to the density of gas molecules. As density increases, the mean free path decreases due to more frequent collisions.
Correct Answer: B — Mean free path decreases with density
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Q. What is the relationship between the mean free path and the diameter of gas molecules?
A.
Mean free path is independent of diameter
B.
Mean free path is directly proportional to diameter
C.
Mean free path is inversely proportional to diameter
D.
Mean free path is equal to diameter
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Solution
The mean free path is inversely proportional to the diameter of gas molecules; as the diameter increases, the mean free path decreases.
Correct Answer: C — Mean free path is inversely proportional to diameter
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Q. What is the relationship between the molality of a solution and its boiling point elevation?
A.
Directly proportional
B.
Inversely proportional
C.
No relationship
D.
Exponential relationship
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Solution
Boiling point elevation is directly proportional to the molality of the solution.
Correct Answer: A — Directly proportional
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Q. What is the relationship between the number of emitted electrons and the intensity of light in the photoelectric effect?
A.
Directly proportional
B.
Inversely proportional
C.
No relationship
D.
Exponential relationship
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Solution
The number of emitted electrons is directly proportional to the intensity of light, provided the frequency is above the threshold frequency.
Correct Answer: A — Directly proportional
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Q. What is the relationship between the number of slits in a diffraction grating and the sharpness of the maxima?
A.
More slits, sharper maxima
B.
More slits, broader maxima
C.
No relationship
D.
Fewer slits, sharper maxima
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Solution
Increasing the number of slits in a diffraction grating results in sharper maxima due to increased constructive interference.
Correct Answer: A — More slits, sharper maxima
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Q. What is the relationship between the number of turns in the primary and secondary coils of a transformer and the voltages across them? (2023)
A.
V_p/V_s = N_p/N_s
B.
V_p/V_s = N_s/N_p
C.
V_p = V_s
D.
V_p + V_s = 0
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Solution
The relationship is given by V_p/V_s = N_p/N_s, where V is voltage and N is the number of turns.
Correct Answer: A — V_p/V_s = N_p/N_s
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Q. What is the relationship between the orbital radius and the period of a satellite in a circular orbit?
A.
T is directly proportional to r
B.
T is inversely proportional to r
C.
T is proportional to r^2
D.
T is proportional to √r
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Solution
The period T of a satellite is proportional to the square root of the orbital radius r (T ∝ √r).
Correct Answer: D — T is proportional to √r
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Q. What is the relationship between the orbital radius and the time period of a satellite?
A.
T ∝ r^2
B.
T ∝ r^3/2
C.
T ∝ r
D.
T ∝ r^1/2
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Solution
The time period T of a satellite is related to the orbital radius r by T ∝ r^(3/2), according to Kepler's third law.
Correct Answer: B — T ∝ r^3/2
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Q. What is the relationship between the period and frequency of a simple harmonic oscillator?
A.
T = f
B.
T = 1/f
C.
T = f^2
D.
T = 2f
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Solution
The period (T) is the reciprocal of frequency (f), so T = 1/f.
Correct Answer: B — T = 1/f
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Q. What is the relationship between the period of a satellite and its orbital radius?
A.
T is directly proportional to r
B.
T is inversely proportional to r
C.
T is proportional to r^2
D.
T is proportional to √r
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Solution
The period T of a satellite is proportional to the square root of the orbital radius r, as given by T = 2π√(r^3/GM).
Correct Answer: D — T is proportional to √r
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Q. What is the relationship between the period of a simple harmonic oscillator and its mass and spring constant?
A.
T = 2π√(m/k)
B.
T = 2π√(k/m)
C.
T = m/k
D.
T = k/m
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Solution
The period T of a mass-spring system is given by T = 2π√(m/k).
Correct Answer: A — T = 2π√(m/k)
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Q. What is the relationship between the potential energy and kinetic energy in simple harmonic motion at maximum displacement?
A.
PE = KE
B.
PE > KE
C.
PE < KE
D.
PE = 0
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Solution
At maximum displacement, all energy is potential energy (PE), and kinetic energy (KE) is zero.
Correct Answer: B — PE > KE
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Q. What is the relationship between the pressure and volume of a gas at constant temperature according to the kinetic theory?
A.
Pressure is directly proportional to volume.
B.
Pressure is inversely proportional to volume.
C.
Pressure is independent of volume.
D.
Pressure is proportional to the square of the volume.
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Solution
According to Boyle's Law, which is derived from the kinetic theory, pressure is inversely proportional to volume at constant temperature.
Correct Answer: B — Pressure is inversely proportional to volume.
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Q. What is the relationship between the pressure and volume of an ideal gas at constant temperature?
A.
Directly proportional
B.
Inversely proportional
C.
Independent
D.
Exponential
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Solution
According to Boyle's law, the pressure and volume of an ideal gas at constant temperature are inversely proportional (PV = constant).
Correct Answer: B — Inversely proportional
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Q. What is the relationship between the principal quantum number (n) and the energy of an electron in a hydrogen atom?
A.
Energy increases with increasing n
B.
Energy decreases with increasing n
C.
Energy is independent of n
D.
Energy is maximum at n=1
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Solution
In a hydrogen atom, the energy of an electron increases with increasing principal quantum number (n).
Correct Answer: A — Energy increases with increasing n
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Q. What is the relationship between the radius and the chord length in a circle?
A.
Chords are always longer than the radius.
B.
Chords can be equal to the radius.
C.
Chords can be shorter than the radius.
D.
All of the above.
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Solution
Chords can vary in length and can be longer, equal to, or shorter than the radius.
Correct Answer: D — All of the above.
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Q. What is the relationship between the radius and the diameter of a circle?
A.
The radius is half of the diameter.
B.
The diameter is half of the radius.
C.
The radius and diameter are equal.
D.
The diameter is the sum of two radii.
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Solution
The radius is defined as half of the diameter.
Correct Answer: A — The radius is half of the diameter.
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Q. What is the relationship between the rate of reaction and temperature according to the Arrhenius equation? (2022)
A.
Inversely proportional
B.
Directly proportional
C.
Exponential
D.
Linear
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Solution
According to the Arrhenius equation, the rate of reaction increases exponentially with temperature.
Correct Answer: C — Exponential
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Q. What is the relationship between the RMS and average value of a sinusoidal AC current? (2023)
A.
RMS = Average
B.
RMS = Average × √2
C.
RMS = Average / √2
D.
RMS = Average × 2
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Solution
For a sinusoidal AC current, the relationship is RMS = Average / √2.
Correct Answer: C — RMS = Average / √2
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Q. What is the relationship between the root mean square speed of gas molecules and the temperature of the gas?
A.
It is independent of temperature.
B.
It is directly proportional to the square root of temperature.
C.
It is inversely proportional to temperature.
D.
It is directly proportional to temperature.
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Solution
The root mean square speed of gas molecules is directly proportional to the square root of the absolute temperature of the gas.
Correct Answer: B — It is directly proportional to the square root of temperature.
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Q. What is the relationship between the slit separation and the angle of diffraction in a double-slit experiment?
A.
Directly proportional
B.
Inversely proportional
C.
No relationship
D.
Quadratic relationship
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Solution
The angle of diffraction is inversely proportional to the slit separation; as the slit separation increases, the angle decreases.
Correct Answer: B — Inversely proportional
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Q. What is the relationship between the slit width and the angle of diffraction in a single-slit experiment?
A.
Directly proportional
B.
Inversely proportional
C.
No relationship
D.
Exponential relationship
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Solution
The angle of diffraction is inversely proportional to the slit width; as the slit width decreases, the angle increases.
Correct Answer: B — Inversely proportional
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Q. What is the relationship between the slit width and the angular position of the first minimum in single-slit diffraction?
A.
Directly proportional
B.
Inversely proportional
C.
No relationship
D.
Exponential relationship
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Solution
The angular position of the first minimum is inversely proportional to the slit width; as the slit width decreases, the angle increases.
Correct Answer: B — Inversely proportional
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Q. What is the relationship between the slit width and the angular width of the central maximum in single-slit diffraction?
A.
Directly proportional
B.
Inversely proportional
C.
Independent
D.
Exponential
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Solution
The angular width of the central maximum is inversely proportional to the slit width; as the slit width increases, the angular width decreases.
Correct Answer: B — Inversely proportional
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Q. What is the relationship between the speed of gas molecules and temperature?
A.
Directly proportional
B.
Inversely proportional
C.
No relationship
D.
Exponential relationship
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Solution
The average speed of gas molecules is directly proportional to the square root of the absolute temperature.
Correct Answer: A — Directly proportional
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Q. What is the relationship between the stopping potential and the maximum kinetic energy of the emitted electrons in the photoelectric effect?
A.
Stopping potential is directly proportional to the work function
B.
Stopping potential is inversely proportional to the maximum kinetic energy
C.
Stopping potential is equal to the maximum kinetic energy
D.
Stopping potential has no relation to the photoelectric effect
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Solution
The stopping potential (V) is related to the maximum kinetic energy (KE) of the emitted electrons by the equation KE = eV, where e is the charge of the electron.
Correct Answer: C — Stopping potential is equal to the maximum kinetic energy
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