Major Competitive Exams
Q. What is the relationship between the angle of diffraction and the wavelength of light in a single-slit diffraction pattern?
A.
Directly proportional
B.
Inversely proportional
C.
No relationship
D.
Depends on slit width
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Solution
The angle of diffraction is inversely proportional to the wavelength; as the wavelength increases, the angle of diffraction increases.
Correct Answer: B — Inversely proportional
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Q. What is the relationship between the angle of incidence and the angle of diffraction in a diffraction grating?
A.
They are equal
B.
They are inversely proportional
C.
They are related by the grating equation
D.
They are independent
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Solution
The angle of incidence and angle of diffraction are related by the grating equation d sin(θ) = mλ.
Correct Answer: C — They are related by the grating equation
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Q. What is the relationship between the angle of incidence and the angle of polarization?
A.
They are equal
B.
They are complementary
C.
They are supplementary
D.
There is no relationship
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Solution
At the angle of polarization, the angle of incidence is equal to the angle of refraction.
Correct Answer: A — They are equal
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Q. What is the relationship between the angle of incidence and the angle of reflection in total internal reflection?
A.
They are equal
B.
They are complementary
C.
They are supplementary
D.
There is no relationship
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Solution
In total internal reflection, the angle of incidence is equal to the angle of reflection.
Correct Answer: A — They are equal
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Q. What is the relationship between the angles of an equilateral triangle? (2023)
A.
All angles are 60 degrees
B.
All angles are 90 degrees
C.
Two angles are equal
D.
No angles are equal
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Solution
In an equilateral triangle, all three angles are equal and measure 60 degrees each.
Correct Answer: A — All angles are 60 degrees
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Q. What is the relationship between the angular velocity (ω) and the linear velocity (v) in circular motion?
A.
v = ωr
B.
v = r/ω
C.
v = ω²r
D.
v = r²ω
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Solution
The relationship is given by v = ωr, where r is the radius of the circular path.
Correct Answer: A — v = ωr
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Q. What is the relationship between the angular velocity and linear velocity of an object moving in a circular path?
A.
v = ωr
B.
v = r/ω
C.
v = ω/r
D.
v = ω²r
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Solution
Linear velocity (v) is related to angular velocity (ω) by the formula v = ωr.
Correct Answer: A — v = ωr
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Q. What is the relationship between the angular velocity and linear velocity of an object in circular motion?
A.
v = ωr
B.
v = r/ω
C.
v = ω/r
D.
v = ω²r
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Solution
Linear velocity (v) is related to angular velocity (ω) by the equation v = ωr.
Correct Answer: A — v = ωr
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Q. What is the relationship between the average kinetic energy of gas molecules and temperature?
A.
KE ∝ T
B.
KE ∝ T^2
C.
KE ∝ 1/T
D.
KE ∝ T^3
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Solution
The average kinetic energy of gas molecules is directly proportional to the absolute temperature (KE ∝ T).
Correct Answer: A — KE ∝ T
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Q. What is the relationship between the average speed and RMS speed of a gas?
A.
RMS speed is always greater than average speed
B.
RMS speed is always less than average speed
C.
RMS speed equals average speed
D.
RMS speed is independent of average speed
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Solution
For an ideal gas, the RMS speed is always greater than the average speed due to the squaring of velocities in the RMS calculation.
Correct Answer: A — RMS speed is always greater than average speed
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Q. What is the relationship between the average speed and RMS speed of gas molecules?
A.
RMS speed is always greater than average speed
B.
RMS speed is always less than average speed
C.
RMS speed equals average speed
D.
RMS speed is independent of average speed
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Solution
For an ideal gas, the RMS speed is always greater than the average speed due to the nature of the distribution of molecular speeds.
Correct Answer: A — RMS speed is always greater than average speed
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Q. What is the relationship between the Celsius and Kelvin scales?
A.
K = C + 273.15
B.
C = K + 273.15
C.
K = C - 273.15
D.
C = K - 273.15
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Solution
The relationship is K = C + 273.15, where K is the temperature in Kelvin and C is the temperature in Celsius.
Correct Answer: A — K = C + 273.15
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Q. What is the relationship between the corresponding angles when two parallel lines are cut by a transversal? (2022)
A.
They are equal
B.
They are supplementary
C.
They are complementary
D.
They are unequal
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Solution
When two parallel lines are cut by a transversal, the corresponding angles are equal.
Correct Answer: A — They are equal
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Q. What is the relationship between the damping coefficient and the type of damping?
A.
Higher coefficient indicates under-damping
B.
Lower coefficient indicates over-damping
C.
Critical damping occurs at a specific coefficient
D.
Damping coefficient has no effect
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Solution
Critical damping occurs at a specific value of the damping coefficient, which separates under-damping from over-damping.
Correct Answer: C — Critical damping occurs at a specific coefficient
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Q. What is the relationship between the damping ratio and the type of damping in a system?
A.
Damping ratio < 1 indicates overdamping
B.
Damping ratio = 1 indicates critical damping
C.
Damping ratio > 1 indicates underdamping
D.
Damping ratio = 0 indicates critical damping
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Solution
A damping ratio of 1 indicates critical damping, while less than 1 indicates underdamping and greater than 1 indicates overdamping.
Correct Answer: B — Damping ratio = 1 indicates critical damping
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Q. What is the relationship between the damping ratio and the type of damping?
A.
Damping ratio < 1: Underdamping
B.
Damping ratio = 1: Overdamping
C.
Damping ratio > 1: Critical damping
D.
Damping ratio = 0: Overdamping
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Solution
A damping ratio less than 1 indicates underdamping, equal to 1 indicates critical damping, and greater than 1 indicates overdamping.
Correct Answer: A — Damping ratio < 1: Underdamping
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Q. What is the relationship between the density of a gas and its molar mass at constant temperature and pressure?
A.
Density is directly proportional to molar mass
B.
Density is inversely proportional to molar mass
C.
Density is independent of molar mass
D.
Density is equal to molar mass
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Solution
At constant temperature and pressure, density is directly proportional to molar mass according to the ideal gas law.
Correct Answer: A — Density is directly proportional to molar mass
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Q. What is the relationship between the electric field and magnetic field in polarized light?
A.
They are always perpendicular to each other
B.
They oscillate in the same direction
C.
They are in phase with each other
D.
They have varying amplitudes
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Solution
In polarized light, the electric field and magnetic field are always perpendicular to each other.
Correct Answer: A — They are always perpendicular to each other
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Q. What is the relationship between the electric field vector and the direction of propagation in linearly polarized light?
A.
They are perpendicular
B.
They are parallel
C.
They are at 45 degrees
D.
They are randomly oriented
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Solution
In linearly polarized light, the electric field vector is perpendicular to the direction of propagation.
Correct Answer: A — They are perpendicular
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Q. What is the relationship between the equilibrium constant (K) and the Gibbs free energy change (ΔG) for a reaction?
A.
ΔG = -RT ln(K)
B.
ΔG = RT ln(K)
C.
ΔG = KRT
D.
ΔG = K/R
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Solution
The relationship is given by the equation ΔG = -RT ln(K), where R is the gas constant and T is the temperature in Kelvin.
Correct Answer: A — ΔG = -RT ln(K)
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Q. What is the relationship between the equilibrium constant (K) and the reaction quotient (Q)?
A.
K = Q at equilibrium
B.
K > Q at equilibrium
C.
K < Q at equilibrium
D.
K is independent of Q
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Solution
At equilibrium, the reaction quotient Q is equal to the equilibrium constant K.
Correct Answer: A — K = Q at equilibrium
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Q. What is the relationship between the equilibrium constants Kp and Kc for a gaseous reaction?
A.
Kp = Kc
B.
Kp = Kc(RT)^(Δn)
C.
Kp = Kc/RT
D.
Kp = Kc(RT)^(Δn) where Δn is the change in moles of gas
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Solution
The relationship between Kp and Kc is given by Kp = Kc(RT)^(Δn), where Δn is the change in the number of moles of gas.
Correct Answer: B — Kp = Kc(RT)^(Δn)
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Q. What is the relationship between the frequency and period of a wave?
A.
Frequency = Period × Speed
B.
Frequency = 1/Period
C.
Frequency = Speed × Wavelength
D.
Frequency = Wavelength/Speed
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Solution
The relationship is given by Frequency = 1/Period.
Correct Answer: B — Frequency = 1/Period
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Q. What is the relationship between the frequency and the period of a simple harmonic oscillator?
A.
f = T
B.
f = 1/T
C.
f = T^2
D.
f = 2T
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Solution
The frequency (f) is the reciprocal of the period (T), so f = 1/T.
Correct Answer: B — f = 1/T
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Q. What is the relationship between the frequency and the period of a wave? (2021)
A.
Frequency is the square of the period
B.
Period is the reciprocal of frequency
C.
Frequency and period are unrelated
D.
Period is the square root of frequency
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Solution
The period T is the reciprocal of frequency f, given by T = 1/f.
Correct Answer: B — Period is the reciprocal of frequency
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Q. What is the relationship between the frequency and wavelength of a wave?
A.
Frequency = Wavelength × Speed
B.
Wavelength = Speed / Frequency
C.
Speed = Frequency × Wavelength
D.
All of the above
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Solution
The relationship is given by the equation Speed = Frequency × Wavelength, which can be rearranged to show the other relationships.
Correct Answer: D — All of the above
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Q. What is the relationship between the frequency of incident light and the number of emitted electrons 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 related to the intensity of light, not the frequency, as long as the frequency is above the threshold.
Correct Answer: C — No relationship
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Q. What is the relationship between the Gibbs free energy change (ΔG) and the equilibrium constant (K) at standard conditions?
A.
ΔG = RT ln K
B.
ΔG = -RT ln K
C.
ΔG = KRT
D.
ΔG = K/R
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Solution
ΔG = -RT ln K relates Gibbs free energy change to the equilibrium constant.
Correct Answer: B — ΔG = -RT ln K
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Q. What is the relationship between the Gibbs free energy change (ΔG) and the equilibrium constant (K)?
A.
ΔG = -RT ln(K)
B.
ΔG = RT ln(K)
C.
ΔG = K - RT
D.
ΔG = 0 at equilibrium
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Solution
The relationship is given by the equation ΔG = -RT ln(K), where R is the gas constant and T is the temperature in Kelvin.
Correct Answer: A — ΔG = -RT ln(K)
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Q. What is the relationship between the height of a satellite and its orbital period?
A.
Directly proportional
B.
Inversely proportional
C.
No relationship
D.
Exponential relationship
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Solution
The orbital period T of a satellite is related to its height h by T ∝ h^(3/2), which indicates that the period is inversely proportional to the square root of the gravitational force acting on it.
Correct Answer: B — Inversely proportional
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