Major Competitive Exams
Q. What is the relationship between electric field E and surface charge density σ on a conductor?
A.
E = σ/ε₀
B.
E = σ/2ε₀
C.
E = 2σ/ε₀
D.
E = σ/4ε₀
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Solution
The electric field just outside a charged conductor is given by E = σ/ε₀.
Correct Answer: A — E = σ/ε₀
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Q. What is the relationship between electric potential (V) and electric field (E) in a uniform field?
A.
V = E × d
B.
V = E/d
C.
E = V × d
D.
E = V/d
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Solution
In a uniform electric field, the electric potential difference V is given by V = E × d, where d is the distance moved in the direction of the field.
Correct Answer: A — V = E × d
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Q. What is the relationship between electric potential and electric field?
A.
E = -dV/dx
B.
E = dV/dx
C.
E = V/d
D.
E = -V/d
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Solution
The electric field E is the negative gradient of the electric potential V, expressed as E = -dV/dx.
Correct Answer: A — E = -dV/dx
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Q. What is the relationship between enthalpy (H), internal energy (U), and pressure-volume work (PV)?
A.
H = U + PV
B.
H = U - PV
C.
H = U * PV
D.
H = U / PV
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Solution
The relationship is given by H = U + PV, where H is enthalpy, U is internal energy, and PV is the pressure-volume work.
Correct Answer: A — H = U + PV
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Q. What is the relationship between enthalpy (H), internal energy (U), pressure (P), and volume (V)?
A.
H = U + PV
B.
H = U - PV
C.
H = U + P/V
D.
H = U - P/V
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Solution
The relationship is given by H = U + PV, where H is enthalpy, U is internal energy, P is pressure, and V is volume.
Correct Answer: A — H = U + PV
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Q. What is the relationship between enthalpy and internal energy?
A.
H = U + PV
B.
H = U - PV
C.
H = U * PV
D.
H = U / PV
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Solution
The relationship is given by the equation H = U + PV, where H is enthalpy, U is internal energy, P is pressure, and V is volume.
Correct Answer: A — H = U + PV
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Q. What is the relationship between enthalpy change and internal energy change at constant pressure?
A.
ΔH = ΔU + PΔV
B.
ΔH = ΔU - PΔV
C.
ΔH = ΔU
D.
ΔH = PΔV
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Solution
At constant pressure, the relationship is given by ΔH = ΔU + PΔV.
Correct Answer: A — ΔH = ΔU + PΔV
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Q. What is the relationship between entropy and spontaneity of a process?
A.
Higher entropy means the process is non-spontaneous.
B.
Lower entropy means the process is spontaneous.
C.
Higher entropy generally indicates a spontaneous process.
D.
Entropy has no relation to spontaneity.
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Solution
A higher entropy generally indicates a spontaneous process, as spontaneous processes tend to increase the overall disorder of the system.
Correct Answer: C — Higher entropy generally indicates a spontaneous process.
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Q. What is the relationship between entropy and temperature?
A.
Entropy increases with decreasing temperature
B.
Entropy decreases with increasing temperature
C.
Entropy increases with increasing temperature
D.
Entropy is independent of temperature
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Solution
Entropy generally increases with increasing temperature due to increased molecular motion and disorder.
Correct Answer: C — Entropy increases with increasing temperature
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Q. What is the relationship between frequency (f) and period (T) of a wave? (2023)
A.
f = T
B.
f = 1/T
C.
f = T^2
D.
f = 2πT
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Solution
The frequency (f) is the reciprocal of the period (T), given by the formula f = 1/T.
Correct Answer: B — f = 1/T
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Q. What is the relationship between frequency and period of a wave? (2020)
A.
Frequency = Period × Speed
B.
Frequency = 1/Period
C.
Frequency = Speed × Wavelength
D.
Frequency = Wavelength/Speed
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Solution
The frequency (f) of a wave is the reciprocal of the period (T), given by the formula f = 1/T.
Correct Answer: B — Frequency = 1/Period
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Q. What is the relationship between frequency and wavelength in a wave traveling at a constant speed?
A.
Directly proportional
B.
Inversely proportional
C.
Independent
D.
None of the above
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Solution
Frequency and wavelength are inversely proportional when the speed of the wave is constant, as given by the equation v = fλ.
Correct Answer: B — Inversely proportional
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Q. What is the relationship between frequency and wavelength in a wave?
A.
Frequency is directly proportional to wavelength
B.
Frequency is inversely proportional to wavelength
C.
Frequency is independent of wavelength
D.
Frequency equals wavelength
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Solution
The relationship is given by the equation v = fλ, where v is the speed of the wave, f is the frequency, and λ is the wavelength. Thus, frequency is inversely proportional to wavelength.
Correct Answer: B — Frequency is inversely proportional to wavelength
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Q. What is the relationship between Gibbs free energy (ΔG) and cell potential (E) in electrochemistry?
A.
ΔG = -nFE
B.
ΔG = nFE
C.
ΔG = -E/nF
D.
ΔG = E/nF
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Solution
The relationship is ΔG = -nFE, where n is the number of moles of electrons transferred.
Correct Answer: A — ΔG = -nFE
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Q. What is the relationship between Gibbs Free Energy and spontaneity?
A.
ΔG < 0 indicates non-spontaneous reactions.
B.
ΔG = 0 indicates spontaneous reactions.
C.
ΔG > 0 indicates spontaneous reactions.
D.
ΔG < 0 indicates spontaneous reactions.
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Solution
A negative ΔG (< 0) indicates that a reaction is spontaneous under the given conditions.
Correct Answer: D — ΔG < 0 indicates spontaneous reactions.
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Q. What is the relationship between Gibbs Free Energy and the equilibrium constant (K)?
A.
ΔG = -RT ln(K)
B.
ΔG = RT ln(K)
C.
ΔG = KRT
D.
ΔG = K - RT
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Solution
The relationship is given by 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 gravitational field strength and gravitational potential?
A.
Field strength is the gradient of potential.
B.
Field strength is the integral of potential.
C.
They are independent.
D.
Field strength is the square of potential.
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Solution
Gravitational field strength is the negative gradient of gravitational potential.
Correct Answer: A — Field strength is the gradient of potential.
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Q. What is the relationship between gravitational potential and gravitational field strength?
A.
V = -g * r
B.
g = -dV/dr
C.
V = g * r
D.
g = dV/dr
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Solution
The gravitational field strength g is the negative gradient of the gravitational potential V, given by g = -dV/dr.
Correct Answer: B — g = -dV/dr
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Q. What is the relationship between heat capacity at constant pressure (Cp) and heat capacity at constant volume (Cv)?
A.
Cp = Cv
B.
Cp > Cv
C.
Cp < Cv
D.
Cp = Cv + R
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Solution
For an ideal gas, Cp is always greater than Cv because it includes the work done against the atmospheric pressure.
Correct Answer: B — Cp > Cv
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Q. What is the relationship between heat capacity at constant pressure (C_p) and at constant volume (C_v)?
A.
C_p = C_v
B.
C_p > C_v
C.
C_p < C_v
D.
C_p = 0
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Solution
For an ideal gas, the heat capacity at constant pressure (C_p) is greater than the heat capacity at constant volume (C_v).
Correct Answer: B — C_p > C_v
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Q. What is the relationship between heat capacity at constant pressure (C_p) and heat capacity at constant volume (C_v)?
A.
C_p = C_v
B.
C_p > C_v
C.
C_p < C_v
D.
C_p = 2C_v
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Solution
For an ideal gas, C_p is always greater than C_v due to the work done during expansion.
Correct Answer: B — C_p > C_v
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Q. What is the relationship between heat capacity at constant volume (Cv) and heat capacity at constant pressure (Cp) for an ideal gas?
A.
Cp = Cv
B.
Cp = Cv + R
C.
Cp = Cv - R
D.
Cp = 2Cv
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Solution
For an ideal gas, the relationship is given by Cp = Cv + R, where R is the universal gas constant.
Correct Answer: B — Cp = Cv + R
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Q. What is the relationship between heat capacity at constant volume (Cv) and heat capacity at constant pressure (Cp)?
A.
Cp = Cv
B.
Cp = Cv + R
C.
Cp = Cv - R
D.
Cp = 2Cv
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Solution
The relationship is Cp = Cv + R for an ideal gas, where R is the gas constant.
Correct Answer: B — Cp = Cv + R
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Q. What is the relationship between Joules and Newton-meters?
A.
They are equal
B.
Joule is greater
C.
Newton-meter is greater
D.
They are unrelated
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Solution
1 Joule is defined as 1 Newton-meter, so they are equal.
Correct Answer: A — They are equal
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Q. What is the relationship between Ka and Kb for a conjugate acid-base pair?
A.
Ka + Kb = Kw
B.
Ka * Kb = Kw
C.
Ka - Kb = Kw
D.
Ka / Kb = Kw
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Solution
For a conjugate acid-base pair, the relationship is Ka * Kb = Kw, where Kw is the ion product of water.
Correct Answer: B — Ka * Kb = Kw
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Q. What is the relationship between Kp and Kc for the reaction aA(g) + bB(g) ⇌ cC(g) + dD(g)?
A.
Kp = Kc(RT)^(d+c-b-a)
B.
Kp = Kc(RT)^(a+b-c-d)
C.
Kp = Kc/(RT)^(d+c-b-a)
D.
Kp = Kc/(RT)^(a+b-c-d)
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Solution
The relationship between Kp and Kc is given by Kp = Kc(RT)^(Δn), where Δn = (d+c) - (a+b).
Correct Answer: A — Kp = Kc(RT)^(d+c-b-a)
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Q. What is the relationship between linear velocity (v) and angular velocity (ω) for a point on a rotating object?
A.
v = ωr
B.
v = r/ω
C.
v = ω/r
D.
v = rω²
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Solution
The relationship is given by v = ωr, where r is the radius of the rotation.
Correct Answer: A — v = ωr
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Q. What is the relationship between mass and weight?
A.
Weight = Mass × Acceleration due to gravity
B.
Weight = Mass / Acceleration due to gravity
C.
Weight = Mass + Acceleration due to gravity
D.
Weight = Mass - Acceleration due to gravity
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Solution
Weight is defined as the force due to gravity acting on a mass, given by the formula Weight = Mass × g (where g is the acceleration due to gravity).
Correct Answer: A — Weight = Mass × Acceleration due to gravity
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Q. What is the relationship between pKa and Ka for a weak acid?
A.
pKa = -log(Ka)
B.
pKa = log(Ka)
C.
pKa = Ka
D.
pKa = 1/Ka
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Solution
The relationship is given by the equation pKa = -log(Ka), where Ka is the acid dissociation constant.
Correct Answer: A — pKa = -log(Ka)
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Q. What is the relationship between pKa and Ka for an acid?
A.
pKa = -log(Ka)
B.
pKa = log(Ka)
C.
pKa = Ka
D.
pKa = 1/Ka
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Solution
The relationship is given by the formula pKa = -log(Ka), where Ka is the acid dissociation constant.
Correct Answer: A — pKa = -log(Ka)
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