Q. What is the refractive index of a medium if the critical angle for total internal reflection is 30° when light travels to air?
A.
1.73
B.
1.00
C.
1.41
D.
1.50
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Solution
Using sin(30°) = 0.5, n = 1/sin(30°) = 1/0.5 = 2. Therefore, the refractive index is 2.
Correct Answer: A — 1.73
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Q. What is the relationship between a function and its inverse?
A.
They are always identical.
B.
The inverse function undoes the action of the original function.
C.
They can never intersect on a graph.
D.
The inverse function is always a polynomial.
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Solution
The inverse function undoes the action of the original function, meaning that applying a function and then its inverse returns the original input.
Correct Answer: B — The inverse function undoes the action of the original function.
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Q. What is the relationship between angular momentum L and moment of inertia I for a rotating object?
A.
L = Iω
B.
L = I²ω
C.
L = ω/I
D.
L = I + ω
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Solution
Angular momentum L is given by L = Iω, where ω is the angular velocity.
Correct Answer: A — L = Iω
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Q. What is the relationship between bulk modulus and compressibility?
A.
Bulk modulus is the inverse of compressibility
B.
Bulk modulus is equal to compressibility
C.
Bulk modulus is the square of compressibility
D.
There is no relationship
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Solution
Bulk modulus is defined as the reciprocal of compressibility, indicating how incompressible a material is.
Correct Answer: A — Bulk modulus is the inverse of compressibility
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Q. What is the relationship between Celsius and Kelvin?
A.
K = C + 273.15
B.
K = C - 273.15
C.
C = K + 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 charge (Q), capacitance (C), and voltage (V) in a capacitor? (2023)
A.
Q = CV
B.
Q = C/V
C.
Q = V/C
D.
Q = C + V
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Solution
The relationship is given by Q = CV, where Q is the charge, C is the capacitance, and V is the voltage across the capacitor.
Correct Answer: A — Q = CV
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Q. What is the relationship between climate change and economic growth as discussed in the passage?
A.
Economic growth is unaffected by climate change.
B.
Climate change hinders economic growth in the long term.
C.
Economic growth accelerates climate change.
D.
There is no relationship between the two.
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Solution
The passage discusses how climate change can hinder economic growth in the long term, emphasizing the need for sustainable practices.
Correct Answer: B — Climate change hinders economic growth in the long term.
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Q. What is the relationship between current (I), charge (Q), and time (t)? (2022)
A.
I = Q × t
B.
I = Q / t
C.
I = t / Q
D.
I = Q + t
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Solution
The relationship is given by I = Q / t, where I is current, Q is charge, and t is time.
Correct Answer: B — I = Q / t
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Q. What is the relationship between current (I), voltage (V), and resistance (R) in a circuit? (2021)
A.
I = V/R
B.
I = R/V
C.
I = V*R
D.
I = V + R
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Solution
The relationship is given by Ohm's law: I = V/R.
Correct Answer: A — I = V/R
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Q. What is the relationship between current and magnetic field in a long straight conductor?
A.
Directly proportional
B.
Inversely proportional
C.
Independent
D.
Exponential
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Solution
The magnetic field around a long straight conductor is directly proportional to the current flowing through it.
Correct Answer: A — Directly proportional
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Q. What is the relationship between current, voltage, and resistance called? (2021)
A.
Ohm's Law
B.
Kirchhoff's Law
C.
Faraday's Law
D.
Ampere's Law
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Solution
The relationship between current, voltage, and resistance is called Ohm's Law.
Correct Answer: A — Ohm's Law
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Q. What is the relationship between current, voltage, and resistance in an electrical circuit?
A.
Ohm's Law
B.
Kirchhoff's Law
C.
Faraday's Law
D.
Ampere's Law
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Solution
Ohm's Law defines the relationship between current (I), voltage (V), and resistance (R) as V = IR.
Correct Answer: A — Ohm's Law
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Q. What is the relationship between digital sum and error detection as mentioned in the passage? (2023)
A.
Digital sum is irrelevant to error detection.
B.
Digital sum can enhance error detection methods.
C.
Error detection methods are based solely on digital sum.
D.
Digital sum complicates error detection processes.
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Solution
The passage indicates that digital sum plays a significant role in improving error detection techniques.
Correct Answer: B — Digital sum can enhance error detection methods.
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Q. What is the relationship between electric field (E) and electric potential (V) in a uniform field? (2022)
A.
E = V/d
B.
E = d/V
C.
E = V^2
D.
E = V/d^2
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Solution
In a uniform electric field, the electric field E is related to the potential difference V and the distance d by the equation E = V/d.
Correct Answer: A — E = V/d
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Q. What is the relationship between electric field and electric potential?
A.
E = -dV/dr
B.
E = dV/dr
C.
E = V/r
D.
E = V^2
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Solution
The electric field E is the negative gradient of the electric potential V, given by E = -dV/dr.
Correct Answer: A — E = -dV/dr
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Q. What is the relationship between electric field E and electric potential V?
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, given by E = -dV/dx.
Correct Answer: A — E = -dV/dx
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Q. What is the relationship between electric field E and potential V in a uniform electric field?
A.
E = -dV/dx
B.
E = dV/dx
C.
E = V/dx
D.
E = -V/dx
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Solution
In a uniform electric field, the relationship is given by E = -dV/dx, indicating that the electric field points in the direction of decreasing potential.
Correct Answer: A — E = -dV/dx
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Q. What is the relationship between electric field E and potential V in electrostatics?
A.
E = -dV/dx
B.
E = dV/dx
C.
E = V/dx
D.
E = -V
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Solution
The electric field is the negative gradient of the electric potential, E = -dV/dx.
Correct Answer: A — E = -dV/dx
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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 the time period of an AC signal? (2023)
A.
Frequency = Time period × 2
B.
Frequency = 1 / Time period
C.
Frequency = Time period / 2
D.
Frequency = Time period × π
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Solution
The frequency (f) is the reciprocal of the time period (T), given by f = 1 / T.
Correct Answer: B — Frequency = 1 / Time period
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