Q. If the frequency of an AC source is 50 Hz, what is the time period of the AC signal? (2019)
A.
0.02 s
B.
0.01 s
C.
0.5 s
D.
1 s
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Solution
The time period (T) is the reciprocal of frequency (f). Therefore, T = 1/f = 1/50 Hz = 0.02 s.
Correct Answer: A — 0.02 s
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Q. If the frequency of an AC source is 60 Hz, what is the time period of the AC signal?
A.
0.0167 s
B.
0.0333 s
C.
0.05 s
D.
0.1 s
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Solution
The time period (T) is the reciprocal of frequency (f). T = 1/f = 1/60 Hz = 0.0167 s.
Correct Answer: B — 0.0333 s
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Q. If the frequency of an AC source is doubled, how does the inductive reactance change? (2020)
A.
Doubles
B.
Halves
C.
Remains the same
D.
Quadruples
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Solution
Xl = 2πfL; if f is doubled, Xl also doubles.
Correct Answer: B — Halves
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Q. If the frequency of an AC source is doubled, what happens to the inductive reactance of an inductor? (2021)
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
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Solution
Inductive reactance Xl = ωL, so if frequency is doubled, Xl halves.
Correct Answer: B — It halves
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Q. If the frequency of an AC source is doubled, what happens to the inductive reactance? (2014)
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
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Solution
Inductive reactance XL = 2πfL, so if frequency f is doubled, XL halves.
Correct Answer: B — It halves
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Q. If the frequency of an AC source is doubled, what happens to the reactance of a capacitor? (2023)
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
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Solution
The capacitive reactance Xc = 1/(2πfC) halves when the frequency f is doubled.
Correct Answer: B — It halves
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Q. If the frequency of an AC source is doubled, what happens to the reactance of an inductor? (2023)
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
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Solution
The reactance of an inductor is given by XL = ωL. If frequency is doubled, reactance also doubles.
Correct Answer: A — It doubles
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Q. If the frequency of an AC source is increased, what happens to the capacitive reactance?
A.
It increases
B.
It decreases
C.
It remains the same
D.
It becomes infinite
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Solution
Capacitive reactance X_C = 1/(ωC) decreases as frequency increases.
Correct Answer: B — It decreases
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Q. If the frequency of an AC source is increased, what happens to the inductive reactance? (2019)
A.
Increases
B.
Decreases
C.
Remains constant
D.
Becomes zero
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Solution
Inductive reactance (X_L) is directly proportional to frequency (f). Therefore, if frequency increases, X_L decreases.
Correct Answer: B — Decreases
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Q. If the frequency of incident light is doubled, what happens to the kinetic energy of the emitted electrons?
A.
It remains the same
B.
It doubles
C.
It quadruples
D.
It decreases
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Solution
The kinetic energy of the emitted electrons is given by KE = hf - φ. If the frequency is doubled, the kinetic energy increases as it is directly proportional to frequency.
Correct Answer: B — It doubles
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Q. If the function f(x) = e^x + x^2 has a minimum at x = 0, then f(0) is:
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Solution
Evaluating f(0) = e^0 + 0^2 = 1 + 0 = 1.
Correct Answer: A — 1
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Q. If the function f(x) = x^2 - 4x + 3 has a minimum value, what is it?
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Solution
The vertex form gives the minimum value at x = 2, f(2) = 1.
Correct Answer: A — -1
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Q. If the function f(x) = x^3 - 3x + 2 has a local maximum, what is the value of x?
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Solution
Setting f'(x) = 0 gives x = 1 as a local maximum.
Correct Answer: C — 1
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Q. If the galvanometer in a Wheatstone bridge has a high resistance, what is the effect on the sensitivity of the bridge?
A.
Increases sensitivity
B.
Decreases sensitivity
C.
No effect
D.
Depends on the resistances
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Solution
A high resistance in the galvanometer increases the sensitivity of the bridge.
Correct Answer: A — Increases sensitivity
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Q. If the galvanometer in a Wheatstone bridge has a resistance of 5Ω and the bridge is balanced, what is the current through the galvanometer?
A.
Zero.
B.
5A.
C.
1A.
D.
10A.
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Solution
In a balanced Wheatstone bridge, the current through the galvanometer is zero.
Correct Answer: A — Zero.
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Q. If the galvanometer in a Wheatstone bridge shows a deflection, what does it indicate?
A.
The bridge is balanced.
B.
The bridge is unbalanced.
C.
The resistances are equal.
D.
The circuit is open.
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Solution
A deflection in the galvanometer indicates that the bridge is unbalanced, meaning the ratios of resistances are not equal.
Correct Answer: B — The bridge is unbalanced.
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Q. If the galvanometer shows a deflection in a Wheatstone bridge, what can be inferred?
A.
The bridge is balanced
B.
The bridge is unbalanced
C.
The resistances are equal
D.
The circuit is open
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Solution
A deflection in the galvanometer indicates that there is a potential difference across it, meaning the bridge is unbalanced.
Correct Answer: B — The bridge is unbalanced
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Q. If the galvanometer shows a deflection when the Wheatstone bridge is not balanced, what does it indicate?
A.
The bridge is balanced
B.
The resistances are equal
C.
There is a potential difference
D.
The circuit is open
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Solution
A deflection in the galvanometer indicates that there is a potential difference across it, meaning the bridge is not balanced.
Correct Answer: C — There is a potential difference
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Q. If the GCD of two numbers is 1, which of the following statements is true?
A.
The numbers are multiples of each other
B.
The numbers are co-prime
C.
The numbers are both even
D.
The numbers are both odd
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Solution
If the GCD of two numbers is 1, it means they have no common factors other than 1, hence they are co-prime.
Correct Answer: B — The numbers are co-prime
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Q. If the graph of a function f(x) is symmetric about the y-axis, which of the following must be true?
A.
f(x) = f(-x) for all x.
B.
f(x) = -f(-x) for all x.
C.
f(x) is always positive.
D.
f(x) has a maximum value.
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Solution
A function that is symmetric about the y-axis satisfies the property f(x) = f(-x) for all x.
Correct Answer: A — f(x) = f(-x) for all x.
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Q. If the graph of a function is symmetric about the y-axis, which of the following types of functions could it represent?
A.
Linear function
B.
Odd function
C.
Even function
D.
Exponential function
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Solution
A function is symmetric about the y-axis if it is an even function, which satisfies the condition f(x) = f(-x).
Correct Answer: C — Even function
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Q. If the graph of a function is symmetric about the y-axis, which of the following types of functions could it be?
A.
Linear function
B.
Odd function
C.
Even function
D.
Exponential function
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Solution
A function is symmetric about the y-axis if it is an even function, which satisfies the condition f(x) = f(-x).
Correct Answer: C — Even function
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Q. If the graph of a function is symmetric about the y-axis, which of the following must be true?
A.
The function is linear.
B.
The function is even.
C.
The function is odd.
D.
The function has no intercepts.
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Solution
A function is even if it is symmetric about the y-axis, meaning f(x) = f(-x) for all x.
Correct Answer: B — The function is even.
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Q. If the gravitational field strength at a point is 10 N/kg, what is the gravitational potential at that point assuming it is at infinity?
A.
0 J/kg
B.
-10 J/kg
C.
10 J/kg
D.
-5 J/kg
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Solution
The gravitational potential is negative and is given by V = -g * r. At infinity, V approaches 0, so at a field strength of 10 N/kg, V = -10 J/kg.
Correct Answer: B — -10 J/kg
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Q. If the gravitational field strength at a point is 10 N/kg, what is the gravitational potential at that point assuming the reference point is at infinity?
A.
-10 J/kg
B.
10 J/kg
C.
0 J/kg
D.
-5 J/kg
Show solution
Solution
The gravitational potential V is related to the gravitational field strength g by V = -g * r. If we consider r to be 1 meter, V = -10 * 1 = -10 J/kg.
Correct Answer: A — -10 J/kg
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Q. If the gravitational field strength at a point is 10 N/kg, what is the gravitational potential at that point, assuming it is at a distance of 2 meters from the mass creating the field?
A.
-20 J/kg
B.
-10 J/kg
C.
0 J/kg
D.
-5 J/kg
Show solution
Solution
Gravitational potential V = -g * r = -10 N/kg * 2 m = -20 J/kg.
Correct Answer: A — -20 J/kg
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Q. If the gravitational field strength at a point is 10 N/kg, what is the gravitational potential at that point, assuming it is at a distance of 2 m from the mass creating the field?
A.
-20 J/kg
B.
-10 J/kg
C.
0 J/kg
D.
-5 J/kg
Show solution
Solution
Gravitational potential V = -g * r = -10 N/kg * 2 m = -20 J/kg.
Correct Answer: A — -20 J/kg
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Q. If the gravitational field strength at a point is 10 N/kg, what is the gravitational potential at that point assuming it is 2 meters from the mass?
A.
-20 J/kg
B.
-10 J/kg
C.
0 J/kg
D.
-5 J/kg
Show solution
Solution
Gravitational potential V = -g * r = -10 * 2 = -20 J/kg.
Correct Answer: A — -20 J/kg
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Q. If the gravitational field strength at a point is 10 N/kg, what is the gravitational potential at that point, assuming it is 2 meters above the reference point?
A.
-20 J/kg
B.
-10 J/kg
C.
0 J/kg
D.
-5 J/kg
Show solution
Solution
Gravitational potential V = -g * h = -10 N/kg * 2 m = -20 J/kg.
Correct Answer: A — -20 J/kg
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Q. If the gravitational field strength at a point is 10 N/kg, what is the gravitational potential at that point, assuming it is 2 meters from the mass creating the field?
A.
-20 J/kg
B.
-10 J/kg
C.
0 J/kg
D.
-5 J/kg
Show solution
Solution
Gravitational potential V = -g * r = -10 N/kg * 2 m = -20 J/kg.
Correct Answer: A — -20 J/kg
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