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 function f(x) is defined as f(x) = 2x + 1, what is the value of f(3)?
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Solution
Substituting x = 3 into the function gives f(3) = 2(3) + 1 = 6 + 1 = 7.
Correct Answer:
C
— 7
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Q. If the function g(x) = 2x + 3 is transformed to g(x) = 2(x - 1) + 3, what type of transformation has occurred?
A.
Vertical shift up.
B.
Vertical shift down.
C.
Horizontal shift left.
D.
Horizontal shift right.
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Solution
The transformation g(x) = 2(x - 1) + 3 indicates a horizontal shift to the right by 1 unit.
Correct Answer:
D
— Horizontal shift right.
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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.
Show solution
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
Show solution
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
Show solution
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, what can be inferred about the two numbers? (2023)
A.
They are both even.
B.
They are both odd.
C.
They are coprime.
D.
They are multiples of each other.
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Solution
If the GCD of two numbers is 1, it means they have no common factors other than 1, thus they are coprime.
Correct Answer:
C
— They are coprime.
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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 GDP of a country is $1 trillion and it grows by 5% in a year, what will be the GDP at the end of the year?
A.
$1.05 trillion
B.
$1.1 trillion
C.
$1.2 trillion
D.
$1.15 trillion
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Solution
GDP after growth = 1 trillion * (1 + 0.05) = 1 trillion * 1.05 = $1.05 trillion.
Correct Answer:
A
— $1.05 trillion
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Q. If the GDP of a country is $2 trillion and it decreases by 10% due to a recession, what will be the new GDP?
A.
$1.8 trillion
B.
$1.9 trillion
C.
$2 trillion
D.
$2.1 trillion
Show solution
Solution
New GDP = 2 trillion * (1 - 0.10) = 2 trillion * 0.90 = $1.8 trillion.
Correct Answer:
A
— $1.8 trillion
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Q. If the GDP of a country is $2 trillion and it decreases by 10%, what will be the new GDP?
A.
$1.8 trillion
B.
$1.9 trillion
C.
$2 trillion
D.
$2.1 trillion
Show solution
Solution
New GDP = 2 trillion * (1 - 0.10) = 2 trillion * 0.90 = $1.8 trillion.
Correct Answer:
A
— $1.8 trillion
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Q. If the GDP of a country is $2 trillion and it decreases by 2% in a year, what will be the GDP at the end of the year?
A.
$1.96 trillion
B.
$1.98 trillion
C.
$2 trillion
D.
$2.02 trillion
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Solution
GDP after decrease = 2 trillion * (1 - 0.02) = 2 trillion * 0.98 = $1.96 trillion.
Correct Answer:
B
— $1.98 trillion
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Q. If the GDP of a country is $800 billion and it decreases by 10% due to a recession, what will be the new GDP?
A.
$720 billion
B.
$740 billion
C.
$760 billion
D.
$800 billion
Show solution
Solution
New GDP = 800 * (1 - 0.10) = 800 * 0.90 = $720 billion.
Correct Answer:
A
— $720 billion
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Q. If the government allocates a budget of ₹500 crores for a scheme and 30% of it is spent on infrastructure, how much is spent on infrastructure?
A.
₹100 crores
B.
₹150 crores
C.
₹200 crores
D.
₹250 crores
Show solution
Solution
30% of ₹500 crores = 0.30 * 500 = ₹150 crores.
Correct Answer:
B
— ₹150 crores
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Q. If the graph of a function f(x) intersects the x-axis at x = 1 and x = 3, which of the following can be inferred?
A.
f(1) = 0 and f(3) = 0.
B.
The function is linear.
C.
The function has no real roots.
D.
The function is increasing.
Show solution
Solution
If the graph intersects the x-axis at x = 1 and x = 3, it means that f(1) = 0 and f(3) = 0, indicating the roots of the function.
Correct Answer:
A
— f(1) = 0 and f(3) = 0.
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Q. If the graph of a function f(x) intersects the x-axis at x = 3, what can be concluded?
A.
f(3) = 0.
B.
f(3) > 0.
C.
f(3) < 0.
D.
f(3) is undefined.
Show solution
Solution
The intersection of the graph with the x-axis indicates that the function value at that point is zero.
Correct Answer:
A
— f(3) = 0.
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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.
Show solution
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 a parabola opening upwards, which of the following can be inferred about the function?
A.
The function has a maximum value.
B.
The function has a minimum value.
C.
The function is linear.
D.
The function is constant.
Show solution
Solution
A parabola that opens upwards indicates that the function has a minimum value at its vertex.
Correct Answer:
B
— The function has a minimum value.
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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
Show solution
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.
Show solution
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 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
Show solution
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 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 at infinity?
A.
0 J/kg
B.
-10 J/kg
C.
10 J/kg
D.
-5 J/kg
Show solution
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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