Q. If the wavelength of light is halved, what happens to its frequency? (2021)
A.
It is halved
B.
It remains the same
C.
It is doubled
D.
It is quadrupled
Show solution
Solution
Frequency (f) is inversely proportional to wavelength (λ). If λ is halved, f is doubled.
Correct Answer:
C
— It is doubled
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Q. If the wavelength of light is halved, what happens to the energy of the photons? (2020)
A.
It is halved
B.
It is doubled
C.
It remains the same
D.
It is quadrupled
Show solution
Solution
Energy is inversely proportional to wavelength. Halving the wavelength doubles the energy.
Correct Answer:
B
— It is doubled
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Q. If the wavelength of light used in a diffraction grating is increased, what happens to the angular separation of the fringes? (2023)
A.
Increases
B.
Decreases
C.
Remains the same
D.
Becomes zero
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Solution
The angular separation (θ) is directly proportional to the wavelength (λ). Therefore, increasing λ increases the angular separation.
Correct Answer:
A
— Increases
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Q. If the wavelength of light used in a double-slit experiment is increased, what happens to the fringe separation? (2022)
A.
Increases
B.
Decreases
C.
Remains the same
D.
Becomes zero
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Solution
Fringe separation is directly proportional to the wavelength. If the wavelength increases, the fringe separation also increases.
Correct Answer:
A
— Increases
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Q. If the wavelength of light used in a double-slit experiment is increased, what happens to the distance between the fringes? (2022)
A.
Increases
B.
Decreases
C.
Remains the same
D.
Becomes zero
Show solution
Solution
The fringe width is directly proportional to the wavelength. Therefore, increasing the wavelength increases the distance between the fringes.
Correct Answer:
A
— Increases
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Q. If the wavelength of light used in a single-slit diffraction experiment is increased, what happens to the width of the central maximum? (2023)
A.
It decreases
B.
It increases
C.
It remains the same
D.
It becomes zero
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Solution
The width of the central maximum in single-slit diffraction is directly proportional to the wavelength. Increasing the wavelength increases the width.
Correct Answer:
B
— It increases
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Q. If the wavelength of light used in a single-slit diffraction experiment is increased, what will happen to the position of the first minimum? (2022)
A.
It moves closer to the center
B.
It moves away from the center
C.
It remains unchanged
D.
It disappears
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Solution
The position of the first minimum in single-slit diffraction is given by a sin(θ) = λ. Increasing λ will cause θ to increase, moving the minimum away from the center.
Correct Answer:
B
— It moves away from the center
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Q. If two charges +Q and -Q are placed at a distance 'd' apart, what is the electric field at the midpoint? (2020)
A.
0
B.
kQ/d^2
C.
kQ/(2d^2)
D.
kQ/d
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Solution
At the midpoint, the electric fields due to +Q and -Q cancel each other out, resulting in a net electric field of 0.
Correct Answer:
A
— 0
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Q. If two coins are tossed, what is the probability of getting at least one tail? (2023)
A.
1/4
B.
1/2
C.
3/4
D.
1/3
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Solution
The possible outcomes are HH, HT, TH, TT. The outcomes with at least one tail are HT, TH, TT (3 outcomes). So, the probability is 3/4.
Correct Answer:
C
— 3/4
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Q. If two dice are rolled, what is the probability that the sum is 7?
A.
1/6
B.
1/12
C.
1/36
D.
5/36
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Solution
Possible combinations for sum 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6 combinations. Total outcomes = 36. Probability = 6/36 = 1/6.
Correct Answer:
D
— 5/36
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Q. If two identical capacitors of 4 µF each are connected in series, what is the equivalent capacitance?
A.
2 µF
B.
4 µF
C.
6 µF
D.
8 µF
Show solution
Solution
C_eq = 1 / (1/C1 + 1/C2) = 1 / (1/4 + 1/4) = 2 µF.
Correct Answer:
A
— 2 µF
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Q. If two resistors of 4Ω and 6Ω are connected in series, what is the total resistance? (2023)
A.
10Ω
B.
24Ω
C.
2.4Ω
D.
12Ω
Show solution
Solution
In series, R_eq = R1 + R2 = 4Ω + 6Ω = 10Ω.
Correct Answer:
A
— 10Ω
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Q. If two resistors of 4Ω and 6Ω are connected in series, what is the total voltage across them if the current is 2A? (2022)
A.
20V
B.
12V
C.
8V
D.
10V
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Solution
Total resistance R = 4Ω + 6Ω = 10Ω. Voltage V = I * R = 2A * 10Ω = 20V.
Correct Answer:
A
— 20V
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Q. If U = {1, 2, 3, 4, 5} and A = {1, 2}, what is A'?
A.
{3, 4, 5}
B.
{1, 2}
C.
{1, 2, 3}
D.
{}
Show solution
Solution
The complement A' consists of all elements in U that are not in A. Therefore, A' = {3, 4, 5}.
Correct Answer:
A
— {3, 4, 5}
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Q. If x = 3, what is the value of 2x^2 - 5x + 1? (2022)
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Solution
2(3^2) - 5(3) + 1 = 18 - 15 + 1 = 4.
Correct Answer:
D
— 6
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Q. If x = 5, what is the value of 2x + 3? (2022)
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Solution
Substituting x = 5, we get 2(5) + 3 = 10 + 3 = 13.
Correct Answer:
B
— 13
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Q. If x = 5, what is the value of 3x + 2? (2022)
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Solution
3(5) + 2 = 15 + 2 = 17.
Correct Answer:
A
— 17
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Q. If you have 0.25 moles of sulfuric acid (H2SO4), what is its mass? (2023)
A.
49 g
B.
98 g
C.
25 g
D.
12.5 g
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Solution
Molar mass of H2SO4 = 2*1 + 32 + 4*16 = 98 g/mol. Mass = 0.25 moles x 98 g/mol = 24.5 g.
Correct Answer:
B
— 98 g
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Q. If z = -2 + 2i, what is the value of |z|? (2019)
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Solution
|z| = √((-2)^2 + (2)^2) = √(4 + 4) = √8 = 2√2.
Correct Answer:
A
— 2√2
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Q. If z = 1 + i, what is the value of z^2? (2022)
A.
2i
B.
1 + 2i
C.
2
D.
0
Show solution
Solution
z^2 = (1 + i)^2 = 1^2 + 2(1)(i) + i^2 = 1 + 2i - 1 = 2i.
Correct Answer:
B
— 1 + 2i
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Q. If z = 1 + i, what is the value of z²? (2022)
A.
0
B.
2i
C.
2
D.
1 + 2i
Show solution
Solution
z² = (1 + i)² = 1² + 2(1)(i) + i² = 1 + 2i - 1 = 2i.
Correct Answer:
D
— 1 + 2i
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Q. If z = 1 + √3i, what is the argument of z? (2015)
A.
π/3
B.
π/6
C.
2π/3
D.
3π/4
Show solution
Solution
The argument is given by tan^(-1)(√3/1) = π/3.
Correct Answer:
A
— π/3
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Q. If z = 2 + 2i, what is |z|^2? (2021)
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Solution
|z|^2 = (2^2 + 2^2) = 4 + 4 = 8.
Correct Answer:
A
— 8
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Q. If z = 2 - 3i, what is the conjugate of z? (2020)
A.
2 + 3i
B.
2 - 3i
C.
-2 + 3i
D.
-2 - 3i
Show solution
Solution
The conjugate of z = 2 - 3i is 2 + 3i.
Correct Answer:
A
— 2 + 3i
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Q. If z = 3 + 4i, what is the imaginary part of z? (2022) 2022
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Solution
The imaginary part of the complex number z = 3 + 4i is 4.
Correct Answer:
B
— 4
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Q. If z = 3 + 4i, what is the value of z + z* (where z* is the conjugate of z)? (2017)
Show solution
Solution
z + z* = (3 + 4i) + (3 - 4i) = 6.
Correct Answer:
B
— 8
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Q. If z = 3 + 4i, what is the value of z + z̅? (2022)
Show solution
Solution
z + z̅ = (3 + 4i) + (3 - 4i) = 6.
Correct Answer:
B
— 8
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Q. If z = 3 + 4i, what is the value of |z|^2? (2019)
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Solution
|z|^2 = 3^2 + 4^2 = 9 + 16 = 25.
Correct Answer:
A
— 25
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Q. If z = 4 + 3i, what is the real part of z? (2023)
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Solution
The real part of the complex number z = 4 + 3i is 4.
Correct Answer:
A
— 4
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Q. If z = 5 + 12i, what is the argument of z? (2022)
A.
arctan(12/5)
B.
arctan(5/12)
C.
π/2
D.
0
Show solution
Solution
The argument of z = 5 + 12i is given by arctan(12/5).
Correct Answer:
A
— arctan(12/5)
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