Q. If a machine does 3000 J of work in 10 seconds, what is its power output?
A.
300 W
B.
150 W
C.
600 W
D.
1000 W
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Solution
Power (P) = Work (W) / Time (t) = 3000 J / 10 s = 300 W.
Correct Answer: A — 300 W
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Q. If a magnetic field is increasing at a rate of 0.1 T/s, what is the induced EMF in a coil of 50 turns and area 0.2 m²? (2021)
A.
1 V
B.
0.5 V
C.
0.2 V
D.
0.1 V
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Solution
Induced EMF (ε) = -N * (dB/dt) * A = -50 * 0.1 T/s * 0.2 m² = -1 V.
Correct Answer: A — 1 V
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Q. If a person does 200 J of work in 5 seconds, what is their power output?
A.
40 W
B.
50 W
C.
60 W
D.
30 W
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Solution
Power (P) = Work (W) / Time (t) = 200 J / 5 s = 40 W.
Correct Answer: B — 50 W
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Q. If a person does 300 J of work in 15 seconds, what is their average power output?
A.
20 W
B.
15 W
C.
25 W
D.
30 W
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Solution
Power = Work / Time = 300 J / 15 s = 20 W
Correct Answer: A — 20 W
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Q. If a person does 300 J of work in 15 seconds, what is their power output?
A.
20 W
B.
15 W
C.
25 W
D.
30 W
Show solution
Solution
Power = Work / Time = 300 J / 15 s = 20 W
Correct Answer: A — 20 W
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Q. If a person does 500 J of work in 5 seconds, what is their power output?
A.
100 W
B.
50 W
C.
200 W
D.
150 W
Show solution
Solution
Power (P) = Work (W) / Time (t) = 500 J / 5 s = 100 W.
Correct Answer: A — 100 W
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Q. If a person lifts a 20 kg box to a height of 2 m, what is the work done against gravity? (g = 9.8 m/s²)
A.
392 J
B.
196 J
C.
588 J
D.
784 J
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Solution
Work = m * g * h = 20 kg * 9.8 m/s² * 2 m = 392 J.
Correct Answer: B — 196 J
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Q. If a physical quantity has dimensions [M^0 L^1 T^-1], what is it? (2020)
A.
Velocity
B.
Acceleration
C.
Force
D.
Energy
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Solution
The dimensions [M^0 L^1 T^-1] correspond to velocity, which is defined as distance traveled per unit time.
Correct Answer: A — Velocity
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Q. If a physical quantity has dimensions [M^2 L^3 T^-1], what could it represent? (2020)
A.
Force
B.
Pressure
C.
Volume flow rate
D.
Energy
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Solution
The dimensions [M^2 L^3 T^-1] correspond to volume flow rate, which is volume per unit time.
Correct Answer: C — Volume flow rate
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Q. If a rectangle has a length of 10 and a width of 5, what is its area? (2017)
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Solution
Area = length × width = 10 × 5 = 50.
Correct Answer: A — 50
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Q. If a rectangle has a length of 10 cm and a width of 5 cm, what is its area? (2017)
A.
50 cm²
B.
60 cm²
C.
40 cm²
D.
30 cm²
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Solution
Area = length × width = 10 cm × 5 cm = 50 cm².
Correct Answer: A — 50 cm²
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Q. If a rectangle has a length of 12 cm and a width of 4 cm, what is its perimeter? (2019)
A.
32 cm
B.
28 cm
C.
24 cm
D.
30 cm
Show solution
Solution
Perimeter = 2(length + width) = 2(12 + 4) = 32 cm.
Correct Answer: A — 32 cm
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Q. If a rectangle has a length of 8 cm and a width of 3 cm, what is its area? (2015)
A.
24 cm²
B.
30 cm²
C.
20 cm²
D.
18 cm²
Show solution
Solution
Area = length × width = 8 × 3 = 24 cm².
Correct Answer: A — 24 cm²
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Q. If a rectangle has a length of 8 cm and a width of 3 cm, what is its perimeter? (2019)
A.
22 cm
B.
24 cm
C.
20 cm
D.
26 cm
Show solution
Solution
Perimeter = 2(length + width) = 2(8 + 3) = 22 cm.
Correct Answer: A — 22 cm
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Q. If a student guesses on a multiple-choice test with 4 options per question, what is the probability of guessing correctly?
A.
1/4
B.
1/2
C.
1/3
D.
1/5
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Solution
Probability of guessing correctly = 1/4.
Correct Answer: A — 1/4
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Q. If a student guesses on a multiple-choice test with 4 options, what is the probability of guessing correctly? (2022)
A.
1/4
B.
1/2
C.
1/3
D.
1/5
Show solution
Solution
Probability of guessing correctly = 1/4.
Correct Answer: A — 1/4
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Q. If a student is selected at random from a group of 10 boys and 15 girls, what is the probability that the student is a girl? (2023)
A.
1/2
B.
3/5
C.
2/5
D.
1/3
Show solution
Solution
Total students = 10 + 15 = 25. Probability of girl = 15/25 = 3/5.
Correct Answer: B — 3/5
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Q. If a student is selected at random from a group of 20 students, 12 of whom are girls, what is the probability that the student is a girl?
A.
3/5
B.
2/5
C.
1/2
D.
1/3
Show solution
Solution
Probability of selecting a girl = 12/20 = 3/5.
Correct Answer: A — 3/5
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Q. If a student is selected at random from a group of 20 students, what is the probability that the student is not a girl if there are 12 girls? (2020)
A.
2/5
B.
1/5
C.
3/5
D.
1/2
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Solution
Number of boys = 20 - 12 = 8. Probability = 8/20 = 2/5.
Correct Answer: A — 2/5
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Q. If a student is selected at random from a group of 40 students, 25 of whom are boys, what is the probability that the student is a girl? (2020)
A.
1/2
B.
3/8
C.
3/5
D.
5/8
Show solution
Solution
There are 40 - 25 = 15 girls. The probability of selecting a girl is 15/40 = 3/8.
Correct Answer: D — 5/8
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Q. If a vehicle accelerates from 0 to 60 m/s in 12 seconds, what is its acceleration?
A.
2 m/s²
B.
4 m/s²
C.
5 m/s²
D.
6 m/s²
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Solution
Using the formula: a = (v - u) / t = (60 - 0) / 12 = 5 m/s².
Correct Answer: B — 4 m/s²
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Q. If a wave has a frequency of 50 Hz and a wavelength of 2 m, what is its speed? (2018)
A.
100 m/s
B.
50 m/s
C.
25 m/s
D.
200 m/s
Show solution
Solution
Wave speed = frequency × wavelength = 50 Hz × 2 m = 100 m/s.
Correct Answer: A — 100 m/s
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Q. If a wave has a frequency of 50 Hz, what is its period? (2022)
A.
0.02 s
B.
0.5 s
C.
2 s
D.
20 s
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Solution
Period (T) = 1/Frequency = 1/50 Hz = 0.02 s.
Correct Answer: A — 0.02 s
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Q. If C = [[0, 1], [1, 0]], what is det(C)? (2022)
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Solution
Determinant of C = (0*0) - (1*1) = 0 - 1 = -1.
Correct Answer: C — -1
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Q. If cos(θ) = 0, what is the value of θ? (2017)
A.
0°
B.
90°
C.
180°
D.
270°
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Solution
cos(90°) = 0, so θ = 90°
Correct Answer: B — 90°
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Q. If cos(θ) = 0.5, what is the value of θ in degrees? (2017)
A.
30°
B.
45°
C.
60°
D.
90°
Show solution
Solution
cos(60°) = 0.5, so θ = 60°
Correct Answer: C — 60°
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Q. If cos(θ) = 0.5, what is the value of θ? (2020)
A.
0°
B.
30°
C.
60°
D.
90°
Show solution
Solution
cos(60°) = 0.5, so θ = 60°.
Correct Answer: C — 60°
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Q. If cos(θ) = 0.6, what is sin(θ) using Pythagorean identity? (2017)
A.
0.4
B.
0.5
C.
0.6
D.
0.8
Show solution
Solution
sin²(θ) + cos²(θ) = 1; sin²(θ) = 1 - 0.6² = 0.64; sin(θ) = √0.64 = 0.8.
Correct Answer: A — 0.4
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Q. If cos(θ) = 0.707, what is θ? (2020)
A.
30°
B.
45°
C.
60°
D.
90°
Show solution
Solution
cos(45°) = √2/2 ≈ 0.707, so θ = 45°.
Correct Answer: B — 45°
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Q. If cos(θ) = 1/2, what is θ in degrees?
A.
30°
B.
45°
C.
60°
D.
90°
Show solution
Solution
cos(60°) = 1/2, so θ = 60°
Correct Answer: C — 60°
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