Undergraduate
Q. If a circuit has a voltage of 12 V and a resistance of 3 ohms, what is the current flowing through the circuit? (2022)
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A.
4 A
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B.
3 A
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C.
2 A
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D.
1 A
Solution
Using Ohm's law (I = V/R), I = 12 V / 3 Ω = 4 A.
Correct Answer: A — 4 A
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Q. If a coin is tossed twice, what is the probability of getting at least one head?
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A.
1/4
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B.
1/2
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C.
3/4
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D.
1
Solution
Total outcomes = 4 (HH, HT, TH, TT). Outcomes with at least one head = 3. Probability = 3/4.
Correct Answer: C — 3/4
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Q. If a die is rolled, what is the probability of getting an even number? (2022)
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A.
1/2
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B.
1/3
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C.
1/6
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D.
2/3
Solution
Even numbers on a die = 2, 4, 6. Probability = 3/6 = 1/2.
Correct Answer: A — 1/2
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Q. If a force of 10 N moves an object 5 m in the direction of the force, what is the work done? (2020)
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A.
50 J
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B.
10 J
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C.
5 J
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D.
25 J
Solution
Work Done (W) = Force (F) * Distance (d) = 10 N * 5 m = 50 J
Correct Answer: A — 50 J
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Q. If a force of 15 N is applied to a 3 kg object, what is the net force acting on the object if it is already moving with a velocity of 5 m/s? (2022)
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A.
15 N
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B.
3 N
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C.
0 N
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D.
18 N
Solution
The net force is still 15 N as it does not depend on the velocity of the object.
Correct Answer: A — 15 N
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Q. If a force of 15 N is applied to a mass of 3 kg, what is the acceleration of the mass? (2023)
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A.
3 m/s²
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B.
4 m/s²
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C.
5 m/s²
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D.
6 m/s²
Solution
Using F = ma, a = F/m = 15 N / 3 kg = 5 m/s².
Correct Answer: B — 4 m/s²
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Q. If a force of 20 N moves an object 5 m in the direction of the force, what is the work done?
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A.
100 J
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B.
50 J
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C.
20 J
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D.
200 J
Solution
Work = Force * Distance = 20 N * 5 m = 100 J.
Correct Answer: A — 100 J
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Q. If a machine does 200 J of work in 5 seconds, what is its power? (2022)
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A.
40 W
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B.
50 W
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C.
20 W
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D.
30 W
Solution
Power (P) = Work Done (W) / Time (t) = 200 J / 5 s = 40 W
Correct Answer: B — 50 W
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Q. If a measurement is accurate, it means: (2019)
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A.
It is close to the true value
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B.
It is consistent
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C.
It has a small error
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D.
It is precise
Solution
Accuracy refers to how close a measured value is to the true value.
Correct Answer: A — It is close to the true value
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Q. If a person does 300 J of work in 15 seconds, what is their power output?
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A.
20 W
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B.
15 W
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C.
25 W
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D.
30 W
Solution
Power = Work / Time = 300 J / 15 s = 20 W
Correct Answer: A — 20 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)
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A.
392 J
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B.
196 J
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C.
588 J
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D.
784 J
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 rectangle has a length of 10 cm and a width of 5 cm, what is its area? (2017)
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A.
50 cm²
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B.
60 cm²
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C.
40 cm²
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D.
30 cm²
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)
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A.
32 cm
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B.
28 cm
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C.
24 cm
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D.
30 cm
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)
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A.
24 cm²
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B.
30 cm²
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C.
20 cm²
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D.
18 cm²
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)
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A.
22 cm
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B.
24 cm
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C.
20 cm
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D.
26 cm
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, what is the probability of guessing correctly? (2022)
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A.
1/4
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B.
1/2
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C.
1/3
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D.
1/5
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 20 students, 12 of whom are girls, what is the probability that the student is a girl?
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A.
3/5
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B.
2/5
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C.
1/2
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D.
1/3
Solution
Probability of selecting a girl = 12/20 = 3/5.
Correct Answer: A — 3/5
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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)
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A.
100 m/s
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B.
50 m/s
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C.
25 m/s
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D.
200 m/s
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)
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A.
0.02 s
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B.
0.5 s
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C.
2 s
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D.
20 s
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)
Solution
Determinant of C = (0*0) - (1*1) = 0 - 1 = -1.
Correct Answer: C — -1
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Q. If cos(θ) = 0.5, what is the value of θ in degrees? (2017)
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A.
30°
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B.
45°
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C.
60°
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D.
90°
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)
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A.
0°
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B.
30°
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C.
60°
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D.
90°
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)
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A.
0.4
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B.
0.5
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C.
0.6
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D.
0.8
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) = 1/2, what is θ in degrees?
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A.
30°
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B.
45°
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C.
60°
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D.
90°
Solution
cos(60°) = 1/2, so θ = 60°
Correct Answer: C — 60°
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Q. If E = [[2, 1, 3], [1, 0, 2], [4, 1, 1]], what is det(E)? (2020)
Solution
The determinant of E can be calculated using the rule of Sarrus or cofactor expansion, resulting in 0.
Correct Answer: A — -1
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Q. If F = [[1, 2, 3], [0, 1, 4], [5, 6, 0]], what is det(F)? (2021)
Solution
Det(F) = 1(1*0 - 4*6) - 2(0*0 - 4*5) + 3(0*6 - 1*5) = 1(0 - 24) - 2(0 - 20) + 3(0 - 5) = -24 + 40 - 15 = 1.
Correct Answer: A — -14
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Q. If F = [[2, 0], [0, 3]], what is det(F)? (2020)
Solution
The determinant of F is calculated as (2*3) - (0*0) = 6.
Correct Answer: B — 6
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Q. If F = [[2, 1, 3], [1, 0, 2], [3, 4, 1]], find det(F). (2022)
Solution
Using the determinant formula, det(F) = 2*(0*1 - 2*4) - 1*(1*1 - 2*3) + 3*(1*4 - 0*3) = 2*(-8) - 1*(-5) + 3*4 = -16 + 5 + 12 = 1.
Correct Answer: A — -10
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Q. If F = [[2, 1], [1, 3]], what is the value of det(F)? (2022)
Solution
The determinant of F is (2*3) - (1*1) = 6 - 1 = 5.
Correct Answer: A — 5
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Q. If f(x) = x^3 - 3x^2 + 4, find the critical points. (2022)
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A.
1, 2
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B.
0, 3
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C.
2, 4
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D.
1, 3
Solution
f'(x) = 3x^2 - 6x. Setting f'(x) = 0 gives x(3x - 6) = 0, so x = 0 or x = 2.
Correct Answer: A — 1, 2
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