Engineering Entrance
Q. If a 10Ω resistor is connected in parallel with a 5Ω resistor, what is the total resistance? (2022)
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A.
3.33Ω
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B.
5Ω
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C.
7.5Ω
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D.
15Ω
Solution
For resistors in parallel, 1/R_eq = 1/R1 + 1/R2 = 1/10 + 1/5 = 1/10 + 2/10 = 3/10. Therefore, R_eq = 10/3 = 3.33Ω.
Correct Answer: A — 3.33Ω
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Q. If a 15Ω resistor is connected in parallel with a 5Ω resistor, what is the equivalent resistance? (2023)
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A.
3.75Ω
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B.
4Ω
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C.
5Ω
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D.
10Ω
Solution
1/R_eq = 1/15 + 1/5 = 1/15 + 3/15 = 4/15; R_eq = 15/4 = 3.75Ω.
Correct Answer: A — 3.75Ω
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Q. If a 2 kg object is dropped from a height, what is its velocity just before hitting the ground (g = 10 m/s²)? (2023)
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A.
10 m/s
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B.
20 m/s
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C.
30 m/s
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D.
40 m/s
Solution
Using v = √(2gh), for h = 10 m, v = √(2 * 10 m/s² * 10 m) = √200 = 20 m/s.
Correct Answer: B — 20 m/s
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Q. If a 2 kg object is dropped from a height, what is its velocity just before hitting the ground? (g = 9.8 m/s², h = 20 m) (2023)
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A.
14 m/s
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B.
19.6 m/s
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C.
20 m/s
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D.
28 m/s
Solution
Using v² = u² + 2gh, where u = 0, we find v = √(2 * 9.8 * 20) = 19.6 m/s.
Correct Answer: B — 19.6 m/s
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Q. If a 2 kg object is moving with a velocity of 15 m/s, what is its kinetic energy?
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A.
225 J
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B.
150 J
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C.
300 J
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D.
450 J
Solution
Kinetic Energy = 1/2 * m * v^2 = 1/2 * 2 kg * (15 m/s)^2 = 225 J.
Correct Answer: A — 225 J
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Q. If a 2 kg object is moving with a velocity of 3 m/s, what is its kinetic energy?
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A.
9 J
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B.
6 J
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C.
3 J
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D.
12 J
Solution
Kinetic Energy = 0.5 * m * v² = 0.5 * 2 kg * (3 m/s)² = 9 J.
Correct Answer: A — 9 J
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Q. If a 5 kg object is moving with a velocity of 3 m/s, what is its momentum? (2023)
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A.
5 kg·m/s
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B.
10 kg·m/s
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C.
15 kg·m/s
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D.
20 kg·m/s
Solution
Momentum p = mv = 5 kg * 3 m/s = 15 kg·m/s.
Correct Answer: C — 15 kg·m/s
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Q. If a 5 kg object is subjected to a net force of 20 N, what is its acceleration? (2023)
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A.
2 m/s²
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B.
4 m/s²
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C.
5 m/s²
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D.
10 m/s²
Solution
Using F = ma, we find a = F/m = 20 N / 5 kg = 4 m/s².
Correct Answer: B — 4 m/s²
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Q. If a 5Ω resistor is connected in series with a 10Ω resistor, what is the total resistance? (2022)
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A.
15Ω
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B.
5Ω
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C.
10Ω
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D.
20Ω
Solution
In series, R_eq = R1 + R2 = 5Ω + 10Ω = 15Ω.
Correct Answer: A — 15Ω
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Q. If a 5Ω resistor is connected to a 10V source, what is the power dissipated? (2023)
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A.
2W
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B.
5W
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C.
10W
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D.
20W
Solution
Power P = V²/R = (10V)² / 5Ω = 100 / 5 = 20W.
Correct Answer: C — 10W
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Q. If a 6Ω resistor is connected in parallel with a 3Ω resistor, what is the equivalent resistance? (2023)
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A.
2Ω
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B.
1.5Ω
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C.
4Ω
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D.
9Ω
Solution
Using the formula 1/R_eq = 1/R1 + 1/R2, we get 1/R_eq = 1/6 + 1/3 = 1/6 + 2/6 = 3/6, thus R_eq = 2Ω.
Correct Answer: A — 2Ω
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Q. If a 9V battery is connected to a 3Ω resistor, what is the current flowing through it? (2021)
Solution
Using Ohm's law, I = V/R = 9V / 3Ω = 3A.
Correct Answer: B — 2A
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Q. If a = 2 and b = 3, what is the value of a^3 + b^3? (2021)
Solution
a^3 = 2^3 = 8 and b^3 = 3^3 = 27, so 8 + 27 = 35.
Correct Answer: A — 35
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Q. If A = 2i + 3j and B = 3i + 4j, what is the angle between A and B? (2021)
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A.
0 degrees
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B.
45 degrees
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C.
90 degrees
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D.
180 degrees
Solution
cos(θ) = (A · B) / (|A||B|) = (2*3 + 3*4) / (√(2^2 + 3^2) * √(3^2 + 4^2)) = 0.7071, θ = 45 degrees.
Correct Answer: B — 45 degrees
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Q. If a = 3 and b = 4, what is a^2 + b^2? (2017)
Solution
a^2 = 9 and b^2 = 16, so 9 + 16 = 25.
Correct Answer: A — 25
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Q. If a = 3 and b = 4, what is the value of a^2 + b^2? (2019)
Solution
a^2 = 9 and b^2 = 16, so 9 + 16 = 25.
Correct Answer: A — 25
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Q. If A = 3i + 4j and B = 2i - j, what is A + B? (2021)
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A.
5i + 3j
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B.
5i + 5j
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C.
1i + 5j
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D.
1i + 3j
Solution
A + B = (3i + 4j) + (2i - j) = (3 + 2)i + (4 - 1)j = 5i + 3j.
Correct Answer: A — 5i + 3j
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Q. If A = 4i + 2j and B = -i + 3j, what is the scalar triple product A · (B × A)? (2023)
Solution
B × A = |i j k| |-1 3 0| |4 2 0| = 0, hence A · (B × A) = 0.
Correct Answer: A — 0
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Q. If A = 5i + 12j, what is the unit vector in the direction of A? (2021)
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A.
(5/13)i + (12/13)j
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B.
(12/13)i + (5/13)j
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C.
(5/12)i + (12/5)j
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D.
(12/5)i + (5/12)j
Solution
Unit vector = A / |A| = (5i + 12j) / √(5^2 + 12^2) = (5/13)i + (12/13)j.
Correct Answer: A — (5/13)i + (12/13)j
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Q. If A = i + 2j + 3k and B = 4i + 5j + 6k, what is A - B? (2023)
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A.
-3i - 3j - 3k
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B.
-3i - 3j + 3k
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C.
3i + 3j + 3k
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D.
3i + 3j - 3k
Solution
A - B = (1 - 4)i + (2 - 5)j + (3 - 6)k = -3i - 3j - 3k.
Correct Answer: A — -3i - 3j - 3k
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Q. If a capacitor is charged to 12V and has a capacitance of 6μF, what is the stored energy? (2022)
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A.
0.432 mJ
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B.
0.072 mJ
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C.
0.864 mJ
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D.
0.216 mJ
Solution
Energy = 0.5 × C × V² = 0.5 × 6 × 10^-6 × 12² = 0.432 mJ.
Correct Answer: A — 0.432 mJ
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Q. If a car accelerates from rest to a speed of 20 m/s, and its mass is 1000 kg, what is the kinetic energy of the car at that speed? (2020)
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A.
200 J
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B.
1000 J
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C.
2000 J
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D.
4000 J
Solution
Kinetic Energy = 0.5 × mass × velocity² = 0.5 × 1000 kg × (20 m/s)² = 200000 J = 2000 J
Correct Answer: C — 2000 J
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Q. If a car accelerates from rest to a speed of 20 m/s, what is the kinetic energy of the car if its mass is 1000 kg?
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A.
200,000 J
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B.
100,000 J
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C.
50,000 J
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D.
400,000 J
Solution
Kinetic Energy = 0.5 × mass × velocity² = 0.5 × 1000 kg × (20 m/s)² = 200,000 J
Correct Answer: B — 100,000 J
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Q. If a car travels at a speed of 60 km/h, how far will it travel in 2 hours? (2022)
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A.
120 km
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B.
100 km
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C.
150 km
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D.
90 km
Solution
Distance = Speed × Time = 60 km/h × 2 h = 120 km.
Correct Answer: A — 120 km
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Q. If a car with a mass of 1200 kg is moving at a speed of 15 m/s, what is its kinetic energy? (2021)
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A.
13500 J
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B.
9000 J
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C.
18000 J
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D.
27000 J
Solution
Kinetic Energy = 0.5 × mass × velocity² = 0.5 × 1200 kg × (15 m/s)² = 13500 J
Correct Answer: A — 13500 J
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Q. If a circle has a circumference of 31.4 cm, what is its radius? (2022)
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A.
5 cm
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B.
10 cm
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C.
15 cm
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D.
20 cm
Solution
Circumference = 2πr; 31.4 = 2 * π * r; r = 31.4 / (2 * π) = 5 cm.
Correct Answer: A — 5 cm
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Q. If a circle has a radius of 3 cm, what is its circumference? (Use π = 3.14) (2023)
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A.
6.28 cm
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B.
9.42 cm
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C.
12.56 cm
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D.
15.70 cm
Solution
Circumference = 2πr = 2 * 3.14 * 3 = 18.84 cm.
Correct Answer: C — 12.56 cm
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Q. If a circle's radius is tripled, how does its area change? (2021)
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A.
Increases by 3 times
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B.
Increases by 6 times
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C.
Increases by 9 times
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D.
Remains the same
Solution
Area = πr². If radius is tripled, new area = π(3r)² = 9πr², which is 9 times the original area.
Correct Answer: C — Increases by 9 times
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Q. If a circle's radius is tripled, how does its area change? (2023) 2023
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A.
Increases by 3 times
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B.
Increases by 6 times
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C.
Increases by 9 times
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D.
Remains the same
Solution
Area = πr². If radius is tripled, new area = π(3r)² = 9πr², which is 9 times the original area.
Correct Answer: C — Increases by 9 times
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Q. If a circuit has a resistance of 5 ohms and a current of 2 A, what is the voltage? (2014)
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A.
10 V
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B.
5 V
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C.
2 V
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D.
1 V
Solution
Using Ohm's Law, V = I × R = 2 A × 5 Ω = 10 V.
Correct Answer: A — 10 V
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