Engineering Entrance
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 bag contains 4 green and 6 yellow marbles, what is the probability of picking a green marble?
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A.
2/5
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B.
4/10
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C.
4/6
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D.
1/3
Solution
Total marbles = 4 + 6 = 10. Probability of green marble = 4/10 = 2/5.
Correct Answer: A — 2/5
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Q. If a body is moving in a circular path with a constant speed, what type of acceleration does it experience?
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A.
Centripetal acceleration
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B.
Linear acceleration
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C.
Angular acceleration
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D.
No acceleration
Solution
A body moving in a circular path experiences centripetal acceleration directed towards the center of the circle.
Correct Answer: A — Centripetal acceleration
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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 charge of +2μC is placed in an electric field of 1000 N/C, what is the force experienced by the charge? (2023)
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A.
2 N
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B.
0.002 N
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C.
2000 N
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D.
0.2 N
Solution
The force (F) on a charge in an electric field is given by F = qE. Here, F = 2μC * 1000 N/C = 2 N.
Correct Answer: A — 2 N
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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 has a radius of 4 cm, what is its diameter? (2022)
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A.
4 cm
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B.
8 cm
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C.
12 cm
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D.
16 cm
Solution
Diameter = 2 * radius = 2 * 4 cm = 8 cm.
Correct Answer: B — 8 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
-
A.
Increases by 3 times
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B.
Increases by 6 times
-
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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Q. If a circuit has a total resistance of 12Ω and a current of 1.5A flows through it, what is the voltage across the circuit? (2022)
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A.
18V
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B.
12V
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C.
15V
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D.
10V
Solution
Using Ohm's law, V = IR = 1.5A * 12Ω = 18V.
Correct Answer: A — 18V
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Q. If a circuit has a total resistance of 12Ω and a current of 1.5A, what is the voltage across the circuit? (2021)
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A.
18V
-
B.
12V
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C.
15V
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D.
10V
Solution
Using Ohm's law, V = IR = 1.5A * 12Ω = 18V.
Correct Answer: A — 18V
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Q. If a circuit has a total resistance of 12Ω and a current of 3A flows through it, what is the voltage across the circuit? (2020)
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A.
36V
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B.
12V
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C.
4V
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D.
24V
Solution
Using Ohm's law, V = IR = 3A * 12Ω = 36V.
Correct Answer: A — 36V
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Q. If a circuit has a total resistance of 12Ω and a current of 4A, what is the voltage across the circuit? (2023)
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A.
48V
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B.
36V
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C.
24V
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D.
12V
Solution
Using Ohm's law, V = IR = 4A * 12Ω = 48V.
Correct Answer: A — 48V
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Q. If a circuit has a total resistance of 5Ω and a current of 2A, what is the voltage across the circuit? (2022)
Solution
Using Ohm's law, V = I * R = 2A * 5Ω = 10V.
Correct Answer: A — 10V
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Q. If a circuit has a total resistance of 8Ω and a current of 4A, what is the voltage across the circuit? (2023)
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A.
32V
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B.
24V
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C.
16V
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D.
12V
Solution
Using Ohm's law, V = IR = 4A * 8Ω = 32V.
Correct Answer: A — 32V
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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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