Engineering Entrance
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 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 circle has a circumference of 31.4 cm, what is its radius? (2022)
-
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? (2023) 2023
-
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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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
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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 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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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 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 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)
-
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)
-
A.
0°
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B.
30°
-
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°
-
B.
45°
-
C.
60°
-
D.
90°
Solution
cos(60°) = 1/2, so θ = 60°
Correct Answer: C — 60°
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