Engineering Entrance Exam Preparation Resources

Engineering Entrance

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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)

A. 18V
B. 12V
C. 15V
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)

A. 36V
B. 12V
C. 4V
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)

A. 48V
B. 36V
C. 24V
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)

A. 10V
B. 5V
C. 2V
D. 1V

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)

A. 32V
B. 24V
C. 16V
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?

A. 1/4
B. 1/2
C. 3/4
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)

A. 1/2
B. 1/3
C. 1/6
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 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)

A. 15 N
B. 3 N
C. 0 N
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)

A. 3 m/s²
B. 4 m/s²
C. 5 m/s²
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?

A. 100 J
B. 50 J
C. 20 J
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 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

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)

A. 392 J
B. 196 J
C. 588 J
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)

A. 50 cm²
B. 60 cm²
C. 40 cm²
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)

A. 32 cm
B. 28 cm
C. 24 cm
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)

A. 24 cm²
B. 30 cm²
C. 20 cm²
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)

A. 22 cm
B. 24 cm
C. 20 cm
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)

A. 1/4
B. 1/2
C. 1/3
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?

A. 3/5
B. 2/5
C. 1/2
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)

A. 100 m/s
B. 50 m/s
C. 25 m/s
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)

A. 0.02 s
B. 0.5 s
C. 2 s
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)

A. 0
B. 1
C. -1
D. 2

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°
B. 45°
C. 60°
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°
B. 30°
C. 60°
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)

A. 0.4
B. 0.5
C. 0.6
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?

A. 30°
B. 45°
C. 60°
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)

A. -1
B. 0
C. 1
D. 2

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)

A. -14
B. 14
C. 0
D. 10

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)

A. 0
B. 6
C. 5
D. 2

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)

A. -10
B. 10
C. 0
D. 5

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)

A. 5
B. 6
C. 7
D. 8

Solution

The determinant of F is (2*3) - (1*1) = 6 - 1 = 5.

Correct Answer: A — 5

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Engineering Entrance

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