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Q. If a circle has a circumference of 31.4 cm, what is its radius? (2022)

A. 5 cm
B. 10 cm
C. 15 cm
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)

A. 6.28 cm
B. 9.42 cm
C. 12.56 cm
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 circuit has a resistance of 5 ohms and a current of 2 A, what is the voltage? (2014)

A. 10 V
B. 5 V
C. 2 V
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)

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 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 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 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 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 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 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 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) = 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 f(x) = x^3 - 3x^2 + 4, find the critical points. (2022)

A. 1, 2
B. 0, 3
C. 2, 4
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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Q. If H = [[2, 3], [4, 5]], find det(H). (2022)

A. -2
B. 1
C. 2
D. 7

Solution

Det(H) = (2*5) - (3*4) = 10 - 12 = -2.

Correct Answer: D — 7

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Q. If one root of the equation x² - 7x + k = 0 is 3, find k. (2023)

A. 10
B. 12
C. 15
D. 9

Solution

Using the root, substitute x = 3: 3² - 7*3 + k = 0, which gives k = 10.

Correct Answer: A — 10

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Q. If one root of the equation x² - 7x + k = 0 is 3, what is the value of k? (2020)

A. 10
B. 12
C. 15
D. 9

Solution

Using the root, substitute x = 3: 3² - 7*3 + k = 0, which gives k = 9.

Correct Answer: D — 9

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Q. If sin(θ) = 0.8, what is cos(θ) using Pythagorean identity? (2020)

A. 0.6
B. 0.8
C. 0.4
D. 0.2

Solution

Using sin²(θ) + cos²(θ) = 1, cos²(θ) = 1 - 0.64 = 0.36, cos(θ) = 0.6

Correct Answer: A — 0.6

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Q. If sin(θ) = 0.8, what is cos(θ)? (2022)

A. 0.6
B. 0.8
C. 0.4
D. 0.2

Solution

Using sin²(θ) + cos²(θ) = 1, cos(θ) = √(1 - 0.8²) = √(0.36) = 0.6.

Correct Answer: A — 0.6

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Q. If sin(θ) = 1, what is the value of θ? (2023)

A. 0°
B. 90°
C. 180°
D. 270°

Solution

sin(90°) = 1, so θ = 90°.

Correct Answer: B — 90°

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Q. If sin(θ) = 1/√2, what is θ in degrees?

A. 30°
B. 45°
C. 60°
D. 90°

Solution

sin(45°) = 1/√2, so θ = 45°

Correct Answer: B — 45°

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Q. If tan(θ) = 1, what is the value of θ? (2020)

A. 0°
B. 30°
C. 45°
D. 60°

Solution

tan(45°) = 1, so θ = 45°.

Correct Answer: C — 45°

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Q. If the amplitude of a wave is doubled, how does it affect the energy of the wave? (2020)

A. Remains the same
B. Doubles
C. Increases by four times
D. Halves

Solution

Energy of a wave is proportional to the square of the amplitude. If amplitude is doubled, energy increases by (2^2) = 4 times.

Correct Answer: C — Increases by four times

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Q. If the circumference of a circle is 31.4 cm, what is its radius? (Use π = 3.14) (2015)

A. 5 cm
B. 7 cm
C. 10 cm
D. 8 cm

Solution

Circumference = 2πr, so r = circumference / (2π) = 31.4 / (2 * 3.14) = 5 cm.

Correct Answer: A — 5 cm

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Q. If the concentration of a reactant is tripled in a second-order reaction, how does the rate change? (2023)

A. Increases by 3 times
B. Increases by 6 times
C. Increases by 9 times
D. Increases by 12 times

Solution

For a second-order reaction, if concentration is tripled, the rate increases by 3² = 9 times.

Correct Answer: C — Increases by 9 times

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