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Q. If a 5Ω resistor is connected in series with a 10Ω resistor, what is the total resistance? (2022)

A. 15Ω
B. 5Ω
C. 10Ω
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)

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

A. 2Ω
B. 1.5Ω
C. 4Ω
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)

A. 1A
B. 2A
C. 3A
D. 4A

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)

A. 35
B. 27
C. 10
D. 8

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)

A. 0 degrees
B. 45 degrees
C. 90 degrees
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)

A. 25
B. 20
C. 15
D. 10

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)

A. 25
B. 12
C. 7
D. 16

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)

A. 5i + 3j
B. 5i + 5j
C. 1i + 5j
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)

A. 0
B. 8
C. 12
D. 16

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)

A. (5/13)i + (12/13)j
B. (12/13)i + (5/13)j
C. (5/12)i + (12/5)j
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)

A. -3i - 3j - 3k
B. -3i - 3j + 3k
C. 3i + 3j + 3k
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)

A. 0.432 mJ
B. 0.072 mJ
C. 0.864 mJ
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)

A. 200 J
B. 1000 J
C. 2000 J
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?

A. 200,000 J
B. 100,000 J
C. 50,000 J
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)

A. 120 km
B. 100 km
C. 150 km
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)

A. 13500 J
B. 9000 J
C. 18000 J
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)

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 circle's radius is tripled, how does its area change? (2021)

A. Increases by 3 times
B. Increases by 6 times
C. Increases by 9 times
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
B. Increases by 6 times
C. Increases by 9 times
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 12Ω and a current of 3A, what is the power consumed in the circuit? (2022)

A. 36W
B. 24W
C. 12W
D. 9W

Solution

Power (P) can be calculated using the formula P = I^2 * R = (3A)^2 * 12Ω = 36W.

Correct Answer: A — 36W

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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 2A, what is the voltage across the circuit? (2020)

A. 12V
B. 24V
C. 6V
D. 18V

Solution

Using Ohm's law, V = I * R = 2A * 12Ω = 24V.

Correct Answer: B — 24V

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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 circuit has a total voltage of 24V and a total resistance of 8Ω, what is the total current flowing through the circuit? (2023)

A. 3A
B. 2A
C. 4A
D. 6A

Solution

Using Ohm's law, I = V/R = 24V/8Ω = 3A.

Correct Answer: C — 4A

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