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Q. A box contains 5 white and 3 black balls. If one ball is drawn at random, what is the probability that it is not black?

A. 3/8
B. 5/8
C. 1/2
D. 7/8

Solution

The probability of not drawing a black ball is the probability of drawing a white ball, which is 5/8.

Correct Answer: B — 5/8

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Q. A box contains 5 white and 3 black balls. If two balls are drawn at random, what is the probability that both are white?

A. 1/28
B. 5/28
C. 15/28
D. 3/28

Solution

The probability of drawing 2 white balls = (5/8) * (4/7) = 20/56 = 5/14.

Correct Answer: B — 5/28

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Q. A box contains 5 white and 3 black balls. What is the probability of drawing a black ball?

A. 3/8
B. 5/8
C. 1/2
D. 1/3

Solution

Total balls = 5 + 3 = 8. Probability of black ball = 3/8.

Correct Answer: A — 3/8

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Q. A box contains 5 white and 3 black balls. What is the probability of picking a black ball? (2021)

A. 3/8
B. 5/8
C. 1/2
D. 1/3

Solution

Total balls = 5 + 3 = 8. Probability of black ball = 3/8.

Correct Answer: A — 3/8

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Q. A box is pushed across a floor with a force of 50 N. If the coefficient of kinetic friction is 0.4, what is the net force acting on the box if the normal force is 100 N?

A. 10 N
B. 20 N
C. 30 N
D. 40 N

Solution

Frictional force = μk * N = 0.4 * 100 N = 40 N. Net force = applied force - frictional force = 50 N - 40 N = 10 N.

Correct Answer: C — 30 N

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Q. A box is pushed with a force of 50 N on a surface with a coefficient of kinetic friction of 0.4. What is the acceleration of the box if its mass is 10 kg?

A. 1 m/s²
B. 2 m/s²
C. 3 m/s²
D. 4 m/s²

Solution

Net force = applied force - frictional force. Frictional force = μ_k * N = 0.4 * 10 kg * 9.8 m/s² = 39.2 N. Net force = 50 N - 39.2 N = 10.8 N. Acceleration = F/m = 10.8 N / 10 kg = 1.08 m/s², approximately 1 m/s².

Correct Answer: B — 2 m/s²

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Q. A box is pushed with a force of 50 N on a surface with a coefficient of kinetic friction of 0.3. If the normal force is 100 N, what is the net force acting on the box?

A. 20 N
B. 30 N
C. 50 N
D. 70 N

Solution

Frictional force = μk * N = 0.3 * 100 N = 30 N. Net force = applied force - frictional force = 50 N - 30 N = 20 N.

Correct Answer: B — 30 N

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Q. A building is 100 m tall. From a point 80 m away from the base of the building, the angle of elevation to the top of the building is what?

A. 45 degrees
B. 60 degrees
C. 30 degrees
D. 75 degrees

Solution

Using tan(θ) = height/distance, we have tan(θ) = 100/80 = 1.25, θ = tan⁻¹(1.25) which is approximately 60 degrees.

Correct Answer: B — 60 degrees

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Q. A building is 30 meters tall. From a point 40 meters away from the base of the building, what is the angle of elevation to the top of the building?

A. 30 degrees
B. 36.87 degrees
C. 45 degrees
D. 60 degrees

Solution

Using tan(θ) = height/distance, we have tan(θ) = 30/40 = 0.75. Therefore, θ = tan⁻¹(0.75) ≈ 36.87 degrees.

Correct Answer: B — 36.87 degrees

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Q. A building is 40 m high. From a point on the ground, the angle of elevation to the top of the building is 60 degrees. What is the distance from the point to the base of the building?

A. 20√3 m
B. 40 m
C. 30 m
D. 10√3 m

Solution

Using tan(60°) = height/distance, we have distance = height/tan(60°) = 40/√3 = 20√3 m.

Correct Answer: A — 20√3 m

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Q. A building is 40 m tall. From a point on the ground, the angle of elevation to the top of the building is 45 degrees. How far is the point from the base of the building? (2020)

A. 20 m
B. 30 m
C. 40 m
D. 50 m

Solution

Distance = height / tan(angle) = 40 / tan(45) = 40 / 1 = 40 m.

Correct Answer: C — 40 m

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Q. A building is 40 meters tall. From a point 30 meters away from the base of the building, what is the angle of elevation to the top of the building?

A. 30 degrees
B. 36.87 degrees
C. 45 degrees
D. 53.13 degrees

Solution

Using tan(θ) = height/distance, we have tan(θ) = 40/30. Therefore, θ = tan⁻¹(4/3) ≈ 53.13 degrees.

Correct Answer: B — 36.87 degrees

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Q. A building is 50 m tall. If a person standing 40 m away from the building sees the top at an angle of elevation of θ, what is the value of θ? (2021)

A. 36.87 degrees
B. 45 degrees
C. 53.13 degrees
D. 60 degrees

Solution

tan(θ) = height/distance = 50/40, θ = tan⁻¹(1.25) ≈ 53.13 degrees.

Correct Answer: C — 53.13 degrees

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Q. A building is 50 meters tall. From a point 40 meters away from the base of the building, what is the angle of elevation to the top of the building?

A. 30 degrees
B. 45 degrees
C. 60 degrees
D. 75 degrees

Solution

Using tan(θ) = height/distance, we have θ = tan^(-1)(50/40) = tan^(-1)(1.25) which is approximately 60 degrees.

Correct Answer: C — 60 degrees

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Q. A bus travels 120 km at a speed of 60 km/h and returns at a speed of 40 km/h. What is the average speed for the entire trip? (2023)

A. 48 km/h
B. 50 km/h
C. 52 km/h
D. 54 km/h

Solution

Time for first part = 120/60 = 2 hours. Time for return = 120/40 = 3 hours. Total time = 2 + 3 = 5 hours. Average speed = Total distance / Total time = 240 km / 5 hours = 48 km/h.

Correct Answer: A — 48 km/h

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Q. A bus travels 120 km in 2 hours and then 180 km in 3 hours. What is the average speed of the bus? (2023)

A. 60 km/h
B. 70 km/h
C. 75 km/h
D. 80 km/h

Solution

Total distance = 120 + 180 = 300 km. Total time = 2 + 3 = 5 hours. Average speed = 300 km / 5 hours = 60 km/h.

Correct Answer: C — 75 km/h

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Q. A bus travels from city A to city B, a distance of 120 km, at a speed of 60 km/h. How long does it take to reach city B? (2023)

A. 1 hour
B. 1.5 hours
C. 2 hours
D. 2.5 hours

Solution

Time = Distance / Speed = 120 km / 60 km/h = 2 hours.

Correct Answer: C — 2 hours

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Q. A bus travels from city A to city B, a distance of 120 km, at a speed of 60 km/h. How long does the journey take? (2023)

A. 1 hour
B. 1.5 hours
C. 2 hours
D. 2.5 hours

Solution

Time = Distance / Speed = 120 km / 60 km/h = 2 hours.

Correct Answer: C — 2 hours

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Q. A capacitor has a capacitance of 10 μF and is charged to a potential of 50 V. What is the energy stored in the capacitor?

A. 0.025 J
B. 0.05 J
C. 0.1 J
D. 0.5 J

Solution

Energy stored U = 1/2 * C * V² = 1/2 * 10 × 10^-6 F * (50 V)² = 0.0125 J.

Correct Answer: A — 0.025 J

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Q. A capacitor has a capacitance of 4μF and is charged to 12V. What is the charge on the capacitor?

A. 48μC
B. 12μC
C. 4μC
D. 3μC

Solution

Charge (Q) on a capacitor is given by Q = C * V. Thus, Q = 4μF * 12V = 48μC.

Correct Answer: A — 48μC

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Q. A capacitor has a capacitance of 5 μF and is charged to a potential of 12 V. What is the energy stored in the capacitor?

A. 0.36 mJ
B. 0.72 mJ
C. 0.12 mJ
D. 0.24 mJ

Solution

Energy U = 1/2 * C * V² = 1/2 * 5 × 10^-6 F * (12 V)² = 0.36 mJ.

Correct Answer: B — 0.72 mJ

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Q. A capacitor in an AC circuit has a capacitive reactance of 50 ohms. If the frequency of the AC source is increased, what happens to the capacitive reactance?

A. Increases
B. Decreases
C. Remains the same
D. Becomes infinite

Solution

Capacitive reactance (X_C) is given by X_C = 1/(2πfC). If the frequency (f) increases, X_C decreases.

Correct Answer: B — Decreases

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Q. A capacitor in an AC circuit has a capacitive reactance of 50 ohms. What is the frequency if the capacitance is 10 microfarads?

A. 1 kHz
B. 10 kHz
C. 100 Hz
D. 1000 Hz

Solution

Capacitive reactance (X_C) is given by X_C = 1 / (2πfC). Rearranging gives f = 1 / (2πX_CC). Substituting X_C = 50 ohms and C = 10 x 10^-6 F gives f = 318.31 Hz, approximately 1 kHz.

Correct Answer: A — 1 kHz

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Q. A capacitor is charged to a potential difference of 10V. If the charge on the capacitor is 5μC, what is its capacitance? (2020)

A. 0.5μF
B. 1μF
C. 2μF
D. 5μF

Solution

Capacitance (C) is given by C = Q/V. Here, C = 5μC / 10V = 0.5μF.

Correct Answer: A — 0.5μF

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Q. A capacitor is charged to a potential difference of 12 V. If the capacitance is 4 µF, what is the charge stored in the capacitor?

A. 12 µC
B. 24 µC
C. 48 µC
D. 36 µC

Solution

Charge Q is given by Q = CV. Here, Q = 4 µF * 12 V = 48 µC.

Correct Answer: B — 24 µC

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Q. A capacitor is charged to a potential difference of 12V. If it is disconnected from the battery and the plates are moved apart, what happens to the potential difference? (2021)

A. Increases
B. Decreases
C. Remains the same
D. Becomes zero

Solution

When the plates of a disconnected capacitor are moved apart, the capacitance decreases, leading to an increase in potential difference.

Correct Answer: A — Increases

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Q. A capacitor is charged to a potential difference of 12V. If the charge on the capacitor is 24μC, what is its capacitance? (2019)

A. 2μF
B. 4μF
C. 6μF
D. 8μF

Solution

Capacitance C is given by C = Q/V. Here, C = 24μC / 12V = 2μF.

Correct Answer: B — 4μF

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Q. A capacitor is charged to a potential difference of V. If the charge on the capacitor is Q, what is the capacitance? (2023)

A. Q/V
B. V/Q
C. QV
D. V^2/Q

Solution

The capacitance C is defined as C = Q/V.

Correct Answer: A — Q/V

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Q. A capacitor is charged to a potential difference of V. What is the energy stored in the capacitor?

A. 1/2 CV²
B. CV
C. V²/C
D. 1/2 QV

Solution

The energy (U) stored in a capacitor is given by U = 1/2 CV², where C is the capacitance and V is the potential difference.

Correct Answer: A — 1/2 CV²

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Q. A capacitor is charged to a potential of 12 V. If the capacitance is 3 µF, what is the energy stored in the capacitor?

A. 0.18 mJ
B. 0.36 mJ
C. 0.54 mJ
D. 0.72 mJ

Solution

Energy stored in a capacitor is given by U = 1/2 CV² = 1/2 * 3 x 10^-6 F * (12 V)² = 0.36 mJ.

Correct Answer: B — 0.36 mJ

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Major Competitive Exams

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