NDA Exam Preparation Resources | Soulshift Education

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English General Knowledge Mathematics

Q. A box contains 3 red balls and 2 blue balls. If one ball is drawn at random, what is the probability that it is red?

A. 1/5
B. 2/5
C. 3/5
D. 4/5

Solution

The total number of balls is 3 + 2 = 5. The number of red balls is 3. Therefore, the probability of drawing a red ball is 3/5.

Correct Answer: C — 3/5

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Q. A box contains 3 red balls and 2 blue balls. What is the probability of picking a red ball? (2023)

A. 0.6
B. 0.5
C. 0.4
D. 0.3

Solution

Probability = Number of favorable outcomes / Total outcomes = 3/(3+2) = 3/5 = 0.6.

Correct Answer: A — 0.6

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Q. A box contains 3 red balls and 5 blue balls. If one ball is drawn at random, what is the probability that it is red? (2019)

A. 3/8
B. 5/8
C. 1/2
D. 1/4

Solution

Total balls = 3 + 5 = 8. Probability of red = 3/8.

Correct Answer: A — 3/8

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Q. A box contains 3 red balls and 5 blue balls. What is the probability of drawing a red ball? (2019)

A. 3/8
B. 5/8
C. 1/2
D. 1/4

Solution

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

Correct Answer: A — 3/8

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Q. A box contains 3 red, 5 blue, and 2 green balls. If one ball is drawn at random, what is the probability that it is blue?

A. 1/10
B. 1/5
C. 1/2
D. 1/3

Solution

Total balls = 3 + 5 + 2 = 10. Probability of drawing a blue ball = Number of blue balls / Total balls = 5/10 = 1/2.

Correct Answer: B — 1/5

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Q. A box contains 3 red, 5 blue, and 2 green balls. What is the probability of drawing a blue ball? (2021)

A. 1/2
B. 5/10
C. 1/5
D. 1/3

Solution

Total balls = 3 + 5 + 2 = 10. Probability of blue = Number of blue balls / Total balls = 5/10 = 1/2.

Correct Answer: A — 1/2

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Q. A box contains 5 red balls and 3 blue balls. What is the probability of drawing a red ball? (2021)

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

Solution

Total balls = 5 + 3 = 8. Probability of red = 5/8.

Correct Answer: B — 5/8

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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 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 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 of capacitance 10 microfarads is charged to a voltage of 5 volts. What is the charge stored in the capacitor?

A. 50 microcoulombs
B. 5 microcoulombs
C. 0.5 microcoulombs
D. 100 microcoulombs

Solution

Charge (Q) is given by Q = C * V. Thus, Q = 10 µF * 5 V = 50 µC.

Correct Answer: A — 50 microcoulombs

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Q. A capacitor of capacitance 5 µF is charged to a voltage of 10V. What is the charge stored in the capacitor? (2022)

A. 50 µC
B. 100 µC
C. 500 µC
D. 1000 µC

Solution

Charge (Q) = Capacitance (C) × Voltage (V) = 5µF × 10V = 50µC.

Correct Answer: B — 100 µC

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Q. A capacitor stores 5 microfarads of charge at a voltage of 10 volts. What is the energy stored in the capacitor?

A. 0.25 mJ
B. 0.5 mJ
C. 0.75 mJ
D. 1 mJ

Solution

The energy stored in a capacitor is given by the formula E = 0.5 * C * V^2. Here, E = 0.5 * 5 * 10^-6 F * (10 V)^2 = 0.5 * 5 * 10^-6 * 100 = 0.25 mJ.

Correct Answer: B — 0.5 mJ

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Q. A capacitor stores energy in the form of which type of field?

A. Electric field
B. Magnetic field
C. Gravitational field
D. Electromagnetic field

Solution

A capacitor stores energy in the form of an electric field between its plates.

Correct Answer: A — Electric field

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Q. A car accelerates from rest at a rate of 2 m/s². How far does it travel in 10 seconds? (2020)

A. 50 m
B. 100 m
C. 150 m
D. 200 m

Solution

Using the formula s = ut + (1/2)at²; s = 0 + (1/2)(2)(10²) = 100 m.

Correct Answer: B — 100 m

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Q. A car accelerates uniformly from rest to a speed of 25 m/s in 10 seconds. What is the distance covered during this time? (2020)

A. 100 m
B. 125 m
C. 150 m
D. 200 m

Solution

Using the formula s = ut + (1/2)at². Here, u = 0, a = (25-0)/10 = 2.5 m/s². s = 0 + (1/2)(2.5)(10²) = 125 m.

Correct Answer: B — 125 m

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Q. A car covers a distance of 150 km in 3 hours. What is its speed in km/h? (2023)

A. 45 km/h
B. 50 km/h
C. 55 km/h
D. 60 km/h

Solution

Speed = Distance / Time = 150 km / 3 h = 50 km/h.

Correct Answer: B — 50 km/h

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Q. A car covers a distance of 150 km in 3 hours. What is the speed of the car in km/h? (2022)

A. 45 km/h
B. 50 km/h
C. 55 km/h
D. 60 km/h

Solution

Speed = Distance / Time = 150 km / 3 h = 50 km/h.

Correct Answer: B — 50 km/h

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Q. A car covers a distance of 240 km in 3 hours. What is its average speed? (2021)

A. 80 km/h
B. 70 km/h
C. 60 km/h
D. 90 km/h

Solution

Average Speed = Total Distance / Total Time = 240 km / 3 h = 80 km/h.

Correct Answer: A — 80 km/h

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Q. A car travels 100 km in 1.5 hours. What is its average speed? (2019)

A. 60 km/h
B. 65 km/h
C. 70 km/h
D. 75 km/h

Solution

Average speed = Distance / Time = 100 km / 1.5 hours = 66.67 km/h, which rounds to 60 km/h.

Correct Answer: A — 60 km/h

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Q. A car travels 100 km in 2 hours and then 50 km in 1 hour. What is the average speed of the car for the entire journey? (2021)

A. 50 km/h
B. 60 km/h
C. 70 km/h
D. 75 km/h

Solution

Total distance = 100 km + 50 km = 150 km. Total time = 2 h + 1 h = 3 h. Average speed = Total distance / Total time = 150 km / 3 h = 50 km/h.

Correct Answer: C — 70 km/h

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Q. A car travels 100 km in 2 hours and then 50 km in 1 hour. What is the total average speed of the car? (2019)

A. 50 km/h
B. 60 km/h
C. 70 km/h
D. 80 km/h

Solution

Total distance = 100 + 50 = 150 km. Total time = 2 + 1 = 3 hours. Average speed = Total distance / Total time = 150/3 = 50 km/h.

Correct Answer: B — 60 km/h

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Q. A car travels 150 km in 2 hours and then 100 km in 1 hour. What is the average speed of the car? (2022)

A. 75 km/h
B. 80 km/h
C. 85 km/h
D. 90 km/h

Solution

Total distance = 150 km + 100 km = 250 km. Total time = 2 hours + 1 hour = 3 hours. Average speed = Total distance / Total time = 250 km / 3 hours = 83.33 km/h, which rounds to 80 km/h.

Correct Answer: B — 80 km/h

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Q. A car travels 150 km in 2 hours and then 100 km in 1 hour. What is the average speed of the car for the entire trip? (2020)

A. 75 km/h
B. 80 km/h
C. 85 km/h
D. 90 km/h

Solution

Total distance = 150 + 100 = 250 km. Total time = 2 + 1 = 3 hours. Average speed = Total distance / Total time = 250 km / 3 hours = 83.33 km/h, which rounds to 80 km/h.

Correct Answer: B — 80 km/h

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Q. A car travels 150 km in 2.5 hours. What is its speed in km/h? (2020)

A. 55 km/h
B. 60 km/h
C. 65 km/h
D. 70 km/h

Solution

Speed = Distance / Time = 150 km / 2.5 hours = 60 km/h.

Correct Answer: B — 60 km/h

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Q. A car travels 150 km in 3 hours. What is its average speed? (2022)

A. 40 km/h
B. 50 km/h
C. 60 km/h
D. 70 km/h

Solution

Average speed = Total distance / Total time = 150 km / 3 h = 50 km/h.

Correct Answer: B — 50 km/h

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Q. A car travels 60 km in 1 hour and 30 minutes. What is the average speed of the car in km/h? (2019)

A. 40
B. 50
C. 45
D. 60

Solution

Time taken = 1.5 hours. Average speed = Distance / Time = 60 km / 1.5 h = 40 km/h.

Correct Answer: C — 45

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