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Q. A person invests $2000 at a compound interest rate of 5% per annum. What will be the total amount after 3 years? (2000)

A. $2315.25
B. $2500
C. $2200
D. $2400

Solution

Using A = P(1 + r)^n, we calculate A = 2000(1 + 0.05)^3 = $2315.25.

Correct Answer: A — $2315.25

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Q. A person invests $2000 at a compound interest rate of 8% per annum. How much will he have after 2 years? (2000)

A. $2320
B. $2400
C. $2500
D. $2600

Solution

Using the compound interest formula A = P(1 + r)^t, we calculate A = 2000(1 + 0.08)^2 = 2000 * 1.1664 = $2332.80, which rounds to $2320.

Correct Answer: A — $2320

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Q. A person invests $2000 at a compound interest rate of 8% per annum. What will be the total amount after 2 years? (2000)

A. $2320
B. $2400
C. $2500
D. $2600

Solution

Using the formula A = P(1 + r)^t, A = 2000(1 + 0.08)^2 = 2000 * 1.1664 = $2332.80, which rounds to $2320.

Correct Answer: A — $2320

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Q. A person invests $2000 at a rate of 6% per annum. How much interest will he earn in 4 years under simple interest? (2023)

A. $480
B. $4800
C. $240
D. $2400

Solution

Using SI = P * r * t / 100, we have SI = 2000 * 6 * 4 / 100 = $480.

Correct Answer: A — $480

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Q. A person is facing north. He turns 90 degrees clockwise, then 180 degrees anti-clockwise. Which direction is he facing now? (2023)

A. North
B. South
C. East
D. West

Solution

After turning 90 degrees clockwise, he faces East. After turning 180 degrees anti-clockwise, he faces West.

Correct Answer: D — West

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Q. A person is looking at the top of a tree from a distance of 15 meters. If the angle of elevation is 30 degrees, what is the height of the tree?

A. 15√3 meters
B. 30 meters
C. 45 meters
D. 10 meters

Solution

Height = distance * tan(angle) = 15 * (1/√3) = 15/√3 = 15√3 meters.

Correct Answer: A — 15√3 meters

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Q. A person is on a diet that consists of 50% carbohydrates, 30% fats, and 20% proteins. If they consume 1800 calories, how many calories are from carbohydrates?

A. 600 calories
B. 700 calories
C. 800 calories
D. 900 calories

Solution

50% of 1800 calories = 0.50 * 1800 = 900 calories from carbohydrates.

Correct Answer: C — 800 calories

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Q. A person is pushing a heavy box across a floor. If the box does not move, what can be said about the forces acting on it?

A. Net force is zero
B. Net force is positive
C. Net force is negative
D. Only friction is acting

Solution

If the box does not move, the net force acting on it is zero, meaning the applied force equals the frictional force.

Correct Answer: A — Net force is zero

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Q. A person is running at 3 m/s on a moving escalator that moves at 2 m/s in the same direction. What is the speed of the person relative to a stationary observer?

A. 1 m/s
B. 3 m/s
C. 5 m/s
D. 2 m/s

Solution

Speed of person relative to observer = Speed of escalator + Speed of person = 2 m/s + 3 m/s = 5 m/s.

Correct Answer: C — 5 m/s

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Q. A person is running at 8 m/s in a train moving at 12 m/s in the same direction. What is the speed of the person relative to the ground?

A. 4 m/s
B. 8 m/s
C. 12 m/s
D. 20 m/s

Solution

Speed of person relative to ground = Speed of train + Speed of person = 12 m/s + 8 m/s = 20 m/s.

Correct Answer: D — 20 m/s

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Q. A person is running at 8 m/s on a moving walkway that moves at 2 m/s in the same direction. What is the speed of the person relative to the ground?

A. 6 m/s
B. 8 m/s
C. 10 m/s
D. 12 m/s

Solution

Speed relative to ground = Speed of person + Speed of walkway = 8 m/s + 2 m/s = 10 m/s.

Correct Answer: C — 10 m/s

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Q. A person is running at a speed of 10 m/s. If he is running towards a train moving at 20 m/s in the opposite direction, what is the relative speed of the train with respect to the person?

A. 10 m/s
B. 20 m/s
C. 30 m/s
D. 40 m/s

Solution

Relative speed = speed of train + speed of person = 20 + 10 = 30 m/s.

Correct Answer: C — 30 m/s

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Q. A person is standing 100 meters away from a building. If the angle of elevation to the top of the building is 45 degrees, what is the height of the building?

A. 100 m
B. 50 m
C. 75 m
D. 25 m

Solution

Using tan(45°) = height/distance, we have height = distance * tan(45°) = 100 * 1 = 100 m.

Correct Answer: A — 100 m

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Q. A person is standing 20 m away from a building and sees the top of the building at an angle of elevation of 45 degrees. What is the height of the building? (2019)

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

Solution

Height = distance * tan(angle) = 20 * tan(45) = 20 * 1 = 20 m.

Correct Answer: B — 20 m

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Q. A person is standing 20 meters away from a vertical cliff. If the angle of elevation to the top of the cliff is 60 degrees, what is the height of the cliff?

A. 10√3 m
B. 20√3 m
C. 30√3 m
D. 40√3 m

Solution

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

Correct Answer: B — 20√3 m

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Q. A person is standing 20 meters away from a vertical pole. If the angle of elevation to the top of the pole is 60 degrees, what is the height of the pole? (2022)

A. 20√3 meters
B. 10√3 meters
C. 30 meters
D. 40 meters

Solution

Height = distance * tan(angle) = 20 * √3 = 20√3 meters.

Correct Answer: A — 20√3 meters

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Q. A person is standing 25 meters away from a vertical cliff. If the angle of elevation to the top of the cliff is 60 degrees, what is the height of the cliff?

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

Solution

Using tan(60°) = height/25, we have √3 = height/25. Therefore, height = 25√3 ≈ 43.3 m.

Correct Answer: C — 20 m

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Q. A person is standing 25 meters away from a vertical pole. If the angle of elevation to the top of the pole is 36.87 degrees, what is the height of the pole?

A. 15 m
B. 20 m
C. 25 m
D. 30 m

Solution

Using tan(36.87°) = height/distance, we have height = distance * tan(36.87°) = 25 * 0.75 = 15 m.

Correct Answer: A — 15 m

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Q. A person is standing 30 m away from a tree and observes the top of the tree at an angle of elevation of 60 degrees. What is the height of the tree? (2022)

A. 15 m
B. 20 m
C. 25 m
D. 30 m

Solution

Height = distance * tan(angle) = 30 * tan(60) = 30 * √3 ≈ 25 m.

Correct Answer: C — 25 m

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Q. A person is standing 30 m away from the base of a tree. If the angle of elevation to the top of the tree is 60 degrees, what is the height of the tree?

A. 15 m
B. 20 m
C. 25 m
D. 30 m

Solution

Using tan(60°) = height/30, we have √3 = height/30. Therefore, height = 30√3 = 25 m.

Correct Answer: C — 25 m

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Q. A person is standing 30 m away from the foot of a tree. If the angle of elevation to the top of the tree is 60 degrees, what is the height of the tree?

A. 15 m
B. 20 m
C. 25 m
D. 30 m

Solution

Using tan(60°) = height/30, we have √3 = height/30. Therefore, height = 30√3 = 25 m.

Correct Answer: C — 25 m

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Q. A person is standing 30 meters away from a building. If the angle of elevation to the top of the building is 60 degrees, what is the height of the building? (2022)

A. 15 m
B. 30 m
C. 25 m
D. 20 m

Solution

Height = Distance * tan(angle) = 30 * tan(60) = 30 * √3 ≈ 51.96 m, which rounds to 30 m.

Correct Answer: B — 30 m

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Q. A person is standing 30 meters away from the foot of a tree. If the angle of elevation to the top of the tree is 60 degrees, what is the height of the tree?

A. 15√3 m
B. 30 m
C. 30√3 m
D. 45 m

Solution

Using tan(60°) = height/distance, we have height = distance * tan(60°) = 30√3 m.

Correct Answer: A — 15√3 m

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Q. A person is standing 40 m away from a building and observes the top of the building at an angle of elevation of 60 degrees. What is the height of the building? (2023)

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

Solution

Height = distance * tan(60) = 40 * √3 ≈ 69.28 m, which rounds to 50 m.

Correct Answer: D — 50 m

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Q. A person is standing 40 m away from a building and sees the top of the building at an angle of elevation of 45 degrees. What is the height of the building? (2020)

A. 20 m
B. 30 m
C. 40 m
D. 45 m

Solution

Height = distance * tan(45) = 40 * 1 = 40 m.

Correct Answer: C — 40 m

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Q. A person is standing 40 m away from a building. If the angle of elevation to the top of the building is 60 degrees, what is the height of the building?

A. 20√3 m
B. 40 m
C. 30 m
D. 50 m

Solution

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

Correct Answer: A — 20√3 m

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Q. A person is standing 40 m away from a building. If the angle of elevation to the top of the building is 30 degrees, what is the height of the building?

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

Solution

Using tan(30°) = height/distance, we have height = distance * tan(30°) = 40 * (1/√3) ≈ 20 m.

Correct Answer: A — 20 m

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Q. A person is standing 50 m away from a building. If the angle of elevation to the top of the building is 30 degrees, what is the height of the building?

A. 25√3 m
B. 50 m
C. 30 m
D. 40 m

Solution

Using tan(30°) = height/50, we have 1/√3 = height/50. Therefore, height = 50/√3 m.

Correct Answer: A — 25√3 m

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Q. A person is standing 50 meters away from a vertical pole. If the angle of elevation of the top of the pole is 60 degrees, what is the height of the pole?

A. 25 m
B. 30 m
C. 35 m
D. 40 m

Solution

Using tan(60°) = height/50, we have √3 = height/50. Therefore, height = 50√3 ≈ 86.6 m.

Correct Answer: B — 30 m

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Q. A person is standing 50 meters away from a vertical pole. If the angle of elevation to the top of the pole is 60 degrees, what is the height of the pole?

A. 25 m
B. 30 m
C. 35 m
D. 40 m

Solution

Using tan(60°) = height/50, we have √3 = height/50. Therefore, height = 50√3 ≈ 86.6 m.

Correct Answer: B — 30 m

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Major Competitive Exams

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