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Q. A man invests $5000 at an interest rate of 5% per annum. How much interest will he earn in 3 years?

A. $750
B. $500
C. $150
D. $300

Solution

Interest = Principal × Rate × Time = $5000 × 0.05 × 3 = $750.

Correct Answer: A — $750

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Q. A man invests a sum of money at a rate of 10% per annum. If he receives a total interest of Rs. 600 after 3 years, what was the principal amount? (2000)

A. Rs. 1500
B. Rs. 2000
C. Rs. 2500
D. Rs. 3000

Solution

Using the formula for simple interest, SI = PRT/100. Here, 600 = P * 10 * 3 / 100. Therefore, P = 2000.

Correct Answer: B — Rs. 2000

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Q. A man invests Rs. 5000 at a rate of 5% per annum compounded annually. What will be the amount after 3 years? (2020)

A. Rs. 5750
B. Rs. 6300
C. Rs. 5000
D. Rs. 5798.75

Solution

Amount = P(1 + r)^n = 5000(1 + 0.05)^3 = 5000(1.157625) = 5798.75.

Correct Answer: D — Rs. 5798.75

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Q. A man invests Rs. 5000 at an interest rate of 5% per annum. How much interest will he earn in 3 years? (2020)

A. 750
B. 500
C. 1500
D. 1000

Solution

Simple Interest = Principal * Rate * Time = 5000 * 0.05 * 3 = 750.

Correct Answer: A — 750

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Q. A man is 30 m away from a building and sees the top of the building at an angle of elevation of 60 degrees. What is the height of the building? (2019)

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

Solution

Height = distance * tan(60) = 30 * √3 ≈ 51.96 m, which rounds to 25 m.

Correct Answer: C — 25 m

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Q. A man is facing South. He turns 180 degrees and then turns 90 degrees to his left. Which direction is he facing now? (2023)

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

Solution

Turning 180 degrees from South leads to North. A 90 degrees left turn from North leads to West.

Correct Answer: C — East

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Q. A man is facing South. He turns 45 degrees to his left and then 90 degrees to his right. Which direction is he facing now? (2023)

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

Solution

Facing South, a 45 degrees left turn leads to East-South-East. A 90 degrees right turn from there leads to East.

Correct Answer: A — East

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Q. A man is facing South. He turns 90 degrees to the right and then turns 90 degrees to the left. Which direction is he facing now? (2023)

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

Solution

Turning 90 degrees right from South leads to West. Turning 90 degrees left from West leads back to South.

Correct Answer: B — South

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Q. A man 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 man is standing 30 meters away from a tower. If the angle of elevation of the top of the tower from the man's position is 30 degrees, what is the height of the tower?

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

Solution

Height = distance * tan(angle) = 30 * tan(30°) = 30 * (1/√3) = 10√3 meters.

Correct Answer: A — 15√3 meters

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Q. A man is standing 30 meters away from a tree. If the angle of elevation from his eyes to the top of the tree is 30 degrees, what is the height of the tree?

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

Solution

Height = distance * tan(angle) = 30 * tan(30°) = 30 * (1/√3) = 10√3 meters.

Correct Answer: A — 15√3 meters

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Q. A man is standing 30 meters away from a tree. If the angle of elevation of the top of the tree from his eyes is 60 degrees, what is the height of the tree?

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

Solution

Height = distance * tan(angle) = 30 * √3 = 15√3 meters.

Correct Answer: A — 15√3 meters

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Q. A man is standing 40 meters 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√3 meters
B. 40√3 meters
C. 30 meters
D. 20 meters

Solution

Height = distance * tan(angle) = 40 * (1/√3) = 40/√3 = 20√3 meters.

Correct Answer: A — 20√3 meters

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Q. A man is standing 50 meters away from a vertical pole. If he looks up at an angle of elevation of 60 degrees to the top of the pole, 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 man is standing at a distance of 50 m from a tower. The angle of elevation of the top of the tower from his position is 30 degrees. Find the height of the tower. (2021)

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

Solution

Height = distance * tan(angle) = 50 * tan(30) = 50 * (1/√3) = 50/√3 ≈ 28.87 m, which rounds to 20 m.

Correct Answer: C — 20 m

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Q. A man is standing at a distance of 50 meters from a tower. If the angle of elevation of the top of the tower from his position is 30 degrees, what is the height of the tower? (2021)

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

Solution

Height = distance * tan(angle) = 50 * tan(30) = 50 * (1/√3) = 50/√3 ≈ 25 m.

Correct Answer: A — 25 m

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Q. A man is standing at a distance of 50 meters from a tree. If the angle of elevation of the top of the tree from his position is 30 degrees, what is the height of the tree? (2021)

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

Solution

Height = Distance * tan(angle) = 50 * tan(30) = 50 * (1/√3) = 50/√3 ≈ 28.87 m, which rounds to 25 m.

Correct Answer: A — 25 m

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Q. A man is standing on a hill 100 meters high. If he looks down at an angle of 45 degrees, how far is he from the base of the hill? (2020)

A. 100 meters
B. 50 meters
C. 70 meters
D. 30 meters

Solution

Distance = height / tan(angle) = 100 / 1 = 100 meters.

Correct Answer: A — 100 meters

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Q. A man is standing on a hill 200 meters high. If he looks down at an angle of depression of 30 degrees, how far is he from the base of the hill?

A. 100 m
B. 200 m
C. 300 m
D. 400 m

Solution

Distance = height / tan(angle) = 200 / (1/√3) = 200√3 m.

Correct Answer: A — 100 m

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Q. A man is standing on a hill 80 meters high. If he looks at a point on the ground at an angle of depression of 45 degrees, how far is the point from the base of the hill?

A. 80 meters
B. 40√2 meters
C. 80√2 meters
D. 60 meters

Solution

Distance = height / tan(angle) = 80 / tan(45°) = 80 meters.

Correct Answer: A — 80 meters

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Q. A man is standing on a hill that is 80 m high. If he looks down at an angle of depression of 30 degrees, how far is he from the base of the hill?

A. 40 m
B. 60 m
C. 80 m
D. 100 m

Solution

Using tan(30°) = height/distance, we have 1/√3 = 80/distance. Therefore, distance = 80√3 ≈ 138.56 m.

Correct Answer: A — 40 m

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Q. A man is standing on the ground and looking at the top of a 15 m high pole. If he is 20 m away from the base of the pole, what is the angle of elevation?

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

Solution

Using tan(θ) = height/distance, we have tan(θ) = 15/20. Therefore, θ = tan⁻¹(0.75) which is approximately 36.87 degrees.

Correct Answer: A — 36.87 degrees

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Q. A man is standing on the ground and looking at the top of a 40 m high building. If the angle of elevation is 60 degrees, how far is he from the building?

A. 20 m
B. 40 m
C. 20√3 m
D. 40√3 m

Solution

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

Correct Answer: C — 20√3 m

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Q. A man is standing on the ground and looking at the top of a building. If the angle of elevation is 45 degrees and he is 10 meters away from the building, what is the height of the building?

A. 10 meters
B. 5 meters
C. 15 meters
D. 20 meters

Solution

Height = distance * tan(angle) = 10 * tan(45°) = 10 meters.

Correct Answer: A — 10 meters

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Q. A man is standing on the ground and looking at the top of a tree. If the angle of elevation is 60 degrees and he is 10 meters away from the base of the tree, what is the height of the tree?

A. 5√3 m
B. 10√3 m
C. 15√3 m
D. 20√3 m

Solution

Using tan(60°) = height/10, we have √3 = height/10. Therefore, height = 10√3 m.

Correct Answer: B — 10√3 m

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Q. A man is standing on the ground and observes the top of a building at an angle of elevation of 60 degrees. If he is 50 m away from the building, what is the height of the building?

A. 25 m
B. 43.3 m
C. 50 m
D. 86.6 m

Solution

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

Correct Answer: B — 43.3 m

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Q. A man is standing on the ground and observes the top of a tree at an angle of elevation of 45 degrees. If he is 10 meters away from the tree, what is the height of the tree?

A. 5 m
B. 10 m
C. 15 m
D. 20 m

Solution

Using tan(45°) = height/10, we have 1 = height/10. Therefore, height = 10 m.

Correct Answer: B — 10 m

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Q. A man spends 30% of his salary on rent and 20% on groceries. If his salary is $1000, how much does he spend on groceries?

A. $200
B. $300
C. $400
D. $500

Solution

If the man's salary is $1000, he spends 20% on groceries. Therefore, the amount spent on groceries is 0.2 * 1000 = $200.

Correct Answer: A — $200

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Q. A man spends 40% of his income on necessities and 25% on savings. If he has $200 left, what is his total income? (2020)

A. $500
B. $600
C. $400
D. $300

Solution

Let total income = x. Then, 0.35x = 200. Therefore, x = 200 / 0.35 = $600.

Correct Answer: B — $600

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Q. A man standing on the ground observes the top of a hill at an angle of elevation of 30 degrees. If he is 100 m away from the base of the hill, what is the height of the hill? (2022)

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

Solution

Height = distance * tan(angle) = 100 * tan(30) = 100 * (1/√3) ≈ 25 m.

Correct Answer: A — 25 m

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Major Competitive Exams

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