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Q. A person is standing at a distance of 20 m from a vertical pole. If the angle of elevation to the top of the pole is 45 degrees, what is the height of the pole?

A. 20 m
B. 10 m
C. 30 m
D. 15 m

Solution

Using tan(45°) = height/distance, we have height = distance * tan(45°) = 20 * 1 = 20 m.

Correct Answer: A — 20 m

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

A. 20√3 m
B. 40 m
C. 30 m
D. 10√3 m

Solution

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

Correct Answer: A — 20√3 m

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Q. A person is standing at a distance of 40 meters from the base of 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 m
B. 30 m
C. 40 m
D. 50 m

Solution

Using tan(60°) = height/40, we have √3 = height/40. Therefore, height = 40√3 ≈ 69.28 m.

Correct Answer: C — 40 m

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Q. A person is standing on a hill 100 meters high. If he looks at a point on the ground at an angle of depression of 30 degrees, how far is the point from the base of the hill?

A. 100√3 meters
B. 100 meters
C. 50√3 meters
D. 50 meters

Solution

Distance = height / tan(angle) = 100 / tan(30°) = 100√3 meters.

Correct Answer: A — 100√3 meters

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Q. A person is standing on a hill 80 m high. The angle of depression to a car on the ground is 60 degrees. How far is the car from the base of the hill?

A. 40 m
B. 80 m
C. 20√3 m
D. 40√3 m

Solution

Using tan(60°) = height/distance, we have distance = height/tan(60°) = 80/√3 = 40√3 m.

Correct Answer: D — 40√3 m

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Q. A person is standing on a hill that is 80 meters high. If the angle of depression to a point on the ground is 45 degrees, how far is the point from the base of the hill?

A. 80 m
B. 40 m
C. 80√2 m
D. 40√2 m

Solution

Using tan(45°) = height/distance, we have distance = height/tan(45°) = 80/1 = 80 m.

Correct Answer: A — 80 m

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Q. A person is standing on the ground and looking at the top of a building. If the angle of elevation is 45 degrees and the person is 20 meters away from the building, what is the height of the building?

A. 20 meters
B. 10 meters
C. 30 meters
D. 25 meters

Solution

Height = distance * tan(angle) = 20 * 1 = 20 meters.

Correct Answer: A — 20 meters

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Q. A person is standing on the ground and looking at the top of a tree. If the angle of elevation is 60 degrees and the person is 20 meters away from the tree, what is the height of the tree?

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

Solution

Height = distance * tan(angle) = 20 * tan(60°) = 20 * √3 meters.

Correct Answer: A — 20√3 meters

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Q. A person is walking at 2 m/s on a train moving at 10 m/s. What is the speed of the person relative to the ground?

A. 2 m/s
B. 8 m/s
C. 10 m/s
D. 12 m/s

Solution

Speed of person relative to ground = Speed of train + Speed of person = 10 m/s + 2 m/s = 12 m/s.

Correct Answer: D — 12 m/s

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Q. A person is walking at 4 km/h in a train moving at 36 km/h. What is the speed of the person relative to the ground?

A. 32 km/h
B. 40 km/h
C. 36 km/h
D. 4 km/h

Solution

Speed of person relative to ground = Speed of train + Speed of person = 36 km/h + 4 km/h = 40 km/h.

Correct Answer: B — 40 km/h

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Q. A person jogs at a speed of 8 km/h for 1.5 hours. How far does he jog? (2019)

A. 10 km
B. 12 km
C. 14 km
D. 15 km

Solution

Distance = Speed * Time = 8 km/h * 1.5 hours = 12 km.

Correct Answer: B — 12 km

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Q. A person jogs at a speed of 8 km/h for 45 minutes. How far does he jog? (2022)

A. 5 km
B. 6 km
C. 7 km
D. 8 km

Solution

Time = 45 minutes = 0.75 hours. Distance = Speed * Time = 8 km/h * 0.75 hours = 6 km.

Correct Answer: B — 6 km

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Q. A person lifts a 10 kg box to a height of 2 m. What is the work done against gravity? (g = 9.8 m/s²)

A. 196 J
B. 98 J
C. 20 J
D. 10 J

Solution

Work = mgh = 10 kg * 9.8 m/s² * 2 m = 196 J.

Correct Answer: A — 196 J

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Q. A person lifts a box of mass 10 kg to a height of 2 m in 4 seconds. What is the power exerted by the person?

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

Solution

The work done against gravity is W = mgh = 10 kg * 9.8 m/s² * 2 m = 196 J. Power is P = W/t = 196 J / 4 s = 49 W, approximately 50 W.

Correct Answer: A — 50 W

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Q. A person needs 2000 calories a day and wants to get 15% of their calories from fats. How many grams of fat should they consume (1 gram of fat = 9 calories)? (2000)

A. 33 grams
B. 40 grams
C. 50 grams
D. 60 grams

Solution

15% of 2000 calories = 0.15 * 2000 = 300 calories from fats. 300 calories / 9 calories per gram = 33.33 grams, rounded to 33 grams.

Correct Answer: B — 40 grams

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Q. A person needs 2000 calories a day. If they want to reduce their calorie intake by 20%, how many calories should they consume? (2022)

A. 1600 calories
B. 1700 calories
C. 1800 calories
D. 1900 calories

Solution

20% of 2000 calories = 0.20 * 2000 = 400 calories. 2000 - 400 = 1600 calories.

Correct Answer: A — 1600 calories

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Q. A person pushes a box with a force of 30 N, but the box does not move. If the coefficient of static friction is 0.6, what is the maximum static friction force?

A. 18 N
B. 30 N
C. 36 N
D. 60 N

Solution

The maximum static friction force is equal to the applied force when the box does not move, which is 30 N.

Correct Answer: C — 36 N

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Q. A person requires 2000 calories per day. If they want to reduce their calorie intake by 20%, how many calories should they consume? (2000)

A. 1600 calories
B. 1800 calories
C. 2000 calories
D. 2200 calories

Solution

20% of 2000 calories = 0.20 * 2000 = 400 calories. 2000 - 400 = 1600 calories.

Correct Answer: A — 1600 calories

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Q. A person standing 20 meters away from a vertical cliff observes the top of the cliff at an angle of elevation of 75 degrees. What is the height of the cliff?

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

Solution

Using tan(75°) = height/20, we have height = 20 * tan(75°) ≈ 20 * 3.732 = 74.64 m.

Correct Answer: D — 25 m

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Q. A person standing 40 m away from a building observes the top of the building at an angle of elevation of 30 degrees. What is the height of the building?

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

Solution

Using tan(30°) = height/40, we have 1/√3 = height/40. Therefore, height = 40/√3 ≈ 23.1 m.

Correct Answer: B — 20 m

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Q. A person standing 40 meters away from a building observes the angle of elevation to the top of the building as 30 degrees. What is the height of the building? (2022)

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

Solution

Height = Distance * tan(30) = 40 * (1/√3) ≈ 23.09 m, which rounds to 20 m.

Correct Answer: A — 20 m

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

A. 40√3 meters
B. 20√3 meters
C. 30 meters
D. 50 meters

Solution

Height = distance * tan(angle) = 40 * tan(60°) = 40√3 meters.

Correct Answer: A — 40√3 meters

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Q. A person standing 40 meters away from a building observes the top of the building at an angle of elevation of 45 degrees. What is the height of the building?

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

Solution

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

Correct Answer: B — 40 m

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Q. A person standing 50 m away from a building observes the top of the building at an angle of elevation of 60 degrees. What is the height of the building?

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 standing 50 m away from a tree observes the angle of elevation to the top of the tree as 30 degrees. What is the height of the tree?

A. 25 m
B. 50 m
C. 15 m
D. 20 m

Solution

Using tan(30°) = height/distance, we have height = distance * tan(30°) = 50 * (1/√3) = 25 m.

Correct Answer: A — 25 m

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Q. A person standing 50 meters away from a building observes the top of the building at an angle of elevation of 45 degrees. What is the height of the building?

A. 25 meters
B. 50 meters
C. 35 meters
D. 45 meters

Solution

Height = distance * tan(angle) = 50 * tan(45°) = 50 meters.

Correct Answer: B — 50 meters

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Q. A person standing 60 meters away from a tree sees the top of the tree at an angle of elevation of 30 degrees. What is the height of the tree?

A. 20√3 m
B. 30 m
C. 60 m
D. 10 m

Solution

Height = distance * tan(angle) = 60 * (1/√3) = 20√3 m.

Correct Answer: A — 20√3 m

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Q. A person standing on the ground observes the top of a 40 m high building at an angle of elevation of 60 degrees. How far is he from the building? (2023)

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

Solution

Using tan(60) = √3, distance = height / tan(60) = 40 / √3 ≈ 23.09 m, which rounds to 30 m.

Correct Answer: B — 30 m

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Q. A person standing on the ground observes the top of a pole at an angle of elevation of 75 degrees. If the pole is 10 m high, how far is the person from the base of the pole? (2023)

A. 2.68 m
B. 5.77 m
C. 10 m
D. 15 m

Solution

Distance = height / tan(75) = 10 / 3.732 ≈ 2.68 m.

Correct Answer: B — 5.77 m

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Q. A person standing on the ground observes the top of a tree at an angle of elevation of 45 degrees. If the person 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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Major Competitive Exams

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