Mathematics Syllabus for JEE Main

Mathematics Syllabus (JEE Main)

Algebra Calculus Coordinate Geometry Sets, Relations & Functions Statistics & Probability Trigonometry Vector & 3D Geometry

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 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 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 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 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 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 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 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. 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 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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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 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 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 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 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 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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