Mathematics Syllabus for JEE Main

Mathematics Syllabus (JEE Main)

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

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 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 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 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 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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Q. A student has a 70% chance of passing an exam. What is the probability that the student fails the exam?

A. 0.3
B. 0.7
C. 0.5
D. 0.2

Solution

The probability of failing the exam is 1 - 0.7 = 0.3.

Correct Answer: A — 0.3

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Q. A student is selected at random from a class of 40 students, where 25 are boys and 15 are girls. What is the probability that the student is a girl given that the student is not a boy?

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

Solution

The total number of students that are not boys is 15 (girls). The probability of selecting a girl given that the student is not a boy is 15/15 = 1.

Correct Answer: C — 2/3

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Q. A student is selected at random from a class of 40 students, where 25 are boys and 15 are girls. What is the probability that the student is a boy given that the student is not a girl?

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

Solution

If the student is not a girl, they must be a boy. Therefore, P(Boy | Not Girl) = 1.

Correct Answer: B — 3/4

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Q. A student is selected at random from a group of 40 students, where 25 are studying Mathematics and 15 are studying Physics. What is the probability that the student is studying Mathematics given that they are not studying Physics?

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

Solution

If the student is not studying Physics, they must be studying Mathematics. Therefore, P(Math | Not Physics) = 1.

Correct Answer: A — 5/8

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Q. A student is selected at random from a group of 40 students, where 25 are studying Mathematics and 15 are studying Physics. What is the probability that the student is studying Physics given that the student is not studying Mathematics?

A. 0
B. 1/3
C. 3/8
D. 1/2

Solution

If the student is not studying Mathematics, they must be studying Physics. Therefore, the probability is 1.

Correct Answer: B — 1/3

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Q. A student is selected at random from a group of students who study Mathematics and Physics. If 70% study Mathematics and 40% study both subjects, what is the probability that a student studies Physics given that they study Mathematics?

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

Solution

Using the formula P(Physics|Mathematics) = P(Physics and Mathematics) / P(Mathematics) = 0.4 / 0.7 = 0.571.

Correct Answer: A — 0.4

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Q. A student is selected from a class of 40 students, where 25 are girls and 15 are boys. What is the probability that the student is a girl given that the student is not a boy?

A. 1
B. 0
C. 1/2
D. 3/4

Solution

If the student is not a boy, they must be a girl. Therefore, the probability is 1.

Correct Answer: A — 1

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Q. A tower is 100 meters high. From a point on the ground, the angle of elevation to the top of the tower is 30 degrees. How far is the point from the base of the tower?

A. 100√3 meters
B. 50√3 meters
C. 200 meters
D. 150 meters

Solution

Distance = height / tan(angle) = 100 / (1/√3) = 100√3 meters.

Correct Answer: A — 100√3 meters

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Q. A tower is 40 meters high. From a point on the ground, the angle of elevation to the top of the tower is 60 degrees. How far is the point from the base of the tower?

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

Solution

Distance = height / tan(angle) = 40 / tan(60°) = 40 / √3 = 20√3 meters.

Correct Answer: A — 20√3 meters

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Mathematics Syllabus (JEE Main)

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