Mathematics Syllabus for JEE Main

Mathematics Syllabus (JEE Main)

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

Q. A kite is flying at a height of 30 m. If the angle of elevation from a point on the ground to the kite is 60 degrees, how far is the point from the base of the kite?

A. 15√3 m
B. 30 m
C. 10√3 m
D. 20 m

Solution

Using tan(60°) = height/distance, we have distance = height/tan(60°) = 30/√3 = 15√3 m.

Correct Answer: A — 15√3 m

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Q. A kite is flying at a height of 30 meters. If the angle of elevation from a point on the ground to the kite is 45 degrees, how far is the point from the base of the kite?

A. 15 m
B. 30 m
C. 45 m
D. 60 m

Solution

Using tan(45°) = height/distance, we have 1 = 30/distance. Therefore, distance = 30 m.

Correct Answer: B — 30 m

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Q. A kite is flying at a height of 50 meters. If the angle of elevation from a point on the ground to the kite is 30 degrees, how far is the point from the base of the kite?

A. 50√3 meters
B. 25√3 meters
C. 100 meters
D. 75 meters

Solution

Distance = height / tan(angle) = 50 / (1/√3) = 50√3 meters.

Correct Answer: B — 25√3 meters

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Q. A ladder 10 m long reaches a window 8 m above the ground. What is the angle of elevation of the ladder from the ground?

A. 30 degrees
B. 45 degrees
C. 60 degrees
D. 75 degrees

Solution

Using sin(θ) = opposite/hypotenuse, we have sin(θ) = 8/10. Therefore, θ = sin⁻¹(0.8) ≈ 53.13 degrees.

Correct Answer: C — 60 degrees

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Q. A ladder 15 meters long reaches a window 12 meters above the ground. What is the angle of elevation of the ladder from the ground?

A. 30 degrees
B. 45 degrees
C. 60 degrees
D. 75 degrees

Solution

Using sin(θ) = opposite/hypotenuse, we have sin(θ) = 12/15. Therefore, θ = sin⁻¹(0.8) ≈ 53.13 degrees.

Correct Answer: C — 60 degrees

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Q. A ladder is leaning against a wall. The foot of the ladder is 12 meters away from the wall, and the angle between the ladder and the ground is 60 degrees. What is the height at which the ladder touches the wall?

A. 12√3 m
B. 6 m
C. 12 m
D. 24 m

Solution

Using sin(60°) = height/hypotenuse, we find the height = 12 * tan(60°) = 12√3 m.

Correct Answer: A — 12√3 m

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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 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 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 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 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 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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Mathematics Syllabus (JEE Main) MCQ & Objective Questions

The Mathematics Syllabus for JEE Main is crucial for students aiming to excel in competitive exams. Understanding this syllabus not only helps in grasping key concepts but also enhances your ability to tackle objective questions effectively. Practicing MCQs and important questions from this syllabus is essential for solid exam preparation, ensuring you are well-equipped to score better in your exams.

What You Will Practise Here

Sets, Relations, and Functions
Complex Numbers and Quadratic Equations
Permutations and Combinations
Binomial Theorem
Sequences and Series
Limits and Derivatives
Statistics and Probability

Exam Relevance

The Mathematics Syllabus (JEE Main) is not only relevant for JEE but also appears in CBSE and State Board examinations. Students can expect a variety of question patterns, including direct MCQs, numerical problems, and conceptual questions. Mastery of this syllabus will prepare you for similar topics in NEET and other competitive exams, making it vital for your overall academic success.

Common Mistakes Students Make

Misinterpreting the questions, especially in word problems.
Overlooking the importance of units and dimensions in problems.
Confusing formulas related to sequences and series.
Neglecting to practice derivations, leading to errors in calculus.
Failing to apply the correct methods for solving probability questions.

FAQs

Question: What are the key topics in the Mathematics Syllabus for JEE Main?
Answer: Key topics include Sets, Complex Numbers, Permutations, Binomial Theorem, and Calculus.

Question: How can I improve my performance in Mathematics MCQs?
Answer: Regular practice of MCQs and understanding the underlying concepts are essential for improvement.

Now is the time to take charge of your exam preparation! Dive into solving practice MCQs and test your understanding of the Mathematics Syllabus (JEE Main). Your success is just a question away!

Mathematics Syllabus (JEE Main)

Mathematics Syllabus (JEE Main) MCQ & Objective Questions

What You Will Practise Here

Exam Relevance

Common Mistakes Students Make

FAQs

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