Mathematics Syllabus for JEE Main

Mathematics Syllabus (JEE Main)

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

Q. A tower is 50 meters high. From a point on the ground, the angle of elevation to the top of the tower is 30 degrees. What is the distance from the point to the base of the tower?

A. 25√3 m
B. 50 m
C. 25 m
D. 50√3 m

Solution

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

Correct Answer: A — 25√3 m

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Q. A tower is 60 meters high. From a point on the ground, the angle of elevation to the top of the tower is 45 degrees. How far is the point from the base of the tower?

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

Solution

Distance = height / tan(angle) = 60 / 1 = 60 meters.

Correct Answer: B — 60 meters

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Q. A tower is 80 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. 40 m
B. 80 m
C. 20 m
D. 60 m

Solution

Distance = height / tan(angle) = 80 / √3 = 40 m.

Correct Answer: A — 40 m

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Q. A tower is standing on a horizontal ground. The angle of elevation of the top of the tower from a point on the ground is 30 degrees. If the height of the tower is 10√3 m, how far is the point from the base of the tower?

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

Solution

Using tan(30°) = height/distance, we have 1/√3 = 10√3/distance. Therefore, distance = 10√3 * √3 = 30 m.

Correct Answer: A — 10 m

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Q. A tower is standing on a horizontal ground. The angle of elevation of the top of the tower from a point on the ground is 30 degrees. If the height of the tower is 10√3 meters, how far is the point from the base of the tower?

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

Solution

Using tan(30°) = height/distance, we have 1/√3 = 10√3/distance. Therefore, distance = 10√3 * √3 = 30 m.

Correct Answer: B — 20 m

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Q. A tower is standing on a horizontal ground. The angle of elevation of the top of the tower from a point on the ground is 30 degrees. If the height of the tower is 50 meters, how far is the point from the base of the tower?

A. 50√3 m
B. 100 m
C. 50 m
D. 100√3 m

Solution

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

Correct Answer: A — 50√3 m

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Q. A tree casts a shadow of 20 m when the angle of elevation of the sun is 30 degrees. What is the height of the tree?

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

Solution

Using tan(30°) = height/20, we have 1/√3 = height/20. Therefore, height = 20/√3 ≈ 11.55 m.

Correct Answer: A — 10 m

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Q. A tree casts a shadow of 20 m when the angle of elevation of the sun is 45 degrees. What is the height of the tree?

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

Solution

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

Correct Answer: B — 20 m

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Q. A tree casts a shadow of 20 meters when the angle of elevation of the sun is 30 degrees. What is the height of the tree?

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

Solution

Height = shadow * tan(angle) = 20 * tan(30°) = 20 * (1/√3) = 20√3 meters.

Correct Answer: A — 20√3 meters

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Q. A tree is 15 meters tall. From a point on the ground, the angle of elevation to the top of the tree is 30 degrees. How far is the point from the base of the tree?

A. 15√3 meters
B. 30 meters
C. 45 meters
D. 10 meters

Solution

Distance = height / tan(angle) = 15 / tan(30°) = 15√3 meters.

Correct Answer: A — 15√3 meters

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Q. Calculate the area between the curves y = x and y = x^2 from x = 0 to x = 1.

A. 0.25
B. 0.5
C. 0.75
D. 1

Solution

The area is given by the integral from 0 to 1 of (x - x^2) dx. This evaluates to [x^2/2 - x^3/3] from 0 to 1 = (1/2 - 1/3) = 1/6 = 0.5.

Correct Answer: B — 0.5

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Q. Calculate the area between the curves y = x^2 and y = 2x from x = 0 to x = 2.

A. 2
B. 3
C. 4
D. 5

Solution

The area is given by the integral from 0 to 2 of (2x - x^2) dx. This evaluates to [x^2 - x^3/3] from 0 to 2 = (4 - 8/3) = 4/3.

Correct Answer: A — 2

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Q. Calculate the area between the curves y = x^2 and y = 4 from x = 0 to x = 2.

A. 4
B. 8
C. 6
D. 2

Solution

The area is given by the integral from 0 to 2 of (4 - x^2) dx. This evaluates to [4x - x^3/3] from 0 to 2 = (8 - 8/3) = 16/3.

Correct Answer: A — 4

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Q. Calculate the area under the curve y = cos(x) from x = 0 to x = π/2.

A. 1
B. 0
C. π/2
D. 2

Solution

The area under the curve y = cos(x) from x = 0 to x = π/2 is given by ∫(from 0 to π/2) cos(x) dx = [sin(x)] from 0 to π/2 = 1 - 0 = 1.

Correct Answer: A — 1

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Q. Calculate the area under the curve y = x^2 + 2x from x = 0 to x = 2.

A. 4
B. 6
C. 8
D. 10

Solution

The area under the curve is given by ∫(from 0 to 2) (x^2 + 2x) dx = [x^3/3 + x^2] from 0 to 2 = (8/3 + 4) = 20/3.

Correct Answer: B — 6

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Q. Calculate the area under the curve y = x^4 from x = 0 to x = 2.

A. 4
B. 8
C. 16
D. 32

Solution

The area under the curve y = x^4 from x = 0 to x = 2 is given by ∫(from 0 to 2) x^4 dx = [x^5/5] from 0 to 2 = (32/5) - 0 = 32/5.

Correct Answer: B — 8

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Q. Calculate the derivative of f(x) = e^(2x).

A. 2e^(2x)
B. e^(2x)
C. 2xe^(2x)
D. e^(x)

Solution

Using the chain rule, f'(x) = d/dx(e^(2x)) = 2e^(2x).

Correct Answer: A — 2e^(2x)

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Q. Calculate the derivative of f(x) = x^2 * e^x.

A. (2x + x^2)e^x
B. 2xe^x
C. x^2e^x
D. (x^2 + 2x)e^x

Solution

Using the product rule, f'(x) = d/dx(x^2 * e^x) = (x^2 + 2x)e^x.

Correct Answer: D — (x^2 + 2x)e^x

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Q. Calculate the determinant of the matrix [[1, 2], [3, 4]].

A. -2
B. 2
C. 0
D. 4

Solution

Determinant = (1*4) - (2*3) = 4 - 6 = -2.

Correct Answer: A — -2

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Q. Calculate the determinant of the matrix \( B = \begin{pmatrix} 2 & 3 \\ 5 & 7 \end{pmatrix} \).

A. -1
B. 1
C. 7
D. 10

Solution

The determinant is calculated as \( 2*7 - 3*5 = 14 - 15 = -1 \).

Correct Answer: D — 10

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Q. Calculate the determinant of the matrix \( G = \begin{pmatrix} 2 & 1 & 3 \\ 1 & 0 & 1 \\ 3 & 1 & 2 \end{pmatrix} \).

A. -1
B. 0
C. 1
D. 2

Solution

The determinant is calculated as \( 2(0*2 - 1*1) - 1(1*2 - 3*1) + 3(1*1 - 3*0) = 0 \).

Correct Answer: A — -1

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Q. Calculate the determinant of the matrix \( \begin{pmatrix} 2 & 3 \\ 1 & 4 \end{pmatrix} \).

A. 5
B. 10
C. 7
D. 8

Solution

The determinant is calculated as \( 2*4 - 3*1 = 8 - 3 = 5 \).

Correct Answer: A — 5

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Q. Calculate the determinant of the matrix \( \begin{pmatrix} 2 & 3 \\ 5 & 7 \end{pmatrix} \).

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

Solution

The determinant is calculated as (2*7) - (3*5) = 14 - 15 = -1.

Correct Answer: A — 1

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Q. Calculate the determinant of the matrix: | 1 1 1 | | 2 2 2 | | 3 3 3 |

A. 0
B. 3
C. 6
D. 9

Solution

The rows are linearly dependent, hence the determinant is 0.

Correct Answer: A — 0

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Q. Calculate the determinant \( \begin{vmatrix} 1 & 2 & 1 \\ 2 & 3 & 1 \\ 3 & 4 & 1 \end{vmatrix} \).

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

Solution

The determinant is 0 because the rows are linearly dependent.

Correct Answer: A — 0

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Q. Calculate the determinant \( \begin{vmatrix} 2 & 3 \\ 5 & 7 \end{vmatrix} \)

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

Solution

The determinant is \( 2*7 - 3*5 = 14 - 15 = -1 \).

Correct Answer: A — 1

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Q. Calculate the determinant \( \begin{vmatrix} a & b \\ c & d \end{vmatrix} \)

A. ad - bc
B. ab + cd
C. ac - bd
D. bc - ad

Solution

The determinant is calculated as \( ad - bc \).

Correct Answer: A — ad - bc

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Q. Calculate the determinant | 1 0 0 | | 0 1 0 | | 0 0 1 |.

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

Solution

The determinant of the identity matrix is 1.

Correct Answer: B — 1

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Q. Calculate the determinant | 2 3 | | 4 5 | + | 1 1 | | 1 1 |.

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

Solution

The first determinant is -2 and the second is 0, so the total is -2 + 0 = -2.

Correct Answer: B — 1

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Q. Calculate the determinant: | 2 3 1 | | 1 0 2 | | 0 1 3 |.

A. -1
B. 0
C. 1
D. 2

Solution

The determinant evaluates to 0 as the rows are linearly dependent.

Correct Answer: A — -1

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Showing 121 to 150 of 2847 (95 Pages)

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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