Mathematics Syllabus for JEE Main

Mathematics Syllabus (JEE Main)

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

Q. Calculate the scalar product of the vectors A = (1, 2, 3) and B = (4, 5, 6).

A. 32
B. 30
C. 28
D. 26

Solution

A · B = 1*4 + 2*5 + 3*6 = 4 + 10 + 18 = 32.

Correct Answer: B — 30

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Q. Calculate the scalar product of the vectors A = (4, -1, 2) and B = (2, 3, 1).

A. 10
B. 8
C. 6
D. 12

Solution

A · B = 4*2 + (-1)*3 + 2*1 = 8 - 3 + 2 = 7.

Correct Answer: A — 10

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Q. Calculate the scalar product of the vectors K = (0, 1, 2) and L = (3, 4, 5).

A. 10
B. 11
C. 12
D. 13

Solution

K · L = 0*3 + 1*4 + 2*5 = 0 + 4 + 10 = 14.

Correct Answer: A — 10

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Q. Calculate the variance of the data set {2, 4, 4, 4, 5, 5, 7, 9}.

A. 4
B. 6
C. 5
D. 3

Solution

Mean = 5, Variance = [(2-5)² + (4-5)² + (4-5)² + (4-5)² + (5-5)² + (5-5)² + (7-5)² + (9-5)²] / 8 = 4.

Correct Answer: B — 6

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Q. Calculate the variance of the data set {4, 8, 6, 5, 3}.

A. 2.5
B. 3.2
C. 1.5
D. 4.0

Solution

Mean = (4+8+6+5+3)/5 = 5.2. Variance = [(4-5.2)² + (8-5.2)² + (6-5.2)² + (5-5.2)² + (3-5.2)²]/5 = 2.5.

Correct Answer: A — 2.5

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Q. Calculate the vector product of A = (3, 2, 1) and B = (1, 0, 2).

A. (4, 5, -2)
B. (2, 5, -3)
C. (2, -5, 3)
D. (5, -2, 3)

Solution

A × B = |i  j  k|\n|3  2  1|\n|1  0  2| = (4, 5, -2)

Correct Answer: A — (4, 5, -2)

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Q. Calculate the weighted mean of the following data: (10, 2), (20, 3), (30, 5).

A. 20
B. 25
C. 30
D. 35

Solution

Weighted Mean = (10*2 + 20*3 + 30*5) / (2 + 3 + 5) = 220 / 10 = 22.

Correct Answer: B — 25

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Q. Calculate the weighted mean of the following data: (2, 3), (4, 5), (6, 7) where the first number is the weight.

A. 4.5
B. 5
C. 5.5
D. 6

Solution

Weighted mean = (2*3 + 4*5 + 6*7) / (2 + 4 + 6) = (6 + 20 + 42) / 12 = 68 / 12 = 5.67.

Correct Answer: C — 5.5

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Q. Calculate the weighted mean of the numbers 10, 20, and 30 with weights 1, 2, and 3 respectively.

A. 20
B. 25
C. 30
D. 15

Solution

Weighted mean = (10*1 + 20*2 + 30*3) / (1 + 2 + 3) = 140 / 6 = 23.33.

Correct Answer: B — 25

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Q. Calculate the weighted mean of the scores 70, 80, and 90 with weights 1, 2, and 3 respectively.

A. 80
B. 85
C. 90
D. 75

Solution

Weighted mean = (70*1 + 80*2 + 90*3) / (1 + 2 + 3) = 85.

Correct Answer: B — 85

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Q. Calculate ∫ from 0 to 1 of (1 - x^2) dx.

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

Solution

The integral evaluates to [x - x^3/3] from 0 to 1 = (1 - 1/3) = 2/3.

Correct Answer: B — 1/2

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Q. Calculate ∫ from 0 to 1 of (1/x) dx.

A. 0
B. 1
C. ln(1)
D. ln(2)

Solution

The integral evaluates to [ln(x)] from 0 to 1 = ln(1) - ln(0) which diverges.

Correct Answer: C — ln(1)

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Q. Calculate ∫ from 0 to 1 of (2x^2 + 3x + 1) dx.

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

Solution

The integral evaluates to [2x^3/3 + (3/2)x^2 + x] from 0 to 1 = (2/3 + 3/2 + 1) = 3.

Correct Answer: C — 3

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Q. Calculate ∫ from 0 to 1 of (4x^3 - 2x^2 + x) dx.

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

Solution

The integral evaluates to [x^4 - (2/3)x^3 + (1/2)x^2] from 0 to 1 = (1 - 2/3 + 1/2) = 1/6.

Correct Answer: C — 1/2

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Q. Calculate ∫ from 0 to 1 of (4x^3 - 3x^2 + 2x - 1) dx.

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

Solution

The integral evaluates to [x^4 - x^3 + x^2 - x] from 0 to 1 = (1 - 1 + 1 - 1) = 0.

Correct Answer: B — 1

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Q. Calculate ∫ from 0 to 1 of (4x^3 - 4x^2 + 1) dx.

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

Solution

The integral evaluates to [x^4 - (4/3)x^3 + x] from 0 to 1 = 1 - (4/3) + 1 = 2/3.

Correct Answer: A — 1

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Q. Calculate ∫ from 0 to 1 of (6x^2 - 4x + 1) dx.

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

Solution

The integral evaluates to [2x^3 - 2x^2 + x] from 0 to 1 = (2 - 2 + 1) = 1.

Correct Answer: A — 1

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Q. Calculate ∫ from 0 to 1 of (x^2 * e^x) dx.

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

Solution

Using integration by parts, the integral evaluates to (2/e - 1/e) = 1/e.

Correct Answer: B — 2/e

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Q. Calculate ∫ from 0 to 1 of (x^2 + 1/x^2) dx.

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

Solution

The integral evaluates to [x^3/3 - 1/x] from 0 to 1 = (1/3 - 1) = -2/3.

Correct Answer: C — 3

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Q. Calculate ∫ from 0 to 1 of (x^2 + 2x + 1) dx.

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

Solution

The integral evaluates to [x^3/3 + x^2 + x] from 0 to 1 = (1/3 + 1 + 1) - (0) = 7/3.

Correct Answer: C — 3

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Q. Calculate ∫ from 0 to 1 of (x^2 + 4x + 4) dx.

A. 3
B. 4
C. 5
D. 6

Solution

The integral evaluates to [x^3/3 + 2x^2 + 4x] from 0 to 1 = (1/3 + 2 + 4) = 25/3.

Correct Answer: C — 5

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Q. Calculate ∫ from 0 to 1 of (x^4 - 2x^2 + 1) dx.

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

Solution

The integral evaluates to [x^5/5 - 2x^3/3 + x] from 0 to 1 = (1/5 - 2/3 + 1) = (15/15 - 10/15 + 3/15) = 8/15.

Correct Answer: D — 2/3

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Q. Calculate ∫ from 0 to 1 of (x^4 - 2x^3 + x^2) dx.

A. 0
B. 1/5
C. 1/3
D. 1/2

Solution

The integral evaluates to [x^5/5 - (2/4)x^4 + (1/3)x^3] from 0 to 1 = (1/5 - 1/2 + 1/3) = 1/30.

Correct Answer: B — 1/5

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Q. Calculate ∫ from 0 to 2 of (x^3 - 3x^2 + 4) dx.

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

Solution

The integral evaluates to [x^4/4 - x^3 + 4x] from 0 to 2 = (4 - 8 + 8) - 0 = 4.

Correct Answer: C — 6

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Q. Calculate ∫ from 0 to π of sin(x) dx.

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

Solution

The integral evaluates to [-cos(x)] from 0 to π = [1 - (-1)] = 2.

Correct Answer: C — 2

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Q. Calculate ∫ from 0 to π/2 of sin(x) cos(x) dx.

A. 1/2
B. 1
C. π/4
D. π/2

Solution

Using the identity sin(2x) = 2sin(x)cos(x), the integral becomes 1/2 ∫ from 0 to π/2 of sin(2x) dx = 1/2 [-1/2 cos(2x)] from 0 to π/2 = 1/2 [0 - (-1/2)] = 1/4.

Correct Answer: A — 1/2

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Q. Calculate ∫ from 0 to π/2 of sin^2(x) dx.

A. π/4
B. π/2
C. π/3
D. π/6

Solution

Using the identity sin^2(x) = (1 - cos(2x))/2, the integral evaluates to π/4.

Correct Answer: A — π/4

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Q. Calculate ∫ from 1 to 3 of (2x + 1) dx.

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

Solution

The integral evaluates to [x^2 + x] from 1 to 3 = (9 + 3) - (1 + 1) = 10.

Correct Answer: B — 6

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Q. Calculate ∫_0^1 (4x^3 - 3x^2 + 2) dx.

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

Solution

∫_0^1 (4x^3 - 3x^2 + 2) dx = [x^4 - x^3 + 2x] from 0 to 1 = (1 - 1 + 2) - (0) = 2.

Correct Answer: B — 2

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Q. Calculate ∫_0^1 (e^x) dx.

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

Solution

∫_0^1 e^x dx = [e^x] from 0 to 1 = e - 1.

Correct Answer: A — e - 1

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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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