Mathematics Syllabus for JEE Main

Mathematics Syllabus (JEE Main)

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

Q. In triangle ABC, if AB = 10 cm, AC = 6 cm, and angle A = 30°, what is the length of side BC?

A. 8 cm
B. 7 cm
C. 5 cm
D. 4 cm

Solution

Using the Law of Cosines: BC² = AB² + AC² - 2 * AB * AC * cos(A) = 10² + 6² - 2 * 10 * 6 * (√3/2) = 100 + 36 - 60√3. BC = √(100 + 36 - 60√3) ≈ 7 cm.

Correct Answer: B — 7 cm

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Q. In triangle ABC, if AB = 7 cm, AC = 24 cm, and BC = 25 cm, is triangle ABC a right triangle?

A. Yes
B. No
C. Cannot be determined
D. Only if angle A is 90°

Solution

Using the Pythagorean theorem, 7^2 + 24^2 = 49 + 576 = 625 = 25^2, so triangle ABC is a right triangle.

Correct Answer: A — Yes

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Q. In triangle ABC, if AB = 7 cm, AC = 24 cm, and BC = 25 cm, what is the area of the triangle?

A. 84 cm²
B. 96 cm²
C. 120 cm²
D. 140 cm²

Solution

Using Heron's formula, the semi-perimeter s = (7 + 24 + 25)/2 = 28. Area = √[s(s-a)(s-b)(s-c)] = √[28(28-7)(28-24)(28-25)] = √[28*21*4*3] = 84 cm².

Correct Answer: B — 96 cm²

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Q. In triangle ABC, if AB = 8, AC = 6, and BC = 10, what is the semi-perimeter?

A. 12
B. 14
C. 16
D. 18

Solution

Semi-perimeter s = (AB + AC + BC) / 2 = (8 + 6 + 10) / 2 = 12.

Correct Answer: B — 14

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Q. In triangle ABC, if angle A = 45 degrees and angle B = 45 degrees, what is angle C?

A. 45 degrees
B. 60 degrees
C. 90 degrees
D. 135 degrees

Solution

The sum of angles in a triangle is 180 degrees. Therefore, angle C = 180 - (45 + 45) = 90 degrees.

Correct Answer: C — 90 degrees

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Q. In triangle ABC, if angle A = 45 degrees and angle B = 45 degrees, what is the relationship between sides a, b, and c?

A. a = b
B. a > b
C. a < b
D. a + b = c

Solution

In an isosceles triangle with angles A and B equal, the sides opposite those angles are equal, hence a = b.

Correct Answer: A — a = b

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Q. In triangle ABC, if angle A = 45 degrees and angle B = 45 degrees, what is the type of triangle?

A. Scalene
B. Isosceles
C. Equilateral
D. Right

Solution

Since two angles are equal, triangle ABC is isosceles.

Correct Answer: B — Isosceles

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Q. In triangle ABC, if angle A = 45 degrees and side a = 10 cm, what is the length of side b if angle B = 60 degrees?

A. 8.66 cm
B. 10 cm
C. 12.25 cm
D. 15 cm

Solution

Using the Law of Sines: a/sin(A) = b/sin(B). Therefore, b = a * (sin(B)/sin(A)) = 10 * (sin(60)/sin(45)) = 10 * (√3/2)/(√2/2) = 10 * √3/√2 = 10 * √(3/2) = 8.66 cm.

Correct Answer: A — 8.66 cm

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Q. In triangle ABC, if angle A = 45° and angle B = 45°, what is angle C?

A. 45°
B. 60°
C. 75°
D. 90°

Solution

Angle C = 180° - (angle A + angle B) = 180° - (45° + 45°) = 90°.

Correct Answer: D — 90°

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Q. In triangle ABC, if angle A = 45° and side a = 10, what is the length of side b if angle B = 60°?

A. 8.66
B. 7.5
C. 5
D. 10

Solution

Using the Law of Sines: b/a = sin(B)/sin(A) => b = a * (sin(B)/sin(A)) = 10 * (√3/2)/(√2/2) = 10 * √3/√2 = 10 * 8.66/10 = 8.66.

Correct Answer: A — 8.66

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Q. In triangle ABC, if angle A = 60 degrees and angle B = 70 degrees, what is angle C?

A. 50 degrees
B. 60 degrees
C. 70 degrees
D. 80 degrees

Solution

Angle C = 180 - (angle A + angle B) = 180 - (60 + 70) = 50 degrees.

Correct Answer: A — 50 degrees

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Q. In triangle ABC, if angle A = 60 degrees and angle B = 70 degrees, what is the measure of angle C?

A. 50 degrees
B. 60 degrees
C. 70 degrees
D. 80 degrees

Solution

The sum of angles in a triangle is 180 degrees. Therefore, angle C = 180 - (60 + 70) = 50 degrees.

Correct Answer: A — 50 degrees

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Q. In triangle ABC, if angle A = 60° and angle B = 70°, what is angle C?

A. 50°
B. 60°
C. 70°
D. 80°

Solution

Angle C = 180° - (angle A + angle B) = 180° - (60° + 70°) = 50°.

Correct Answer: A — 50°

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Q. In triangle ABC, if the angles are in the ratio 2:3:4, what is the measure of the largest angle?

A. 60 degrees
B. 80 degrees
C. 90 degrees
D. 120 degrees

Solution

Let the angles be 2x, 3x, and 4x. Then, 2x + 3x + 4x = 180 => 9x = 180 => x = 20. The largest angle = 4x = 80 degrees.

Correct Answer: B — 80 degrees

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Q. In triangle ABC, if the coordinates of A, B, and C are (1, 2), (4, 6), and (7, 2) respectively, what is the length of side AB?

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

Solution

Length of AB = √[(4-1)² + (6-2)²] = √[3² + 4²] = √[9 + 16] = √25 = 5.

Correct Answer: B — 5

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Q. In triangle ABC, if the coordinates of A, B, and C are (1, 2), (4, 6), and (7, 2) respectively, what is the area of triangle ABC?

A. 12
B. 14
C. 16
D. 18

Solution

Using the formula for the area of a triangle given vertices, Area = 1/2 | x1(y2-y3) + x2(y3-y1) + x3(y1-y2) | = 1/2 | 1(6-2) + 4(2-2) + 7(2-6) | = 1/2 | 4 + 0 - 28 | = 12.

Correct Answer: A — 12

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Q. In triangle ABC, if the lengths of sides a = 10, b = 24, and angle C = 60 degrees, find the length of side c.

A. 20
B. 22
C. 24
D. 26

Solution

Using the cosine rule: c^2 = a^2 + b^2 - 2ab*cos(C) = 10^2 + 24^2 - 2*10*24*(1/2) = 100 + 576 - 240 = 436. Thus, c = √436 = 20.

Correct Answer: A — 20

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Q. In triangle ABC, if the lengths of sides a, b, and c are 5, 12, and 13 respectively, what is the perimeter of the triangle?

A. 30
B. 25
C. 20
D. 18

Solution

Perimeter = a + b + c = 5 + 12 + 13 = 30.

Correct Answer: B — 25

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Q. In triangle ABC, if the lengths of sides a, b, and c are 7, 24, and 25 respectively, what type of triangle is it?

A. Acute
B. Obtuse
C. Right
D. Equilateral

Solution

Since 7² + 24² = 49 + 576 = 625 = 25², triangle ABC is a right triangle.

Correct Answer: C — Right

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Q. In triangle ABC, if the lengths of sides a, b, and c are 7, 24, and 25 respectively, what is the area of the triangle?

A. 84
B. 96
C. 120
D. 168

Solution

Using Heron's formula, s = (7 + 24 + 25)/2 = 28. Area = √[s(s-a)(s-b)(s-c)] = √[28(28-7)(28-24)(28-25)] = √[28*21*4*3] = 84.

Correct Answer: B — 96

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Q. In triangle ABC, if the lengths of sides a, b, and c are 8, 15, and 17 respectively, what is the type of triangle?

A. Acute
B. Obtuse
C. Right
D. Equilateral

Solution

Since 8² + 15² = 17², triangle ABC is a right triangle.

Correct Answer: C — Right

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Q. In triangle ABC, if the lengths of sides are 8 cm, 15 cm, and 17 cm, what is the type of triangle?

A. Acute
B. Obtuse
C. Right
D. Isosceles

Solution

Since 8² + 15² = 64 + 225 = 289 = 17², triangle ABC is a right triangle.

Correct Answer: C — Right

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Q. In triangle ABC, if the lengths of the sides are 10 cm, 24 cm, and 26 cm, what is the type of triangle?

A. Acute
B. Obtuse
C. Right
D. Equilateral

Solution

Since 10² + 24² = 100 + 576 = 676 = 26², triangle ABC is a right triangle.

Correct Answer: C — Right

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Q. In triangle ABC, if the lengths of the sides are 5, 12, and 13, what is the perimeter?

A. 30
B. 25
C. 20
D. 18

Solution

Perimeter = a + b + c = 5 + 12 + 13 = 30.

Correct Answer: B — 25

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Q. In triangle ABC, if the lengths of the sides are 8 cm, 15 cm, and 17 cm, what is the perimeter?

A. 30 cm
B. 40 cm
C. 50 cm
D. 60 cm

Solution

Perimeter = 8 + 15 + 17 = 40 cm.

Correct Answer: A — 30 cm

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Q. In triangle ABC, if the lengths of the sides are 8 cm, 15 cm, and 17 cm, what is the type of triangle?

A. Acute
B. Obtuse
C. Right
D. Equilateral

Solution

Since 8² + 15² = 64 + 225 = 289 = 17², triangle ABC is a right triangle.

Correct Answer: C — Right

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Q. In triangle ABC, if the lengths of the sides are 8, 15, and 17, what is the area of the triangle?

A. 60
B. 80
C. 120
D. 150

Solution

Using Heron's formula, the semi-perimeter s = (8 + 15 + 17)/2 = 20. Area = √[s(s-a)(s-b)(s-c)] = √[20(20-8)(20-15)(20-17)] = √[20*12*5*3] = 60.

Correct Answer: A — 60

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Q. In triangle ABC, if the lengths of the sides are 8, 15, and 17, what is the type of triangle?

A. Acute
B. Obtuse
C. Right
D. Equilateral

Solution

Since 8² + 15² = 64 + 225 = 289 = 17², triangle ABC is a right triangle.

Correct Answer: C — Right

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Q. In triangle ABC, if the lengths of the sides are a = 5, b = 12, and c = 13, what is the perimeter of the triangle?

A. 30
B. 25
C. 20
D. 18

Solution

The perimeter of a triangle is the sum of its sides. Therefore, perimeter = a + b + c = 5 + 12 + 13 = 30.

Correct Answer: B — 25

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Q. In triangle ABC, if the lengths of the sides are a = 8, b = 15, and c = 17, what is the perimeter?

A. 30
B. 40
C. 50
D. 60

Solution

The perimeter of a triangle is the sum of its sides: a + b + c = 8 + 15 + 17 = 40.

Correct Answer: A — 30

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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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