Mathematics Syllabus for JEE Main

Mathematics Syllabus (JEE Main)

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

Q. For which value of a is the function f(x) = { ax + 1, x < 0; 2, x = 0; 3x - 1, x > 0 } continuous at x = 0?

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

Solution

Setting ax + 1 = 2 at x = 0 gives a = 2.

Correct Answer: A — -1

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Q. For which value of a is the function f(x) = { ax + 1, x < 0; 2x + a, x >= 0 } continuous at x = 0?

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

Solution

Setting the two pieces equal at x = 0 gives 1 = a, hence a = 1.

Correct Answer: A — -1

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Q. For which value of a is the function f(x) = { ax + 2, x < 1; 3, x >= 1 } continuous at x = 1?

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

Solution

Setting ax + 2 = 3 at x = 1 gives a = 1.

Correct Answer: B — 2

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Q. For which value of a is the function f(x) = { x^2 + a, x < 1; 3, x >= 1 } continuous at x = 1?

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

Solution

To ensure continuity at x = 1, we set limit as x approaches 1 from left (1 + a) equal to f(1) = 3, thus a = 2.

Correct Answer: B — 2

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Q. For which value of a is the function f(x) = { x^2 - a, x < 0; 2x + 1, x >= 0 } continuous at x = 0?

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

Solution

Setting the two pieces equal at x = 0 gives -a = 1, so a = -1.

Correct Answer: A — -1

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Q. For which value of a is the function f(x) = { x^2 - a, x < 1; 3x - 2, x >= 1 } continuous at x = 1?

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

Solution

Setting the two pieces equal at x = 1 gives 1 - a = 1. Thus, a = 0.

Correct Answer: C — 2

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Q. For which value of a is the function f(x) = { x^2, x < 1; ax + 1, x >= 1 } continuous at x = 1?

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

Solution

Setting the two pieces equal at x = 1 gives 1 = a(1) + 1, leading to a = 0.

Correct Answer: C — 2

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Q. For which value of b is the function f(x) = { 2x + 1, x < 1; b, x = 1; x^2 + 1, x > 1 continuous at x = 1?

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

Solution

Setting the left limit (2(1) + 1 = 3) equal to the right limit (1^2 + 1 = 2), we find b = 3.

Correct Answer: B — 2

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Q. For which value of b is the function f(x) = { x^2 - 1, x < 1; b, x = 1; 3x - 2, x > 1 continuous at x = 1?

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

Solution

Setting limit as x approaches 1 gives b = 2 for continuity.

Correct Answer: C — 2

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Q. For which value of b is the function f(x) = { x^2 - 4, x < 2; bx + 2, x >= 2 } continuous at x = 2?

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

Solution

Setting the two pieces equal at x = 2 gives us 0 = 2b + 2. Solving for b gives b = -1.

Correct Answer: B — 4

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Q. For which value of b is the function f(x) = { x^3 - 3x + b, x < 1; 2x + 1, x >= 1 continuous at x = 1?

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

Solution

Setting 1 - 3 + b = 2 gives b = 4 for continuity.

Correct Answer: A — 0

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Q. For which value of c is the function f(x) = { 3x + c, x < 1; 2x^2, x >= 1 continuous at x = 1?

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

Solution

Setting 3(1) + c = 2(1)^2 gives c = -1 for continuity.

Correct Answer: B — 0

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Q. For which value of c is the function f(x) = { x^2 - 4, x < c; 3x - 5, x >= c } continuous at x = c?

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

Solution

Setting the two pieces equal at x = c: c^2 - 4 = 3c - 5. Solving gives c = 3.

Correct Answer: C — 3

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Q. For which value of c is the function f(x) = { x^2 - c, x < 1; 2x + 1, x >= 1 continuous at x = 1?

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

Solution

Setting x^2 - c = 2x + 1 at x = 1 gives c = 2.

Correct Answer: C — 2

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Q. For which value of c is the function f(x) = { x^2, x < c; 2x + 1, x >= c continuous at x = c?

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

Solution

Setting x^2 = 2x + 1 at x = c gives c = 2.

Correct Answer: C — 2

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Q. For which value of k does the equation x^2 + kx + 16 = 0 have real and distinct roots?

A. -8
B. -4
C. 0
D. 4

Solution

The discriminant must be positive: k^2 - 4*1*16 > 0 => k^2 > 64 => k > 8 or k < -8. Thus, k = -4 is valid.

Correct Answer: B — -4

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Q. For which value of k does the equation x^2 + kx + 4 = 0 have one root equal to 2?

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

Solution

Substituting x = 2 into the equation gives 2^2 + 2k + 4 = 0, leading to k = -4.

Correct Answer: B — -2

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Q. For which value of k does the equation x^2 - 4x + k = 0 have roots that differ by 2?

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

Solution

Let the roots be r and r+2. Then, r + (r+2) = 4 and r(r+2) = k leads to k = 4.

Correct Answer: C — 4

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Q. For which value of k does the equation x^2 - kx + 9 = 0 have roots that are both positive?

A. k < 6
B. k > 6
C. k = 6
D. k = 0

Solution

For both roots to be positive, k must be greater than 6, as the sum of the roots must be positive.

Correct Answer: B — k > 6

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Q. For which value of k does the quadratic equation x^2 - kx + 4 = 0 have no real roots?

A. k < 4
B. k = 4
C. k > 4
D. k ≤ 4

Solution

The discriminant must be negative: k^2 - 16 < 0, hence k > 4.

Correct Answer: C — k > 4

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Q. For which value of k is the function f(x) = kx^2 + 2x + 1 differentiable at x = -1?

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

Solution

f'(x) = 2kx + 2; f'(-1) = -2k + 2 must exist for any k.

Correct Answer: A — 0

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Q. For which value of m is the function f(x) = { 3x + m, x < 1; 2, x = 1; mx + 1, x > 1 continuous at x = 1?

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

Solution

Setting 3 + m = 2 and 2 = m + 1 gives m = 1 for continuity.

Correct Answer: B — 0

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Q. For which value of p is the function f(x) = { x^2 + p, x < 0; 3x - 1, x >= 0 } continuous at x = 0?

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

Solution

Setting the two pieces equal at x = 0 gives us p = -1.

Correct Answer: B — 0

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Q. From a group of 10 people, how many ways can a committee of 4 be formed?

A. 210
B. 120
C. 150
D. 180

Solution

The number of ways to choose 4 people from 10 is given by 10C4 = 210.

Correct Answer: A — 210

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Q. From a point A, the angle of elevation of the top of a building is 45 degrees. If the height of the building is 20 meters, how far is point A from the base of the building?

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

Solution

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

Correct Answer: B — 20 m

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Q. From a point on the ground, the angle of elevation of the top of a hill is 30 degrees. If the distance from the point to the base of the hill is 100 meters, what is the height of the hill?

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

Solution

Using tan(30°) = height/100, we have 1/√3 = height/100. Therefore, height = 100/√3 ≈ 57.74 m.

Correct Answer: A — 50 m

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Q. From a point on the ground, the angle of elevation of the top of a hill is 30 degrees. If the height of the hill is 50 meters, how far is the point from the base of the hill?

A. 50 m
B. 75 m
C. 100 m
D. 125 m

Solution

Using tan(30°) = height/distance, we have 1/√3 = 50/distance. Therefore, distance = 50√3 ≈ 86.6 m.

Correct Answer: C — 100 m

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Q. From a point on the ground, the angle of elevation to the top of a 40 m high building is 45 degrees. How far is the point from the base of the building?

A. 40 m
B. 20 m
C. 30 m
D. 50 m

Solution

Using tan(45°) = height/distance, we have distance = height/tan(45°) = 40/1 = 40 m.

Correct Answer: A — 40 m

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Q. From a point on the ground, the angle of elevation to the top of a 75 m high building is 45 degrees. How far is the point from the building?

A. 75 m
B. 50 m
C. 100 m
D. 25 m

Solution

Using tan(45°) = height/distance, we have distance = height/tan(45°) = 75/1 = 75 m.

Correct Answer: A — 75 m

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Q. From a point on the ground, the angle of elevation to the top of a building is 45 degrees. If the building is 50 meters tall, how far is the point from the base of the building?

A. 50 m
B. 25 m
C. 100 m
D. 75 m

Solution

Distance = height / tan(angle) = 50 / 1 = 50 m.

Correct Answer: A — 50 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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