JEE Main Preparation Resources for Competitive Exams

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JEE Main MCQ & Objective Questions

The JEE Main exam is a crucial step for students aspiring to enter prestigious engineering colleges in India. It tests not only knowledge but also the ability to apply concepts effectively. Practicing MCQs and objective questions is essential for scoring better, as it helps in familiarizing students with the exam pattern and enhances their problem-solving skills. Engaging with practice questions allows students to identify important questions and strengthen their exam preparation.

What You Will Practise Here

Fundamental concepts of Physics, Chemistry, and Mathematics
Key formulas and their applications in problem-solving
Important definitions and theories relevant to JEE Main
Diagrams and graphical representations for better understanding
Numerical problems and their step-by-step solutions
Previous years' JEE Main questions for real exam experience
Time management strategies while solving MCQs

Exam Relevance

The topics covered in JEE Main are not only significant for the JEE exam but also appear in various CBSE and State Board examinations. Many concepts are shared with the NEET syllabus, making them relevant across multiple competitive exams. Common question patterns include conceptual applications, numerical problems, and theoretical questions that assess a student's understanding of core subjects.

Common Mistakes Students Make

Misinterpreting the question stem, leading to incorrect answers
Neglecting units in numerical problems, which can change the outcome
Overlooking negative marking and not managing time effectively
Relying too heavily on rote memorization instead of understanding concepts
Failing to review and analyze mistakes from practice tests

FAQs

Question: How can I improve my speed in solving JEE Main MCQ questions?
Answer: Regular practice with timed quizzes and focusing on shortcuts can significantly enhance your speed.

Question: Are the JEE Main objective questions similar to previous years' papers?
Answer: Yes, many questions are based on previous years' patterns, so practicing them can be beneficial.

Question: What is the best way to approach JEE Main practice questions?
Answer: Start with understanding the concepts, then attempt practice questions, and finally review your answers to learn from mistakes.

Now is the time to take charge of your preparation! Dive into solving JEE Main MCQs and practice questions to test your understanding and boost your confidence for the exam.

Chemistry Syllabus (JEE Main) Mathematics Syllabus (JEE Main) Physics Syllabus (JEE Main)

Q. For which of the following molecules is the bond order equal to 0?

A. He2
B. H2
C. Li2
D. Be2

Solution

He2 has a bond order of 0, as it has equal bonding and antibonding electrons.

Correct Answer: A — He2

Q. For which of the following molecules is the molecular orbital diagram similar to that of O2?

A. N2
B. F2
C. C2
D. Ne2

Solution

The molecular orbital diagram of F2 is similar to that of O2, with the same energy level arrangement.

Correct Answer: B — F2

Q. For which of the following pairs of molecules is the bond order the same?

A. N2 and C2
B. O2 and F2
C. B2 and C2
D. N2 and O2

Solution

O2 and F2 both have a bond order of 2.

Correct Answer: B — O2 and F2

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

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

Solution

To ensure differentiability at x = -1, we find f'(-1) exists. Setting a = 0 ensures the derivative is defined.

Correct Answer: B — 0

Q. For which value of a is the function f(x) = x^2 + ax + 1 differentiable everywhere?

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

Solution

The function is a polynomial and is differentiable for all real numbers, hence any value of a works.

Correct Answer: B — 0

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

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

Solution

Setting the derivative f'(1) = 0 gives a = 1 for differentiability.

Correct Answer: B — 1

Q. For which value of a is the function f(x) = x^2 - ax + 4 differentiable at x = 2?

A. 0
B. 2
C. 4
D. 6

Solution

f(x) is a polynomial and is differentiable for all a, hence any value of a works.

Correct Answer: A — 0

Q. For which value of a is the function f(x) = x^3 - 3ax + 2 differentiable at x = 1?

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

Solution

Setting f'(1) = 0 gives a = 1, ensuring differentiability at that point.

Correct Answer: B — 1

Q. For which value of a is the function f(x) = x^3 - 3ax^2 + 3a^2x + 1 differentiable at x = 1?

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

Solution

Setting f'(1) = 0 gives a = 1 for differentiability at x = 1.

Correct Answer: B — 1

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

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

Solution

Setting a = 1 gives continuity at x = 0.

Correct Answer: B — 0

Q. For which value of a is the function f(x) = { 3x + a, x < 2; 4x - 1, x >= 2 continuous at x = 2?

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

Solution

Setting 3(2) + a = 4(2) - 1 gives a = 1.

Correct Answer: A — -1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Q. For which value of k does the equation x^2 + kx + 16 = 0 have no real roots?

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

Solution

The discriminant must be less than zero: k^2 - 4*1*16 < 0 => k^2 < 64 => k < 8 and k > -8.

Correct Answer: A — -8

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

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

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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