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. What is the value of gravitational acceleration at the height equal to the radius of the Earth?

A. g/2
B. g/4
C. g/3
D. g/8

Solution

At height R, g' = g / (2^2) = g / 4.

Correct Answer: B — g/4

Q. What is the value of gravitational acceleration at the surface of the Earth?

A. 9.8 m/s^2
B. 10 m/s^2
C. 9.81 m/s^2
D. 8.9 m/s^2

Solution

The standard value of gravitational acceleration at the surface of the Earth is approximately 9.81 m/s^2.

Correct Answer: C — 9.81 m/s^2

Q. What is the value of gravitational acceleration on the surface of the Earth?

A. 9.8 m/s²
B. 10 m/s²
C. 9.81 m/s²
D. 9.6 m/s²

Solution

The standard value of gravitational acceleration on the surface of the Earth is approximately 9.8 m/s².

Correct Answer: A — 9.8 m/s²

Q. What is the value of i^4?

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

Solution

i^4 = (i^2)^2 = (-1)^2 = 1.

Correct Answer: A — 1

Q. What is the value of k for which the equation x^2 + kx + 16 = 0 has equal roots?

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

Solution

For equal roots, the discriminant must be zero: k^2 - 4*1*16 = 0, thus k^2 = 64, giving k = -8 or 8. The answer is -4.

Correct Answer: B — -4

Q. What is the value of k for which the equation x^2 + kx + 9 = 0 has no real roots?

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

Solution

The discriminant must be negative: k^2 - 4*1*9 < 0 => k^2 < 36 => |k| < 6, hence k > 6.

Correct Answer: B — k > 6

Q. What is the value of k for which the equation x^2 - 2kx + 3 = 0 has roots that are reciprocals of each other?

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

Solution

If the roots are reciprocals, then k = sum of roots = 0 and product = 1. Thus, k = 2.

Correct Answer: B — 2

Q. What is the value of k for which the equation x^2 - 4x + k = 0 has roots that are equal?

A. 4
B. 8
C. 16
D. 0

Solution

For equal roots, the discriminant must be zero: (-4)^2 - 4*1*k = 0 => 16 - 4k = 0 => k = 4.

Correct Answer: A — 4

Q. What is the value of k for which the function f(x) = { kx + 2, x < 2; x^2 - 4, x >= 2 is continuous at x = 2?

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

Solution

Setting 2k + 2 = 0 gives k = 2.

Correct Answer: C — 2

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

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

Solution

Setting k(0) = 0^2 + 1 gives k = 1.

Correct Answer: B — 0

Q. What is the value of k for which the function f(x) = { kx, x < 2; x^2, x >= 2 } is continuous at x = 2?

A. 0
B. 2
C. 4
D. 1

Solution

Setting k(2) = 2^2 gives 2k = 4, thus k = 2.

Correct Answer: C — 4

Q. What is the value of k if f(x) = kx^2 + 2x + 1 has a minimum value of -3?

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

Solution

The minimum value occurs at x = -b/(2a) = -2/(2k). Setting f(-1) = -3 gives k = -2.

Correct Answer: B — -2

Q. What is the value of k if the equation x^2 + kx + 16 = 0 has no real roots?

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

Solution

For no real roots, the discriminant must be less than zero: k^2 - 4*1*16 < 0 => k^2 < 64 => |k| < 8.

Correct Answer: B — -4

Q. What is the value of k if the quadratic equation x^2 + kx + 16 = 0 has equal roots?

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

Solution

For equal roots, the discriminant must be zero: k^2 - 4*1*16 = 0, thus k^2 = 64, giving k = -8 or k = 8. The answer is -8.

Correct Answer: B — -4

Q. What is the value of k if the quadratic equation x^2 + kx + 16 = 0 has no real roots?

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

Solution

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

Correct Answer: B — -4

Q. What is the value of k if the quadratic equation x^2 + kx + 25 = 0 has one real root?

A. -10
B. -5
C. 5
D. 10

Solution

For one real root, the discriminant must be zero: k^2 - 4*1*25 = 0, thus k^2 = 100, giving k = -10 or k = 10.

Correct Answer: A — -10

Q. What is the value of k if the quadratic equation x^2 + kx + 9 = 0 has no real roots?

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

Solution

For no real roots, the discriminant must be less than zero: k^2 - 4*1*9 < 0, thus k > 6.

Correct Answer: B — k > 6

Q. What is the value of k if the quadratic equation x^2 + kx + 9 = 0 has one real root?

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

Solution

For one real root, the discriminant must be zero: k^2 - 4*1*9 = 0 => k^2 = 36 => k = ±6.

Correct Answer: B — -3

Q. What is the value of k if the roots of the equation x^2 + kx + 16 = 0 are equal?

A. 4
B. 8
C. 16
D. 0

Solution

For equal roots, the discriminant must be zero: k^2 - 4*1*16 = 0 => k^2 = 64 => k = 8 or k = -8.

Correct Answer: B — 8

Q. What is the value of k if the roots of the equation x^2 - kx + 12 = 0 are 3 and 4?

A. 7
B. 12
C. 9
D. 10

Solution

Using Vieta's formulas, k = 3 + 4 = 7.

Correct Answer: A — 7

Q. What is the value of l for a d orbital?

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

Solution

For d orbitals, the azimuthal quantum number l is equal to 2.

Correct Answer: C — 2

Q. What is the value of log2(8)?

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

Solution

log2(8) = 3 because 2^3 = 8.

Correct Answer: B — 3

Q. What is the value of log_10(1000) + log_10(0.01)?

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

Solution

log_10(1000) = 3 and log_10(0.01) = -2, thus 3 - 2 = 1.

Correct Answer: C — -1

Q. What is the value of log_10(1000)?

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

Solution

log_10(1000) = log_10(10^3) = 3.

Correct Answer: C — 3

Q. What is the value of log_2(32) - log_2(4)?

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

Solution

log_2(32) = 5 and log_2(4) = 2. Therefore, 5 - 2 = 3.

Correct Answer: C — 3

Q. What is the value of log_2(32) - log_2(8)?

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

Solution

log_2(32) = 5 and log_2(8) = 3. Therefore, 5 - 3 = 2.

Correct Answer: C — 3

Q. What is the value of log_2(32)?

A. 4
B. 5
C. 6
D. 7

Solution

Since 32 = 2^5, log_2(32) = 5.

Correct Answer: B — 5

Q. What is the value of log_3(27) - log_3(9)?

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

Solution

log_3(27) = 3 and log_3(9) = 2. Therefore, 3 - 2 = 1.

Correct Answer: B — 1

Q. What is the value of log_3(27)?

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

Solution

Since 27 = 3^3, log_3(27) = 3.

Correct Answer: B — 3

Q. What is the value of log_3(81)?

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

Solution

log_3(81) = log_3(3^4) = 4.

Correct Answer: C — 4

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