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. If f(x) = x^4 - 4x^3 + 6x^2 - 4x + 1, what is f'(1)?

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

Solution

f'(x) = 4x^3 - 12x^2 + 12x - 4; f'(1) = 0.

Correct Answer: A — 0

Q. If f(x) = x^4 - 4x^3 + 6x^2, find f'(2).

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

Solution

f'(x) = 4x^3 - 12x^2 + 12x; f'(2) = 4(2^3) - 12(2^2) + 12(2) = 32 - 48 + 24 = 8.

Correct Answer: A — 0

Q. If f(x) = x^4 - 8x^2 + 16, then the points of inflection are at:

A. x = 0
B. x = ±2
C. x = ±4
D. x = 2

Solution

To find points of inflection, we find f''(x) = 12x^2 - 16. Setting f''(x) = 0 gives x^2 = 4, so x = ±2 are points of inflection.

Correct Answer: B — x = ±2

Q. If f(x) = { 2x + 3, x < 0; kx + 1, x >= 0 } is continuous at x = 0, what is the value of k?

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

Solution

Setting the two pieces equal at x = 0: 3 = k(0) + 1. Solving gives k = -3/2.

Correct Answer: A — -3/2

Q. If f(x) = { x^2 + 1, x < 0; k, x = 0; 2x + 1, x > 0 } is continuous at x = 0, what is k?

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

Solution

For continuity at x = 0, we need the left limit (1) to equal k. Thus, k = 1.

Correct Answer: A — 1

Q. If f(x) = { x^2 + 1, x < 0; k, x = 0; 2x + 1, x > 0 }, what value of k makes f continuous at x = 0?

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

Solution

To be continuous at x = 0, k must equal the limit from the left, which is 1.

Correct Answer: B — 1

Q. If f(x) = { x^2 + 1, x < 0; k, x = 0; 2x, x > 0 }, for f(x) to be continuous at x = 0, k must be:

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

Solution

For continuity at x = 0, k must equal the limit as x approaches 0, which is 1.

Correct Answer: B — 1

Q. If f(x) = { x^2 + 1, x < 0; kx + 2, x = 0; 3 - x, x > 0 is continuous at x = 0, find k.

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

Solution

For continuity at x = 0, we need 1 = 2, thus k must be 1.

Correct Answer: B — 2

Q. If f(x) = { x^2 + 1, x < 0; kx + 3, x = 0; 2x - 1, x > 0 is continuous at x = 0, find k.

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

Solution

For continuity at x = 0, we need 1 = 3 and 1 = -1 + 3k, solving gives k = 1.

Correct Answer: C — 1

Q. If f(x) = { x^2, x < 0; 2x + 3, x >= 0 }, find f(0).

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

Solution

At x = 0, we use the second piece: f(0) = 2(0) + 3 = 3.

Correct Answer: B — 3

Q. If f(x) = { x^2, x < 0; kx + 1, x >= 0 } is differentiable at x = 0, what is k?

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

Solution

Setting the derivatives equal at x = 0 gives k = 0.

Correct Answer: B — 0

Q. If f(x) = { x^2, x < 0; kx + 1, x = 0; 2x + 3, x > 0 is continuous at x = 0, find k.

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

Solution

To ensure continuity at x = 0, we set k(0) + 1 = 0^2, leading to k = 2.

Correct Answer: C — 1

Q. If f(x) = { x^2, x < 1; kx + 1, x >= 1 } is continuous at x = 1, find k.

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

Solution

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

Correct Answer: B — 1

Q. If f(x) = { x^2, x < 2; 4, x = 2; 2x, x > 2 } is continuous at x = 2, what is the value of f(2)?

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

Solution

For continuity at x = 2, f(2) must equal the limit from both sides, which is 4.

Correct Answer: B — 4

Q. If f(x) = { x^2, x < 3; k, x = 3; 2x, x > 3 } is continuous at x = 3, what is the value of k?

A. 3
B. 9
C. 6
D. 0

Solution

For continuity at x = 3, we need limit as x approaches 3 from left (9) to equal f(3) = k, thus k = 9.

Correct Answer: C — 6

Q. If f(x) = { x^2, x < 3; k, x = 3; 3x - 2, x > 3 } is continuous at x = 3, what is k?

A. 7
B. 9
C. 8
D. 6

Solution

For continuity at x = 3, we need k to equal the limit from both sides, which is 9.

Correct Answer: C — 8

Q. If f(x) = |x - 2|, what is f(2)?

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

Solution

f(2) = |2 - 2| = |0| = 0.

Correct Answer: A — 0

Q. If f(x) = |x|, is f differentiable at x = 0?

A. Yes
B. No
C. Only from the right
D. Only from the left

Solution

The left and right derivatives at x = 0 do not match, hence f is not differentiable at that point.

Correct Answer: B — No

Q. If f(x) = |x|, what is f(-3)?

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

Solution

f(-3) = |-3| = 3.

Correct Answer: B — 3

Q. If f(x) is continuous on [a, b], which of the following must be true?

A. f(a) = f(b)
B. f(x) takes every value between f(a) and f(b)
C. f(x) is increasing
D. f(x) is decreasing

Solution

By the Intermediate Value Theorem, a continuous function on a closed interval takes every value between f(a) and f(b).

Correct Answer: B — f(x) takes every value between f(a) and f(b)

Q. If f: A → B is a function and |A| = 5, |B| = 3, what is the maximum number of distinct functions f?

A. 3^5
B. 5^3
C. 15
D. 8

Solution

The number of distinct functions from set A to set B is given by |B|^|A|. Here, |B| = 3 and |A| = 5, so the maximum number of distinct functions is 3^5 = 243.

Correct Answer: A — 3^5

Q. If f: A → B is a function and |A| = 5, |B| = 3, what is the maximum number of distinct functions that can be formed?

A. 3^5
B. 5^3
C. 15
D. 8

Solution

The maximum number of distinct functions is |B|^|A| = 3^5 = 243.

Correct Answer: A — 3^5

Q. If G = (1, 0, 1) and H = (0, 1, 0), find G · H.

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

Solution

G · H = 1*0 + 0*1 + 1*0 = 0 + 0 + 0 = 0.

Correct Answer: A — 0

Q. If G = (1, 1, 1) and H = (1, -1, 1), what is G · H?

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

Solution

G · H = 1*1 + 1*(-1) + 1*1 = 1 - 1 + 1 = 1.

Correct Answer: A — 0

Q. If G = (1, 1, 1) and H = (2, 2, 2), what is G · H?

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

Solution

G · H = 1*2 + 1*2 + 1*2 = 2 + 2 + 2 = 6.

Correct Answer: A — 3

Q. If G = (2, 2) and H = (3, -1), what is G · H?

A. -1
B. 1
C. 5
D. 7

Solution

G · H = 2*3 + 2*(-1) = 6 - 2 = 4.

Correct Answer: C — 5

Q. If G = {1, 2, 3, 4, 5}, how many subsets have exactly 3 elements?

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

Solution

The number of ways to choose 3 elements from 5 is given by the combination formula C(5, 3) = 10.

Correct Answer: A — 10

Q. If G = {1, 2, 3, 4, 5}, what is the total number of subsets of G?

A. 32
B. 64
C. 16
D. 8

Solution

The number of subsets of a set with n elements is 2^n. Here, n = 5, so 2^5 = 32.

Correct Answer: A — 32

Q. If G = {1, 2, 3}, how many subsets contain the element '1'?

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

Solution

The subsets containing '1' can be formed by including '1' and choosing from the remaining elements {2, 3}. There are 2^2 = 4 subsets, but we need to exclude the empty subset, so there are 4 - 1 = 3 subsets containing '1'.

Correct Answer: C — 6

Q. If G = {1, 2, 3}, how many subsets of G have exactly 2 elements?

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

Solution

The subsets with exactly 2 elements are {1, 2}, {1, 3}, and {2, 3}. So, there are 3 such subsets.

Correct Answer: C — 5

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