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. Determine the length of the latus rectum of the parabola y^2 = 16x.

A. 4
B. 8
C. 16
D. 32

Solution

The length of the latus rectum for the parabola y^2 = 4px is given by 4p. Here, p = 4, so the length is 16.

Correct Answer: B — 8

Q. Determine the local maxima and minima of f(x) = x^3 - 3x.

A. Maxima at (1, -2)
B. Minima at (0, 0)
C. Maxima at (0, 0)
D. Minima at (1, -2)

Solution

f'(x) = 3x^2 - 3. Setting f'(x) = 0 gives x = ±1. f''(1) = 6 > 0 (min), f''(-1) = 6 > 0 (min). Local maxima at (0, 0).

Correct Answer: A — Maxima at (1, -2)

Q. Determine the local maxima and minima of the function f(x) = x^3 - 6x^2 + 9x.

A. (0, 0)
B. (2, 0)
C. (3, 0)
D. (1, 0)

Solution

f'(x) = 3x^2 - 12x + 9. Setting f'(x) = 0 gives x = 1, 3. f''(1) > 0 (min), f''(3) < 0 (max).

Correct Answer: C — (3, 0)

Q. Determine the local maxima and minima of the function f(x) = x^4 - 4x^3 + 4x.

A. Maxima at (0, 0)
B. Minima at (2, 0)
C. Maxima at (2, 0)
D. Minima at (0, 0)

Solution

f'(x) = 4x^3 - 12x^2 + 4. Setting f'(x) = 0 gives x = 0 and x = 2. f''(0) = 4 > 0 (min), f''(2) = -8 < 0 (max).

Correct Answer: B — Minima at (2, 0)

Q. Determine the maximum value of f(x) = -x^2 + 4x + 1.

A. 1
B. 5
C. 9
D. 13

Solution

The vertex occurs at x = 2. f(2) = -2^2 + 4(2) + 1 = 5, which is the maximum value.

Correct Answer: B — 5

Q. Determine the minimum value of the function f(x) = x^2 - 4x + 5.

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

Solution

The vertex occurs at x = 2. f(2) = 2^2 - 4*2 + 5 = 1. Thus, the minimum value is 1.

Correct Answer: A — 1

Q. Determine the moment of inertia of a solid sphere of mass M and radius R about an axis through its center.

A. 2/5 MR^2
B. 3/5 MR^2
C. 4/5 MR^2
D. MR^2

Solution

The moment of inertia of a solid sphere about an axis through its center is I = 2/5 MR^2.

Correct Answer: A — 2/5 MR^2

Q. Determine the nature of the lines represented by the equation 7x^2 + 2xy + 3y^2 = 0.

A. Parallel
B. Intersecting
C. Coincident
D. Perpendicular

Solution

The discriminant indicates that the lines intersect at two distinct points.

Correct Answer: B — Intersecting

Q. Determine the point at which the function f(x) = x^3 - 3x^2 + 4 has a local minimum.

A. (1, 2)
B. (2, 1)
C. (0, 4)
D. (3, 4)

Solution

Find f'(x) = 3x^2 - 6x. Setting f'(x) = 0 gives x(x - 2) = 0, so x = 0 or x = 2. f''(2) = 6 > 0, so (2, 1) is a local minimum.

Correct Answer: A — (1, 2)

Q. Determine the point at which the function f(x) = |x - 1| is not differentiable.

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

Solution

The function |x - 1| is not differentiable at x = 1 due to a cusp.

Correct Answer: B — x = 1

Q. Determine the point at which the function f(x) = |x - 3| is not differentiable.

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

Solution

The function f(x) = |x - 3| is not differentiable at x = 3 because it has a sharp corner.

Correct Answer: C — x = 3

Q. Determine the point at which the function f(x) = |x^2 - 4| is differentiable.

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

Solution

f(x) is not differentiable at x = -2 and x = 2, but is differentiable everywhere else.

Correct Answer: A — x = -2

Q. Determine the point of inflection for the function f(x) = x^4 - 4x^3 + 6.

A. (1, 3)
B. (2, 2)
C. (3, 1)
D. (0, 6)

Solution

f''(x) = 12x^2 - 24x. Setting f''(x) = 0 gives x = 0 and x = 2. The point of inflection is at (1, 3).

Correct Answer: A — (1, 3)

Q. Determine the point of inflection for the function f(x) = x^4 - 4x^3 + 6x^2.

A. (1, 3)
B. (2, 2)
C. (3, 1)
D. (0, 0)

Solution

Find f''(x) = 12x^2 - 24x + 12. Setting f''(x) = 0 gives x = 1 and x = 2. Testing intervals shows a change in concavity at x = 1.

Correct Answer: A — (1, 3)

Q. Determine the point of intersection of the lines y = 2x + 1 and y = -x + 4.

A. (1, 3)
B. (2, 5)
C. (3, 7)
D. (4, 9)

Solution

Setting 2x + 1 = -x + 4 gives 3x = 3, hence x = 1. Substituting back gives y = 3.

Correct Answer: A — (1, 3)

Q. Determine the points where f(x) = x^3 - 3x is not differentiable.

A. x = 0
B. x = 1
C. x = -1
D. Nowhere

Solution

The function is a polynomial and is differentiable everywhere, hence nowhere.

Correct Answer: D — Nowhere

Q. Determine the points where the function f(x) = x^4 - 4x^3 is not differentiable.

A. x = 0
B. x = 1
C. x = 2
D. None

Solution

The function is a polynomial and is differentiable everywhere. Thus, there are no points where it is not differentiable.

Correct Answer: D — None

Q. Determine the scalar product of the vectors (0, 1, 2) and (3, 4, 5).

A. 10
B. 11
C. 12
D. 13

Solution

Scalar product = 0*3 + 1*4 + 2*5 = 0 + 4 + 10 = 14.

Correct Answer: B — 11

Q. Determine the scalar product of the vectors A = (1, 1, 1) and B = (2, 2, 2).

A. 3
B. 4
C. 6
D. 8

Solution

A · B = 1*2 + 1*2 + 1*2 = 2 + 2 + 2 = 6.

Correct Answer: C — 6

Q. Determine the scalar product of the vectors A = (2, 2, 2) and B = (3, 3, 3).

A. 12
B. 18
C. 6
D. 9

Solution

A · B = 2*3 + 2*3 + 2*3 = 6 + 6 + 6 = 18.

Correct Answer: A — 12

Q. Determine the solution for the inequality -2x + 6 > 0.

A. x < 3
B. x > 3
C. x < -3
D. x > -3

Solution

-2x + 6 > 0 => -2x > -6 => x < 3.

Correct Answer: B — x > 3

Q. Determine the solution for the inequality -2x + 6 ≥ 0.

A. x ≤ 3
B. x ≥ 3
C. x ≤ -3
D. x ≥ -3

Solution

-2x + 6 ≥ 0 => -2x ≥ -6 => x ≤ 3.

Correct Answer: B — x ≥ 3

Q. Determine the solution for the inequality -3x + 1 ≤ 4.

A. x ≥ -1
B. x ≤ -1
C. x ≥ 1
D. x ≤ 1

Solution

-3x + 1 ≤ 4 => -3x ≤ 3 => x ≥ -1.

Correct Answer: B — x ≤ -1

Q. Determine the solution for the inequality -3x + 4 ≤ 1.

A. x ≥ 1
B. x ≤ 1
C. x ≥ -1
D. x ≤ -1

Solution

-3x + 4 ≤ 1 => -3x ≤ -3 => x ≥ 1.

Correct Answer: B — x ≤ 1

Q. Determine the solution for the inequality 2x + 3 ≤ 7.

A. x ≤ 2
B. x ≥ 2
C. x ≤ 3
D. x ≥ 3

Solution

2x + 3 ≤ 7 => 2x ≤ 4 => x ≤ 2.

Correct Answer: A — x ≤ 2

Q. Determine the solution for the inequality 6 - x > 2.

A. x < 4
B. x > 4
C. x < 6
D. x > 6

Solution

6 - x > 2 => -x > -4 => x < 4.

Correct Answer: A — x < 4

Q. Determine the solution for the inequality 6 - x ≤ 3.

A. x ≥ 3
B. x ≤ 3
C. x ≥ 6
D. x ≤ 6

Solution

6 - x ≤ 3 => -x ≤ -3 => x ≥ 3.

Correct Answer: B — x ≤ 3

Q. Determine the solution for the inequality 7 - 3x < 1.

A. x < 2
B. x > 2
C. x ≤ 2
D. x ≥ 2

Solution

7 - 3x < 1 => -3x < -6 => x > 2.

Correct Answer: A — x < 2

Q. Determine the solution for the inequality 7x - 2 ≤ 5x + 6.

A. x ≤ 4
B. x ≥ 4
C. x ≤ 3
D. x ≥ 3

Solution

7x - 2 ≤ 5x + 6 => 2x ≤ 8 => x ≤ 4.

Correct Answer: A — x ≤ 4

Q. Determine the solution set for the inequality 2(x - 1) ≥ 3.

A. x ≤ 2
B. x ≥ 2
C. x ≤ 3
D. x ≥ 3

Solution

2(x - 1) ≥ 3 => x - 1 ≥ 1.5 => x ≥ 2.

Correct Answer: B — x ≥ 2

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