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. The function f(x) = x^2 for x < 1 and f(x) = 2x - 1 for x ≥ 1 is differentiable at x = 1?

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

Solution

f'(1) from left = 2 and from right = 2; hence, f is continuous but not differentiable at x = 1.

Correct Answer: B — No

Q. The function f(x) = x^2 sin(1/x) for x ≠ 0 and f(0) = 0 is differentiable at x = 0. True or False?

A. True
B. False
C. Depends on x
D. Not enough information

Solution

True, as the limit of f'(x) as x approaches 0 exists and equals 0.

Correct Answer: A — True

Q. The function f(x) = x^3 - 3x + 2 is differentiable at x = 1?

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

Solution

f(x) is a polynomial function, hence it is differentiable everywhere including at x = 1.

Correct Answer: A — Yes

Q. The function f(x) = x^3 - 3x + 2 is differentiable everywhere. Find its critical points.

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

Solution

f'(x) = 3x^2 - 3 = 0 gives x = ±1, thus critical points are x = -1 and x = 1.

Correct Answer: B — 0

Q. The function f(x) = x^3 - 3x + 2 is differentiable everywhere. What is f'(1)?

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

Solution

f'(x) = 3x^2 - 3, thus f'(1) = 0.

Correct Answer: A — 0

Q. The function f(x) = x^3 - 6x^2 + 9x has how many local extrema?

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

Solution

Finding f'(x) = 3x^2 - 12x + 9. Setting f'(x) = 0 gives x = 1 and x = 3. Checking the second derivative shows one local maximum and one local minimum.

Correct Answer: B — 1

Q. The function f(x) = { 1/x, x != 0; 0, x = 0 } is continuous at x = 0?

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

Solution

The limit as x approaches 0 does not equal f(0) = 0, hence it is not continuous at x = 0.

Correct Answer: B — No

Q. The function f(x) = { 1/x, x ≠ 0; 0, x = 0 } is:

A. Continuous at x = 0
B. Not continuous at x = 0
C. Continuous everywhere
D. None of the above

Solution

The function is not continuous at x = 0 since the limit does not equal f(0).

Correct Answer: B — Not continuous at x = 0

Q. The function f(x) = { 2x + 3, x < 1; x^2 + 1, x >= 1 } is continuous at x = ?

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

Solution

To check continuity at x = 1, we find the left limit (5) and the right limit (2). They are not equal, hence f(x) is not continuous at x = 1.

Correct Answer: B — 1

Q. The function f(x) = { 3x + 1, x < 1; 2, x = 1; x^2, x > 1 } is continuous at x = 1 if which condition holds?

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

Solution

For continuity at x = 1, the left limit (3) must equal f(1) (2), which is not true.

Correct Answer: A — 3 = 2

Q. The function f(x) = { 3x + 1, x < 1; 2x + 3, x >= 1 } is continuous at x = 1 if:

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

Solution

For continuity at x = 1, both pieces must equal 4, hence the function is continuous.

Correct Answer: A — 3

Q. The function f(x) = { x + 2, x < 1; 3, x = 1; x^2, x > 1 } is continuous at x = ?

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

Solution

To check continuity at x = 1, we find the left limit (3) and the right limit (3). Both equal 3, hence f(x) is continuous at x = 1.

Correct Answer: B — 1

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

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

Solution

Limit as x approaches 0 from left is 0, and f(0) = 1, hence it is not continuous at x = 0.

Correct Answer: A — Yes

Q. The function f(x) = { x^2, x < 0; 2x + 1, x >= 0 } is continuous at which point?

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

Solution

To check continuity at x = 0, we find f(0) = 1 and limit as x approaches 0 is also 1.

Correct Answer: B — x = 0

Q. The function f(x) = { x^2, x < 1; 2, x = 1; x + 1, x > 1 } is:

A. Continuous everywhere
B. Continuous at x = 1
C. Not continuous at x = 1
D. Continuous for x < 1

Solution

The function is not continuous at x = 1 because the left-hand limit does not equal the function value.

Correct Answer: C — Not continuous at x = 1

Q. The function f(x) = { x^2, x < 1; 2x - 1, x >= 1 } is continuous at which point?

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

Solution

To check continuity at x = 1, we find f(1) = 1, limit as x approaches 1 from left is 1, and from right is also 1.

Correct Answer: B — x = 1

Q. The function f(x) = { x^2, x < 1; 2x - 1, x >= 1 } is continuous at x = ?

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

Solution

To check continuity at x = 1, we find the limit from both sides. Both limits equal 1, hence f(x) is continuous at x = 1.

Correct Answer: B — 1

Q. The function f(x) = { x^2, x < 1; 2x - 1, x ≥ 1 } is differentiable at x = 1 if which condition holds?

A. f(1) = 1
B. f'(1) = 1
C. f'(1) = 2
D. f(1) = 2

Solution

For differentiability, the left and right derivatives must equal at x = 1, hence f'(1) = 1.

Correct Answer: B — f'(1) = 1

Q. The function f(x) = { x^2, x < 2; 4, x = 2; 2x, x > 2 } is continuous at x = 2 if:

A. f(2) = 4
B. lim x->2 f(x) = 4
C. Both a and b
D. None of the above

Solution

Both conditions must hold true for continuity at x = 2.

Correct Answer: C — Both a and b

Q. The function f(x) = { x^2, x < 2; k, x = 2; 3x - 4, x > 2 } is continuous at x = 2 for which value of k?

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

Solution

To be continuous at x = 2, k must equal f(2) = 2^2 = 4.

Correct Answer: C — 4

Q. The function f(x) = |x - 3| is continuous at which of the following points?

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

Solution

The function |x - 3| is continuous everywhere, including at x = 3.

Correct Answer: C — x = 3

Q. The function f(x) = |x| is differentiable at x = 0?

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

Solution

f(x) = |x| is not differentiable at x = 0 because the left-hand and right-hand derivatives do not match.

Correct Answer: B — No

Q. The general form of the family of curves for circles is given by:

A. (x - h)^2 + (y - k)^2 = r^2
B. x^2 + y^2 = r^2
C. x^2 + y^2 + Dx + Ey + F = 0
D. y = mx + b

Solution

The equation x^2 + y^2 + Dx + Ey + F = 0 represents a family of circles.

Correct Answer: C — x^2 + y^2 + Dx + Ey + F = 0

Q. The general form of the family of curves y^2 = 4ax is known as:

A. Circle
B. Ellipse
C. Parabola
D. Hyperbola

Solution

The equation y^2 = 4ax represents a parabola.

Correct Answer: C — Parabola

Q. The general form of the family of curves y^2 = 4ax represents:

A. Ellipses
B. Hyperbolas
C. Parabolas
D. Circles

Solution

The equation y^2 = 4ax represents a parabola that opens to the right.

Correct Answer: C — Parabolas

Q. The general form of the family of exponential curves is given by:

A. y = a^x
B. y = ax^2 + bx + c
C. y = mx + c
D. y = log(x)

Solution

The equation y = a^x represents an exponential function where a is a constant.

Correct Answer: A — y = a^x

Q. The gravitational field inside a uniform spherical shell is:

A. Zero
B. Constant
C. Increases linearly
D. Decreases linearly

Solution

The gravitational field inside a uniform spherical shell is zero.

Correct Answer: A — Zero

Q. The gravitational field strength at the surface of a planet is 9.8 N/kg. What is the gravitational potential at the surface if the radius of the planet is 6.4 x 10^6 m?

A. -62.72 x 10^6 J/kg
B. -9.8 J/kg
C. -19.6 x 10^6 J/kg
D. -39.2 x 10^6 J/kg

Solution

V = -g * r = -9.8 N/kg * 6.4 x 10^6 m = -62.72 x 10^6 J/kg.

Correct Answer: A — -62.72 x 10^6 J/kg

Q. The gravitational field strength at the surface of the Earth is approximately 9.8 N/kg. What is the gravitational potential at the surface of the Earth?

A. 0 J/kg
B. -9.8 J/kg
C. -19.6 J/kg
D. -39.2 J/kg

Solution

The gravitational potential at the surface of the Earth is negative, approximately -9.8 J/kg.

Correct Answer: B — -9.8 J/kg

Q. The gravitational force acting on a satellite in orbit is dependent on which of the following?

A. Mass of the satellite only
B. Mass of the Earth only
C. Distance from the Earth
D. All of the above

Solution

The gravitational force acting on a satellite depends on the mass of the satellite, the mass of the Earth, and the distance from the Earth according to Newton's law of gravitation.

Correct Answer: D — All of the above

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