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. Is the function f(x) = x^2 - 4x + 4 differentiable everywhere?

A. Yes
B. No
C. Only at x = 0
D. Only at x = 2

Solution

This is a polynomial function, which is differentiable everywhere on its domain.

Correct Answer: A — Yes

Q. Is the function f(x) = x^2 sin(1/x) differentiable at x = 0?

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

Solution

Using the limit definition, f'(0) = lim (h -> 0) [(h^2 sin(1/h) - 0)/h] = 0. Thus, f(x) is differentiable at x = 0.

Correct Answer: A — Yes

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

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

Solution

The function is a polynomial and hence differentiable everywhere, including at x = 1.

Correct Answer: A — Yes

Q. Is the function f(x) = { e^x, x < 0; ln(x + 1), x >= 0 } continuous at x = 0?

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

Solution

Both limits as x approaches 0 from the left and right are equal to 1, hence f(x) is continuous at x = 0.

Correct Answer: A — Yes

Q. Is the function f(x) = { sin(x), x < 0; x^2, x >= 0 } continuous at x = 0?

A. Yes
B. No
C. Depends on x
D. Not defined

Solution

Both limits as x approaches 0 from the left and right are equal to 0, hence f(x) is continuous at x = 0.

Correct Answer: A — Yes

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

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

Solution

Both limits as x approaches 1 from the left and right are equal to 2, hence f(x) is continuous at x = 1.

Correct Answer: A — Yes

Q. Is the function f(x) = |x|/x continuous at x = 0?

A. Yes
B. No
C. Depends on direction
D. None of the above

Solution

The left limit is -1 and the right limit is 1, which are not equal. Therefore, f(x) is not continuous at x = 0.

Correct Answer: B — No

Q. Lenz's law states that the direction of induced current is such that it opposes what?

A. The change in magnetic flux
B. The flow of electric current
C. The resistance in the circuit
D. The applied voltage

Solution

Lenz's law states that the direction of induced current will oppose the change in magnetic flux that produced it.

Correct Answer: A — The change in magnetic flux

Q. Let A = {1, 2, 3, 4} and R be the relation defined by R = {(a, b) | a < b}. How many ordered pairs are in R?

A. 4
B. 6
C. 8
D. 10

Solution

The pairs are (1,2), (1,3), (1,4), (2,3), (2,4), (3,4). Thus, there are 6 ordered pairs.

Correct Answer: B — 6

Q. Let A = {1, 2, 3, 4} and R be the relation defined by R = {(x, y) | x < y}. How many ordered pairs are in R?

A. 4
B. 6
C. 8
D. 10

Solution

The ordered pairs are (1,2), (1,3), (1,4), (2,3), (2,4), (3,4). Thus, there are 6 ordered pairs.

Correct Answer: B — 6

Q. Let R be a relation on the set of natural numbers defined by R = {(m, n) | m divides n}. Is R a partial order?

A. Yes
B. No
C. Only reflexive
D. Only transitive

Solution

R is reflexive, antisymmetric, and transitive, thus it is a partial order.

Correct Answer: A — Yes

Q. Solve for x: 2x^2 - 8x + 6 = 0.

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

Solution

Using the quadratic formula x = [8 ± √(64 - 48)] / 4 = [8 ± 4] / 4, giving x = 3 or x = 1.

Correct Answer: B — 3

Q. Solve for x: 3(x - 1) = 2(x + 4).

A. -10
B. 10
C. 2
D. 3

Solution

Expanding gives 3x - 3 = 2x + 8. Rearranging gives x = 11.

Correct Answer: A — -10

Q. Solve for x: 3(x - 2) = 12.

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

Solution

Dividing both sides by 3 gives x - 2 = 4, thus x = 6.

Correct Answer: C — 6

Q. Solve for x: 3(x - 2) = 2(x + 1).

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

Solution

Expanding both sides gives 3x - 6 = 2x + 2. Rearranging gives x = 8.

Correct Answer: B — 0

Q. Solve for x: 5x + 2 = 3x + 10.

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

Solution

Subtracting 3x from both sides gives 2x + 2 = 10, then subtracting 2 gives 2x = 8, leading to x = 4.

Correct Answer: A — 4

Q. Solve for x: log_3(x + 1) - log_3(x - 1) = 1.

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

Solution

Using properties of logarithms, log_3((x + 1)/(x - 1)) = 1 => (x + 1)/(x - 1) = 3 => x + 1 = 3(x - 1) => x = 2.

Correct Answer: A — 2

Q. Solve for x: log_3(x) = 2.

A. 6
B. 9
C. 3
D. 2

Solution

log_3(x) = 2 implies x = 3^2 = 9.

Correct Answer: B — 9

Q. Solve for x: log_5(x + 1) - log_5(x - 1) = 1.

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

Solution

Using properties of logarithms: log_5((x + 1)/(x - 1)) = 1 => (x + 1)/(x - 1) = 5 => x + 1 = 5(x - 1) => 4x = 6 => x = 2.

Correct Answer: A — 2

Q. Solve for x: log_5(x) = 2.

A. 5
B. 10
C. 25
D. 50

Solution

log_5(x) = 2 implies x = 5^2 = 25.

Correct Answer: C — 25

Q. Solve for x: x^2 - 9 = 0.

A. -3
B. 3
C. 0
D. ±3

Solution

The equation factors to (x - 3)(x + 3) = 0, giving solutions x = 3 and x = -3.

Correct Answer: D — ±3

Q. Solve for y: 4y + 8 = 24.

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

Solution

Subtracting 8 from both sides gives 4y = 16, then dividing by 4 gives y = 4.

Correct Answer: B — 3

Q. Solve the differential equation dy/dx + 2y = 4.

A. y = 2 - Ce^(-2x)
B. y = 2 + Ce^(-2x)
C. y = 4 - Ce^(-2x)
D. y = 4 + Ce^(2x)

Solution

This is a linear first-order differential equation. The integrating factor is e^(2x). Solving gives y = 2 - Ce^(-2x).

Correct Answer: A — y = 2 - Ce^(-2x)

Q. Solve the differential equation dy/dx = 3x^2.

A. y = x^3 + C
B. y = 3x^3 + C
C. y = x^2 + C
D. y = 3x + C

Solution

Integrating both sides gives y = x^3 + C.

Correct Answer: A — y = x^3 + C

Q. Solve the differential equation dy/dx = x^2 + y^2.

A. y = x^3/3 + C
B. y = x^2 + C
C. y = x^2 + x + C
D. y = Cx^2 + C

Solution

This is a non-linear differential equation. The solution can be found using substitution methods.

Correct Answer: A — y = x^3/3 + C

Q. Solve the differential equation y' = 3y + 6.

A. y = Ce^(3x) - 2
B. y = Ce^(3x) + 2
C. y = 2e^(3x)
D. y = 3e^(3x) + 2

Solution

Using the integrating factor method, we find y = Ce^(3x) + 2.

Correct Answer: B — y = Ce^(3x) + 2

Q. Solve the differential equation y'' + 4y = 0.

A. y = C1 cos(2x) + C2 sin(2x)
B. y = C1 e^(2x) + C2 e^(-2x)
C. y = C1 cos(x) + C2 sin(x)
D. y = C1 e^(x) + C2 e^(-x)

Solution

The characteristic equation is r^2 + 4 = 0, giving complex roots. The solution is y = C1 cos(2x) + C2 sin(2x).

Correct Answer: A — y = C1 cos(2x) + C2 sin(2x)

Q. Solve the differential equation y'' - 5y' + 6y = 0.

A. y = C1 e^(2x) + C2 e^(3x)
B. y = C1 e^(3x) + C2 e^(2x)
C. y = C1 e^(x) + C2 e^(2x)
D. y = C1 e^(2x) + C2 e^(x)

Solution

The characteristic equation is r^2 - 5r + 6 = 0, which factors to (r - 2)(r - 3) = 0, giving the solution y = C1 e^(2x) + C2 e^(3x).

Correct Answer: B — y = C1 e^(3x) + C2 e^(2x)

Q. Solve the equation 2sin(x) + √3 = 0 for x in the interval [0, 2π].

A. 5π/3
B. π/3
C. 2π/3
D. 4π/3

Solution

Rearranging gives sin(x) = -√3/2, so x = 4π/3 and x = 5π/3.

Correct Answer: A — 5π/3

Q. Solve the equation 2sin(x) - 1 = 0 for x in the interval [0, 2π].

A. π/6
B. 5π/6
C. π/2
D. 7π/6

Solution

The solution is x = π/2.

Correct Answer: C — π/2

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