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 induced EMF in a loop of wire if the magnetic flux through it changes at a rate of dΦ/dt?

A. -dΦ/dt
B. dΦ/dt
C. Φ
D. 0

Solution

According to Faraday's law of electromagnetic induction, the induced EMF is given by ε = -dΦ/dt.

Correct Answer: A — -dΦ/dt

Q. What is the induced EMF in a loop of wire when the magnetic field changes at a rate of 5 T/s?

A. 0 V
B. 5 V
C. 10 V
D. 15 V

Solution

The induced EMF (ε) is given by Faraday's law of electromagnetic induction: ε = -dΦ/dt. If the change in magnetic field is 5 T/s, then ε = 5 V.

Correct Answer: B — 5 V

Q. What is the induced EMF in a loop of wire when the magnetic field through it changes at a rate of 5 T/s?

A. 0 V
B. 5 V
C. 10 V
D. 15 V

Solution

The induced EMF (ε) is given by Faraday's law of electromagnetic induction: ε = -dΦ/dt. If the rate of change of magnetic field is 5 T/s, then ε = 5 V.

Correct Answer: B — 5 V

Q. What is the induced EMF in a loop of wire when the magnetic field through it changes at a rate of dB/dt?

A. -dB/dt
B. dB/dt
C. μ₀dB/dt
D. 0

Solution

According to Faraday's law of electromagnetic induction, the induced EMF is given by ε = -dΦ/dt, where Φ is the magnetic flux.

Correct Answer: A — -dB/dt

Q. What is the inradius of a triangle with sides 7 cm, 8 cm, and 9 cm?

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

Solution

Using the formula r = A/s, where A is the area and s is the semi-perimeter. Area = 26 cm², s = 12 cm, so r = 26/12 = 4 cm.

Correct Answer: B — 4 cm

Q. What is the integral form of Ampere's Law?

A. ∮B·dl = μ₀I_enclosed
B. ∮E·dl = -dΦ/dt
C. ∮F·dl = m*a
D. ∮V·dl = Q/C

Solution

The integral form of Ampere's Law states that the line integral of the magnetic field B around a closed loop is equal to μ₀ times the enclosed current I.

Correct Answer: A — ∮B·dl = μ₀I_enclosed

Q. What is the integral of 1/x dx?

A. ln
B. x
C. + C
D. x + C
. 1/x + C
. x^2/2 + C

Solution

The integral of 1/x dx is ln|x| + C.

Correct Answer: A — ln

Q. What is the integral of cos(x)dx?

A. sin(x) + C
B. cos(x) + C
C. -sin(x) + C
D. -cos(x) + C

Solution

The integral of cos(x) is sin(x) + C.

Correct Answer: A — sin(x) + C

Q. What is the integral of f(x) = 2x from 0 to 3?

A. 9
B. 6
C. 3
D. 12

Solution

∫(2x)dx from 0 to 3 = [x^2] from 0 to 3 = 9 - 0 = 9.

Correct Answer: B — 6

Q. What is the integral of f(x) = 2x with respect to x?

A. x^2 + C
B. 2x^2 + C
C. x^2 + 2C
D. 2x + C

Solution

The integral ∫2x dx = x^2 + C.

Correct Answer: A — x^2 + C

Q. What is the integral of f(x) = 2x?

A. x^2 + C
B. 2x^2 + C
C. x^2 + 2C
D. 2x + C

Solution

∫2x dx = x^2 + C.

Correct Answer: A — x^2 + C

Q. What is the integral of f(x) = 4x^3?

A. x^4 + C
B. x^4
C. x^3 + C
D. 4x^4 + C

Solution

The integral ∫4x^3 dx = x^4 + C.

Correct Answer: A — x^4 + C

Q. What is the integral of f(x) = cos(x)?

A. sin(x) + C
B. -sin(x) + C
C. tan(x) + C
D. sec(x) + C

Solution

The integral is sin(x) + C.

Correct Answer: A — sin(x) + C

Q. What is the integrated rate law for a first-order reaction?

A. ln[A] = -kt + ln[A]0
B. [A] = [A]0 - kt
C. [A] = [A]0e^(-kt)
D. 1/[A] = kt + 1/[A]0

Solution

The integrated rate law for a first-order reaction is ln[A] = -kt + ln[A]0.

Correct Answer: A — ln[A] = -kt + ln[A]0

Q. What is the integrating factor for the equation dy/dx + 2y = 3x?

A. e^(2x)
B. e^(-2x)
C. e^(3x)
D. e^(-3x)

Solution

The integrating factor is e^(∫2dx) = e^(2x).

Correct Answer: A — e^(2x)

Q. What is the integrating factor for the equation dy/dx + 3y = 6x?

A. e^(3x)
B. e^(-3x)
C. e^(6x)
D. e^(-6x)

Solution

The integrating factor is e^(∫3dx) = e^(3x).

Correct Answer: A — e^(3x)

Q. What is the interquartile range (IQR) of the data set {1, 3, 5, 7, 9, 11, 13, 15}?

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

Solution

Q1 = 4, Q3 = 10. IQR = Q3 - Q1 = 10 - 4 = 6.

Correct Answer: B — 6

Q. What is the interquartile range (IQR) of the data set {1, 3, 7, 8, 9, 10}?

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

Solution

IQR = Q3 - Q1; Q1 = 3, Q3 = 8; IQR = 8 - 3 = 5.

Correct Answer: A — 5

Q. What is the interquartile range (IQR) of the data set {1, 3, 7, 8, 9}?

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

Solution

Q1 = 3, Q3 = 8. IQR = Q3 - Q1 = 8 - 3 = 5.

Correct Answer: A — 6

Q. What is the interquartile range (IQR) of the data set: 1, 2, 3, 4, 5, 6, 7, 8, 9?

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

Solution

Q1 = 3, Q3 = 7; IQR = Q3 - Q1 = 7 - 3 = 4.

Correct Answer: A — 4

Q. What is the interquartile range (IQR) of the data set: 1, 3, 5, 7, 9, 11, 13?

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

Solution

Q1 = 3, Q3 = 9. IQR = Q3 - Q1 = 9 - 3 = 6.

Correct Answer: B — 6

Q. What is the intersection of the sets A = {1, 2, 3} and B = {2, 3, 4}?

A. {1, 2, 3}
B. {2, 3}
C. {4}
D. {1, 4}

Solution

The intersection of two sets includes only the elements that are present in both sets. Here, the intersection is {2, 3}.

Correct Answer: B — {2, 3}

Q. What is the inverse of the function f(x) = 2x + 3?

A. (x - 3)/2
B. (x + 3)/2
C. 2x - 3
D. 2(x - 3)

Solution

To find the inverse, set y = 2x + 3, solve for x: x = (y - 3)/2.

Correct Answer: A — (x - 3)/2

Q. What is the inverse of the function f(x) = 2x + 5?

A. f^-1(x) = (x - 5)/2
B. f^-1(x) = 2x - 5
C. f^-1(x) = (x + 5)/2
D. f^-1(x) = 5 - 2x

Solution

To find the inverse, set y = 2x + 5, solve for x: x = (y - 5)/2, thus f^-1(x) = (x - 5)/2.

Correct Answer: A — f^-1(x) = (x - 5)/2

Q. What is the inverse of the function f(x) = 3x + 1?

A. (x-1)/3
B. (x-1)/3
C. (x-3)/1
D. 3(x-1)

Solution

To find the inverse, set y = 3x + 1, solve for x: x = (y - 1)/3.

Correct Answer: A — (x-1)/3

Q. What is the inverse of the function f(x) = 3x + 4?

A. (x - 4)/3
B. (x + 4)/3
C. 3/x - 4
D. 3/x + 4

Solution

To find the inverse, set y = 3x + 4, solve for x: x = (y - 4)/3, hence the inverse is (x - 4)/3.

Correct Answer: A — (x - 4)/3

Q. What is the inverse of the function f(x) = 3x - 5?

A. (x + 5)/3
B. (x - 5)/3
C. 3(x + 5)
D. 3(x - 5)

Solution

To find the inverse, set y = 3x - 5, solve for x: x = (y + 5)/3, hence f^(-1)(x) = (x + 5)/3.

Correct Answer: A — (x + 5)/3

Q. What is the inverse of the matrix A = [[0, 1], [1, 0]]?

A. [[0, 1], [1, 0]]
B. [[1, 0], [0, 1]]
C. [[0, 0], [0, 0]]
D. [[1, 1], [1, 1]]

Solution

The inverse of A is A itself since A is an involutory matrix.

Correct Answer: A — [[0, 1], [1, 0]]

Q. What is the inverse of the matrix A = [[1, 2], [3, 4]]?

A. [[4, -2], [-3, 1]]
B. [[-2, 1], [1.5, -0.5]]
C. [[-2, 1], [1.5, -0.5]]
D. [[2, -1], [-1.5, 0.5]]

Solution

The inverse of A is (1/det(A)) * adj(A) = (1/-2) * [[4, -2], [-3, 1]] = [[-2, 1], [1.5, -0.5]].

Correct Answer: A — [[4, -2], [-3, 1]]

Q. What is the isoelectric point (pI) of a protein?

A. The pH at which the protein is positively charged
B. The pH at which the protein is negatively charged
C. The pH at which the protein has no net charge
D. The pH at which the protein is denatured

Solution

The isoelectric point (pI) of a protein is the pH at which the protein has no net charge, leading to minimal solubility.

Correct Answer: C — The pH at which the protein has no net charge

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