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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 the mode of the data set 1, 2, 2, 3, 4, 4, 4, 5 is removed, what will be the new mode?

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

Solution

New mode = 2 (as 4 is removed, 2 is the next most frequent).

Correct Answer: A — 2

Q. If the mode of the data set 1, 2, 2, 3, 4, 4, 4, 5 is?

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

Solution

Mode is the number that appears most frequently. Here, 4 appears 3 times.

Correct Answer: D — 4

Q. If the mode of the data set 2, 3, 3, 5, 7, 8 is 3, what is the mode of the data set 1, 1, 2, 2, 3, 3, 3, 4?

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

Solution

Mode = 3 (most frequent value).

Correct Answer: C — 3

Q. If the mode of the data set 2, 3, 4, 4, 5, 5, 5, 6 is removed, what is the new mode?

A. 4
B. 5
C. 6
D. No mode

Solution

Removing 5 leaves 2, 3, 4, 4, 6. The new mode is 4.

Correct Answer: D — No mode

Q. If the mode of the data set 2, 3, 4, 4, 5, 5, 5, 6 is?

A. 2
B. 4
C. 5
D. 6

Solution

Mode is the value that appears most frequently. Here, 5 appears 3 times.

Correct Answer: C — 5

Q. If the mode of the data set 3, 4, 4, 5, 6, 6, 6, 7 is removed, what is the new mode?

A. 4
B. 5
C. 6
D. 7

Solution

Removing mode 6 leaves 3, 4, 4, 5, 7. New mode = 4.

Correct Answer: A — 4

Q. If the mode of the data set 3, 7, 7, 2, 5, 7, 8 is x, what is the value of x?

A. 2
B. 3
C. 7
D. 8

Solution

Mode is the most frequent value. Here, 7 appears most frequently.

Correct Answer: C — 7

Q. If the mode of the data set {1, 2, 2, 3, 4, 4, 4, 5} is removed, what is the new mode?

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

Solution

Removing mode 4 leaves {1, 2, 2, 3, 5}. New mode = 2.

Correct Answer: B — 2

Q. If the mode of the data set {3, 5, 7, 3, 9, 3, 5} is x, what is the value of x?

A. 3
B. 5
C. 7
D. 9

Solution

Mode is the number that appears most frequently. Here, 3 appears 3 times.

Correct Answer: A — 3

Q. If the molar mass of a gas is doubled, how does its RMS speed change?

A. Increases by sqrt(2)
B. Decreases by sqrt(2)
C. Remains the same
D. Increases by 2

Solution

RMS speed is inversely proportional to the square root of molar mass, so if M is doubled, v_rms decreases by sqrt(2).

Correct Answer: B — Decreases by sqrt(2)

Q. If the molar mass of a gas is doubled, how does the RMS speed change?

A. Increases by sqrt(2)
B. Decreases by sqrt(2)
C. Remains the same
D. Increases by 2

Solution

The RMS speed is inversely proportional to the square root of the molar mass. If M is doubled, v_rms decreases by sqrt(2).

Correct Answer: B — Decreases by sqrt(2)

Q. If the molar mass of a gas is halved, what happens to its RMS speed?

A. Increases by a factor of sqrt(2)
B. Increases by a factor of 2
C. Decreases by a factor of sqrt(2)
D. Remains the same

Solution

If the molar mass is halved, the RMS speed increases by a factor of sqrt(2) because RMS speed is inversely proportional to the square root of molar mass.

Correct Answer: A — Increases by a factor of sqrt(2)

Q. If the mole fraction of a solute in a solution is 0.2, what is the mole fraction of the solvent?

A. 0.8
B. 0.2
C. 0.5
D. 0.6

Solution

Mole fraction of solvent = 1 - mole fraction of solute = 1 - 0.2 = 0.8.

Correct Answer: A — 0.8

Q. If the mole fraction of a solvent in a solution is 0.75, what is the vapor pressure of the solvent if its pure vapor pressure is 100 mmHg?

A. 75 mmHg
B. 100 mmHg
C. 25 mmHg
D. 50 mmHg

Solution

According to Raoult's Law, the vapor pressure of the solvent in the solution is 0.75 * 100 mmHg = 75 mmHg.

Correct Answer: A — 75 mmHg

Q. If the mole fraction of a solvent in a solution is 0.8, what is the mole fraction of the solute?

A. 0.2
B. 0.8
C. 0.5
D. 0.1

Solution

The mole fraction of the solute is 1 - X_solvent = 1 - 0.8 = 0.2.

Correct Answer: A — 0.2

Q. If the mole fraction of solute in a solution is 0.2, what is the mole fraction of the solvent?

A. 0.8
B. 0.2
C. 0.5
D. 0.6

Solution

The mole fraction of the solvent is 1 - X_solute = 1 - 0.2 = 0.8.

Correct Answer: A — 0.8

Q. If the moment of inertia of a body is 10 kg m², what is the angular momentum when it rotates with an angular velocity of 5 rad/s?

A. 50 kg m²/s
B. 10 kg m²/s
C. 5 kg m²/s
D. 2 kg m²/s

Solution

Angular momentum L = Iω = 10 kg m² * 5 rad/s = 50 kg m²/s.

Correct Answer: A — 50 kg m²/s

Q. If the moment of inertia of a body is 10 kg m², what is the rotational kinetic energy when it rotates with an angular velocity of 5 rad/s?

A. 125 J
B. 50 J
C. 100 J
D. 75 J

Solution

Rotational kinetic energy is given by KE = 1/2 I ω² = 1/2 * 10 * 5² = 125 J.

Correct Answer: A — 125 J

Q. If the moment of inertia of a body is 10 kg·m² and it is subjected to a torque of 20 N·m, what is the angular acceleration?

A. 2 rad/s²
B. 0.5 rad/s²
C. 5 rad/s²
D. 10 rad/s²

Solution

Using τ = Iα, we have α = τ/I = 20 N·m / 10 kg·m² = 2 rad/s².

Correct Answer: A — 2 rad/s²

Q. If the moment of inertia of a body is doubled, what happens to its rotational kinetic energy if the angular velocity remains constant?

A. Doubles
B. Halves
C. Remains the same
D. Quadruples

Solution

Rotational kinetic energy is given by KE = 1/2 I ω^2. If I is doubled and ω remains constant, KE also doubles.

Correct Answer: A — Doubles

Q. If the moment of inertia of a body is doubled, what will be the effect on its angular acceleration if the torque applied remains constant?

A. Doubles
B. Halves
C. Remains the same
D. Increases by a factor of four

Solution

Angular acceleration α = τ/I. If I is doubled and τ remains constant, α is halved.

Correct Answer: B — Halves

Q. If the moment of inertia of a body is doubled, what will happen to its angular momentum if the angular velocity remains constant?

A. Doubles
B. Halves
C. Remains the same
D. Quadruples

Solution

Angular momentum L = Iω; if I is doubled and ω remains constant, L also doubles.

Correct Answer: A — Doubles

Q. If the moment of inertia of a body is increased, what happens to its angular acceleration for a constant torque?

A. Increases
B. Decreases
C. Remains the same
D. Becomes zero

Solution

According to Newton's second law for rotation, τ = Iα, if I increases and τ is constant, α must decrease.

Correct Answer: B — Decreases

Q. If the natural frequency of a damped oscillator is 5 rad/s and the damping ratio is 0.2, what is the damped frequency?

A. 4.8 rad/s
B. 5 rad/s
C. 5.2 rad/s
D. 5.5 rad/s

Solution

Damped frequency (ω_d) = ω_n√(1-ζ^2) = 5√(1-0.2^2) = 5√(0.96) ≈ 4.8 rad/s.

Correct Answer: A — 4.8 rad/s

Q. If the nth term of a sequence is given by a_n = n^2 + n, what is a_4?

A. 20
B. 24
C. 16
D. 18

Solution

a_4 = 4^2 + 4 = 16 + 4 = 20.

Correct Answer: A — 20

Q. If the object distance is equal to the focal length of a convex lens, what is the nature of the image formed?

A. Real and inverted
B. Virtual and upright
C. At infinity
D. No image formed

Solution

When the object distance equals the focal length, the image is formed at infinity.

Correct Answer: C — At infinity

Q. If the object distance is equal to the focal length of a convex lens, what type of image is formed?

A. Real and inverted
B. Virtual and upright
C. At infinity
D. No image formed

Solution

When the object is at the focal length, the image is formed at infinity.

Correct Answer: C — At infinity

Q. If the odds in favor of an event are 3:2, what is the probability of the event occurring?

A. 0.6
B. 0.4
C. 0.5
D. 0.3

Solution

Probability = Odds in favor / (Total odds) = 3 / (3 + 2) = 3/5 = 0.6.

Correct Answer: A — 0.6

Q. If the osmotic pressure of a solution is 3.0 atm at 25 °C, what is the molarity of the solution? (R = 0.0821 L atm/(K mol))

A. 0.12 M
B. 0.15 M
C. 0.18 M
D. 0.20 M

Solution

Molarity = π / (RT) = 3.0 / (0.0821 * 298) = 0.12 M

Correct Answer: C — 0.18 M

Q. If the osmotic pressure of a solution is 3.0 atm, what is the molarity of the solution? (R = 0.0821 L atm/(K mol), T = 298 K)

A. 0.12 M
B. 0.15 M
C. 0.10 M
D. 0.20 M

Solution

Molarity = π / (RT) = 3.0 / (0.0821 * 298) = 0.12 M

Correct Answer: B — 0.15 M

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