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. If a torque of 25 Nm is applied to a wheel with a radius of 0.5 m, what is the force applied at the edge of the wheel?

A. 50 N
B. 40 N
C. 30 N
D. 20 N

Solution

Force = Torque / Radius = 25 Nm / 0.5 m = 50 N.

Correct Answer: A — 50 N

Q. If a torque of 25 Nm is generated by a force acting at a distance of 0.5 m, what is the force applied?

A. 50 N
B. 40 N
C. 30 N
D. 20 N

Solution

Force = Torque / Distance = 25 Nm / 0.5 m = 50 N.

Correct Answer: A — 50 N

Q. If a torque of 30 Nm is applied to a lever arm of 3 m, what is the force applied?

A. 5 N
B. 10 N
C. 15 N
D. 20 N

Solution

Force = Torque / Distance = 30 Nm / 3 m = 10 N.

Correct Answer: B — 10 N

Q. If a torque of 5 Nm is applied to a rotating object with a moment of inertia of 2 kg·m², what is the angular acceleration?

A. 2.5 rad/s²
B. 5 rad/s²
C. 10 rad/s²
D. 1 rad/s²

Solution

Angular acceleration α = Torque / Moment of inertia = 5 Nm / 2 kg·m² = 2.5 rad/s².

Correct Answer: A — 2.5 rad/s²

Q. If a torque of 8 Nm is produced by a force acting at a distance of 0.2 m, what is the force?

A. 20 N
B. 30 N
C. 40 N
D. 50 N

Solution

Force = Torque / Distance = 8 Nm / 0.2 m = 40 N.

Correct Answer: A — 20 N

Q. If a train travels at a speed of 72 km/h, how long will it take to cover a distance of 180 km?

A. 2 h
B. 2.5 h
C. 3 h
D. 3.5 h

Solution

Time = distance / speed = 180 km / (72 km/h) = 2.5 h.

Correct Answer: C — 3 h

Q. If a triangle has sides of lengths 3, 4, and 5, what is its area?

A. 6
B. 12
C. 8
D. 10

Solution

The area of a right triangle is (1/2) * base * height = (1/2) * 3 * 4 = 6.

Correct Answer: A — 6

Q. If a triangle has sides of lengths 3, 4, and 5, what type of triangle is it?

A. Acute
B. Obtuse
C. Right
D. Equilateral

Solution

A triangle with sides 3, 4, and 5 satisfies the Pythagorean theorem, thus it is a right triangle.

Correct Answer: C — Right

Q. If a volume is measured as 200 L with an error of 5 L, what is the range of possible volumes?

A. 195 L to 205 L
B. 200 L to 205 L
C. 195 L to 210 L
D. 200 L to 210 L

Solution

Range of possible volumes = 200 - 5 to 200 + 5 = 195 L to 205 L.

Correct Answer: A — 195 L to 205 L

Q. If a weight is measured as 10 kg with a 0.2 kg error, what is the maximum possible true weight?

A. 10.2 kg
B. 9.8 kg
C. 10 kg
D. 10.4 kg

Solution

Maximum true weight = Measured weight + Error = 10 kg + 0.2 kg = 10.2 kg.

Correct Answer: A — 10.2 kg

Q. If a wheel of radius R rolls without slipping, what is the distance traveled by the center of mass after one complete rotation?

A. 2πR
B. πR
C. 4R
D. R/2

Solution

The distance traveled by the center of mass after one complete rotation is equal to the circumference of the wheel, which is 2πR.

Correct Answer: A — 2πR

Q. If a wire carries a current of 5 A and is placed in a magnetic field of 0.1 T, what is the force per unit length on the wire?

A. 0.5 N/m
B. 1 N/m
C. 0.2 N/m
D. 0.1 N/m

Solution

Using the formula F = BIL, where B is the magnetic field, I is the current, and L is the length of the wire (1 m), F = 0.1 T * 5 A * 1 m = 0.5 N.

Correct Answer: B — 1 N/m

Q. If a wire carries a current of 5 A, what is the magnetic field at a distance of 0.1 m from the wire?

A. 0.1 T
B. 0.2 T
C. 0.5 T
D. 1.0 T

Solution

Using Ampere's Law, B = μ₀I/2πr, where μ₀ = 4π × 10^-7 Tm/A, we find B = (4π × 10^-7)(5)/(2π(0.1)) = 0.1 T.

Correct Answer: B — 0.2 T

Q. If a wire carrying current I is bent into a semicircular arc of radius R, what is the magnetic field at the center of the arc?

A. μ₀I/(4R)
B. μ₀I/(2R)
C. μ₀I/(8R)
D. μ₀I/(πR)

Solution

The magnetic field at the center of a semicircular arc of radius R carrying current I is given by B = μ₀I/(4R).

Correct Answer: A — μ₀I/(4R)

Q. If a wire is bent into a semicircular shape, what is the magnetic field at the center of the semicircle due to current I?

A. μ₀I/(4R)
B. μ₀I/(2R)
C. μ₀I/(πR)
D. μ₀I/(8R)

Solution

The magnetic field at the center of a semicircular wire carrying current I is given by B = μ₀I/(4R) for the semicircle, which is half of the full circular loop.

Correct Answer: C — μ₀I/(πR)

Q. If a wire is bent into a semicircular shape, what is the magnetic field at the center of the semicircle due to the current I?

A. μ₀I/(4R)
B. μ₀I/(2R)
C. μ₀I/(8R)
D. μ₀I/(6R)

Solution

The magnetic field at the center of a semicircular wire carrying current I is given by B = μ₀I/(4R).

Correct Answer: A — μ₀I/(4R)

Q. If a wire is stretched and its length increases by 2%, what is the strain?

A. 0.02
B. 0.2
C. 2
D. 200

Solution

Strain is defined as the change in length divided by the original length, so 2% = 0.02.

Correct Answer: A — 0.02

Q. If a wire of length L and cross-sectional area A is stretched by a force F, what is the expression for the elongation?

A. F * L / (A * E)
B. A * F / (L * E)
C. E * F / (A * L)
D. L * E / (A * F)

Solution

The elongation (ΔL) can be expressed as ΔL = F * L / (A * E).

Correct Answer: A — F * L / (A * E)

Q. If a wire's length is doubled while keeping its cross-sectional area constant, how does its resistance change?

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

Solution

Resistance is directly proportional to length; doubling the length doubles the resistance.

Correct Answer: B — Doubles

Q. If A(1, 2, 3) and B(4, 5, 6) are two points in space, what is the vector AB?

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

Solution

Vector AB = B - A = (4-1, 5-2, 6-3) = (3, 3, 3).

Correct Answer: A — (3, 3, 3)

Q. If A(1, 2, 3) and B(4, 5, 6) are two points, what is the vector AB?

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

Solution

Vector AB = B - A = (4-1, 5-2, 6-3) = (3, 3, 3).

Correct Answer: A — (3, 3, 3)

Q. If A(2, 3, 4) and B(1, 0, -1) are two points in space, find the vector AB.

A. (1, 3, 5)
B. (1, -3, -5)
C. (1, 3, -5)
D. (1, -3, 5)

Solution

AB = B - A = (1 - 2, 0 - 3, -1 - 4) = (-1, -3, -5) = (1, 3, 5) in the opposite direction.

Correct Answer: A — (1, 3, 5)

Q. If an electron has quantum numbers n=2, l=0, and m_l=0, which orbital does it occupy?

A. 2s
B. 2p
C. 1s
D. 3s

Solution

The quantum numbers correspond to the 2s orbital, where l=0 indicates an s orbital.

Correct Answer: A — 2s

Q. If an electron has quantum numbers n=3, l=1, and m_l=-1, what is the possible value of the spin quantum number?

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

Solution

The spin quantum number can be either +1/2 or -1/2, so both values are possible.

Correct Answer: A — +1/2

Q. If an electron has the quantum numbers n=3, l=1, m_l=0, what type of orbital does it occupy?

A. s
B. p
C. d
D. f

Solution

For l=1, the electron occupies a p orbital.

Correct Answer: B — p

Q. If an electron has the quantum numbers n=3, l=1, m_l=0, what type of orbital is it in?

A. s
B. p
C. d
D. f

Solution

For l=1, the orbital is a p orbital.

Correct Answer: B — p

Q. If an electron has the quantum numbers n=3, l=1, what is the possible range of m_l?

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

Solution

For l=1, m_l can take values -1, 0, +1.

Correct Answer: A — -1, 0, +1

Q. If an electron is in the state characterized by the quantum numbers n=4, l=0, what is the value of m_l?

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

Solution

For l=0, m_l can only be 0.

Correct Answer: A — 0

Q. If an electron is in the state characterized by the quantum numbers n=4, l=2, what is the value of m_l?

A. -2
B. 0
C. 2
D. All of the above

Solution

For l=2, m_l can take values -2, -1, 0, 1, 2. Therefore, all of the options are valid.

Correct Answer: D — All of the above

Q. If an ellipse has a semi-major axis of 10 and a semi-minor axis of 6, what is the value of b^2?

A. 36
B. 64
C. 100
D. 60

Solution

For an ellipse, b is the semi-minor axis. Here, b = 6, so b^2 = 6^2 = 36.

Correct Answer: A — 36

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