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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 common oxidation state of Chromium in chromates?

A. +2
B. +3
C. +4
D. +6

Solution

Chromium commonly exhibits a +6 oxidation state in chromates (CrO4^2-).

Correct Answer: D — +6

Q. What is the common oxidation state of chromium in Cr2O7^2-?

A. +2
B. +3
C. +6
D. +7

Solution

In Cr2O7^2-, chromium has a common oxidation state of +6.

Correct Answer: C — +6

Q. What is the common oxidation state of Chromium in its compounds?

A. +2
B. +3
C. +6
D. +5

Solution

Chromium commonly exhibits a +6 oxidation state in compounds such as chromium trioxide (CrO3).

Correct Answer: C — +6

Q. What is the common oxidation state of Group 17 elements?

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

Solution

Group 17 elements, also known as halogens, commonly exhibit an oxidation state of -1.

Correct Answer: A — -1

Q. What is the common oxidation state of nitrogen in ammonia (NH3)?

A. -3
B. 0
C. +1
D. +3

Solution

In ammonia, nitrogen has an oxidation state of -3.

Correct Answer: A — -3

Q. What is the common oxidation state of the p-block elements in group 13?

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

Solution

The common oxidation state of group 13 elements, such as Aluminum, is +3.

Correct Answer: C — +3

Q. What is the common oxidation state of transition metals in their compounds?

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

Solution

Transition metals commonly exhibit a +2 oxidation state due to the loss of two 4s electrons.

Correct Answer: B — +2

Q. What is the common ratio of the geometric series 4, 12, 36, ...?

A. 3
B. 2
C. 1.5
D. 4

Solution

The common ratio r = 12/4 = 3.

Correct Answer: A — 3

Q. What is the composition of functions f(g(x)) if f(x) = x + 1 and g(x) = 2x?

A. 2x + 1
B. 2x - 1
C. x + 2
D. x + 1

Solution

f(g(x)) = f(2x) = 2x + 1.

Correct Answer: A — 2x + 1

Q. What is the concentration in g/L of a solution containing 0.5 moles of KCl in 1.5 L of solution? (Molar mass of KCl = 74.5 g/mol)

A. 24.83 g/L
B. 49.67 g/L
C. 37.25 g/L
D. 50 g/L

Solution

Mass of KCl = 0.5 moles × 74.5 g/mol = 37.25 g. Concentration = 37.25 g / 1.5 L = 24.83 g/L.

Correct Answer: B — 49.67 g/L

Q. What is the concentration in molality of a solution made by dissolving 5 moles of solute in 3 kg of solvent?

A. 1.67 m
B. 2 m
C. 1.5 m
D. 2.5 m

Solution

Molality (m) = moles of solute / kg of solvent = 5 moles / 3 kg = 1.67 m.

Correct Answer: B — 2 m

Q. What is the concentration in molarity of a solution that contains 0.5 moles of solute in 1.5 liters of solution?

A. 0.33 M
B. 0.5 M
C. 0.75 M
D. 1 M

Solution

Molarity (M) = moles of solute / liters of solution = 0.5 moles / 1.5 L = 0.33 M.

Correct Answer: C — 0.75 M

Q. What is the concentration in ppm of a solution containing 1 gram of solute in 1 liter of solution?

A. 1000 ppm
B. 100 ppm
C. 10 ppm
D. 1 ppm

Solution

PPM = (mass of solute in grams / volume of solution in liters) * 10^6 = (1 g / 1 L) * 10^6 = 1000 ppm.

Correct Answer: A — 1000 ppm

Q. What is the concentration of a solution if 10 grams of NaCl is dissolved in 500 mL of water? (Molar mass of NaCl = 58.5 g/mol)

A. 0.34 M
B. 0.17 M
C. 0.50 M
D. 0.25 M

Solution

Molarity (M) = moles of solute / liters of solution = (10 g / 58.5 g/mol) / 0.5 L = 0.34 M.

Correct Answer: A — 0.34 M

Q. What is the concentration of H+ ions in a solution with a pH of 3?

A. 0.001 M
B. 0.01 M
C. 0.1 M
D. 1 M

Solution

[H+] = 10^(-pH) = 10^(-3) = 0.001 M

Correct Answer: A — 0.001 M

Q. What is the condition for a system to be critically damped?

A. Damping coefficient equals zero
B. Damping coefficient is less than the natural frequency
C. Damping coefficient equals the square root of the product of mass and spring constant
D. Damping coefficient is greater than the natural frequency

Solution

A system is critically damped when the damping coefficient equals the square root of the product of mass and spring constant.

Correct Answer: C — Damping coefficient equals the square root of the product of mass and spring constant

Q. What is the condition for a Wheatstone bridge to be balanced?

A. R1/R2 = R3/R4
B. R1 + R2 = R3 + R4
C. R1 - R2 = R3 - R4
D. R1 * R2 = R3 * R4

Solution

The condition for a Wheatstone bridge to be balanced is R1/R2 = R3/R4.

Correct Answer: A — R1/R2 = R3/R4

Q. What is the condition for a Wheatstone bridge to be in a balanced state?

A. R1/R2 = R3/R4
B. R1 + R2 = R3 + R4
C. R1 - R2 = R3 - R4
D. R1 * R4 = R2 * R3

Solution

The condition for balance is R1/R2 = R3/R4.

Correct Answer: A — R1/R2 = R3/R4

Q. What is the condition for a Wheatstone bridge to be in equilibrium?

A. R1/R2 = R3/R4
B. R1 + R2 = R3 + R4
C. R1 - R2 = R3 - R4
D. R1 * R3 = R2 * R4

Solution

In a Wheatstone bridge, the bridge is in equilibrium when the ratio of the resistances in one branch is equal to the ratio in the other branch, i.e., R1/R2 = R3/R4.

Correct Answer: A — R1/R2 = R3/R4

Q. What is the condition for an object to be in rotational equilibrium?

A. Net force is zero
B. Net torque is zero
C. Both net force and net torque are zero
D. None of the above

Solution

For rotational equilibrium, the net torque acting on the object must be zero.

Correct Answer: B — Net torque is zero

Q. What is the condition for constructive interference in a double-slit experiment?

A. Path difference is an odd multiple of lambda/2
B. Path difference is an even multiple of lambda
C. Path difference is an odd multiple of lambda
D. Path difference is zero

Solution

Constructive interference occurs when the path difference between the two waves is an even multiple of the wavelength (nλ, where n is an integer).

Correct Answer: B — Path difference is an even multiple of lambda

Q. What is the condition for constructive interference in a thin film?

A. 2t = (m + 1/2)λ
B. 2t = mλ
C. t = mλ/2
D. t = (m + 1/2)λ/2

Solution

For constructive interference, the condition is 2t = mλ, where t is the thickness of the film and m is an integer.

Correct Answer: B — 2t = mλ

Q. What is the condition for constructive interference in two waves?

A. Path difference = (n + 1/2)λ
B. Path difference = nλ
C. Path difference = (n - 1/2)λ
D. Path difference = 0

Solution

Constructive interference occurs when the path difference is nλ, where n is an integer.

Correct Answer: B — Path difference = nλ

Q. What is the condition for critical damping in a damped harmonic oscillator?

A. Damping coefficient equals zero
B. Damping coefficient equals mass times natural frequency
C. Damping coefficient equals twice the mass times natural frequency
D. Damping coefficient is less than mass times natural frequency

Solution

Critical damping occurs when the damping coefficient equals twice the mass times the natural frequency of the system.

Correct Answer: C — Damping coefficient equals twice the mass times natural frequency

Q. What is the condition for critical damping in a damped oscillator?

A. Damping coefficient equals zero
B. Damping coefficient equals mass times natural frequency
C. Damping coefficient is less than mass times natural frequency
D. Damping coefficient is greater than mass times natural frequency

Solution

Critical damping occurs when the damping coefficient equals the mass times the natural frequency.

Correct Answer: B — Damping coefficient equals mass times natural frequency

Q. What is the condition for light to be completely polarized by reflection?

A. Angle of incidence equals angle of refraction
B. Angle of incidence equals Brewster's angle
C. Angle of incidence is 45 degrees
D. Light must be monochromatic

Solution

Light is completely polarized when it is reflected at Brewster's angle, which is given by θ_B = arctan(n2/n1).

Correct Answer: B — Angle of incidence equals Brewster's angle

Q. What is the condition for light to be polarized by reflection?

A. Angle of incidence equals angle of refraction
B. Angle of incidence equals Brewster's angle
C. Angle of incidence is 45 degrees
D. Light must be monochromatic

Solution

Light is polarized by reflection when the angle of incidence equals Brewster's angle.

Correct Answer: B — Angle of incidence equals Brewster's angle

Q. What is the condition for rolling without slipping?

A. v = Rω
B. v = 2Rω
C. v = 0
D. v = R^2ω

Solution

The condition for rolling without slipping is that the linear velocity v of the center of mass is equal to the product of the radius R and the angular velocity ω, i.e., v = Rω.

Correct Answer: A — v = Rω

Q. What is the condition for the first minimum in single-slit diffraction?

A. a = λ
B. a = 2λ
C. a = λ/2
D. a = 3λ

Solution

The first minimum occurs at a = λ, where 'a' is the slit width and 'λ' is the wavelength.

Correct Answer: A — a = λ

Q. What is the condition for the lines 2x + 3y = 6 and 4x + 6y = 12 to be parallel?

A. They have the same slope
B. They intersect
C. They are identical
D. None of the above

Solution

Both lines can be rewritten in slope-intercept form. The first line has slope -2/3 and the second line has the same slope, hence they are parallel.

Correct Answer: A — They have the same slope

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