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 value of the principal quantum number (n) for the outermost electron in potassium (K)?

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

Solution

Potassium has the electronic configuration [Ar] 4s1, so the outermost electron is in n=4.

Correct Answer: B — 4

Q. What is the value of the principal quantum number for an electron in the ground state of a hydrogen atom?

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

Solution

The ground state of hydrogen corresponds to n=1.

Correct Answer: A — 1

Q. What is the value of the principal quantum number for the outermost electrons in a sodium atom?

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

Solution

Sodium has an atomic number of 11, and its outermost electrons are in the n=3 shell.

Correct Answer: C — 3

Q. What is the value of the principal quantum number for the outermost electrons in potassium (K)?

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

Solution

Potassium has an atomic number of 19, and its outermost electrons are in the n=4 shell.

Correct Answer: D — 4

Q. What is the value of the series 1 + 1/2 + 1/3 + ... + 1/n as n approaches infinity?

A. 0
B. 1
C. ∞
D. undefined

Solution

The series diverges to infinity as n approaches infinity.

Correct Answer: C — ∞

Q. What is the value of the universal gas constant R in J/(mol·K)?

A. 8.314
B. 0.0821
C. 1.987
D. 22.414

Solution

The universal gas constant R is 8.314 J/(mol·K).

Correct Answer: A — 8.314

Q. What is the value of the universal gas constant R in L·atm/(K·mol)?

A. 0.0821
B. 8.314
C. 62.36
D. 1.987

Solution

The universal gas constant R is 0.0821 L·atm/(K·mol).

Correct Answer: A — 0.0821

Q. What is the value of x if 2x + 3 = 11?

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

Solution

Subtract 3 from both sides: 2x = 8. Then divide by 2: x = 4.

Correct Answer: C — 4

Q. What is the value of x if 3x - 5 = 16?

A. 7
B. 5
C. 4
D. 3

Solution

Solving for x: 3x = 21 => x = 7.

Correct Answer: A — 7

Q. What is the value of x in the equation 2x^2 - 8x + 6 = 0?

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

Solution

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

Correct Answer: C — 3

Q. What is the value of x in the equation 3x - 5 = 7?

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

Solution

Solving for x: 3x = 12, thus x = 4.

Correct Answer: A — 4

Q. What is the value of x in the equation 5(x - 2) = 3x + 4?

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

Solution

Expanding gives 5x - 10 = 3x + 4. Rearranging gives 2x = 14, thus x = 7.

Correct Answer: A — -1

Q. What is the value of x in the equation 5x - 3 = 2x + 12?

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

Solution

Rearranging gives 5x - 2x = 12 + 3 => 3x = 15 => x = 5.

Correct Answer: B — 4

Q. What is the value of x in the equation 5x - 3 = 2x + 6?

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

Solution

Rearranging gives 5x - 2x = 6 + 3 => 3x = 9 => x = 3.

Correct Answer: B — 2

Q. What is the value of z if z^2 = -1?

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

Solution

The solutions to z^2 = -1 are z = i and z = -i.

Correct Answer: A — i

Q. What is the value of \( \begin{vmatrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 3 & 6 \end{vmatrix} \)?

A. 0
B. 1
C. 2
D. 3

Solution

The determinant is 0 because the first column is repeated.

Correct Answer: A — 0

Q. What is the value of \( \tan(\tan^{-1}(3)) \)?

A. 0
B. 1
C. 3
D. undefined

Solution

By definition, \( \tan(\tan^{-1}(x)) = x \). Therefore, \( \tan(\tan^{-1}(3)) = 3 \).

Correct Answer: C — 3

Q. What is the value of |z| if z = -3 + 4i?

A. 5
B. 7
C. 4
D. 3

Solution

|z| = √((-3)^2 + (4)^2) = √(9 + 16) = √25 = 5.

Correct Answer: A — 5

Q. What is the value of |z| if z = 4 - 3i?

A. 5
B. 7
C. 4
D. 3

Solution

|z| = √(4^2 + (-3)^2) = √(16 + 9) = √25 = 5.

Correct Answer: A — 5

Q. What is the value of |z| if z = 4e^(iπ/3)?

A. 4
B. 8
C. 2
D. 1

Solution

The modulus |z| = 4, as it is the coefficient in the polar form.

Correct Answer: A — 4

Q. What is the value of |z|^2 if z = 4 - 3i?

A. 25
B. 16
C. 7
D. 12

Solution

|z|^2 = 4^2 + (-3)^2 = 16 + 9 = 25.

Correct Answer: A — 25

Q. What is the van 't Hoff factor (i) for a strong electrolyte like NaCl in solution?

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

Solution

NaCl dissociates into two ions (Na+ and Cl-), so the van 't Hoff factor (i) is 2.

Correct Answer: B — 2

Q. What is the van 't Hoff factor (i) for a strong electrolyte that completely dissociates into 3 ions?

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

Solution

The van 't Hoff factor (i) is equal to the number of particles the solute dissociates into. For a strong electrolyte that dissociates into 3 ions, i = 3.

Correct Answer: C — 3

Q. What is the van 't Hoff factor (i) for glucose in solution?

A. 1
B. 2
C. 3
D. 0

Solution

The van 't Hoff factor (i) for glucose is 1, as it does not dissociate in solution.

Correct Answer: A — 1

Q. What is the van 't Hoff factor for a non-electrolyte solute?

A. 0
B. 1
C. 2
D. 3

Solution

For a non-electrolyte solute, the van 't Hoff factor (i) is 1, as it does not dissociate into ions.

Correct Answer: B — 1

Q. What is the vapor pressure of a solution containing 0.1 mol of a non-volatile solute in 1 kg of water? (Vapor pressure of pure water = 23.76 mmHg)

A. 22.88 mmHg
B. 21.76 mmHg
C. 20.76 mmHg
D. 19.76 mmHg

Solution

Vapor pressure = P°_solvent * (n_solvent / (n_solvent + n_solute)) = 23.76 * (55.5 / (55.5 + 0.1)) = 22.88 mmHg

Correct Answer: A — 22.88 mmHg

Q. What is the vapor pressure of a solution containing 1 mole of a non-volatile solute in 9 moles of solvent, if the vapor pressure of the pure solvent is 100 mmHg?

A. 90 mmHg
B. 100 mmHg
C. 10 mmHg
D. 80 mmHg

Solution

Using Raoult's law, P_solution = X_solvent * P°_solvent = (9/10) * 100 mmHg = 90 mmHg.

Correct Answer: A — 90 mmHg

Q. What is the vapor pressure of a solution containing 1 mole of a non-volatile solute in 10 moles of solvent, assuming ideal behavior?

A. 0.1 P0
B. 0.9 P0
C. 1.0 P0
D. 0.5 P0

Solution

Using Raoult's law, the vapor pressure of the solution = (moles of solvent / total moles) * P0 = (10 / 11) * P0 = 0.909 P0.

Correct Answer: B — 0.9 P0

Q. What is the vapor pressure of a solution containing 1 mole of a non-volatile solute in 3 moles of solvent, assuming ideal behavior?

A. 0.25 P0
B. 0.75 P0
C. 1.0 P0
D. 0.5 P0

Solution

Vapor pressure lowering = (moles of solute / total moles) * P0 = (1 / (1 + 3)) * P0 = 0.25 P0, so vapor pressure = P0 - 0.25 P0 = 0.75 P0.

Correct Answer: B — 0.75 P0

Q. What is the vapor pressure of a solution containing 1 mole of non-volatile solute in 3 moles of solvent if the vapor pressure of the pure solvent is 100 mmHg?

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

Solution

Using Raoult's law, P_solution = X_solvent * P°_solvent. X_solvent = 3/(1+3) = 0.75, so P_solution = 0.75 * 100 mmHg = 75 mmHg.

Correct Answer: A — 75 mmHg

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