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 n=4 and l=2, what is the type of orbital?

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

Solution

For l=2, the orbital type is d.

Correct Answer: C — d

Q. If one of the resistors in a Wheatstone bridge is replaced with a variable resistor, what is the effect on the balance condition?

A. It cannot be balanced
B. It can be balanced by adjusting the variable resistor
C. It will always be unbalanced
D. It will short-circuit the bridge

Solution

The variable resistor allows for adjustment to achieve balance in the bridge.

Correct Answer: B — It can be balanced by adjusting the variable resistor

Q. If one root of the equation x^2 - 3x + p = 0 is 2, what is the value of p?

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

Solution

Substituting x = 2 into the equation gives 2^2 - 3*2 + p = 0 => 4 - 6 + p = 0 => p = 2.

Correct Answer: D — 4

Q. If one root of the equation x^2 - 6x + k = 0 is 2, what is the value of k?

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

Solution

Using the root, we substitute: 2^2 - 6*2 + k = 0 => 4 - 12 + k = 0 => k = 8.

Correct Answer: A — 4

Q. If one root of the equation x^2 - 7x + k = 0 is 3, what is the value of k?

A. 6
B. 9
C. 12
D. 15

Solution

Using Vieta's formulas, if one root is 3, the other root is 7 - 3 = 4. Thus, k = 3 * 4 = 12.

Correct Answer: B — 9

Q. If R is a relation defined on set A = {1, 2, 3} such that R = {(1, 2), (2, 3)}, is R a function?

A. Yes
B. No
C. Depends on A
D. Not enough information

Solution

A relation is a function if every element in the domain (set A) maps to exactly one element in the codomain. Here, 1 maps to 2, and 2 maps to 3, but 3 has no mapping, so R is not a function.

Correct Answer: B — No

Q. If R is a relation on set A = {1, 2, 3} defined by R = {(1, 1), (2, 2), (3, 3)}, is R reflexive?

A. Yes
B. No
C. Depends on A
D. None of the above

Solution

A relation R is reflexive if every element in set A is related to itself. Since R contains (1, 1), (2, 2), and (3, 3), R is reflexive.

Correct Answer: A — Yes

Q. If R is a relation on set A = {1, 2, 3} defined by R = {(1, 1), (2, 2), (3, 3)}, is R symmetric?

A. Yes
B. No
C. Depends on A
D. None of the above

Solution

A relation is symmetric if for every (a, b) in R, (b, a) is also in R. Since R only contains pairs of the form (a, a), it is symmetric.

Correct Answer: A — Yes

Q. If R is a relation on set A = {1, 2, 3} defined by R = {(1, 2), (2, 3)}, is R transitive?

A. Yes
B. No
C. Not enough information
D. None of the above

Solution

A relation R is transitive if whenever (a, b) ∈ R and (b, c) ∈ R, then (a, c) must also be in R. Here, (1, 2) and (2, 3) are in R, but (1, 3) is not, so R is not transitive.

Correct Answer: B — No

Q. If R is a relation on the set A = {1, 2, 3} defined by R = {(1, 2), (2, 3), (3, 1)}, which of the following properties does R possess?

A. Reflexive
B. Symmetric
C. Transitive
D. All of the above

Solution

R is not reflexive as (1,1), (2,2), (3,3) are not in R. It is symmetric as (2,3) implies (3,2) is not in R. It is transitive as (1,2) and (2,3) implies (1,3) is not in R. Thus, R is not all of the above.

Correct Answer: C — Transitive

Q. If R is a relation on the set {1, 2, 3, 4} defined by R = {(1, 1), (2, 2), (3, 3), (4, 4), (1, 2), (2, 1)}, what type of relation is R?

A. Reflexive
B. Symmetric
C. Transitive
D. Both reflexive and symmetric

Solution

R is reflexive because it contains all pairs (a, a) and symmetric because (1,2) implies (2,1).

Correct Answer: D — Both reflexive and symmetric

Q. If R is a relation on the set {1, 2, 3} defined by R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)}, which of the following is true?

A. R is reflexive
B. R is symmetric
C. R is transitive
D. Both 1 and 2

Solution

R is reflexive and symmetric, but not transitive. Thus, both 1 and 2 are true.

Correct Answer: D — Both 1 and 2

Q. If R is a relation on the set {1, 2, 3} defined by R = {(1, 1), (2, 2), (3, 3), (1, 2)}, is R a partial order?

A. Yes
B. No
C. Only reflexive
D. Only transitive

Solution

R is not a partial order because it is not transitive; (1,2) and (2,2) do not imply (1,2).

Correct Answer: B — No

Q. If R is a relation on the set {a, b, c} defined by R = {(a, b), (b, c)}, what can be said about R?

A. Reflexive
B. Symmetric
C. Transitive
D. None of the above

Solution

R is neither reflexive, symmetric, nor transitive as it does not satisfy any of the properties.

Correct Answer: D — None of the above

Q. If R is a relation on the set {a, b, c} defined by R = {(a, b), (b, c)}, which property does R NOT have?

A. Reflexive
B. Symmetric
C. Transitive
D. None of the above

Solution

R is not symmetric as (b,c) does not imply (c,b) is in R. It is reflexive and transitive.

Correct Answer: B — Symmetric

Q. If R is a relation on the set {x, y, z} defined by R = {(x, y), (y, z), (z, x)}, what can be said about R?

A. Reflexive
B. Symmetric
C. Transitive
D. None of the above

Solution

R is neither reflexive, symmetric, nor transitive.

Correct Answer: D — None of the above

Q. If R1 = 10Ω, R2 = 15Ω, R3 = 5Ω, what should R4 be for the Wheatstone bridge to be balanced?

A. 7.5Ω
B. 10Ω
C. 12.5Ω
D. 15Ω

Solution

Using the balance condition R1/R2 = R3/R4, we find R4 = (R2 * R3) / R1 = (15 * 5) / 10 = 7.5Ω.

Correct Answer: C — 12.5Ω

Q. If R1 = 10Ω, R2 = 20Ω, and R3 = 30Ω in a Wheatstone bridge, what should R4 be for the bridge to be balanced?

A. 15Ω
B. 20Ω
C. 25Ω
D. 30Ω

Solution

For balance, R1/R2 = R3/R4, thus R4 = (R2 * R3) / R1 = (20 * 30) / 10 = 60Ω.

Correct Answer: B — 20Ω

Q. If R1 = 10Ω, R2 = 20Ω, R3 = 30Ω, and R4 = 60Ω in a Wheatstone bridge, is the bridge balanced?

A. Yes
B. No
C. Depends on the voltage
D. Depends on the current

Solution

The bridge is not balanced because 10/20 ≠ 30/60.

Correct Answer: B — No

Q. If R1 = 2Ω, R2 = 3Ω, and R3 = 6Ω in a Wheatstone bridge, what is the value of R4 for balance?

A. 4Ω
B. 5Ω
C. 6Ω
D. 9Ω

Solution

Using the balance condition R1/R2 = R3/R4, we have 2/3 = 6/R4. Solving gives R4 = 4Ω.

Correct Answer: A — 4Ω

Q. If R1 = 2Ω, R2 = 3Ω, and R3 = 6Ω, what is the value of R4 for the Wheatstone bridge to be balanced?

A. 4Ω
B. 5Ω
C. 6Ω
D. 8Ω

Solution

Using the balance condition R1/R2 = R3/R4, we have 2/3 = 6/R4. Solving gives R4 = 4Ω.

Correct Answer: A — 4Ω

Q. If R1 = 5Ω, R2 = 10Ω, and R3 = 15Ω in a Wheatstone bridge, what is the value of R4 for balance?

A. 7.5Ω
B. 10Ω
C. 15Ω
D. 20Ω

Solution

Using the balance condition R1/R2 = R3/R4, we find R4 = (R2 * R3) / R1 = (10 * 15) / 5 = 30Ω.

Correct Answer: B — 10Ω

Q. If R1 = 5Ω, R2 = 15Ω, R3 = 10Ω, what should R4 be for the Wheatstone bridge to be balanced?

A. 30Ω
B. 10Ω
C. 15Ω
D. 5Ω

Solution

For balance, R4 must be 30Ω since 5/15 = 10/30.

Correct Answer: B — 10Ω

Q. If sec A = 2, what is the value of cos A?

A. 1/2
B. 2
C. √2
D. 1

Solution

Since sec A = 1/cos A, we have cos A = 1/2.

Correct Answer: A — 1/2

Q. If sec θ = 2, what is the value of cos θ?

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

Solution

Since sec θ = 1/cos θ, if sec θ = 2, then cos θ = 1/2.

Correct Answer: A — 1/2

Q. If sec(x) = 2, what is the value of cos(x)?

A. 1/2
B. 2
C. √3/2
D. 1

Solution

sec(x) = 1/cos(x), so cos(x) = 1/2.

Correct Answer: A — 1/2

Q. If sin A = 0.6, what is cos A?

A. 0.8
B. 0.6
C. 0.4
D. 0.2

Solution

Using the identity sin^2 A + cos^2 A = 1, we have cos A = sqrt(1 - (0.6)^2) = sqrt(1 - 0.36) = sqrt(0.64) = 0.8.

Correct Answer: A — 0.8

Q. If sin A = 0.6, what is the value of cos A?

A. 0.8
B. 0.6
C. 0.4
D. 0.2

Solution

Using the identity sin^2 A + cos^2 A = 1, we have cos A = sqrt(1 - (0.6)^2) = sqrt(1 - 0.36) = sqrt(0.64) = 0.8.

Correct Answer: A — 0.8

Q. If sin A = 0.6, what is the value of tan A?

A. 0.8
B. 1.2
C. 0.75
D. 1.5

Solution

Using the identity tan A = sin A / cos A, we find cos A = sqrt(1 - (0.6)^2) = 0.8, thus tan A = 0.6 / 0.8 = 0.75.

Correct Answer: B — 1.2

Q. If sin A = 1/2, what are the possible values of A in the range [0°, 360°]?

A. 30°, 150°
B. 45°, 135°
C. 60°, 300°
D. 90°, 270°

Solution

sin A = 1/2 at A = 30° and A = 150°.

Correct Answer: A — 30°, 150°

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