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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 true value of a measurement is 50.0 units and the measured value is 48.0 units, what is the percentage error?

A. 4.0%
B. 2.0%
C. 5.0%
D. 3.0%

Solution

Percentage error = |(True value - Measured value) / True value| * 100 = |(50.0 - 48.0) / 50.0| * 100 = 4.0%.

Correct Answer: A — 4.0%

Q. If the true value of a quantity is 100 and the measured value is 98, what is the percentage error?

A. 2%
B. 1%
C. 3%
D. 0.5%

Solution

Percentage error = (|True value - Measured value| / True value) * 100 = (|100 - 98| / 100) * 100 = 2%.

Correct Answer: A — 2%

Q. If the true value of a quantity is 200 and the measured value is 198, what is the percentage error?

A. 1%
B. 0.5%
C. 2%
D. 0.25%

Solution

Percentage error = (|True value - Measured value| / True value) * 100 = (|200 - 198| / 200) * 100 = 1%.

Correct Answer: A — 1%

Q. If the universal set U = {1, 2, 3, 4, 5} and A = {1, 2}, what is A'?

A. {3, 4, 5}
B. {1, 2}
C. {1, 2, 3}
D. {2, 3, 4, 5}

Solution

The complement of A, denoted A', includes all elements in U that are not in A. Thus, A' = {3, 4, 5}.

Correct Answer: A — {3, 4, 5}

Q. If the value of one of the resistances in a Wheatstone bridge is doubled, what effect does it have on the balance condition?

A. It remains balanced
B. It becomes unbalanced
C. It depends on other resistances
D. It cannot be determined

Solution

Doubling one resistance will change the ratio, thus making the bridge unbalanced.

Correct Answer: B — It becomes unbalanced

Q. If the value of one of the resistances in a Wheatstone bridge is increased, what effect does it have on the balance of the bridge?

A. It remains balanced
B. It becomes unbalanced
C. It depends on the other resistances
D. It becomes short-circuited

Solution

Increasing one resistance will generally cause the bridge to become unbalanced.

Correct Answer: B — It becomes unbalanced

Q. If the vapor pressure of a pure solvent is 80 mmHg and a non-volatile solute is added, resulting in a vapor pressure of 60 mmHg, what is the mole fraction of the solvent in the solution?

A. 0.75
B. 0.50
C. 0.25
D. 0.80

Solution

Using Raoult's Law, P_solution = X_solvent * P_pure_solvent; 60 mmHg = X_solvent * 80 mmHg; X_solvent = 60/80 = 0.75.

Correct Answer: A — 0.75

Q. If the vapor pressure of a solution is 80 mmHg and the vapor pressure of the pure solvent is 120 mmHg, what is the mole fraction of the solvent in the solution?

A. 0.67
B. 0.33
C. 0.50
D. 0.75

Solution

Using Raoult's Law, P_solution = X_solvent * P_solvent^0; 80 = X_solvent * 120; X_solvent = 80/120 = 0.67.

Correct Answer: A — 0.67

Q. If the vapor pressure of pure solvent A is 100 mmHg, and the mole fraction of A in the solution is 0.6, what is the vapor pressure of the solution according to Raoult's Law?

A. 60 mmHg
B. 100 mmHg
C. 40 mmHg
D. 80 mmHg

Solution

Using Raoult's Law, P_solution = X_A * P_A^0 = 0.6 * 100 mmHg = 60 mmHg.

Correct Answer: A — 60 mmHg

Q. If the vapor pressure of pure solvent A is 100 mmHg, and the mole fraction of A in the solution is 0.5, what is the vapor pressure of the solution according to Raoult's Law?

A. 50 mmHg
B. 100 mmHg
C. 150 mmHg
D. 200 mmHg

Solution

According to Raoult's Law, P_solution = X_A * P_A^0 = 0.5 * 100 mmHg = 50 mmHg.

Correct Answer: A — 50 mmHg

Q. If the vapor pressure of pure solvent A is 100 mmHg, what is the vapor pressure of a solution containing 0.5 mole fraction of A?

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

Solution

According to Raoult's Law, the vapor pressure of the solution is 0.5 * 100 mmHg = 50 mmHg.

Correct Answer: A — 50 mmHg

Q. If the vapor pressure of pure solvent is 120 mmHg, what will be the vapor pressure of a solution containing 0.2 moles of solute in 1 mole of solvent?

A. 100 mmHg
B. 110 mmHg
C. 120 mmHg
D. 80 mmHg

Solution

Using Raoult's Law, the vapor pressure of the solution is P_solution = P_solvent * X_solvent = 120 * (1/(1+0.2)) = 120 * (1/1.2) = 100 mmHg.

Correct Answer: B — 110 mmHg

Q. If the vapor pressure of pure solvent is 80 mmHg and the mole fraction of the solvent in the solution is 0.75, what is the vapor pressure of the solution?

A. 60 mmHg
B. 80 mmHg
C. 75 mmHg
D. 20 mmHg

Solution

Using Raoult's Law, P_solution = X_solvent * P_solvent^0 = 0.75 * 80 mmHg = 60 mmHg.

Correct Answer: A — 60 mmHg

Q. If the vapor pressure of pure water is 23.8 mmHg at 25°C, what is the vapor pressure of a solution containing 1 mole of NaCl in 1 kg of water?

A. 20.0 mmHg
B. 22.0 mmHg
C. 23.0 mmHg
D. 23.8 mmHg

Solution

Using Raoult's law, the vapor pressure lowering is calculated considering the van 't Hoff factor for NaCl.

Correct Answer: B — 22.0 mmHg

Q. If the variance of a data set is 16, what is the standard deviation?

A. 4
B. 8
C. 16
D. 2

Solution

Standard deviation = √variance = √16 = 4.

Correct Answer: A — 4

Q. If the vector A = (1, 2) and B = (2, 1), what is the angle between them?

A. 0 degrees
B. 90 degrees
C. 45 degrees
D. 180 degrees

Solution

Cosine of angle = (A · B) / (|A| |B|) = (1*2 + 2*1) / (√5 * √5) = 4/5, angle = cos^(-1)(4/5).

Correct Answer: C — 45 degrees

Q. If the vector a = (1, 2) and b = (3, 4), find the angle between them using the dot product.

A. 0 degrees
B. 90 degrees
C. 45 degrees
D. 60 degrees

Solution

cos(θ) = (a · b) / (|a| |b|). a · b = 1*3 + 2*4 = 11, |a| = √(1^2 + 2^2) = √5, |b| = √(3^2 + 4^2) = 5. Thus, cos(θ) = 11 / (√5 * 5) = 11 / (5√5), θ = 60 degrees.

Correct Answer: D — 60 degrees

Q. If the vector a = (2, -1) and b = (1, 3), what is a + b?

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

Solution

a + b = (2 + 1, -1 + 3) = (3, 2)

Correct Answer: A — (3, 2)

Q. If the vector a = (2, -1) and b = (1, 3), what is the cross product a × b?

A. 5
B. 7
C. 1
D. 0

Solution

Cross product in 2D = a1*b2 - a2*b1 = 2*3 - (-1)*1 = 6 + 1 = 7

Correct Answer: A — 5

Q. If the vector a = (2, 2) and b = (2, -2), what is the angle between them?

A. 90 degrees
B. 45 degrees
C. 0 degrees
D. 180 degrees

Solution

Angle = cos⁻¹((a·b) / (|a||b|)) = cos⁻¹(0) = 90 degrees

Correct Answer: A — 90 degrees

Q. If the vector a = (2, 2) is scaled by a factor of 3, what is the resulting vector?

A. (6, 6)
B. (3, 3)
C. (2, 2)
D. (1, 1)

Solution

Scaled vector = 3 * a = 3 * (2, 2) = (6, 6)

Correct Answer: A — (6, 6)

Q. If the vector a = (2, 3) and b = (4, 1), what is the cross product a × b?

A. -10
B. 10
C. 0
D. 5

Solution

Cross product a × b = 2*1 - 3*4 = 2 - 12 = -10.

Correct Answer: A — -10

Q. If the vector a = (2, 3) and b = (4, 1), what is the resultant vector a + b?

A. (6, 4)
B. (2, 4)
C. (4, 2)
D. (6, 2)

Solution

Resultant vector a + b = (2+4, 3+1) = (6, 4).

Correct Answer: A — (6, 4)

Q. If the vector A = (2, 3) is multiplied by 2, what is the resulting vector?

A. (4, 6)
B. (2, 3)
C. (1, 1.5)
D. (0, 0)

Solution

Resulting vector = 2 * A = 2 * (2, 3) = (4, 6).

Correct Answer: A — (4, 6)

Q. If the vector A = (2, 3) is reflected across the line y = x, what is the resulting vector?

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

Solution

Reflection across y = x gives vector (3, 2).

Correct Answer: A — (3, 2)

Q. If the vector A = (2, 3) is scaled by a factor of 2, what is the resulting vector?

A. (4, 6)
B. (2, 3)
C. (1, 1.5)
D. (0, 0)

Solution

Scaled vector = 2 * A = 2 * (2, 3) = (4, 6).

Correct Answer: A — (4, 6)

Q. If the vector a = (2, 3, 4) and b = (1, 0, -1), what is a + b?

A. (3, 3, 3)
B. (1, 3, 3)
C. (2, 3, 3)
D. (2, 3, 5)

Solution

a + b = (2+1, 3+0, 4-1) = (3, 3, 3).

Correct Answer: A — (3, 3, 3)

Q. If the vector a = (2, 3, 4) and b = (1, 0, -1), what is the scalar triple product a · (b × a)?

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

Solution

The scalar triple product is 0 because a · (b × a) = 0.

Correct Answer: A — 0

Q. If the vector a = (2, 3, 4) is scaled by a factor of 2, what is the resulting vector?

A. (4, 6, 8)
B. (2, 3, 4)
C. (1, 1.5, 2)
D. (0, 0, 0)

Solution

Scaling the vector a by 2 gives (2*2, 2*3, 2*4) = (4, 6, 8).

Correct Answer: A — (4, 6, 8)

Q. If the vector a = (3, 4) and b = (1, 2), find the cross product a × b.

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

Solution

In 2D, a × b = a1*b2 - a2*b1 = 3*2 - 4*1 = 6 - 4 = 2.

Correct Answer: A — -2

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