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. The quadratic equation x^2 + 6x + 9 = 0 has roots that are:

A. Real and equal
B. Real and distinct
C. Complex
D. None of these

Solution

The discriminant is 0, hence the roots are real and equal.

Correct Answer: A — Real and equal

Q. The quadratic equation x^2 + kx + 16 = 0 has equal roots. What is the value of k?

A. -8
B. -4
C. 4
D. 8

Solution

For equal roots, the discriminant must be zero: k^2 - 4*1*16 = 0, solving gives k = -8.

Correct Answer: A — -8

Q. The quadratic equation x^2 + px + q = 0 has roots 3 and -2. What is the value of p?

A. 1
B. 5
C. -1
D. -5

Solution

Using the sum of roots: p = -(3 + (-2)) = -1.

Correct Answer: B — 5

Q. The quadratic equation x^2 - 3x + 2 = 0 can be factored as?

A. (x-1)(x-2)
B. (x-2)(x-1)
C. (x+1)(x+2)
D. (x-3)(x+2)

Solution

The equation factors to (x-1)(x-2) = 0.

Correct Answer: A — (x-1)(x-2)

Q. The quadratic equation x^2 - 4x + 4 = 0 has how many distinct real roots?

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

Solution

The discriminant is 0, indicating one distinct real root.

Correct Answer: B — 1

Q. The quadratic equation x^2 - 6x + 9 = 0 has how many distinct real roots?

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

Solution

The discriminant is 0, indicating that there is exactly one distinct real root.

Correct Answer: B — 1

Q. The quadratic equation x^2 - 6x + k = 0 has roots that are both positive. What is the condition on k?

A. k > 0
B. k < 0
C. k > 9
D. k < 9

Solution

For both roots to be positive, k must be greater than the square of half the coefficient of x: k > (6/2)^2 = 9.

Correct Answer: C — k > 9

Q. The quadratic equation x^2 - 6x + k = 0 has roots that differ by 2. What is the value of k?

A. 8
B. 10
C. 12
D. 14

Solution

Let the roots be r and r+2. Then, r + (r+2) = 6 and r(r+2) = k. Solving gives k = 10.

Correct Answer: B — 10

Q. The range of sin^(-1)(x) is:

A. [-π/2, π/2]
B. [0, π]
C. [-1, 1]
D. [0, 1]

Solution

The range of sin^(-1)(x) is [-π/2, π/2].

Correct Answer: A — [-π/2, π/2]

Q. The range of the data set 1, 3, 5, 7, 9 is:

A. 8
B. 6
C. 4
D. 2

Solution

Range = Maximum - Minimum = 9 - 1 = 8.

Correct Answer: A — 8

Q. The range of the data set {10, 15, 20, 25, 30} is?

A. 15
B. 20
C. 25
D. 30

Solution

Range = Maximum value - Minimum value = 30 - 10 = 20.

Correct Answer: A — 15

Q. The range of the function f(x) = |x - 1| is:

A. (-∞, 1)
B. [0, ∞)
C. (-1, 1)
D. [1, ∞)

Solution

The absolute value function has a minimum value of 0, hence the range is [0, ∞).

Correct Answer: B — [0, ∞)

Q. The range of the function y = sin^(-1)(x) is:

A. (0, π)
B. [-π/2, π/2]
C. [-1, 1]
D. [0, 1]

Solution

The range of y = sin^(-1)(x) is [-π/2, π/2].

Correct Answer: B — [-π/2, π/2]

Q. The rate law for a reaction is determined experimentally and is dependent on which of the following?

A. Stoichiometry of the reaction
B. Mechanism of the reaction
C. Equilibrium constant
D. Temperature only

Solution

The rate law for a reaction is determined experimentally and is dependent on the mechanism of the reaction.

Correct Answer: B — Mechanism of the reaction

Q. The rate law for a reaction is determined experimentally. Which of the following is true?

A. It can be derived from stoichiometry
B. It is always first-order
C. It depends on the mechanism
D. It is independent of temperature

Solution

The rate law for a reaction depends on the mechanism of the reaction.

Correct Answer: C — It depends on the mechanism

Q. The rate law for a reaction is given as rate = k[A][B]². What is the overall order of the reaction?

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

Solution

The overall order of the reaction is the sum of the powers of the concentration terms, which is 1 + 2 = 3.

Correct Answer: C — 3

Q. The rate of a reaction doubles when the temperature is increased by 10°C. This is an example of which rule?

A. Arrhenius equation
B. Van 't Hoff rule
C. Le Chatelier's principle
D. Gibbs free energy

Solution

This is an example of Van 't Hoff rule, which states that the rate of reaction doubles for every 10°C increase in temperature.

Correct Answer: B — Van 't Hoff rule

Q. The rate of a reaction is defined as the change in concentration of a reactant or product per unit time. What is the unit of rate?

A. mol/L
B. mol/L·s
C. L/mol·s
D. 1/s

Solution

The rate of reaction is expressed in terms of concentration change per unit time, hence the unit is mol/L·s.

Correct Answer: B — mol/L·s

Q. The rate of a reaction is directly proportional to the product of the concentrations of the reactants raised to their respective powers. This is known as what?

A. Rate law
B. Equilibrium constant
C. Reaction quotient
D. Catalytic law

Solution

This relationship is known as the rate law of the reaction.

Correct Answer: A — Rate law

Q. The rate of heat transfer by conduction is directly proportional to the area and the temperature gradient. This is described by which law?

A. Newton's Law of Cooling
B. Fourier's Law of Heat Conduction
C. Stefan-Boltzmann Law
D. Ohm's Law

Solution

Fourier's Law of Heat Conduction states that the rate of heat transfer by conduction is directly proportional to the area and the temperature gradient.

Correct Answer: B — Fourier's Law of Heat Conduction

Q. The rate of heat transfer by conduction is directly proportional to which of the following?

A. Temperature difference
B. Surface area
C. Material thickness
D. All of the above

Solution

The rate of heat transfer by conduction is directly proportional to the temperature difference between the two ends.

Correct Answer: A — Temperature difference

Q. The real part of the complex number z = 4 - 3i is?

A. 4
B. -3
C. 3
D. 0

Solution

The real part of z = 4 - 3i is 4.

Correct Answer: A — 4

Q. The restoring force in a simple harmonic motion is directly proportional to:

A. Displacement
B. Velocity
C. Time
D. Mass

Solution

Restoring force F = -kx, where k is the spring constant and x is the displacement.

Correct Answer: A — Displacement

Q. The right-hand rule is used to determine the direction of?

A. Magnetic field
B. Current
C. Force
D. All of the above

Solution

The right-hand rule can be used to determine the direction of the magnetic field, current, and force in electromagnetic situations.

Correct Answer: D — All of the above

Q. The RMS speed of a gas is 250 m/s. What is the kinetic energy per molecule of the gas?

A. 0.5 * m * (250)^2
B. 0.25 * m * (250)^2
C. 0.75 * m * (250)^2
D. 1.5 * m * (250)^2

Solution

The kinetic energy per molecule is given by KE = (1/2) * m * v^2. Thus, KE = 0.5 * m * (250)^2.

Correct Answer: A — 0.5 * m * (250)^2

Q. The RMS speed of a gas is 300 m/s. What is the speed of sound in the gas if the ratio of specific heats is 1.4?

A. 300 m/s
B. 400 m/s
C. 500 m/s
D. 600 m/s

Solution

Speed of sound = sqrt(γRT/M) = sqrt(1.4 * (300^2)) = 400 m/s.

Correct Answer: B — 400 m/s

Q. The RMS speed of a gas is 400 m/s. What is the speed of sound in the gas if the ratio of specific heats is 1.4?

A. 400 m/s
B. 560 m/s
C. 700 m/s
D. 800 m/s

Solution

The speed of sound in a gas is given by c = sqrt(γRT/M). For an ideal gas, c is approximately 1.4 times the RMS speed.

Correct Answer: B — 560 m/s

Q. The roots of the equation 2x^2 - 4x + 1 = 0 are:

A. 1
B. 2
C. 1/2
D. None of these

Solution

Using the quadratic formula, x = [4 ± √(16 - 8)] / 4 = [4 ± 2√2] / 4 = 1 ± √2/2. Hence, the roots are not simple fractions.

Correct Answer: C — 1/2

Q. The roots of the equation 2x^2 - 4x + k = 0 are 1 and 2. Find the value of k.

A. 2
B. 4
C. 6
D. 8

Solution

Using Vieta's formulas, sum of roots = 1 + 2 = 3 = -(-4)/2 => k = 2*1*2 = 4.

Correct Answer: C — 6

Q. The roots of the equation 5x^2 - 20x + 15 = 0 are:

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

Solution

Using the quadratic formula, the roots are x = [20 ± √(400 - 300)] / 10 = [20 ± 10] / 10 = 3 and 1.

Correct Answer: B — 2

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