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. Calculate the integral ∫ (x^2 + 2x + 1) dx.

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

Solution

The integral of x^2 is (1/3)x^3, the integral of 2x is x^2, and the integral of 1 is x. Thus, ∫ (x^2 + 2x + 1) dx = (1/3)x^3 + x^2 + x + C.

Correct Answer: A — (1/3)x^3 + x^2 + x + C

Q. Calculate the integral ∫ (x^2 + 2x + 1)/(x + 1) dx.

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

Solution

The integrand simplifies to x + 1. Therefore, ∫ (x + 1) dx = (1/2)x^2 + x + C.

Correct Answer: A — (1/3)x^3 + x^2 + C

Q. Calculate the integral ∫ (x^3 - 4x) dx.

A. (1/4)x^4 - 2x^2 + C
B. (1/4)x^4 - 2x^2
C. (1/4)x^4 - 4x^2 + C
D. (1/4)x^4 - 2x^2 + 1

Solution

The integral of x^3 is (1/4)x^4 and the integral of -4x is -2x^2. Therefore, ∫ (x^3 - 4x) dx = (1/4)x^4 - 2x^2 + C.

Correct Answer: A — (1/4)x^4 - 2x^2 + C

Q. Calculate the integral ∫ cos^2(x) dx.

A. (1/2)x + (1/4)sin(2x) + C
B. (1/2)x + C
C. (1/2)x - (1/4)sin(2x) + C
D. (1/2)x + (1/2)sin(2x) + C

Solution

Using the identity cos^2(x) = (1 + cos(2x))/2, we find that ∫ cos^2(x) dx = (1/2)x + (1/4)sin(2x) + C.

Correct Answer: A — (1/2)x + (1/4)sin(2x) + C

Q. Calculate the integral ∫ from 0 to π of sin(x) dx.

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

Solution

The integral evaluates to [-cos(x)] from 0 to π = [1 - (-1)] = 2.

Correct Answer: C — 2

Q. Calculate the interquartile range (IQR) for the data set: 1, 3, 7, 8, 9, 10.

A. 4
B. 5
C. 6
D. 7

Solution

Q1 = 3, Q3 = 9; IQR = Q3 - Q1 = 9 - 3 = 6.

Correct Answer: A — 4

Q. Calculate the limit: lim (x -> 0) (1 - cos(x))/(x^2)

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

Solution

Using the identity 1 - cos(x) = 2sin^2(x/2), we have lim (x -> 0) (2sin^2(x/2))/(x^2) = 1.

Correct Answer: B — 1/2

Q. Calculate the limit: lim (x -> 0) (e^x - 1)/x

A. 0
B. 1
C. Infinity
D. Undefined

Solution

Using the definition of the derivative of e^x at x = 0, we find that lim (x -> 0) (e^x - 1)/x = e^0 = 1.

Correct Answer: B — 1

Q. Calculate the limit: lim (x -> 0) (tan(3x)/x)

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

Solution

Using the standard limit lim (x -> 0) (tan(kx)/x) = k, we have k = 3, so the limit is 3.

Correct Answer: A — 3

Q. Calculate the limit: lim (x -> 1) (x^2 - 1)/(x - 1)

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

Solution

This is an indeterminate form (0/0). Factor the numerator: (x-1)(x+1)/(x-1) = x + 1. Thus, lim (x -> 1) (x + 1) = 2.

Correct Answer: C — 2

Q. Calculate the limit: lim (x -> 1) (x^2 - 1)/(x - 1)^2

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

Solution

Factoring gives (x - 1)(x + 1)/(x - 1)^2 = (x + 1)/(x - 1). Thus, lim (x -> 1) (x + 1)/(x - 1) = 2.

Correct Answer: C — 2

Q. Calculate the limit: lim (x -> 1) (x^3 - 1)/(x - 1)

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

Solution

Factoring gives (x - 1)(x^2 + x + 1)/(x - 1). Canceling (x - 1) gives lim (x -> 1) (x^2 + x + 1) = 3.

Correct Answer: C — 3

Q. Calculate the limit: lim (x -> 2) (x^2 - 2x)/(x - 2)

A. 0
B. 2
C. 4
D. Undefined

Solution

Factoring gives (x(x - 2))/(x - 2), canceling gives lim (x -> 2) x = 2.

Correct Answer: D — Undefined

Q. Calculate the mean absolute deviation for the data set: 1, 2, 3, 4, 5.

A. 1
B. 1.5
C. 2
D. 2.5

Solution

Mean = 3. Mean Absolute Deviation = (|1-3| + |2-3| + |3-3| + |4-3| + |5-3|)/5 = (2 + 1 + 0 + 1 + 2)/5 = 1.5.

Correct Answer: B — 1.5

Q. Calculate the mean of the following data: 5, 10, 15, 20.

A. 10
B. 12.5
C. 15
D. 17.5

Solution

Mean = (5 + 10 + 15 + 20) / 4 = 50 / 4 = 12.5.

Correct Answer: B — 12.5

Q. Calculate the mean of the following numbers: 10, 20, 30, 40, 50.

A. 30
B. 35
C. 40
D. 45

Solution

Mean = (10 + 20 + 30 + 40 + 50) / 5 = 150 / 5 = 30.

Correct Answer: A — 30

Q. Calculate the mean of the following numbers: 4, 8, 12, 16, 20.

A. 10
B. 12
C. 14
D. 16

Solution

Mean = (4 + 8 + 12 + 16 + 20) / 5 = 60 / 5 = 12.

Correct Answer: C — 14

Q. Calculate the molality of a solution if the boiling point elevation is 1.024 °C. (K_b for water = 0.512 °C kg/mol)

A. 1 mol/kg
B. 2 mol/kg
C. 0.5 mol/kg
D. 0.25 mol/kg

Solution

Molality = ΔT_b / (i * K_b) = 1.024 / (2 * 0.512) = 1 mol/kg

Correct Answer: B — 2 mol/kg

Q. Calculate the moment of inertia of a hollow sphere of mass M and radius R about an axis through its center.

A. 2/5 MR^2
B. 3/5 MR^2
C. 2/3 MR^2
D. MR^2

Solution

The moment of inertia of a hollow sphere about an axis through its center is I = 2/5 MR^2.

Correct Answer: B — 3/5 MR^2

Q. Calculate the pH of a 0.1 M acetic acid solution (Ka = 1.8 x 10^-5).

A. 2.87
B. 3.87
C. 4.87
D. 5.87

Solution

Using the formula for weak acids, pH = 0.5(pKa - log[C]), where pKa = -log(1.8 x 10^-5) ≈ 4.74. Thus, pH = 0.5(4.74 - log(0.1)) = 3.87.

Correct Answer: B — 3.87

Q. Calculate the pH of a buffer solution containing 0.1 M acetic acid and 0.1 M sodium acetate.

A. 4.76
B. 5.76
C. 6.76
D. 7.76

Solution

Using Henderson-Hasselbalch equation: pH = pKa + log([A-]/[HA]); pKa of acetic acid = 4.76, so pH = 4.76 + log(1) = 4.76

Correct Answer: B — 5.76

Q. Calculate the pH of a solution that is 0.1 M in acetic acid (Ka = 1.8 x 10^-5).

A. 2.87
B. 3.87
C. 4.87
D. 5.87

Solution

Using the formula for weak acids, pH = 0.5(pKa - logC) = 0.5(4.74 - log(0.1)) = 3.87.

Correct Answer: B — 3.87

Q. Calculate the range of the data set: 12, 15, 22, 30, 5.

A. 25
B. 27
C. 30
D. 22

Solution

Range = Maximum - Minimum = 30 - 5 = 25.

Correct Answer: A — 25

Q. Calculate the range of the data set: 4, 8, 15, 16, 23, 42.

A. 38
B. 36
C. 34
D. 32

Solution

Range = Maximum - Minimum = 42 - 4 = 38.

Correct Answer: A — 38

Q. Calculate the range of the data set: 8, 12, 15, 20, 22.

A. 10
B. 12
C. 14
D. 15

Solution

Range = Max - Min = 22 - 8 = 14.

Correct Answer: A — 10

Q. Calculate the range of the following data set: 12, 15, 20, 22, 30.

A. 10
B. 12
C. 18
D. 20

Solution

Range = Maximum - Minimum = 30 - 12 = 18.

Correct Answer: C — 18

Q. Calculate the range of the following data set: 15, 22, 8, 19, 30.

A. 7
B. 15
C. 22
D. 30

Solution

Range = max - min = 30 - 8 = 22.

Correct Answer: D — 30

Q. Calculate the range of the following data set: 4, 8, 15, 16, 23, 42.

A. 38
B. 36
C. 34
D. 32

Solution

Range = Maximum - Minimum = 42 - 4 = 38.

Correct Answer: A — 38

Q. Calculate the range of the following data set: 8, 12, 15, 7, 10.

A. 5
B. 8
C. 10
D. 12

Solution

Range = Maximum - Minimum = 15 - 7 = 8.

Correct Answer: A — 5

Q. Calculate the RMS speed of a gas with molar mass 0.028 kg/mol at 300 K. (R = 8.314 J/(mol K))

A. 500 m/s
B. 600 m/s
C. 700 m/s
D. 800 m/s

Solution

Using v_rms = sqrt(3RT/M), we find v_rms = sqrt(3 * 8.314 * 300 / 0.028) = 600 m/s.

Correct Answer: B — 600 m/s

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