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 standard entropy change (ΔS°) for the reaction: 2SO2(g) + O2(g) → 2SO3(g)?

A. Increases
B. Decreases
C. Remains constant
D. Cannot be determined

Solution

The reaction decreases the number of gas molecules from 3 to 2, leading to a decrease in entropy.

Correct Answer: B — Decreases

Q. What is the standard form of the equation of a parabola that opens upwards with vertex at the origin?

A. y^2 = 4ax
B. x^2 = 4ay
C. y^2 = -4ax
D. x^2 = -4ay

Solution

The standard form of a parabola that opens upwards is given by x^2 = 4ay.

Correct Answer: B — x^2 = 4ay

Q. What is the standard Gibbs Free Energy change (ΔG°) for a reaction at standard conditions?

A. Always zero
B. Depends on the reaction
C. Is a constant value
D. Is always positive

Solution

ΔG° depends on the specific reaction and its conditions.

Correct Answer: B — Depends on the reaction

Q. What is the standard molar entropy of a substance?

A. Entropy at 0 K
B. Entropy at 25 °C and 1 atm
C. Entropy at boiling point
D. Entropy at melting point

Solution

Standard molar entropy is defined as the entropy of 1 mole of a substance at 25 °C and 1 atm pressure.

Correct Answer: B — Entropy at 25 °C and 1 atm

Q. What is the standard state of a substance?

A. The most stable form at 1 atm and 25°C
B. Any form of the substance
C. The gaseous form only
D. The liquid form only

Solution

The standard state of a substance is defined as its most stable form at 1 atm pressure and 25°C.

Correct Answer: A — The most stable form at 1 atm and 25°C

Q. What is the standard unit of temperature in the SI system?

A. Celsius
B. Fahrenheit
C. Kelvin
D. Rankine

Solution

The standard unit of temperature in the SI system is Kelvin (K).

Correct Answer: C — Kelvin

Q. What is the Stefan-Boltzmann law related to?

A. Conduction
B. Convection
C. Radiation
D. Thermal expansion

Solution

The Stefan-Boltzmann law states that the total energy radiated per unit surface area of a black body is proportional to the fourth power of its absolute temperature.

Correct Answer: C — Radiation

Q. What is the structural formula for 2-methylpropane?

A. CH3-CH2-CH(CH3)-CH3
B. CH3-CH(CH3)-CH2-CH3
C. CH3-CH2-CH2-CH3
D. CH3-CH2-CH(CH2)-CH3

Solution

The structural formula for 2-methylpropane is CH3-CH(CH3)-CH2-CH3.

Correct Answer: B — CH3-CH(CH3)-CH2-CH3

Q. What is the structural formula for hexane?

A. C6H14
B. C5H12
C. C4H10
D. C3H8

Solution

The structural formula for hexane is C6H14.

Correct Answer: A — C6H14

Q. What is the structural formula of 2-methylpropane?

A. CH3-CH2-CH(CH3)-CH3
B. CH3-CH(CH3)-CH2-CH3
C. CH3-CH2-CH2-CH3
D. CH3-CH2-CH(CH2)-CH3

Solution

The structural formula of 2-methylpropane is CH3-CH(CH3)-CH2-CH3.

Correct Answer: B — CH3-CH(CH3)-CH2-CH3

Q. What is the structural formula of propane?

A. C3H8
B. C2H6
C. C4H10
D. C5H12

Solution

The structural formula of propane is C3H8, indicating three carbon atoms.

Correct Answer: A — C3H8

Q. What is the structure of DNA?

A. Single-stranded
B. Double helix
C. Triple helix
D. Linear

Solution

DNA has a double helix structure, consisting of two strands that coil around each other.

Correct Answer: B — Double helix

Q. What is the sum of the coefficients in the expansion of (2 + 3x)^4?

A. 81
B. 64
C. 100
D. 125

Solution

The sum of the coefficients is found by substituting x = 1: (2 + 3*1)^4 = 5^4 = 625.

Correct Answer: A — 81

Q. What is the sum of the coefficients in the expansion of (x + 1)^5?

A. 5
B. 6
C. 31
D. 32

Solution

The sum of the coefficients is found by substituting x = 1, so (1 + 1)^5 = 2^5 = 32.

Correct Answer: D — 32

Q. What is the sum of the coefficients in the expansion of (x + 1)^7?

A. 128
B. 64
C. 32
D. 16

Solution

The sum of the coefficients is found by substituting x = 1, giving (1 + 1)^7 = 2^7 = 128.

Correct Answer: A — 128

Q. What is the sum of the complex numbers 2 + 3i and 4 - 5i?

A. 6 - 2i
B. 6 + 2i
C. 2 - 2i
D. 2 + 2i

Solution

The sum is (2 + 4) + (3 - 5)i = 6 - 2i.

Correct Answer: A — 6 - 2i

Q. What is the sum of the first 5 natural numbers?

A. 10
B. 15
C. 20
D. 25

Solution

Sum = 1 + 2 + 3 + 4 + 5 = 15.

Correct Answer: B — 15

Q. What is the sum of the first 5 terms of the series 1, 1/2, 1/4, ...?

A. 1.5
B. 2
C. 1
D. 3

Solution

S_5 = 1 + 1/2 + 1/4 + 1/8 + 1/16 = 1.5.

Correct Answer: A — 1.5

Q. What is the sum of the first 6 terms of the arithmetic series 10, 15, 20, ...?

A. 90
B. 100
C. 110
D. 120

Solution

The sum S_n = n/2 * (2a + (n-1)d) = 6/2 * (2*10 + 5*5) = 3 * (20 + 25) = 135.

Correct Answer: A — 90

Q. What is the sum of the first n terms of the arithmetic series 2, 5, 8, ...?

A. n/2 * (2 + (n-1) * 3)
B. n * (2 + 3n)/2
C. 3n^2/2 + n/2
D. n * (n + 1)

Solution

The first term a = 2, common difference d = 3. The sum of the first n terms S_n = n/2 * (2a + (n-1)d) = n/2 * (2 + (n-1) * 3).

Correct Answer: A — n/2 * (2 + (n-1) * 3)

Q. What is the sum of the infinite geometric series 1 + 1/2 + 1/4 + ...?

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

Solution

The sum S = a/(1 - r) = 1/(1 - 1/2) = 1/(1/2) = 2.

Correct Answer: A — 2

Q. What is the sum of the roots of the equation 2x^2 - 3x + 1 = 0?

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

Solution

The sum of the roots is given by -b/a = 3/2.

Correct Answer: B — 3/2

Q. What is the sum of the roots of the equation 2x^2 - 4x + 1 = 0?

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

Solution

The sum of the roots is given by -b/a = 4/2 = 2.

Correct Answer: B — 1

Q. What is the sum of the roots of the equation 3x^2 - 12x + 9 = 0?

A. 3
B. 4
C. 6
D. 9

Solution

Using Vieta's formulas, the sum of the roots is -(-12)/3 = 4.

Correct Answer: B — 4

Q. What is the sum of the roots of the equation f(x) = x^2 - 5x + 6?

A. 5
B. 6
C. 10
D. 3

Solution

The sum of the roots of ax^2 + bx + c = 0 is -b/a. Here, sum = 5.

Correct Answer: A — 5

Q. What is the sum of the roots of the equation x^2 - 4x + 3 = 0?

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

Solution

The sum of the roots is given by -b/a = 4/1 = 4.

Correct Answer: D — 4

Q. What is the sum of the roots of the quadratic equation f(x) = x^2 - 5x + 6?

A. 5
B. 6
C. 10
D. 3

Solution

The sum of the roots is given by -b/a = 5/1 = 5.

Correct Answer: A — 5

Q. What is the sum of the roots of the quadratic equation x^2 - 4x + 3 = 0?

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

Solution

The sum of the roots is given by -b/a = 4/1 = 4.

Correct Answer: D — 4

Q. What is the sum of the roots of the quadratic equation x^2 - 5x + 6 = 0?

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

Solution

The sum of the roots is given by -b/a = 5/1 = 5.

Correct Answer: A — 5

Q. What is the sum of the roots of the quadratic equation x^2 - 7x + 10 = 0?

A. 5
B. 6
C. 7
D. 8

Solution

The sum of the roots is given by -b/a = 7/1 = 7.

Correct Answer: C — 7

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