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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. For an ideal gas, which of the following equations is correct?

A. PV = nRT
B. PV = nR/T
C. PV = nT/R
D. PV = nRT^2

Solution

The ideal gas law is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature.

Correct Answer: A — PV = nRT

Q. For an ideal gas, which of the following is true at constant temperature?

A. PV = nRT
B. P1V1 = P2V2
C. P/T = constant
D. V/T = constant

Solution

At constant temperature, Boyle's law states that the product of pressure and volume (PV) is constant, hence P1V1 = P2V2.

Correct Answer: B — P1V1 = P2V2

Q. For an ideal solution, if the mole fraction of the solvent is 0.75, what is the vapor pressure of the solution if the vapor pressure of the pure solvent is 100 mmHg?

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

Solution

According to Raoult's Law, the vapor pressure of the solution is 0.75 * 100 mmHg = 75 mmHg.

Correct Answer: A — 75 mmHg

Q. For an infinite plane sheet of charge with surface charge density σ, what is the electric field at any point?

A. σ/2ε₀
B. σ/ε₀
C. 0
D. σ/4πε₀

Solution

The electric field due to an infinite plane sheet of charge is constant and given by E = σ/2ε₀ on either side of the sheet.

Correct Answer: A — σ/2ε₀

Q. For an infinite plane sheet of charge with surface charge density σ, what is the electric field at a point near the sheet?

A. σ/2ε₀
B. σ/ε₀
C. 0
D. σ/4πε₀

Solution

Using Gauss's law, the electric field due to an infinite plane sheet of charge is E = σ/2ε₀ on either side of the sheet.

Correct Answer: A — σ/2ε₀

Q. For destructive interference to occur in a thin film, the path difference must be equal to:

A. nλ/2 (n is an integer)
B. nλ (n is an integer)
C. λ/4
D. λ/2

Solution

Destructive interference occurs when the path difference is an odd multiple of λ/2 (i.e., (2n+1)λ/2).

Correct Answer: A — nλ/2 (n is an integer)

Q. For f(x) = { x^2, x < 1; 2x - 1, x ≥ 1 }, is f differentiable at x = 1?

A. Yes
B. No
C. Only left
D. Only right

Solution

f'(1) from left = 2, from right = 2; hence f is differentiable at x = 1.

Correct Answer: B — No

Q. For the data set 10, 20, 30, 40, 50, what is the mean deviation?

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

Solution

Mean = 30; Mean Deviation = (|10-30| + |20-30| + |30-30| + |40-30| + |50-30|) / 5 = 10.

Correct Answer: B — 15

Q. For the data set {10, 12, 23, 23, 16, 23, 21}, what is the mode?

A. 10
B. 12
C. 23
D. 21

Solution

The mode is the number that appears most frequently, which is 23.

Correct Answer: C — 23

Q. For the data set {12, 15, 20, 22, 25}, what is the mode?

A. 12
B. 15
C. 20
D. No mode

Solution

There is no mode as all values appear only once.

Correct Answer: D — No mode

Q. For the data set {2, 4, 6, 8, 10}, what is the mean deviation?

A. 2
B. 1.6
C. 3
D. 2.5

Solution

Mean = 6; Mean deviation = (|2-6| + |4-6| + |6-6| + |8-6| + |10-6|)/5 = (4 + 2 + 0 + 2 + 4)/5 = 12/5 = 2.4.

Correct Answer: B — 1.6

Q. For the data set {4, 8, 6, 5, 3}, what is the mean?

A. 4.5
B. 5.5
C. 6.0
D. 5.0

Solution

Mean = (4 + 8 + 6 + 5 + 3) / 5 = 26 / 5 = 5.0.

Correct Answer: D — 5.0

Q. For the data set: 1, 2, 3, 4, 5, what is the interquartile range?

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

Solution

Q1 = 2, Q3 = 4; Interquartile Range = Q3 - Q1 = 4 - 2 = 2.

Correct Answer: B — 2

Q. For the data set: 5, 7, 8, 9, 10, what is the mean absolute deviation?

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

Solution

Mean = 7.5; MAD = (|5-7.5| + |7-7.5| + |8-7.5| + |9-7.5| + |10-7.5|) / 5 = 1.

Correct Answer: B — 2

Q. For the data set: 5, 7, 8, 9, 10, what is the standard deviation?

A. 1.5
B. 2
C. 2.5
D. 3

Solution

Mean = 7.5; Variance = [(5-7.5)^2 + (7-7.5)^2 + (8-7.5)^2 + (9-7.5)^2 + (10-7.5)^2] / 5 = 2; Standard Deviation = sqrt(2) = 1.41

Correct Answer: B — 2

Q. For the ellipse defined by the equation 9x^2 + 16y^2 = 144, what are the lengths of the semi-major and semi-minor axes?

A. 3, 4
B. 4, 3
C. 6, 8
D. 8, 6

Solution

The semi-major axis is 4 and the semi-minor axis is 3 after rewriting the equation in standard form.

Correct Answer: A — 3, 4

Q. For the equation x^2 + 2x + k = 0 to have one root equal to 1, what is the value of k?

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

Solution

Substituting x = 1 into the equation gives 1^2 + 2*1 + k = 0 => 1 + 2 + k = 0 => k = -3.

Correct Answer: B — 1

Q. For the equation x^2 + kx + 9 = 0 to have real roots, what must be true about k?

A. k < 6
B. k > 6
C. k < 0
D. k > 0

Solution

The discriminant must be non-negative: k^2 - 4*1*9 >= 0 => k^2 >= 36 => k <= -6 or k >= 6.

Correct Answer: A — k < 6

Q. For the equilibrium 2A(g) ⇌ B(g) + C(g), how many moles of gas are on the reactant side?

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

Solution

There are 2 moles of gas on the reactant side (2A).

Correct Answer: B — 2

Q. For the equilibrium 2A(g) ⇌ B(g) + C(g), if the concentration of B is increased, what will happen to the concentration of A?

A. Increase
B. Decrease
C. Remain the same
D. Cannot be determined

Solution

According to Le Chatelier's principle, increasing the concentration of B will shift the equilibrium to the left, resulting in a decrease in the concentration of A.

Correct Answer: B — Decrease

Q. For the equilibrium 2A(g) ⇌ B(g) + C(g), if the volume of the container is decreased, what will happen?

A. Shift to the left
B. Shift to the right
C. No change
D. Depends on the temperature

Solution

Decreasing the volume increases the pressure, and the equilibrium will shift towards the side with fewer moles of gas, which is the right side in this case.

Correct Answer: B — Shift to the right

Q. For the equilibrium 2A(g) ⇌ B(g) + C(g), if the volume of the container is doubled, what will happen to the equilibrium concentrations?

A. Concentrations of A will increase
B. Concentrations of B and C will increase
C. Equilibrium will not change
D. Concentrations of A will decrease

Solution

Doubling the volume decreases the pressure, which shifts the equilibrium towards the side with more moles of gas (B and C).

Correct Answer: B — Concentrations of B and C will increase

Q. For the equilibrium 2A(g) ⇌ B(g) + C(g), if the volume of the container is doubled, what will happen to the equilibrium position?

A. Shift to the left
B. Shift to the right
C. No change
D. Depends on the temperature

Solution

Doubling the volume decreases the pressure, which shifts the equilibrium towards the side with more moles of gas, in this case, the right side.

Correct Answer: B — Shift to the right

Q. For the equilibrium reaction 4HCl(g) ⇌ 2H2(g) + 2Cl2(g), how will the equilibrium shift if the temperature is decreased?

A. Shift to the right
B. Shift to the left
C. No change
D. Increase in pressure

Solution

Decreasing the temperature for an endothermic reaction will shift the equilibrium to the left, favoring the formation of HCl.

Correct Answer: B — Shift to the left

Q. For the equilibrium reaction CO(g) + 2H2(g) ⇌ CH3OH(g), if the temperature is decreased, what will be the effect?

A. Shift to the right
B. Shift to the left
C. No change
D. Increase in pressure

Solution

Decreasing the temperature for an exothermic reaction will shift the equilibrium to the right, favoring the formation of products.

Correct Answer: A — Shift to the right

Q. For the equilibrium reaction N2(g) + 3H2(g) ⇌ 2NH3(g), how will the equilibrium shift if H2 is added?

A. Shift to the right
B. Shift to the left
C. No change
D. Increase in temperature

Solution

Adding H2 will shift the equilibrium to the right to produce more NH3.

Correct Answer: A — Shift to the right

Q. For the equilibrium reaction N2(g) + 3H2(g) ⇌ 2NH3(g), if the pressure is increased, what will be the effect on the equilibrium?

A. Shift to the right
B. Shift to the left
C. No change
D. Increase in temperature

Solution

Increasing the pressure will shift the equilibrium to the right, favoring the formation of NH3, which has fewer moles of gas.

Correct Answer: A — Shift to the right

Q. For the equilibrium reaction N2(g) + 3H2(g) ⇌ 2NH3(g), what happens if the volume of the container is decreased?

A. Shift to the right
B. Shift to the left
C. No change
D. Increase in temperature

Solution

Decreasing the volume increases the pressure, which shifts the equilibrium to the side with fewer moles of gas, favoring the production of NH3.

Correct Answer: A — Shift to the right

Q. For the equilibrium reaction: H2(g) + I2(g) ⇌ 2HI(g), what is the effect of adding more HI?

A. Shifts to the right
B. Shifts to the left
C. No change
D. Increases the rate of reaction

Solution

Adding more HI increases the concentration of products, which shifts the equilibrium to the left to form more reactants.

Correct Answer: B — Shifts to the left

Q. For the equilibrium reaction: H2(g) + I2(g) ⇌ 2HI(g), what is the effect of adding more I2?

A. Equilibrium shifts to the right
B. Equilibrium shifts to the left
C. No effect
D. Equilibrium constant changes

Solution

Adding more I2 increases its concentration, which shifts the equilibrium to the right to produce more HI.

Correct Answer: A — Equilibrium shifts to the right

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