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. If the entropy of a system increases, what can be inferred about the spontaneity of the process?

A. The process is non-spontaneous
B. The process is spontaneous
C. The process is at equilibrium
D. None of the above

Solution

An increase in entropy indicates that the process is spontaneous, as per the second law of thermodynamics.

Correct Answer: B — The process is spontaneous

Q. If the entropy of a system increases, what is the effect on Gibbs Free Energy at constant temperature?

A. ΔG increases
B. ΔG decreases
C. ΔG remains constant
D. ΔG becomes zero

Solution

If entropy increases, ΔG decreases, making the reaction more favorable.

Correct Answer: B — ΔG decreases

Q. If the equation 2x^2 + 3x + k = 0 has one root equal to 1, what is the value of k?

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

Solution

Substituting x = 1 gives 2(1)^2 + 3(1) + k = 0 => 2 + 3 + k = 0 => k = -5.

Correct Answer: A — -1

Q. If the equation 2x^2 + 3x + k = 0 has roots 1 and -2, what is the value of k?

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

Solution

Using Vieta's formulas, k = 2*1*(-2) = -4.

Correct Answer: D — 4

Q. If the equation 2x^2 + 3x - 5 = 0 has roots r1 and r2, what is the value of r1 + r2?

A. -3/2
B. 3/2
C. 5/2
D. -5/2

Solution

Using Vieta's formulas, r1 + r2 = -b/a = -3/2.

Correct Answer: A — -3/2

Q. If the equation of a parabola is given by y^2 = 12x, what is the value of 'p'?

A. 3
B. 6
C. 4
D. 12

Solution

In the equation y^2 = 4px, p = 3, hence the value of 'p' is 3.

Correct Answer: B — 6

Q. If the equation of an ellipse is 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

Rewriting the equation in standard form gives (x^2/16) + (y^2/9) = 1, so semi-major axis a = 4 and semi-minor axis b = 3.

Correct Answer: A — 3, 4

Q. If the equation x^2 + px + q = 0 has roots 2 and 3, what is the value of p?

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

Solution

Using Vieta's formulas, p = -(2 + 3) = -5.

Correct Answer: A — -5

Q. If the equation x^2 - 5x + k = 0 has equal roots, what is the value of k?

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

Solution

For equal roots, the discriminant must be zero. Thus, (-5)^2 - 4*1*k = 0 => 25 - 4k = 0 => k = 25/4 = 6.25.

Correct Answer: A — 5

Q. If the equilibrium constant Kc for a reaction is 10 at a certain temperature, what is the value of Kc for the reverse reaction?

A. 0.1
B. 1
C. 10
D. 100

Solution

The equilibrium constant for the reverse reaction is the reciprocal of the forward reaction, so Kc' = 1/Kc = 0.1.

Correct Answer: A — 0.1

Q. If the equilibrium constant Kc for a reaction is 10, what can be said about the position of equilibrium?

A. Products are favored
B. Reactants are favored
C. Equilibrium is at the center
D. No conclusion can be drawn

Solution

A Kc value greater than 1 indicates that the products are favored at equilibrium.

Correct Answer: A — Products are favored

Q. If the equilibrium constant Kc for a reaction is less than 1, what does it indicate about the equilibrium position?

A. Products are favored
B. Reactants are favored
C. Equal amounts of reactants and products
D. Reaction does not occur

Solution

A Kc value less than 1 indicates that at equilibrium, the concentration of reactants is greater than that of products, thus reactants are favored.

Correct Answer: B — Reactants are favored

Q. If the expansion of (x + a)^n has a term 15x^3a^2, what is the value of n?

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

Solution

The term is given by C(n, 3) * a^2 * x^3. Setting C(n, 3) * a^2 = 15 gives n = 6.

Correct Answer: B — 6

Q. If the family of curves is given by y = k/x, what type of curves does it represent?

A. Linear
B. Hyperbolic
C. Circular
D. Exponential

Solution

The equation y = k/x represents a family of hyperbolas.

Correct Answer: B — Hyperbolic

Q. If the first term of an arithmetic series is 5 and the common difference is 3, what is the 15th term?

A. 44
B. 45
C. 43
D. 42

Solution

a_n = a + (n-1)d = 5 + (15-1) * 3 = 5 + 42 = 47.

Correct Answer: A — 44

Q. If the focal length of a concave lens is -10 cm, what is the nature of the image formed when an object is placed at 15 cm?

A. Real and inverted
B. Virtual and erect
C. Real and erect
D. Virtual and inverted

Solution

Concave lenses always produce virtual and erect images regardless of the object distance.

Correct Answer: B — Virtual and erect

Q. If the focal length of a concave mirror is 10 cm, what is the radius of curvature?

A. 5 cm
B. 10 cm
C. 15 cm
D. 20 cm

Solution

The radius of curvature (R) is twice the focal length (f). Therefore, R = 2f = 2 * 10 cm = 20 cm.

Correct Answer: B — 10 cm

Q. If the focal length of a concave mirror is 20 cm, what is the radius of curvature?

A. 10 cm
B. 20 cm
C. 30 cm
D. 40 cm

Solution

The radius of curvature (R) is twice the focal length (f). Therefore, R = 2f = 2 * 20 cm = 40 cm.

Correct Answer: B — 20 cm

Q. If the focal length of a lens is -10 cm, what type of lens is it?

A. Convex lens
B. Concave lens
C. Bifocal lens
D. Cylindrical lens

Solution

A negative focal length indicates that the lens is a concave lens.

Correct Answer: B — Concave lens

Q. If the focal length of a lens is 20 cm, what is the power of the lens?

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

Solution

Power (P) = 1/f (in meters). Here, f = 0.2 m, so P = 1/0.2 = +5 D.

Correct Answer: B — +10 D

Q. If the focal length of a lens is 25 cm, what is the power of the lens?

A. +2 D
B. +4 D
C. +5 D
D. +10 D

Solution

Power (P) is given by P = 1/f (in meters). Thus, P = 1/0.25 m = +4 D.

Correct Answer: C — +5 D

Q. If the focal length of a lens is doubled, how does the power of the lens change?

A. Doubles
B. Halves
C. Remains the same
D. Quadruples

Solution

Power is inversely proportional to focal length. If f is doubled, P = 1/f will halve.

Correct Answer: B — Halves

Q. If the following numbers are arranged in ascending order: 3, 7, 8, 12, 14, what is the range?

A. 11
B. 10
C. 12
D. 9

Solution

Range = Maximum - Minimum = 14 - 3 = 11

Correct Answer: A — 11

Q. If the forward reaction is exothermic, what effect does increasing the temperature have on the equilibrium position?

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

Solution

According to Le Chatelier's principle, increasing the temperature of an exothermic reaction shifts the equilibrium position to the left, favoring the reactants.

Correct Answer: B — Shifts to the left

Q. If the frequency of a simple harmonic motion is doubled, what happens to the time period?

A. It doubles
B. It halves
C. It remains the same
D. It quadruples

Solution

The time period T is inversely proportional to the frequency f. If the frequency is doubled, the time period halves.

Correct Answer: B — It halves

Q. If the frequency of a simple harmonic oscillator is halved, what happens to the period?

A. It doubles
B. It halves
C. It remains the same
D. It quadruples

Solution

Period T = 1/f, if frequency is halved, period doubles.

Correct Answer: A — It doubles

Q. If the frequency of a sound wave is doubled, what happens to its wavelength in a given medium?

A. Doubles
B. Halves
C. Remains the same
D. Increases by a factor of four

Solution

Wavelength is inversely proportional to frequency; if frequency is doubled, wavelength is halved.

Correct Answer: B — Halves

Q. If the frequency of a sound wave is doubled, what happens to its wavelength?

A. It doubles
B. It halves
C. It remains the same
D. It quadruples

Solution

Wavelength is inversely proportional to frequency; if frequency is doubled, wavelength halves.

Correct Answer: B — It halves

Q. If the frequency of a wave is doubled, what happens to its wavelength, assuming the speed of the wave remains constant?

A. Wavelength doubles
B. Wavelength halves
C. Wavelength remains the same
D. Wavelength quadruples

Solution

According to the wave equation v = fλ, if frequency (f) is doubled and speed (v) remains constant, the wavelength (λ) must halve.

Correct Answer: B — Wavelength halves

Q. If the frequency of a wave is doubled, what happens to its wavelength?

A. It doubles
B. It halves
C. It remains the same
D. It quadruples

Solution

The speed of a wave is given by the product of its frequency and wavelength (v = fλ). If the frequency is doubled, the wavelength must be halved to keep the speed constant.

Correct Answer: B — It halves

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