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 vector a = (3, 4) is scaled by a factor of 2, what is the new vector?

A. (6, 8)
B. (3, 4)
C. (1.5, 2)
D. (0, 0)

Solution

New vector = 2 * (3, 4) = (6, 8).

Correct Answer: A — (6, 8)

Q. If the vector a = (3, 4, 0) and b = (0, 0, 5), what is the magnitude of a × b?

A. 15
B. 20
C. 12
D. 10

Solution

Magnitude of a × b = |a||b|sin(90) = |(3, 4, 0)|| (0, 0, 5)| = 5√(3^2 + 4^2) = 15.

Correct Answer: A — 15

Q. If the vector A = (a, b) is perpendicular to B = (b, -a), what is the relationship between a and b?

A. a = b
B. a = -b
C. a + b = 0
D. a - b = 0

Solution

A·B = ab - ab = 0, hence A and B are perpendicular if a = -b.

Correct Answer: B — a = -b

Q. If the vectors A = (1, 2) and B = (2, 1) are given, what is the angle between them?

A. 90 degrees
B. 45 degrees
C. 60 degrees
D. 30 degrees

Solution

Cosine of angle θ = (A · B) / (|A| |B|) = (1*2 + 2*1) / (√5 * √5) = 4/5, θ = cos⁻¹(4/5).

Correct Answer: B — 45 degrees

Q. If the vectors A = (2, 3) and B = (4, 5) are given, what is the scalar product A · B?

A. 23
B. 22
C. 20
D. 21

Solution

A · B = 2*4 + 3*5 = 8 + 15 = 23.

Correct Answer: C — 20

Q. If the vectors A = (3, -2, 1) and B = (k, 4, -2) are orthogonal, find the value of k.

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

Solution

A · B = 3k - 8 - 2 = 0; 3k - 10 = 0; k = 10/3.

Correct Answer: A — -1

Q. If the vectors A = (x, 2, 3) and B = (4, y, 6) are orthogonal, what is the value of y?

A. 2
B. 3
C. 4
D. 5

Solution

A · B = x*4 + 2*y + 3*6 = 0. Thus, 4x + 2y + 18 = 0. If x = 0, then y = -9. If x = 1, y = -10. The only integer solution is y = 3.

Correct Answer: B — 3

Q. If the vectors A = (x, 2, 3) and B = (4, y, 6) are orthogonal, what is the value of x + y?

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

Solution

A · B = x*4 + 2*y + 3*6 = 0. Thus, 4x + 2y + 18 = 0. Solving gives x + y = -9/2, which is not an option. Correcting gives x + y = 0.

Correct Answer: A — -2

Q. If the vertex of the parabola y = ax^2 + bx + c is at (1, -2), what is the value of a if b = 4 and c = -6?

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

Solution

The vertex form of a parabola is given by x = -b/(2a). Here, 1 = -4/(2a) => 2a = -4 => a = -2.

Correct Answer: A — 1

Q. If the viscosity of a fluid is doubled, what happens to the flow rate through a constant diameter pipe?

A. Doubles
B. Halves
C. Remains the same
D. Increases fourfold

Solution

If viscosity is doubled, the flow rate through a constant diameter pipe is halved.

Correct Answer: B — Halves

Q. If the viscosity of a fluid is doubled, what happens to the flow rate through a pipe, assuming all other factors remain constant?

A. Doubles
B. Halves
C. Remains the same
D. Increases fourfold

Solution

If viscosity is doubled, the flow rate through a pipe will halve, as flow rate is inversely proportional to viscosity.

Correct Answer: B — Halves

Q. If the viscosity of a fluid is high, what does it imply about the fluid's flow?

A. It flows easily
B. It flows slowly
C. It is incompressible
D. It is a gas

Solution

A high viscosity indicates that the fluid flows slowly.

Correct Answer: B — It flows slowly

Q. If the viscosity of a liquid is doubled, how does it affect the flow rate through a pipe?

A. Flow rate doubles
B. Flow rate halves
C. Flow rate remains the same
D. Flow rate quadruples

Solution

According to Poiseuille's law, if viscosity is doubled, the flow rate is halved, assuming all other factors remain constant.

Correct Answer: B — Flow rate halves

Q. If the viscosity of a liquid is doubled, what happens to the flow rate through a pipe, assuming all other factors remain constant?

A. Flow rate doubles
B. Flow rate halves
C. Flow rate remains the same
D. Flow rate quadruples

Solution

According to Poiseuille's law, if viscosity is doubled, the flow rate will be halved, assuming other factors remain constant.

Correct Answer: B — Flow rate halves

Q. If the voltage across a conductor is 15 volts and the current is 3 amperes, what is the resistance?

A. 5 Ω
B. 10 Ω
C. 15 Ω
D. 20 Ω

Solution

Using Ohm's Law, R = V / I = 15 V / 3 A = 5 Ω.

Correct Answer: A — 5 Ω

Q. If the voltage across a resistor is doubled, what happens to the current through it?

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

Solution

According to Ohm's law, if voltage is doubled and resistance remains constant, current also doubles.

Correct Answer: A — It doubles

Q. If the voltage across a resistor is doubled, what happens to the current through the resistor, assuming resistance remains constant?

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

Solution

According to Ohm's Law (V = IR), if voltage is doubled and resistance remains constant, current also doubles.

Correct Answer: A — Doubles

Q. If the voltage across a resistor is tripled, what happens to the current through it, assuming resistance remains constant?

A. It triples.
B. It doubles.
C. It remains the same.
D. It decreases.

Solution

According to Ohm's Law (I = V/R), if voltage (V) is tripled and resistance (R) remains constant, the current (I) will also triple.

Correct Answer: A — It triples.

Q. If the volume of a gas is doubled while keeping the temperature constant, what happens to the pressure?

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

Solution

According to Boyle's Law, if the volume is doubled, the pressure is halved.

Correct Answer: B — It halves

Q. If the volume of a gas is halved while keeping the temperature constant, what happens to the pressure?

A. Pressure is halved
B. Pressure remains constant
C. Pressure doubles
D. Pressure quadruples

Solution

According to Boyle's Law, if the volume of a gas is halved at constant temperature, the pressure will double.

Correct Answer: C — Pressure doubles

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

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

Solution

Frequency is inversely proportional to wavelength. If the wavelength is halved, the frequency doubles.

Correct Answer: B — It doubles

Q. If the wavelength of light in a vacuum is 600 nm, what is its wavelength in glass (n = 1.5)?

A. 400 nm
B. 600 nm
C. 900 nm
D. 300 nm

Solution

The wavelength in a medium is given by λ' = λ/n. Thus, λ' = 600 nm / 1.5 = 400 nm.

Correct Answer: A — 400 nm

Q. If the wavelength of light in air is 600 nm, what is its wavelength in glass (n=1.5)?

A. 400 nm
B. 450 nm
C. 600 nm
D. 900 nm

Solution

Wavelength in glass (λ') = λ/n = 600 nm / 1.5 = 400 nm.

Correct Answer: A — 400 nm

Q. If the wavelength of light is halved, what happens to the frequency of the light?

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

Solution

Frequency (f) is inversely proportional to wavelength (λ). If λ is halved, f doubles.

Correct Answer: A — It doubles

Q. If the wavelength of light used in a diffraction experiment is halved, what happens to the position of the minima?

A. They move closer together
B. They move further apart
C. They remain unchanged
D. They disappear

Solution

Halving the wavelength causes the minima to move closer together, as the angle for minima is directly proportional to the wavelength.

Correct Answer: A — They move closer together

Q. If the wavelength of light used in a diffraction experiment is halved, what happens to the angular position of the first minimum in a single-slit diffraction pattern?

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

Solution

Halving the wavelength will halve the angle for the first minimum, as the position of minima is directly proportional to the wavelength.

Correct Answer: C — It halves

Q. If the wavelength of light used in a diffraction experiment is halved, what happens to the position of the first diffraction minimum?

A. It moves closer to the center
B. It moves further from the center
C. It remains unchanged
D. It disappears

Solution

Halving the wavelength results in the first minimum moving closer to the center, as the position of minima is directly related to the wavelength.

Correct Answer: A — It moves closer to the center

Q. If the wavelength of light used in a diffraction experiment is increased, what happens to the diffraction pattern?

A. It becomes sharper
B. It becomes broader
C. It remains unchanged
D. It disappears

Solution

Increasing the wavelength results in a broader diffraction pattern as the angles for minima and maxima increase.

Correct Answer: B — It becomes broader

Q. If the wavelength of light used in a double-slit experiment is 600 nm and the distance between the slits is 0.3 mm, what is the distance between the first and second bright fringes on the screen placed 2 m away?

A. 0.4 m
B. 0.6 m
C. 0.8 m
D. 0.2 m

Solution

Distance between fringes = (λD)/d = (600 x 10^-9 m * 2 m) / (0.3 x 10^-3 m) = 0.004 m = 0.4 m.

Correct Answer: A — 0.4 m

Q. If the wavelength of light used in a double-slit experiment is increased, what happens to the position of the interference fringes?

A. Fringes move closer together
B. Fringes move further apart
C. Fringes disappear
D. Fringes become brighter

Solution

Increasing the wavelength increases the fringe width, causing the fringes to move further apart.

Correct Answer: B — Fringes move further apart

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