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 two resistors of resistivity ρ are connected in series, what is the total resistivity of the combination?

A. ρ
B. 2ρ
C. ρ/2
D. Depends on the configuration

Solution

Resistivity is a property of the material and does not change with series or parallel connections.

Correct Answer: A — ρ

Q. If two rigid bodies have the same mass and shape but one is rotating faster than the other, how does their moment of inertia compare?

A. The same
B. The faster one has a larger moment of inertia
C. The slower one has a larger moment of inertia
D. Cannot be determined

Solution

The moment of inertia depends only on the mass distribution and shape, not on the angular velocity.

Correct Answer: A — The same

Q. If two sound waves of the same frequency interfere constructively, what happens to the resultant amplitude?

A. It decreases
B. It remains the same
C. It doubles
D. It becomes zero

Solution

In constructive interference, the amplitudes of the waves add up, resulting in a doubled amplitude.

Correct Answer: C — It doubles

Q. If two waves have a phase difference of π radians, what type of interference occurs?

A. Constructive interference
B. Destructive interference
C. No interference
D. Complete interference

Solution

A phase difference of π radians results in destructive interference.

Correct Answer: B — Destructive interference

Q. If two waves interfere constructively, what is the condition for the path difference?

A. (n + 1/2)λ
B. nλ
C. (n - 1/2)λ
D. n/2 λ

Solution

Constructive interference occurs when the path difference is nλ, where n is an integer.

Correct Answer: B — nλ

Q. If two waves of equal amplitude interfere destructively, what is the phase difference between them?

A. 0 rad
B. π/2 rad
C. π rad
D. 3π/2 rad

Solution

Destructive interference occurs when the phase difference is π rad.

Correct Answer: C — π rad

Q. If two waves of equal amplitude interfere destructively, what is the resultant amplitude?

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

Solution

For destructive interference, the resultant amplitude is zero when two equal amplitudes cancel each other out.

Correct Answer: A — 0

Q. If two waves of equal amplitude interfere, what is the maximum intensity observed?

A. A^2
B. 2A^2
C. 4A^2
D. A

Solution

Maximum intensity (I_max) = 4A^2 for two waves of equal amplitude A.

Correct Answer: B — 2A^2

Q. If two waves of the same frequency interfere constructively, what is the result?

A. A wave of lower amplitude
B. A wave of higher amplitude
C. No wave
D. A standing wave

Solution

Constructive interference results in a wave of higher amplitude.

Correct Answer: B — A wave of higher amplitude

Q. If two waves traveling in opposite directions interfere constructively, what is the result?

A. A smaller amplitude wave
B. A larger amplitude wave
C. No wave
D. A standing wave

Solution

Constructive interference occurs when two waves meet in phase, resulting in a wave with a larger amplitude.

Correct Answer: B — A larger amplitude wave

Q. If two wires of the same material are connected in series, how does their combined resistance compare to the individual resistances?

A. Less than both
B. Equal to the sum
C. Greater than both
D. Depends on length

Solution

In series, the total resistance is the sum of individual resistances.

Correct Answer: B — Equal to the sum

Q. If u = (1, 2) and v = (3, 4), what is the dot product u · v?

A. 10
B. 11
C. 12
D. 7

Solution

Dot product u · v = 1*3 + 2*4 = 3 + 8 = 11.

Correct Answer: A — 10

Q. If u = (1, 2) and v = (3, 4), what is u + v?

A. (4, 6)
B. (2, 3)
C. (1, 2)
D. (3, 4)

Solution

u + v = (1 + 3, 2 + 4) = (4, 6)

Correct Answer: A — (4, 6)

Q. If u = (1, 2, 3) and v = (4, 5, 6), what is the dot product u · v?

A. 32
B. 27
C. 26
D. 30

Solution

Dot product u · v = 1*4 + 2*5 + 3*6 = 4 + 10 + 18 = 32.

Correct Answer: B — 27

Q. If u = (2, 3, 1) and v = (1, 0, -1), find the dot product u · v.

A. 5
B. 2
C. 1
D. 0

Solution

u · v = 2*1 + 3*0 + 1*(-1) = 2 + 0 - 1 = 1.

Correct Answer: A — 5

Q. If U = {1, 2, 3, 4, 5}, A = {1, 2}, and B = {2, 3}, what is A ∪ B?

A. {1, 2}
B. {1, 2, 3}
C. {1, 2, 3, 4, 5}
D. {2, 3, 4, 5}

Solution

The union A ∪ B includes all elements from both sets, which are {1, 2, 3}.

Correct Answer: B — {1, 2, 3}

Q. If unpolarized light passes through a polarizer, what fraction of the light intensity is transmitted?

A. 0%
B. 25%
C. 50%
D. 100%

Solution

When unpolarized light passes through a polarizer, 50% of the light intensity is transmitted.

Correct Answer: C — 50%

Q. If unpolarized light passes through a polarizer, what is the intensity of the transmitted light?

A. Zero
B. Half of the original intensity
C. Equal to the original intensity
D. Twice the original intensity

Solution

According to Malus's law, the intensity of transmitted light is half of the original intensity when unpolarized light passes through a polarizer.

Correct Answer: B — Half of the original intensity

Q. If unpolarized light passes through a polarizer, what percentage of the light intensity will emerge?

A. 0%
B. 25%
C. 50%
D. 100%

Solution

When unpolarized light passes through a polarizer, 50% of the light intensity will emerge, according to Malus's law.

Correct Answer: C — 50%

Q. If unpolarized light passes through two polarizers at 90 degrees to each other, what is the intensity of the transmitted light?

A. Same as incident light
B. Half of the incident light
C. Zero
D. One quarter of the incident light

Solution

When unpolarized light passes through two polarizers at 90 degrees, no light is transmitted, resulting in zero intensity.

Correct Answer: C — Zero

Q. If unpolarized light passes through two polarizers, what is the maximum intensity of light transmitted?

A. Zero
B. Half of the original intensity
C. Equal to the original intensity
D. Dependent on the angle between the polarizers

Solution

The maximum intensity transmitted through two polarizers is given by Malus's law, which states that I = I0 * cos²(θ), where θ is the angle between the polarizers.

Correct Answer: D — Dependent on the angle between the polarizers

Q. If vector A = (1, 2, 3) and vector B = (4, 5, 6), what is A + B?

A. (5, 7, 9)
B. (4, 5, 6)
C. (1, 2, 3)
D. (0, 0, 0)

Solution

A + B = (1+4, 2+5, 3+6) = (5, 7, 9).

Correct Answer: A — (5, 7, 9)

Q. If vector A = (1, 2, 3) and vector B = (4, 5, 6), what is the angle between them?

A. 0 degrees
B. 30 degrees
C. 60 degrees
D. 90 degrees

Solution

Cosine of angle θ = (A . B) / (|A| |B|) = (1*4 + 2*5 + 3*6) / (√14 * √77) = 0, hence θ = 90 degrees.

Correct Answer: D — 90 degrees

Q. If vector A = (1, 2, 3) and vector B = (4, 5, 6), what is the vector A - B?

A. (-3, -3, -3)
B. (3, 3, 3)
C. (5, 7, 9)
D. (0, 0, 0)

Solution

A - B = (1-4, 2-5, 3-6) = (-3, -3, -3).

Correct Answer: A — (-3, -3, -3)

Q. If vector A = (2, 2, 2) and vector B = (1, 1, 1), what is the scalar triple product A . (B × A)?

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

Solution

A . (B × A) = 0, since B × A = 0.

Correct Answer: A — 0

Q. If vector A = (3, -2, 1) and vector B = (1, 4, -3), what is the cross product A × B?

A. (-5, -10, 14)
B. (5, 10, -14)
C. (10, 14, 5)
D. (14, -5, 10)

Solution

A × B = |i  j  k|\n|3 -2  1|\n|1  4 -3| = (-5, -10, 14).

Correct Answer: A — (-5, -10, 14)

Q. If vectors A = (x, 2, 3) and B = (1, y, 4) are perpendicular, what is the value of x + y?

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

Solution

A · B = x*1 + 2*y + 3*4 = 0. Thus, x + 2y + 12 = 0. Solving gives x + y = -6.

Correct Answer: B — 2

Q. If vectors A = 3i + 4j and B = 2i - j, what is the scalar product A · B?

A. -1
B. 2
C. 10
D. 11

Solution

A · B = (3)(2) + (4)(-1) = 6 - 4 = 2.

Correct Answer: C — 10

Q. If x + 2y = 10 and 2x - y = 3, what is the value of x?

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

Solution

From the first equation, x = 10 - 2y. Substituting into the second gives 2(10 - 2y) - y = 3, solving gives y = 4, x = 2.

Correct Answer: C — 3

Q. If x + 4 = 10, what is the value of x?

A. 4
B. 6
C. 8
D. 10

Solution

Subtracting 4 from both sides gives x = 6.

Correct Answer: B — 6

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