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 pair of lines represented by ax^2 + 2hxy + by^2 = 0 are perpendicular, then:

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

Solution

For the lines to be perpendicular, the condition a + b = 0 must hold.

Correct Answer: A — a + b = 0

Q. If the pair of lines represented by the equation ax^2 + 2hxy + by^2 = 0 are perpendicular, then:

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

Solution

For the lines to be perpendicular, the condition a*b + h^2 = 0 must hold.

Correct Answer: A — a + b = 0

Q. If the parabola y = ax^2 + bx + c has its vertex at (1, -2), what is the value of a if it passes through the point (0, 0)?

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

Solution

Using the vertex form y = a(x - 1)^2 - 2 and substituting (0, 0), we get 0 = a(0 - 1)^2 - 2 => 2 = a => a = 2.

Correct Answer: B — 2

Q. If the parabola y^2 = 16x opens to the right, what is the value of p?

A. 2
B. 4
C. 8
D. 16

Solution

In the equation y^2 = 4px, we have 4p = 16, thus p = 4.

Correct Answer: B — 4

Q. If the parabola y^2 = 20x opens to the right, what is the value of p?

A. 5
B. 10
C. 20
D. 2

Solution

In the equation y^2 = 4px, we have 4p = 20, thus p = 20/4 = 5.

Correct Answer: A — 5

Q. If the peak current in an AC circuit is 5 A, what is the average current over one complete cycle?

A. 5 A
B. 2.5 A
C. 0 A
D. 7.07 A

Solution

The average current over one complete cycle is I_avg = I_peak/√2 = 5/√2 = 2.5 A.

Correct Answer: B — 2.5 A

Q. If the peak voltage of an AC source is 200 V, what is the RMS voltage?

A. 100 V
B. 141.42 V
C. 200 V
D. 282.84 V

Solution

The RMS voltage (V_rms) is given by V_rms = V_peak / √2. Therefore, V_rms = 200 V / √2 = 141.42 V.

Correct Answer: B — 141.42 V

Q. If the peak voltage of an AC source is 220 V, what is the RMS voltage?

A. 110 V
B. 154 V
C. 220 V
D. 311 V

Solution

The RMS voltage (V_rms) is given by V_rms = V_peak / √2. Therefore, V_rms = 220 V / √2 = 110 V.

Correct Answer: A — 110 V

Q. If the period of a satellite in a circular orbit is T, what is the relationship between T and the radius r of the orbit?

A. T ∝ r
B. T ∝ r²
C. T ∝ √r
D. T ∝ 1/√r

Solution

T = 2π√(r³/GM), thus T ∝ √r.

Correct Answer: C — T ∝ √r

Q. If the photoelectric effect is observed, what can be inferred about the incident light?

A. It has a frequency below the threshold
B. It has a frequency equal to the threshold
C. It has a frequency above the threshold
D. It has any frequency

Solution

The photoelectric effect occurs only when the frequency of the incident light is above the threshold frequency.

Correct Answer: C — It has a frequency above the threshold

Q. If the points (1, 2), (3, 4), and (5, 6) are collinear, what is the slope of the line?

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

Solution

Slope = (4-2)/(3-1) = 1, and it remains the same for other points.

Correct Answer: A — 1

Q. If the points A(1, 2), B(3, 4), and C(5, 6) are collinear, what is the area of triangle ABC?

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

Solution

Area = 1/2 | x1(y2-y3) + x2(y3-y1) + x3(y1-y2) | = 0.

Correct Answer: A — 0

Q. If the polynomial P(x) = x^3 - 6x^2 + 11x - 6 has a root at x = 1, what is P(2)?

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

Solution

P(2) = 2^3 - 6(2^2) + 11(2) - 6 = 8 - 24 + 22 - 6 = 0.

Correct Answer: D — 3

Q. If the position vector of a point is (5, 12), what is its distance from the origin?

A. 13
B. 12
C. 11
D. 10

Solution

Distance = √(5^2 + 12^2) = √(25 + 144) = √169 = 13

Correct Answer: A — 13

Q. If the position vector of a point is given by r = (2t, 3t, 4t), what is the velocity vector?

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

Solution

Velocity vector = dr/dt = (2, 3, 4)

Correct Answer: A — (2, 3, 4)

Q. If the position vector of a point P is (2, 3, 4), what is the distance from the origin to point P?

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

Solution

Distance = √(2^2 + 3^2 + 4^2) = √(4 + 9 + 16) = √29 ≈ 5.385.

Correct Answer: B — 6

Q. If the position vector of a point P is (x, y, z) and the vector a = (1, 2, 3), what is the projection of P onto a?

A. (1, 2, 3)
B. (2, 4, 6)
C. (0, 0, 0)
D. (x, y, z)

Solution

Projection of P onto a = ((P · a) / |a|^2) * a.

Correct Answer: D — (x, y, z)

Q. If the position vector of a point P is given by r = (2t, 3t, 4t), find the coordinates of P when t = 1.

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

Solution

Substituting t = 1, r = (2*1, 3*1, 4*1) = (2, 3, 4).

Correct Answer: A — (2, 3, 4)

Q. If the position vector of point P is (3, -2) and Q is (1, 4), what is the vector PQ?

A. (-2, 6)
B. (2, -6)
C. (4, -6)
D. (6, 2)

Solution

Vector PQ = Q - P = (1 - 3, 4 - (-2)) = (-2, 6).

Correct Answer: A — (-2, 6)

Q. If the position vector of point P is (3, 4) and Q is (1, 2), what is the vector PQ?

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

Solution

Vector PQ = Q - P = (1 - 3, 2 - 4) = (-2, -2).

Correct Answer: A — (2, 2)

Q. If the principal quantum number n = 4 and the azimuthal quantum number l = 2, what is the maximum number of electrons in this subshell?

A. 8
B. 10
C. 14
D. 16

Solution

The maximum number of electrons in a subshell is given by 2(2l + 1). For l = 2, it is 2(2*2 + 1) = 10.

Correct Answer: C — 14

Q. If the principal quantum number n = 4, what are the possible values of l?

A. 0, 1, 2, 3
B. 1, 2, 3, 4
C. 0, 1, 2, 3, 4
D. 0, 1, 2

Solution

For n=4, l can take values 0, 1, 2, or 3.

Correct Answer: A — 0, 1, 2, 3

Q. If the principal quantum number n = 4, what are the possible values of the azimuthal quantum number l?

A. 0, 1, 2, 3
B. 1, 2, 3, 4
C. 0, 1, 2, 3, 4
D. 0, 1, 2

Solution

For n=4, l can take values from 0 to n-1, which are 0, 1, 2, and 3.

Correct Answer: A — 0, 1, 2, 3

Q. If the probability of an event A is 0.3, what is the probability of the event not occurring?

A. 0.7
B. 0.3
C. 0.5
D. 0.2

Solution

Probability of not A = 1 - P(A) = 1 - 0.3 = 0.7.

Correct Answer: A — 0.7

Q. If the probability of an event A is 0.7, what is the probability of the event not occurring?

A. 0.3
B. 0.7
C. 0.5
D. 0.1

Solution

Probability of not A = 1 - P(A) = 1 - 0.7 = 0.3.

Correct Answer: A — 0.3

Q. If the probability of an event is 0.7, what is the probability of its complement?

A. 0.3
B. 0.7
C. 1
D. 0.5

Solution

Probability of complement = 1 - P(event) = 1 - 0.7 = 0.3.

Correct Answer: A — 0.3

Q. If the probability of an event is 0.7, what is the probability of the event not occurring?

A. 0.3
B. 0.7
C. 0.5
D. 0.1

Solution

Probability of not occurring = 1 - P(event) = 1 - 0.7 = 0.3.

Correct Answer: A — 0.3

Q. If the probability of event A is 0.4 and event B is 0.5, what is the probability of both events occurring if they are independent?

A. 0.2
B. 0.4
C. 0.5
D. 0.6

Solution

P(A and B) = P(A) * P(B) = 0.4 * 0.5 = 0.2.

Correct Answer: A — 0.2

Q. If the quadratic equation ax^2 + bx + c = 0 has roots 3 and -2, what is the value of a?

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

Solution

Using the fact that the product of the roots is c/a and the sum is -b/a, we can set a = 1, b = -1, c = -6.

Correct Answer: A — 1

Q. If the quadratic equation x^2 + 2px + p^2 - 4 = 0 has real roots, what is the condition on p?

A. p > 2
B. p < 2
C. p = 2
D. p >= 2

Solution

The discriminant must be non-negative: (2p)^2 - 4(1)(p^2 - 4) >= 0 => 4p^2 - 4p^2 + 16 >= 0, which is always true. Thus, p can be any real number.

Correct Answer: D — p >= 2

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