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. The roots of the equation x^2 + 2x + 1 = 0 are:

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

Solution

The equation can be factored as (x + 1)^2 = 0, giving a double root at x = -1.

Correct Answer: A — -1

Q. The roots of the equation x^2 + 4x + 4 = 0 are:

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

Solution

The equation can be factored as (x + 2)^2 = 0, giving a double root at x = -2.

Correct Answer: A — -2, -2

Q. The roots of the equation x^2 - 3x + 2 = 0 are:

A. 1 and 2
B. 2 and 3
C. 0 and 1
D. None of these

Solution

Factoring gives (x-1)(x-2) = 0, so the roots are 1 and 2.

Correct Answer: A — 1 and 2

Q. The scalar product of two unit vectors is 0. What can be said about these vectors?

A. They are parallel
B. They are orthogonal
C. They are collinear
D. They are equal

Solution

If the scalar product is 0, the vectors are orthogonal.

Correct Answer: B — They are orthogonal

Q. The scalar product of vectors A = (a, b, c) and B = (1, 2, 3) is 14. If a = 2, find b and c.

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

Solution

A · B = 2*1 + b*2 + c*3 = 14. Thus, 2 + 2b + 3c = 14, leading to 2b + 3c = 12.

Correct Answer: B — 4, 3

Q. The scalar product of vectors A = (a, b, c) and B = (1, 2, 3) is 14. If a = 2, what is the value of b + c?

A. 4
B. 5
C. 6
D. 7

Solution

A · B = 2*1 + b*2 + c*3 = 14. Thus, 2 + 2b + 3c = 14, leading to 2b + 3c = 12. Solving gives b + c = 6.

Correct Answer: C — 6

Q. The shape of a soap bubble is spherical because:

A. It minimizes volume
B. It maximizes surface area
C. It minimizes surface area for a given volume
D. It is the only stable shape

Solution

A soap bubble adopts a spherical shape because it minimizes the surface area for a given volume, which is energetically favorable due to surface tension.

Correct Answer: C — It minimizes surface area for a given volume

Q. The slope of the line represented by the equation 2x - 3y + 6 = 0 is:

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

Solution

Rearranging gives y = (2/3)x + 2, so slope = 2/3.

Correct Answer: B — -2/3

Q. The slope of the line represented by the equation 3x - 4y + 12 = 0 is:

A. 3/4
B. 4/3
C. -3/4
D. -4/3

Solution

Rearranging gives y = (3/4)x + 3. Slope = 3/4.

Correct Answer: C — -3/4

Q. The slope of the tangent to the curve y = sin(x) at x = π/4 is:

A. 1
B. √2/2
C. √3/3
D. √2

Solution

The derivative f'(x) = cos(x). At x = π/4, f'(π/4) = cos(π/4) = √2/2.

Correct Answer: B — √2/2

Q. The slope of the tangent to the curve y = x^3 - 3x at x = 1 is:

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

Solution

The derivative f'(x) = 3x^2 - 3. At x = 1, f'(1) = 3(1)^2 - 3 = 0, so the slope is 0.

Correct Answer: B — 1

Q. The slopes of the lines represented by the equation 2x^2 + 3xy + y^2 = 0 are:

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

Solution

The slopes can be found by solving the quadratic equation derived from the given equation.

Correct Answer: A — -1, -2

Q. The slopes of the lines represented by the equation 5x^2 + 6xy + 2y^2 = 0 are given by:

A. -3/5 and -2/5
B. 2/5 and -5/2
C. 1/2 and -2
D. None of the above

Solution

Using the quadratic formula, the slopes are found to be -3/5 and -2/5.

Correct Answer: A — -3/5 and -2/5

Q. The slopes of the lines represented by the equation 5x^2 + 6xy + 2y^2 = 0 are:

A. -3/5, -2/5
B. 2/5, 3/5
C. 1, -1
D. 0, ∞

Solution

The slopes can be calculated using the quadratic formula, yielding -3/5 and -2/5.

Correct Answer: A — -3/5, -2/5

Q. The Stefan-Boltzmann Law relates to which mode of heat transfer?

A. Conduction
B. Convection
C. Radiation
D. Insulation

Solution

The Stefan-Boltzmann Law relates to radiation, stating that the total energy radiated per unit surface area is proportional to the fourth power of the black body's temperature.

Correct Answer: C — Radiation

Q. The sum of the first n natural numbers is given by which formula?

A. n(n+1)/2
B. n^2
C. n(n-1)/2
D. n(n+1)/3

Solution

The sum of the first n natural numbers is given by the formula n(n+1)/2.

Correct Answer: A — n(n+1)/2

Q. The sum of the first n terms of an arithmetic series is given by S_n = 3n^2 + 2n. What is the 10th term?

A. 32
B. 34
C. 36
D. 38

Solution

The nth term a_n = S_n - S_(n-1) = (3n^2 + 2n) - (3(n-1)^2 + 2(n-1)). For n=10, a_10 = 32.

Correct Answer: C — 36

Q. The sum of the roots of the equation 2x^2 - 3x + 1 = 0 is equal to what?

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

Solution

Using Vieta's formulas, the sum of the roots is -(-3)/2 = 3/2.

Correct Answer: B — 3/2

Q. The sum of the roots of the equation 2x^2 - 4x + k = 0 is 3. What is the value of k?

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

Solution

The sum of the roots is given by -b/a = 4/2 = 2. Setting this equal to 3 gives k = 1.

Correct Answer: A — 1

Q. The sum of the roots of the equation 3x^2 - 12x + 9 = 0 is:

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

Solution

The sum of the roots is given by -b/a = 12/3 = 4.

Correct Answer: C — 4

Q. The sum of the roots of the equation x^2 - 7x + 10 = 0 is?

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

Solution

The sum of the roots is given by -b/a = 7/1 = 7.

Correct Answer: C — 7

Q. The sum of the roots of the quadratic equation 2x^2 - 4x + k = 0 is 3. What is the value of k?

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

Solution

Using the sum of roots formula -b/a, we have 4/2 = 2, thus 2 + 1 = 3, so k = 1.

Correct Answer: B — 2

Q. The sum of the roots of the quadratic equation 3x^2 - 12x + 9 = 0 is equal to what?

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

Solution

Using Vieta's formulas, the sum of the roots is -(-12)/3 = 4.

Correct Answer: B — 4

Q. The sum of the roots of the quadratic equation 3x^2 - 12x + 9 = 0 is:

A. 3
B. 4
C. 2
D. 6

Solution

Using Vieta's formulas, the sum of the roots is -(-12)/3 = 4.

Correct Answer: B — 4

Q. The sum of the roots of the quadratic equation 3x^2 - 12x + k = 0 is 4. What is the value of k?

A. 0
B. 4
C. 8
D. 12

Solution

Using Vieta's formulas, sum of roots = -b/a = 12/3 = 4, hence k = 8.

Correct Answer: C — 8

Q. The sum of the roots of the quadratic equation x^2 - 7x + 10 = 0 is:

A. 10
B. 7
C. 5
D. 3

Solution

The sum of the roots is given by -b/a = 7/1 = 7.

Correct Answer: B — 7

Q. The surface tension of a liquid can be measured using which of the following methods?

A. Barometer method
B. Capillary rise method
C. Hydrometer method
D. Manometer method

Solution

The capillary rise method is commonly used to measure surface tension by observing the height to which a liquid rises in a capillary tube.

Correct Answer: B — Capillary rise method

Q. The temperature is measured as 25°C with an error of 1°C. What is the range of possible true values?

A. 24°C to 26°C
B. 25°C to 27°C
C. 23°C to 25°C
D. 26°C to 28°C

Solution

True value can be in the range of (Measured value - Error) to (Measured value + Error) = 25°C ± 1°C = 24°C to 26°C.

Correct Answer: A — 24°C to 26°C

Q. The time period of a satellite in a low Earth orbit is approximately how many minutes?

A. 90 minutes
B. 60 minutes
C. 120 minutes
D. 30 minutes

Solution

The time period of a satellite in a low Earth orbit is approximately 90 minutes due to its close proximity to the Earth.

Correct Answer: A — 90 minutes

Q. The time period of a simple harmonic oscillator is given by T = 2π√(m/k). If the mass is doubled, what will be the new time period?

A. T
B. 2T
C. √2 T
D. T/√2

Solution

If the mass is doubled, the new time period T' = 2π√(2m/k) = √2 * (2π√(m/k)) = √2 * T. Thus, the time period increases.

Correct Answer: B — 2T

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