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 gravitational force between two objects is 10 N. If the distance between them is halved, what will be the new force?

A. 20 N
B. 40 N
C. 10 N
D. 5 N

Solution

If the distance is halved, the gravitational force increases by a factor of 4, so the new force is 40 N.

Correct Answer: B — 40 N

Q. The gravitational potential at a point is defined as the work done in bringing a unit mass from infinity to that point. What is the unit of gravitational potential?

A. J/kg
B. N/kg
C. J/m
D. N/m

Solution

The unit of gravitational potential is Joules per kilogram (J/kg).

Correct Answer: A — J/kg

Q. The gravitational potential at infinity is defined as what value?

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

Solution

The gravitational potential at infinity is defined to be 0.

Correct Answer: A — 0

Q. The gravitational potential energy of a system of two masses is negative. What does this imply?

A. The masses are repelling each other
B. The masses are attracting each other
C. The system is in equilibrium
D. The potential energy is zero

Solution

A negative gravitational potential energy indicates that the masses are attracting each other.

Correct Answer: B — The masses are attracting each other

Q. The gravitational potential energy of an object at height h is given by which formula?

A. mgh
B. gh
C. mg/h
D. mgh^2

Solution

The gravitational potential energy U at height h is given by U = mgh.

Correct Answer: A — mgh

Q. The gravitational potential energy of an object is given by which formula?

A. U = mgh
B. U = -GMm/r
C. U = 1/2 mv^2
D. U = Fd

Solution

The gravitational potential energy U of an object in a gravitational field is given by U = -GMm/r.

Correct Answer: B — U = -GMm/r

Q. The gravitational potential energy of two masses m1 and m2 separated by a distance r is given by which formula?

A. -G(m1*m2)/r
B. G(m1*m2)/r
C. -G(m1+m2)/r
D. G(m1+m2)/r

Solution

The gravitational potential energy U = -G(m1*m2)/r.

Correct Answer: A — -G(m1*m2)/r

Q. The half-life of a first-order reaction is dependent on which of the following?

A. Initial concentration
B. Rate constant
C. Temperature
D. All of the above

Solution

The half-life of a first-order reaction is given by t1/2 = 0.693/k, which depends only on the rate constant.

Correct Answer: B — Rate constant

Q. The heat transfer coefficient in convection depends on which of the following?

A. Surface area
B. Fluid velocity
C. Temperature difference
D. All of the above

Solution

The heat transfer coefficient in convection depends on surface area, fluid velocity, and temperature difference.

Correct Answer: D — All of the above

Q. The interquartile range of the data set: 1, 2, 3, 4, 5, 6, 7, 8 is:

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

Solution

Q1 = 3, Q3 = 6. Interquartile Range = Q3 - Q1 = 6 - 3 = 3.

Correct Answer: B — 3

Q. The Langmuir adsorption isotherm assumes that:

A. Adsorption occurs on a surface with infinite sites
B. Adsorption sites are equivalent
C. Adsorption is a multilayer process
D. Adsorption is independent of pressure

Solution

The Langmuir isotherm assumes that adsorption sites are equivalent and that the process is monolayer.

Correct Answer: B — Adsorption sites are equivalent

Q. The Langmuir adsorption isotherm assumes which of the following?

A. Adsorption occurs on a surface with infinite sites
B. Adsorption sites are equivalent
C. Adsorption is a multilayer process
D. Adsorption is temperature independent

Solution

The Langmuir isotherm assumes that adsorption occurs on a surface with a finite number of equivalent sites.

Correct Answer: B — Adsorption sites are equivalent

Q. The Langmuir isotherm assumes that adsorption occurs at specific sites on the adsorbent. What is the maximum number of molecules that can be adsorbed at a given temperature called?

A. Adsorption capacity
B. Saturation capacity
C. Equilibrium constant
D. Adsorption energy

Solution

The maximum number of molecules that can be adsorbed at a given temperature is referred to as the saturation capacity.

Correct Answer: B — Saturation capacity

Q. The length of a rod is measured as 50 cm with an error of 1 cm. What is the minimum possible length?

A. 49 cm
B. 50 cm
C. 51 cm
D. 48 cm

Solution

Minimum possible length = Measured value - Error = 50 - 1 = 49 cm.

Correct Answer: A — 49 cm

Q. The lengths of the sides of triangle ABC are 7 cm, 24 cm, and 25 cm. What type of triangle is it?

A. Acute
B. Obtuse
C. Right
D. Equilateral

Solution

Since 7^2 + 24^2 = 25^2, triangle ABC is a right triangle.

Correct Answer: C — Right

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

A. Coincident
B. Parallel
C. Intersecting
D. Perpendicular

Solution

To determine the nature of the lines, we can analyze the discriminant of the quadratic equation.

Correct Answer: C — Intersecting

Q. The lines represented by the equation 4x^2 - 12xy + 9y^2 = 0 are:

A. Parallel
B. Coincident
C. Intersecting
D. Perpendicular

Solution

The lines are perpendicular if the product of their slopes is -1. We can find the slopes from the equation and check this condition.

Correct Answer: D — Perpendicular

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

A. Parallel
B. Perpendicular
C. Coincident
D. Intersecting

Solution

The discriminant is negative, indicating that the lines are perpendicular.

Correct Answer: B — Perpendicular

Q. The lines represented by the equation 5x^2 - 6xy + 5y^2 = 0 intersect at:

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

Solution

The lines intersect at the origin (0,0) as derived from the equation.

Correct Answer: A — (0,0)

Q. The lines represented by the equation 5x^2 - 6xy + y^2 = 0 intersect at which point?

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

Solution

The lines intersect at the origin, which can be verified by substituting x = 0 and y = 0 into the equation.

Correct Answer: A — (0,0)

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

A. Parallel
B. Coincident
C. Intersecting
D. Perpendicular

Solution

The lines are perpendicular if the product of their slopes is -1, which can be verified from the equation.

Correct Answer: D — Perpendicular

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

A. Parallel
B. Intersecting
C. Coincident
D. Perpendicular

Solution

The lines intersect at the origin and are not parallel, hence they are intersecting.

Correct Answer: B — Intersecting

Q. The lines represented by the equation x^2 - 6x + y^2 - 8y + 9 = 0 are:

A. Parallel
B. Coincident
C. Intersecting
D. Perpendicular

Solution

Completing the square shows that the lines intersect at two distinct points.

Correct Answer: C — Intersecting

Q. The lines represented by the equation x^2 - 6xy + 9y^2 = 0 are:

A. Coincident
B. Parallel
C. Intersecting
D. Perpendicular

Solution

The equation can be factored as (x - 3y)^2 = 0, indicating that the lines are coincident.

Correct Answer: A — Coincident

Q. The magnetic field inside a long solenoid is?

A. Zero
B. Uniform
C. Non-uniform
D. Depends on the current

Solution

The magnetic field inside a long solenoid is uniform and parallel to the axis of the solenoid.

Correct Answer: B — Uniform

Q. The maximum value of the function f(x) = -x^2 + 4x + 1 is at x = ?

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

Solution

To find the maximum, we calculate f'(x) = -2x + 4. Setting f'(x) = 0 gives x = 2. Since f''(x) = -2 < 0, this is a maximum point.

Correct Answer: B — 2

Q. The maximum value of the function f(x) = -x^2 + 4x + 1 is:

A. 5
B. 9
C. 7
D. 6

Solution

The vertex form of a parabola gives the maximum value at x = -b/(2a) = 2. Evaluating f(2) = -2^2 + 4*2 + 1 = 9.

Correct Answer: A — 5

Q. The maximum value of the function f(x) = -x^2 + 4x + 1 occurs at:

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

Solution

The vertex of the parabola given by f(x) = -x^2 + 4x + 1 occurs at x = -b/(2a) = -4/(-2) = 2, which gives the maximum value.

Correct Answer: A — x = 2

Q. The mean free path of gas molecules is defined as:

A. The average distance traveled between collisions
B. The distance traveled in one second
C. The distance between two gas containers
D. The average distance of gas molecules in a container

Solution

The mean free path is the average distance a molecule travels before colliding with another molecule.

Correct Answer: A — The average distance traveled between collisions

Q. The mean of a data set is 50 and the standard deviation is 5. What is the coefficient of variation?

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

Solution

Coefficient of Variation = (Standard Deviation / Mean) * 100 = (5 / 50) * 100 = 10%.

Correct Answer: B — 10%

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