JEE Main maths practice questions by section

Original questions for all nine sections, Section A multiple choice and Section B numerical value, each with a full worked solution.

Section A practice	Multiple choice, worked or timed
Section B practice	Type one integer, checked at once
Solutions	Every step, and why each wrong option is wrong

Try 4 questions

Question 1Section A: multiple choice

A

is a

3 \times 3

matrix with

\det(A)

=3

. The value of

\det(2\operatorname{adj}A)

Question 2Section A: multiple choice

\displaystyle\int_{-2}^{2} \left(x^3+3x+4\right)\sqrt{4-x^2}\,dx

is equal to

Question 3Section A: multiple choice

What is the shortest distance between the lines

\frac{x+1}{2}

= \frac{y-1}{2}

= \frac{z}{-3}

and

\frac{x-2}{2}

= \frac{y}{-3}

= \frac{z-4}{2}

Question 4Section A: multiple choice

Find

\sin^{-1}(\sin 5)

{}+\cos^{-1}(\cos 10)

, where the angles

5

and

10

are measured in radians, not degrees. (Inverse trigonometric functions take their principal values.)

How hard are the questions?

From standard questions to a hardest tier: questions that join two ideas or hide a trap in the setting.