Practice/Question bank/JEE Advanced

JEE Advanced practice questions

IIT-level single/multiple correct and numericals from past papers. 713 questions in the bank.

1. 1Let $\alpha$ and $\beta$ be real numbers such that $-\frac{\pi}{4}<\beta<0<\alpha<\frac{\pi}{4}$. If $\sin (\alpha+\beta)=\frac{1}{3}$ and…Mathematics· JEE Adv 2022 Paper 2· Challenging
2. 2For a complex number $z$, let $\operatorname{Re}(z)$ denote the real part of $z$. Let $S$ be the set of all complex numbers $z$ satisfying…Mathematics· JEE Adv 2020 Paper 2· Challenging
3. 3The probability that a missile hits a target successfully is 0.75 . In order to destroy the target completely, at least three successful…Mathematics· JEE Adv 2020 Paper 2· Challenging
4. 4Let $O$ be the centre of the circle $x^{2}+y^{2}=r^{2}$, where $r>\frac{\sqrt{5}}{2}$. Suppose $P Q$ is a chord of this circle and the…Mathematics· JEE Adv 2020 Paper 2· Challenging
5. 5The trace of a square matrix is defined to be the sum of its diagonal entries. If $A$ is a $2 \times 2$ matrix such that the trace of $A$…Mathematics· JEE Adv 2020 Paper 2· Challenging
6. 6Three numbers are chosen at random, one after another with replacement, from the set $S=\{1,2,3, \ldots, 100\}$. Let $p_1$ be the…Mathematics· JEE Adv 2021 Paper 1· Challenging
7. 7Three numbers are chosen at random, one after another with replacement, from the set $S=\{1,2,3, \ldots, 100\}$. Let $p_1$ be the…Mathematics· JEE Adv 2021 Paper 1· Challenging
8. 8Consider the region $R=\left\{(x, y) \in \mathbb{R} \times \mathbb{R}: x \geq 0\right.$ and $\left.y^2 \leq 4-x\right\}$. Let $\mathcal{F}$…Mathematics· JEE Adv 2021 Paper 2· Challenging
9. 9Consider the region $R=\left\{(x, y) \in \mathbb{R} \times \mathbb{R}: x \geq 0\right.$ and $\left.y^2 \leq 4-x\right\}$. Let $\mathcal{F}$…Mathematics· JEE Adv 2021 Paper 2· Challenging
10. 10Let $f_1:(0, \infty) \rightarrow \mathbb{R}$ and $f_2:(0, \infty) \rightarrow \mathbb{R}$ be defined by \[f_1(x)=\int_0^x…Mathematics· JEE Adv 2021 Paper 2· Challenging
11. 11Let $f_1:(0, \infty) \rightarrow \mathbb{R}$ and $f_2:(0, \infty) \rightarrow \mathbb{R}$ be defined by \[f_1(x)=\int_0^x…Mathematics· JEE Adv 2021 Paper 2· Challenging
12. 12Let $\mathrm{g}_i:\left[\frac{\pi}{8}, \frac{3 \pi}{8}\right] \rightarrow \mathbb{R}, \mathrm{i}=1,2$, and $f:\left[\frac{\pi}{8}, \frac{3…Mathematics· JEE Adv 2021 Paper 2· Challenging
13. 13What is the value of \[ \sec ^{-1}\left(\frac{1}{4} \sum_{k=0}^{10} \sec \left(\frac{7 \pi}{12}+\frac{k \pi}{2}\right) \sec \left(\frac{7…Mathematics· JEE Adv 2019 Paper 2· Challenging
14. 14An engineer is required to visit a factory for exactly four days during the first 15 days of every month and it is mandatory that no two…Mathematics· JEE Adv 2020 Paper 2· Challenging
15. 15In a hotel, four rooms are available. Six persons are to be accommodated in these four rooms in such a way that each of these rooms…Mathematics· JEE Adv 2020 Paper 2· Challenging
16. 16Two fair dice, each with faces numbered 1,2,3,4,5 and 6, are rolled together and the sum of the numbers on the faces is observed. This…Mathematics· JEE Adv 2020 Paper 2· Challenging
17. 17Let the function $f:[0,1] \rightarrow \mathbb{R}$ be defined by \[ f(x)=\frac{4^{x}}{4^{x}+2} \] Then what is the value of \[…Mathematics· JEE Adv 2020 Paper 2· Challenging
18. 18For $x \in \mathbb{R}$, what is the number of real roots of the equation \[ 3 x^{2}-4\left|x^{2}-1\right|+x-1=0 \]?Mathematics· JEE Adv 2021 Paper 1· Challenging
19. 19In a triangle $A B C$, let $A B=\sqrt{23}, B C=3$ and $C A=4$. Then what is the value of \[ \frac{\cot A+\cot C}{\cot B} \]?Mathematics· JEE Adv 2021 Paper 1· Challenging