Practice/Question bank/JEE Advanced

JEE Advanced practice questions

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

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  1. 1Consider 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
  2. 2Consider 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
  3. 3Let $f_1:(0, \infty) \rightarrow \mathbb{R}$ and $f_2:(0, \infty) \rightarrow \mathbb{R}$ be defined by \[f_1(x)=\int_0^x…Mathematics· JEE Adv 2021 Paper 2· Challenging
  4. 4Let $f_1:(0, \infty) \rightarrow \mathbb{R}$ and $f_2:(0, \infty) \rightarrow \mathbb{R}$ be defined by \[f_1(x)=\int_0^x…Mathematics· JEE Adv 2021 Paper 2· Challenging
  5. 5Let $\mathrm{g}_i:\left[\frac{\pi}{8}, \frac{3 \pi}{8}\right] \rightarrow \mathbb{R}, \mathrm{i}=1,2$, and $f:\left[\frac{\pi}{8}, \frac{3…Mathematics· JEE Adv 2021 Paper 2· Challenging
  6. 6What 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
  7. 7An 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
  8. 8In 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
  9. 9Two 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
  10. 10Let 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
  11. 11For $x \in \mathbb{R}$, 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
  12. 12In 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