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2025 JEE PYQ

Get chapter-wise JEE Main & Advanced questions with solutions

Q JEE MAIN 2025
If the equation of the parabola with vertex $\mathrm{V}\left(\frac{3}{2}, 3\right)$ and the directrix $x+2 y=0$ is $\alpha x^{2}+\beta y^{2}-\gamma x y-30 x-60 y+225=0$, then $a+\beta+\gamma$...
JEE Main Mathematics Easy
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Q JEE MAIN 2025
The function $f:(-\infty, \infty) \rightarrow(-\infty, 1)$, defined by $f(x)=\frac{2^{x}-2^{-x}}{2^{x}+2^{-x}}$ is :
JEE Main Mathematics Easy
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Q JEE MAIN 2025
Let $\overrightarrow{\mathrm{a}}=3 \hat{i}-\hat{j}+2 \hat{k}, \overrightarrow{\mathrm{~b}}=\overrightarrow{\mathrm{a}} \times(\hat{i}-2 \hat{k})$ and $\overrightarrow{\mathrm{c}}=\overrightarrow{\mathrm{b}} \times \hat{k}$. Then the projection of $\overrightarrow{\mathrm{c}}-2 \hat{j}$ on $\vec{a}$ is:
JEE Main Mathematics Easy
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Q JEE MAIN 2025
Let $\mathrm{A}=\left\{x \in(0, \pi)-\left\{\frac{\pi}{2}\right\}: \log _{(2 / \pi)}|\sin x|+\log _{(2 / \pi)}|\cos x|=2\right\}$ and $B=\{x \geq 0: \sqrt{x}(\sqrt{x}-4)-3|\sqrt{x}-2|+6=0\}$. Then $n(A \cup B)$ is equal to...
JEE Main Mathematics Medium
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Q JEE MAIN 2025
Let $\mathrm{A}=\left[a_{i j}\right]$ be a square matrix of order 2 with entries either 0 or 1 . Let E be the event that A is...
JEE Main Mathematics Easy
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Q JEE MAIN 2025
The number of real solution(s) of the equation $x^{2}+3 x+2=\min \{|x-3|,|x+2|\}$ is :
JEE Main Mathematics Easy
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Q JEE MAIN 2025
For some a, b, let $$ f(x)=\left|\begin{array}{ccc} a+\frac{\sin x}{x} & 1 & \mathbf{b} \\ \mathbf{a} & 1+\frac{\sin x}{x} & \mathbf{b} \\ \mathbf{a} & 1 &...
JEE Main Mathematics Easy
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Q JEE MAIN 2025
If $7=5+\frac{1}{7}(5+\alpha)+\frac{1}{7^{2}}(5+2 \alpha)+\frac{1}{7^{3}}(5+3 \alpha)+\ldots \ldots \ldots$, then the value of $\alpha$ is :
JEE Main Mathematics Easy
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Q JEE MAIN 2025
The area of the region enclosed by the curves $y=\mathbf{e}^{x}, y=\left|\mathbf{e}^{x}-1\right|$ and $y$-axis is :
JEE Main Mathematics Medium
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Q JEE MAIN 2025
If the system of equations $x+2 y-3 z=2$ $2 x+\lambda y+5 z=5$ $14 x+3 y+\mu z=33$ has infinitely many solutions, then $\lambda+\mu$ is equal to:
JEE Main Mathematics Easy
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