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2025 JEE PYQ

Get chapter-wise JEE Main & Advanced questions with solutions

Q JEE MAIN 2025
Let $f(x)=\lim _{\mathrm{n} \rightarrow \infty} \sum_{\mathrm{r}=0}^{\mathrm{n}}\left(\frac{\tan \left(x / 2^{r+1}\right)+\tan ^{3}\left(x / 2^{r+1}\right)}{1-\tan ^{2}\left(x / 2^{r+1}\right)}\right)$. Then $\lim _{x \rightarrow 0} \frac{\mathrm{e}^{x}-\mathrm{e}^{f(x)}}{(x-f(x))}$ is equal to
JEE Main Mathematics Easy
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Q JEE MAIN 2025
Let $[x]$ denote the greatest integer less than or equal to $x$. Then the domain of $f(x)=\sec ^{-1}(2[x]+1)$ is :
JEE Main Mathematics Easy
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Q JEE MAIN 2025
If the midpoint of a chord of the ellipse $\frac{x^{2}}{9}+\frac{y^{2}}{4}=1$ is $(\sqrt{2}, 4 / 3)$, and the length of the chord is $\frac{2 \sqrt{\alpha}}{3}$, then...
JEE Main Mathematics Easy
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Q JEE MAIN 2025
If $f(x)=\int \frac{1}{x^{1 / 4}\left(1+x^{1 / 4}\right)} \mathrm{d} x, f(0)=-6$, then $f(1)$ is equal to :
JEE Main Mathematics Easy
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Q JEE MAIN 2025
Let $f: \mathbf{R}-\{0\} \rightarrow(-\infty, 1)$ be a polynomial of degree 2 , satisfying $f(x) f\left(\frac{1}{x}\right)=f(x)+f\left(\frac{1}{x}\right)$. If $f(\mathrm{~K})=-2 \mathrm{~K}$, then the sum of squares of all...
JEE Main Mathematics Medium
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Q JEE MAIN 2025
The area of the region bounded by the curves $x\left(1+y^{2}\right)=1$ and $y^{2}=2 x$ is:
JEE Main Mathematics Easy
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Q JEE MAIN 2025
If $\sum_{r=1}^{13}\left\{\frac{1}{\sin \left(\frac{\pi}{4}+(r-1) \frac{\pi}{6}\right) \sin \left(\frac{\pi}{4}+\frac{r \pi}{6}\right)}\right\}=a \sqrt{3}+b, a, b \in Z$, then $a^{2}+b^{2}$ is equal to :
JEE Main Mathematics Easy
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Q JEE MAIN 2025
If $\alpha+i \beta$ and $\gamma+i \delta$ are the roots of $x^{2}-(3-2 i) x-(2 i-2)=0, i=\sqrt{-1}$, then $\alpha \gamma+\beta \delta$ is equal to :
JEE Main Mathematics Easy
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Q JEE MAIN 2025
For $n \ge 2$, let ${S_n}$ denote the set of all subsets of $\{ 1,2, \ldots ,n\} $ with no two consecutive numbers. For example...
JEE Main Mathematics Hard
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