JEE MAIN 2025 Previous Year Questions (PYQs) – Page 1 of 38

Let $\mathrm{I}(x)=\int \frac{d x}{(x-11)^{\frac{11}{13}}(x+15)^{\frac{15}{13}}}$. If $\mathrm{I}(37)-\mathrm{I}(24)=\frac{1}{4}\left(\frac{1}{\mathrm{~b}^{\frac{1}{13}}}-\frac{1}{\mathrm{c}^{\frac{1}{13}}}\right), \mathrm{b}, \mathrm{c} \in \mathcal{N}$, then $3(\mathrm{~b}+\mathrm{c})$ is equal to

Let the three sides of a triangle be on the lines $4x-7y+10=0$, $x+y=5$ and $7x+4y=15$. Then the distance of its orthocentre from the orthocentre of the triangle formed by the lines $x=0$, $y=0$ and $x+y=1$ is

If the line $3x - 2y + 12 = 0$ intersects the parabola $4y = 3x^2$ at the points $A$ and $B$, then at the vertex of the parabola, the line segment $AB$ subtends an angle equal to:

In the expansion of $\left(\sqrt[3]{2}+\dfrac{1}{\sqrt[3]{3}}\right)^{n},\ n\in\mathbb{N}$, if the ratio of $15^{\text{th}}$ term from the beginning to the $15^{\text{th}}$ term from the end is $\dfrac{1}{6}$, then the value of ${}^nC_3$ is

If the first term of an A.P. is $3$ and the sum of its first four terms is equal to one-fifth of the sum of the next four terms, then the sum of the first $20$ terms is:

Considering the principal values of the inverse trigonometric functions, $\sin ^{-1}\left(\frac{\sqrt{3}}{2} x+\frac{1}{2} \sqrt{1-x^2}\right),-\frac{1}{2}< x<\frac{1}{\sqrt{2}}$, is equal to

Let the arc $AC$ of a circle subtend a right angle at the centre $O$. If the point $B$ on the arc $AC$ divides the arc $AC$ such that $\dfrac{\text{length of arc }AB}{\text{length of arc }BC}=\dfrac{1}{5}$, and $\overrightarrow{OC}=\alpha\,\overrightarrow{OA}+\beta\,\overrightarrow{OB}$, then $\alpha+\sqrt{2}\,(\sqrt{3}-1)\,\beta$ is equal to:

Let $A={-3,-2,-1,0,1,2,3}$ and $R$ be a relation on $A$ defined by $xRy$ iff $2x-y\in{0,1}$. Let $l$ be the number of elements in $R$. Let $m$ and $n$ be the minimum number of elements required to be added in $R$ to make it reflexive and symmetric relations, respectively. Then $l+m+n$ is equal to

Let the area of $\triangle PQR$ with vertices $P(5,4),\ Q(-2,4)$ and $R(a,b)$ be $35$ square units. If its orthocenter and centroid are $O\!\left(2,\dfrac{14}{5}\right)$ and $C(c,d)$ respectively, then $c+2d$ is equal to:

Let the domains of the functions $f(x)=\log_{4}\big(\log_{3}\big(\log_{7}\big(8-\log_{2}(x^{2}+4x+5)\big)\big)\big)$ and $g(x)=\sin^{-1}\left(\dfrac{7x+10}{x-2}\right)$ be $(\alpha,\beta)$ and $[\gamma,\delta]$, respectively. Then $\alpha^{2}+\beta^{2}+\gamma^{2}+\delta^{2}$ is equal to