JEE Mains JEE Advance BITSAT
JEE Mains | PYQ

Year

All years 2026 2025 2024 2023 2022 2021

Let $ f(\alpha) $ denote the area of the region in the first quadrant bounded by $ x=0, x=1, y^{2}=x $ and $ y=|\alpha x-5|-|1-\alpha x|+\alpha x^{2} $. Then $ \left(f(0)+f(1)\right) $ is equal to:

If $\int \left( \frac{1 - 5\cos^2 x}{\sin^5 x \cos^2 x} \right) dx = f(x) + C$, where $C$ is the constant of integration, then $f\left(\frac{\pi}{6}\right) - f\left(\frac{\pi}{4}\right)$ is equal to:

Let $ f(x) = \int \frac{(2 - x^2)e^x}{\sqrt{1 + x}(1 - x)^{3/2}} \, dx $. If $ f(0) = 0 $, then $ f\!\left(\frac{1}{2}\right) $ is equal to:

If $\int (\sin x)^{-\frac{11}{2}} (\cos x)^{-\frac{5}{2}} dx = -\frac{p_1}{q_1}(\cot x)^{\frac{9}{2}} - \frac{p_2}{q_2}(\cot x)^{\frac{5}{2}} - \frac{p_3}{q_3}(\cot x)^{\frac{1}{2}} + \frac{p_4}{q_4}(\cot x)^{-\frac{3}{2}} + C$, where $p_i$ and $q_i$ are positive integers with $\gcd(p_i, q_i)=1$ for $i=1,2,3,4$ and $C$ is the constant of integration, then $\frac{15p_1p_2p_3p_4}{q_1q_2q_3q_4}$ is equal to _________.

$ f(x)=\displaystyle \int \dfrac{7x^{10}+9x^{8}}{(1+x^{2}+2x^{9})^{2}} \, dx,\ x>0, \ \lim_{x\to 0} f(x)=0 $ and $ f(1)=\dfrac{1}{4} $. . and $ B=\operatorname{adj}(\operatorname{adj}A) $ be such that $ |B|=81 $, then $ \alpha^{2} $ is equal to:

← PreviousQuestion 3 of 8Next →

JEE Main 2026 23rd Jan Morning Shift

Let $ f(x) = \int \frac{(2 - x^2)e^x}{\sqrt{1 + x}(1 - x)^{3/2}} \, dx $. If $ f(0) = 0 $, then $ f\!\left(\frac{1}{2}\right) $ is equal to:

Let $ f(t)=\int \frac{(1-\sin (\log_{e} t))}{(1-\cos (\log_{e} t))}\,dt,\; t>1 $. If $ f\!\left(e^{\pi/2}\right)=-e^{-\pi/2} $ and $ f\!\left(e^{\pi/4}\right)=\alpha e^{\pi/4} $, then $ \alpha $ equals:

Let $ f:\mathbb{R}\to \mathbb{R} $ be a differentiable function such that $ f\!\left(\frac{x+y}{3}\right)=\frac{f(x)+f(y)}{3} $ for all $ x,y\in \mathbb{R} $, and $ f'(0)=3 $. Then the minimum value of the function $ g(x)=3+e^{x}f(x) $, is:

Let $ f(x)=\displaystyle \int \left(\dfrac{16x+24}{x^{2}+2x-15}\right)dx $. If $ f(4)=14\log_{e}(3) $ and $ f(7)=\log_{e}\!\left(2^{\alpha}\cdot3^{\beta}\right),\,\alpha,\beta\in\mathbb{N} $, then $ \alpha+\beta $ is equal to:

JEE MainsJEE AdvanceBITSATJEE Mains | PYQ

JEE Mains JEE Advance BITSAT
JEE Mains | PYQ