JEE Maths PYQ Practice, chapter-wise

JEE Main 2021 (Online) 25th February Evening ShiftQuestion 1

The integral $\int\frac{e^{3\log_e2x}+5e^{2\log_e2x}}{e^{4\log_ex}+5e^{3\log_ex}-7e^{2\log_ex}}dx$, $x>0$, is equal to : (where $c$ is a constant of integration)

Indefinite Integration

$\log_e\left|x^{2}+5x-7\right|+c$$4\log_e\left|x^{2}+5x-7\right|+c$$\frac{1}{4}\log_e\left|x^{2}+5x-7\right|+c$$\log_e\sqrt{\left|x^{2}+5x-7\right|}+c$

JEE Main 2021 (Online) 3rd August Evening ShiftQuestion 2

The integral $\int\frac{dx}{\sqrt{2x+5}-\sqrt{2x+3}}$ is equal to (where $C$ is a constant of integration)

Indefinite Integration

$\frac{1}{3}\left[(2x+5)^{\frac{3}{2}}+(2x+3)^{\frac{3}{2}}\right]+C$$\frac{1}{6}\left[(2x+5)^{\frac{2}{3}}+(2x+3)^{\frac{2}{3}}\right]+C$$\frac{1}{6}\left[(2x+5)^{\frac{3}{2}}+(2x+3)^{\frac{3}{2}}\right]+C$$\frac{1}{12}\left[(2x+5)^{\frac{2}{3}}+(2x+3)^{\frac{2}{3}}\right]+C$

JEE Main 2021 (Online) 25th February Morning ShiftQuestion 3

The value of the integral $\int\frac{\sin\theta\cdot\sin2\theta\left(\sin^{6}\theta+\sin^{4}\theta+\sin^{2}\theta\right)\sqrt{2\sin^{4}\theta+3\sin^{2}\theta+6}}{1-\cos2\theta}\,d\theta$ is : (where $c$ is a constant of integration)

Indefinite Integration

$\frac{1}{18}\left[9-2\sin^{6}\theta-3\sin^{4}\theta-6\sin^{2}\theta\right]^{3/2}+c$$\frac{1}{18}\left[9-2\cos^{6}\theta-3\cos^{4}\theta-6\cos^{2}\theta\right]^{3/2}+c$$\frac{1}{18}\left[11-18\sin^{2}\theta+9\sin^{4}\theta-2\sin^{6}\theta\right]^{3/2}+c$$\frac{1}{18}\left[11-18\cos^{2}\theta+9\cos^{4}\theta-2\cos^{6}\theta\right]^{3/2}+c$

JEE Main 2021 (Online) 18th March Morning ShiftQuestion 4

The integral $\int\frac{(2x-1)\cos\sqrt{(2x-1)^{2}+5}}{\sqrt{4x^{2}-4x+6}}dx$ is equal to : (where $c$ is a constant of integration)

Indefinite Integration

$\frac{1}{2}\sin\sqrt{(2x+1)^{2}+5}+c$$\frac{1}{2}\sin\sqrt{(2x-1)^{2}+5}+c$$\frac{1}{2}\cos\sqrt{(2x-1)^{2}+5}+c$$\frac{1}{2}\cos\sqrt{(2x+1)^{2}+5}+c$

JEE Main 2026 (Online) 2nd April Evening ShiftQuestion 5

Let $f(x)=\int\left(\frac{16x+24}{x^{2}+2x-15}\right)dx$. If $f(4)=14\log_e(3)$ and $f(7)=\log_e(2^{\alpha}\cdot 3^{\beta})$, $\alpha,\beta\in\mathbf{N}$, then $\alpha+\beta$ is equal to :

Indefinite Integration

$31$$37$$39$$41$