$ \text{If } 0 < x < \tfrac{1}{\sqrt{2}} \text{ and } \tfrac{\sin^{-1}x}{\alpha} = \tfrac{\cos^{-1}x}{\beta}, \text{ then the value of } \sin!\left(\tfrac{2\pi\alpha}{\alpha+\beta}\right) \text{ is :}$

1

If the line $x-1=0$ is a directrix of the hyperbola $kx^{2}-y^{2}=6$, then the hyperbola passes through the point:

Topic: JEE Main 2022 (26 July Evening Shift)

2

Let the abscissae of the two points $P$ and $Q$ on a circle be the roots of $x^{2}-4x-6=0$ and the ordinates of $P$ a…

Topic: JEE Main 2022 (26 July Evening Shift)

3

Let the solution curve $y=f(x)$ of the differential equation $\dfrac{dy}{dx}+\dfrac{xy}{x^{2}-1}=\dfrac{x^{4}+2x}{\sqrt…

Topic: JEE Main 2022 (26 July Evening Shift)

4

$\int_{0}^{20\pi} (|\sin x| + |\cos x|)^{2} \, dx$ is equal to:

Topic: JEE Main 2022 (26 July Evening Shift)

5

The value of $\log_{e}2 \, \dfrac{d}{dx}\!\big(\log_{\cos x} \csc x\big)$ at $x=\tfrac{\pi}{4}$ is:

Topic: JEE Main 2022 (26 July Evening Shift)

6

Let $\beta=\lim_{x\to 0}\dfrac{\alpha x-(e^{3x}-1)}{\alpha x(e^{3x}-1)}$ for some $\alpha\in\mathbb{R}$. Then the val…

Topic: JEE Main 2022 (26 July Evening Shift)

7

If the maximum value of $a$, for which the function $f_a(x)=\tan^{-1}(2x)-3ax+7$ is non-decreasing in $\left(-\tfrac{\p…

Topic: JEE Main 2022 (26 July Evening Shift)

8

Let $P$ and $Q$ be any points on the curves $(x-1)^{2}+(y+1)^{2}=1$ and $y=x^{2}$, respectively. The distance between…

Topic: JEE Main 2022 (26 July Evening Shift)

9

Let $A=\begin{bmatrix}1\\1\\1\end{bmatrix}$ and $B=\begin{bmatrix} 9^{2} & -10^{2} & 11^{2}\\ 12^{2} & 13^{2} & -14^{2…

Topic: JEE Main 2022 (26 July Evening Shift)

10

If $z = x+iy$ satisfies $|z|-2=0$ and $|z-i|-|z+5i|=0$, then :

Topic: JEE Main 2022 (26 July Evening Shift)

1

$ \text{The integral } \int \dfrac{\left(1-\tfrac{1}{\sqrt{3}}\right)(\cos x-\sin x)}{1+\tfrac{2}{\sqrt{3}}\sin 2x},dx …

Topic: JEE Main 2022 (26 July Evening Shift)

2

$ \text{The area bounded by the curves } y=\lvert x^{2}-1\rvert \text{ and } y=1 \text{ is :}$

Topic: JEE Main 2022 (26 July Evening Shift)