The domain of the function $ f(x)=\sin^{-1}\!\left(\frac{x^{2}-3x+2}{x^{2}+2x+7}\right) $ is:

1

Let $\vec{a},\vec{b},\vec{c}$ be three coplanar concurrent vectors such that the angles between any two of them are the…

Topic: JEE Main 2022 (29 July Evening Shift)

2

Let $S=\{\,z=x+iy:\ |z-1+i|\ge |z|,\ |z|

Topic: JEE Main 2022 (29 July Evening Shift)

3

Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One ball is tra…

Topic: JEE Main 2022 (29 July Evening Shift)

4

Let $A(\alpha,-2)$, $B(\alpha,6)$ and $C\!\left(\dfrac{\alpha}{4},-2\right)$ be vertices of $\triangle ABC$. If $\left…

Topic: JEE Main 2022 (29 July Evening Shift)

5

Let $m_1, m_2$ be the slopes of two adjacent sides of a square of side $a$ such that $a^{2}+11a+3\left(m_{1}^{2}+m_{2}…

Topic: JEE Main 2022 (29 July Evening Shift)

6

Let $y=y(x)$ be the solution curve of the differential equation $ \frac{dy}{dx}+\left(\frac{2x^{2}+11x+13}{x^{3}+6x^{2}…

Topic: JEE Main 2022 (29 July Evening Shift)

7

If the solution curve of the differential equation $ \dfrac{dy}{dx}=\dfrac{x+y-2}{x-y} $ passes through the points $(…

Topic: JEE Main 2022 (29 July Evening Shift)

8

For $ I(x) = \int \frac{\sec^{2}x - 2022}{\sin^{2022}x} \, dx, $ if $ I\!\left(\frac{\pi}{4}\right) = 2^{1011}, $ then

Topic: JEE Main 2022 (29 July Evening Shift)

9

If $[t]$ denotes the greatest integer $\leq t$, then the value of $ \int_{0}^{1} \left[ 2x - |3x^{2} - 5x + 2| + 1 \ri…

Topic: JEE Main 2022 (29 July Evening Shift)

10

Which of the following matrices can NOT be obtained from the matrix $\begin{bmatrix}-1 & 2 \\ 1 & -1\end{bmatrix}$ by…

Topic: JEE Main 2022 (29 July Evening Shift)

1

If the system of equations $x+y+z=6$ $2x+5y+\alpha z=\beta$ $x+2y+3z=14$ has infinitely many solutions, then $\al…

Topic: JEE Main 2022 (29 July Evening Shift)