Let $S = \left\{ {x \in R:0 < x < 1\,\mathrm{and}\,2{{\tan }^{ - 1}}\left( {{{1 - x} \over {1 + x}}} \right) = {{\cos }^{ - 1}}\left( {{{1 - {x^2}} \over {1 + {x^2}}}} \right)} \right\}$.

If $\mathrm{n(S)}$ denotes the number of elements in $\mathrm{S}$ then :

1

Let $f:\mathbb{R}-\{0,1\}\to\mathbb{R}$ be a function such that $f(x)+f\!\left(\frac{1}{1-x}\right)=1+x.$ Then $f(2)$…

Topic: JEE Main 2023 (1 February Evening Shift)

2

Let $\alpha x = \exp(x^{\beta} y^{\gamma})$ be the solution of the differential equation $2x^{2}y\,dy - (1 - xy^{2})\…

Topic: JEE Main 2023 (1 February Evening Shift)

3

Let \(\vec a = 2\hat i - 7\hat j + 5\hat k\), \(\vec b = \hat i + \hat k\) and \(\vec c = \hat i + 2\hat j - 3\hat k\) …

Topic: JEE Main 2023 (1 February Evening Shift)

4

Two dice are thrown independently. Let \(A\) be the event that the number on the \(1^{\text{st}}\) die is less than t…

Topic: JEE Main 2023 (1 February Evening Shift)

5

If $A=\dfrac12\begin{bmatrix}1 & \sqrt{3}\\ -\sqrt{3} & 1\end{bmatrix}$, then:

Topic: JEE Main 2023 (1 February Evening Shift)

6

Let $a,b$ be two real numbers such that $ab

Topic: JEE Main 2023 (1 February Evening Shift)

7

The number of integral values of $k$ for which one root of the equation $2x^{2}-8x+k=0$ lies in the interval $(1,2)$ an…

Topic: JEE Main 2023 (1 February Evening Shift)

8

The area of the region given by $\{(x,y):\, xy\le 8,\ 1\le y\le x^{2}\}$ is:

Topic: JEE Main 2023 (1 February Evening Shift)

9

If $y(x)=x^{x},\ x>0$, then $y''(2)-2y'(2)$ is equal to:

Topic: JEE Main 2023 (1 February Evening Shift)

10

The value of the integral $\displaystyle \int_{-\pi/4}^{\pi/4}\frac{x+\pi/4}{\,2-\cos 2x\,}\,dx$ is:

Topic: JEE Main 2023 (1 February Evening Shift)