The domain of the function $f(x)=\sin^{-1}!\big([,2x^{2}-3,]\big)+\log_{2}!\left(\log_{1/2}(x^{2}-5x+5)\right)$, where $[,\cdot,]$ is the greatest integer function, is:

1

Let $S$ be the set of all $(\alpha,\beta)$ with $\pi

Topic: JEE Main 2022 (27 July Evening Shift)

2

If $\alpha, \beta$ are the roots of the equation $x^{2} - \left(5 + 3\sqrt{\log_{3}5} - 5\sqrt{\log_{5}3}\right)x + 3\l…

Topic: JEE Main 2022 (27 July Evening Shift)

3

If for $p\ne q\ne 0$, the function $f(x)=\dfrac{\sqrt[7]{p(729+x)}-3}{\sqrt[3]{729+qx}-9}$ is continuous at $x=0$, then:

Topic: JEE Main 2022 (27 July Evening Shift)

4

Let $f(x)=2+|x|-|x-1|+|x+1|,;x\in\mathbb{R}$. Consider (S1): $f'!\left(-\tfrac{3}{2}\right)+f'!\left(-\tfrac{1}{2}\righ…

Topic: JEE Main 2022 (27 July Evening Shift)

5

Let the sum of an infinite G.P., whose first term is $a$ and the common ratio is $r$, be $5$. Let the sum of its first …

Topic: JEE Main 2022 (27 July Evening Shift)

6

The area of the region enclosed by $y\le 4x^{2}$, $x^{2}\le 9y$ and $y\le 4$ is equal to:

Topic: JEE Main 2022 (27 July Evening Shift)

7

The value of $\displaystyle \int_{0}^{2}!\left(,|2x^{2}-3x|+\big[x-\tfrac{1}{2}\big]\right),dx$, where $[\cdot]$ is the…

Topic: JEE Main 2022 (27 July Evening Shift)

8

Consider a curve $y=y(x)$ in the first quadrant as shown in the figure. Let the area $A_{1}$ be twice the area $A_{2}$.…

Topic: JEE Main 2022 (27 July Evening Shift)

9

The equations of the sides $AB$, $BC$ and $CA$ of a triangle $ABC$ are $2x+y=0$, $x+py=39$ and $x-y=3$ respectively and…

Topic: JEE Main 2022 (27 July Evening Shift)

10

If the length of the perpendicular drawn from the point $P(a,4,2),;a>0$ on the line $\dfrac{x+1}{2}=\dfrac{y-3}{3}=\…

Topic: JEE Main 2022 (27 July Evening Shift)