$ \text{Let } f(x)=3^{(x^{2}-2)^{3}+4},; x\in\mathbb{R}. \text{ Then which of the following statements are true?} $ $P: x=0 \text{ is a point of local minima of } f$ $Q: x=\sqrt{2} \text{ is a point of inflection of } f$ $R: f' \text{ is increasing for } x>\sqrt{2}$

1

$ \text{The number of points where the function } f:\mathbb{R}\to\mathbb{R},\quad f(x)=|x-1|\cos|x-2|\sin|x-1|+(x-3),|x…

Topic: JEE Main 2022 (29 July Morning Shift)

2

$ \text{The number of points where the function } f:\mathbb{R}\to\mathbb{R},\quad f(x)=|x-1|\cos|x-2|\sin|x-1|+(x-3),|x…

Topic: JEE Main 2022 (29 July Morning Shift)

3

$ \text{Let the focal chord of the parabola } P: y^{2}=4x \text{ along the line } L: y=mx+c,; m>0 \text{ meet the parab…

Topic: JEE Main 2022 (29 July Morning Shift)

4

The area of the region$\left\{(x, y):|x-1| \leq y \leq \sqrt{5-x^{2}}\right\}$ is equal to :

Topic: JEE Main 2022 (29 July Morning Shift)

5

The area of the region$\left\{(x, y):|x-1| \leq y \leq \sqrt{5-x^{2}}\right\}$ is equal to :

Topic: JEE Main 2022 (29 July Morning Shift)

6

If $f(\alpha)=\int\limits_{1}^{\alpha} \frac{\log _{10} \mathrm{t}}{1+\mathrm{t}} \mathrm{dt}, \alpha>0$ then $f\left(\…

Topic: JEE Main 2022 (29 July Morning Shift)

7

Let $\hat{a}$ and $\hat{b}$ be two unit vectors such that the angle between them is $\frac{\pi}{4}$. If $\theta$ is the…

Topic: JEE Main 2022 (29 July Morning Shift)

8

Let the circumcentre of a triangle with vertices A(a, 3), B(b, 5) and C(a, b), ab > 0 be P(1,1). If the line AP interse…

Topic: JEE Main 2022 (29 July Morning Shift)

9

Let a line L pass through the point of intersection of the lines $b x+10 y-8=0$ and $2 x-3 y=0, \mathrm{~b} \in \mathbf…

Topic: JEE Main 2022 (29 July Morning Shift)

10

$ \text{Let the solution curve } y=y(x) \text{ of the differential equation } (1+e^{2x})!\left(\dfrac{dy}{dx}+y\right)=…

Topic: JEE Main 2022 (29 July Morning Shift)