1

JEE Main 2022 (Online) 29th July Morning Shift

MCQ (Single Correct Answer)

+4

-1

Let $$f(x)=3^{\left(x^{2}-2\right)^{3}+4}, x \in \mathrm{R}$$. Then which of the following statements are true?

$$\mathrm{P}: x=0$$ is a point of local minima of $$f$$

$$\mathrm{Q}: x=\sqrt{2}$$ is a point of inflection of $$f$$

$$R: f^{\prime}$$ is increasing for $$x>\sqrt{2}$$

2

JEE Main 2022 (Online) 28th July Evening Shift

MCQ (Single Correct Answer)

+4

-1

The function $$f(x)=x \mathrm{e}^{x(1-x)}, x \in \mathbb{R}$$, is :

3

JEE Main 2022 (Online) 28th July Morning Shift

MCQ (Single Correct Answer)

+4

-1

If the minimum value of $$f(x)=\frac{5 x^{2}}{2}+\frac{\alpha}{x^{5}}, x>0$$, is 14 , then the value of $$\alpha$$ is equal to :

4

JEE Main 2022 (Online) 26th July Evening Shift

MCQ (Single Correct Answer)

+4

-1

If the maximum value of $$a$$, for which the function $$f_{a}(x)=\tan ^{-1} 2 x-3 a x+7$$ is non-decreasing in $$\left(-\frac{\pi}{6}, \frac{\pi}{6}\right)$$, is $$\bar{a}$$, then $$f_{\bar{a}}\left(\frac{\pi}{8}\right)$$ is equal to :

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