When an unpolarized light of intensity $I_0$ is incident on a polarizing sheet,the intensity of the light which does not get transmitted is

The extreme values of $4 \cos \left(x^2\right) \cos \left(\frac{\pi}{3}+x^2\right) \cos \left(\frac{\pi}{3}-x^2\right)$ over $\mathbb{R}$ are

The solution of the differential equation $\frac{dy}{dx} + \frac{3x^2}{1+x^3}y = \frac{\sin^2 x}{1+x^3}$ is

The monomer of neoprene is

Consider two statements $S_1$ and $S_2$.
$S_1$: If $f(x)$ is a differentiable function with $f'(x) = 0$ in $(a, b)$ and $f(x)$ is increasing in $(a, b)$,then $\frac{f(x)}{f'(x)}$ is also increasing in $(a, b)$.
$S_2$: Both $\sin x$ and $\tan x$ are increasing functions in $(0, \frac{\pi}{2})$.
Which of the following is true?

Which of the following is an insecticide?