What is the optimal soil $pH$ for plant growth?

If $a>0$,then $\int_{-\pi}^\pi \frac{\sin ^2 x}{1+a^x} d x$ is equal to

$A$ water barrel having water up to a depth $d$ is placed on a table of height $h$. $A$ small hole is made on the wall of the barrel at its bottom. If the stream of water coming out of the hole falls on the ground at a horizontal distance $R$ from the barrel,then the value of $d$ is

The approximate value of $(1.0002)^{3000}$ is

If $y = \sec(\tan^{-1}x)$,then $\frac{dy}{dx}$ at $x = 1$ is equal to:

If $f(x) = \frac{1}{x^2} \int_3^x (2t - 3f'(t)) dt$,then $f'(3)$ is equal to