The integral $\int \frac{3x^{13} + 2x^{11}}{(2x^4 + 3x^2 + 1)^4} dx$ is equal to (where $C$ is a constant of integration)

The ascending limb of the Loop of Henle is permeable to which of the following?

One mole of $A_{(g)}$ is heated to $200^{\circ} C$ in a one litre closed flask,till the following equilibrium is reached.
$A_{(g)} \rightleftharpoons B_{(g)}$
The rate of forward reaction at equilibrium is $0.02 \ mol \ L^{-1} \ min^{-1}$. What is the rate (in $mol \ L^{-1} \ min^{-1}$) of the backward reaction at equilibrium?

In a compound microscope,the focal lengths of the objective and the eye lens are $2.5 \, cm$ and $5 \, cm$ respectively. An object is placed at $3.75 \, cm$ before the objective and the image is formed at the least distance of distinct vision. Then,the distance between the two lenses (i.e.,the length of the microscope tube) will be......$cm$.

If $\int \frac{d x}{\sqrt{\sin ^3 x \cos x}}=g(x)+c$,then $g(x)$ is equal to

The equation of a stationary wave along a stretched string is given by $y = 5 \sin \frac{\pi x}{3} \cos 40 \pi t$,where $x$ and $y$ are in $cm$ and $t$ is in $s$. The separation between two adjacent nodes is .... $cm$.