If $\int \frac{x^2-1}{(x+1)^2 \sqrt{x(x^2+x+1)}} dx = A \tan^{-1}\left(\sqrt{\frac{x^2+x+1}{x}}\right) + C$,where $C$ is a constant,then $A$ equals to

Which of the following anthropogenic actions leads to evolution?

A positive ion $A$ and a negative ion $B$ has charges $6.67 \times 10^{-19}\ {C}$ and $9.6 \times 10^{-10}\ {C}$, and masses $19.2 \times 10^{-27}\ {kg}$ and $9 \times 10^{-27}\ {kg}$ respectively. At an instant, the ions are separated by a certain distance $r$. At that instant the ratio of the magnitudes of electrostatic force to gravitational force is ${P} \times 10^{-13}$, where the value of $P$ is _________ .
(Take $\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9\ {Nm}^2 {C}^{-1}$ and universal gravitational constant as $6.67 \times 10^{-11}\ {Nm}^2 {kg}^{-2}$)

The radius of which of the following orbits is the same as that of the $1^{st}$ orbit of $H$ atom?

The given diagram shows an ideal gas taken from state $1$ to $2$ through optional paths $A, B, C$. Let $Q, W$,and $\Delta U$ represent the heat supplied to the gas,work done by the gas,and the change in internal energy of the gas,respectively. Which of the following conditions is true?

The standard e.m.f. of a cell,involving one electron change is found to be $0.591 \ V$ at $25 \ ^oC$. The equilibrium constant of the reaction is ($F = 96,500 \ C \ mol^{-1}$; $R = 8.314 \ JK^{-1} \ mol^{-1}$)