If $\int \frac{5\tan x}{\tan x - 2} dx = x + a \ln |\sin x - 2\cos x| + k$,then $a$ is equal to

Which of the following compounds is an optically inactive compound?

The cell reaction $Mn + 2Ag_{(C_1)}^{+} (aq) \to Mn_{(C_2)}^{+2} (aq) + 2Ag$ is represented by

The formation of the oxide ion $O^{2-}_{(g)}$ requires first an exothermic and then an endothermic step as shown below:
$O_{(g)} + e^- \to O^-_{(g)}; \Delta H = -142 \ kJ/mol$
$O^-_{(g)} + e^- \to O^{2-}_{(g)}; \Delta H = 844 \ kJ/mol$
This is because:

The bob of a simple pendulum is displaced from its equilibrium position $O$ to a position $Q$ which is at height $h$ above $O$ and the bob is then released. Assuming the mass of the bob to be $m$ and time period of oscillations to be $2.0\ s$,the tension in the string when the bob passes through $O$ is

If $x^y=y^x$,then $x(x-y \log x) \frac{d y}{d x}$ is equal to :