If $\sin^{-1}(\frac{x}{5}) + \csc^{-1}(\frac{5}{4}) = \frac{\pi}{2}$,then $x = $

Adsorption of phenol from its aqueous solution on to fly ash obeys Freundlich isotherm. At a given temperature, from $10 \ mg \ g ^{-1}$ and $16 \ mg \ g ^{-1}$ aqueous phenol solutions, the concentrations of adsorbed phenol are measured to be $4 \ mg \ g ^{-1}$ and $10 \ mg \ g ^{-1}$, respectively. At this temperature, the concentration (in $mg \ g ^{-1}$ ) of adsorbed phenol from $20 \ mg \ g ^{-1}$ aqueous solution of phenol will be $.....$ .
Use : $\log _{10} 2=0.3$

In the $lac$ operon model,lactose molecules function as:

To which group does the plant shown in the given figure belong?

$X$-rays are used in:

$A$ $500\,\mu F$ capacitor is charged at a steady rate of $100\,\mu C/s$. The potential difference across the capacitor will be $10\,V$ after an interval of $......\,s$.