The technique used to make numerous copies of a specific segment of $DNA$ quickly and accurately is

If $|x| < 1$ and $y = x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4} + \ldots$,then $x$ is equal to :

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 : $\log _{10} 2=0.3$

If $p$ and $q$ are the perpendicular distances from the origin to the straight lines $x \sec \theta - y \operatorname{cosec} \theta = a$ and $x \cos \theta + y \sin \theta = a \cos 2 \theta$,then

If the geometric mean between $a$ and $b$ is $\frac{a^{n+1} + b^{n+1}}{a^n + b^n}$,then the value of $n$ is

The slopes of the lines represented by $x^2+2 h x y+2 y^2=0$ are in the ratio $1:2$,then $h$ is equal to: