If $(2, 0)$ is the vertex and the $y$-axis is the directrix of a parabola,then its focus is

If $1, \log_9(3^{1-x} + 2), \log_3(4 \cdot 3^x - 1)$ are in $A.P.$,then $x$ equals

$5$ moles of Hydrogen $\left(\gamma=\frac{7}{5}\right)$ initially at $S.T.P.$ are compressed adiabatically so that its temperature becomes $400^{\circ} C$. The increase in the internal energy of the gas in kilo-joules is $(R=8.30 \ J \ mol^{-1} \ K^{-1})$.

In which of the following compounds,the transition metal is in oxidation state of zero?

The number of unit cells present in $39 \ g$ of potassium if it crystallizes as body-centered cubic $(BCC)$ is ($N = \text{Avogadro number}$,$\text{At. wt. of potassium} = 39$).

Two different radioactive elements with half-lives $T_{1}$ and $T_{2}$ have undecayed atoms $N_{1}$ and $N_{2}$ respectively,present at a given instant. The ratio of their activities at this instant is