The method of zone refining of metals is based on the principle of:

In the conversion of limestone to lime,$CaCO_{3(s)} \rightarrow CaO_{(s)} + CO_{2(g)}$,the values of $\Delta H^o$ and $\Delta S^o$ are $+179.1 \ kJ \ mol^{-1}$ and $160.2 \ J \ K^{-1} \ mol^{-1}$ respectively at $298 \ K$ and $1 \ bar$. Assuming that $\Delta H^o$ and $\Delta S^o$ do not change with temperature,the temperature above which the conversion of limestone to lime will be spontaneous is ............. $K$.

Consider a system of three charges $\frac{q}{3}, \frac{q}{3}$ and $-\frac{2q}{3}$ placed at points $A, B$ and $C$ respectively,as shown in the figure. Take $O$ to be the centre of the circle of radius $R$ and $\angle CAB = 60^\circ$.

If a point $(x, y) = (\tan \theta + \sin \theta, \tan \theta - \sin \theta)$,then the locus of $(x, y)$ is

In which of the following reactions does $H_2O_2$ act as a reducing agent?

For any integer $n \geq 1$, the number of positive divisors of $n$ is denoted by $d(n)$. Then, for a prime $P$, $d(d(d(P^7)))$ is equal to