From a solid sphere of mass $M$ and radius $R$,a cube of maximum possible volume is cut. The moment of inertia of the cube about an axis passing through its centre and perpendicular to one of its faces is

If we completely remove the decomposers from an ecosystem,its functioning will be adversely affected because

For the gaseous reactions $(I)$ and $(II)$,the equilibrium constants are $X$ and $Y$ respectively.
$I$. $\frac{1}{2} N_{2(g)} + O_{2(g)} \rightleftharpoons NO_{2(g)}$
$II$. $2 NO_{2(g)} \rightleftharpoons N_2 O_{4(g)}$
Using the above reactions,the equilibrium constant $Z$ for the reaction $(III)$ given below is:
$III$. $N_2 O_{4(g)} \rightleftharpoons N_{2(g)} + 2 O_{2(g)}$

Suppose a pure $Si$ crystal has $5 \times 10^{28} \text{ atoms } m^{-3}$. It is doped by $1 \text{ ppm}$ concentration of pentavalent $As$. Calculate the number of electrons and holes. Given that $n_{i} = 1.5 \times 10^{16} \text{ m}^{-3}$.

The equation of the pair of lines passing through the point $(2, 1)$ and perpendicular to the pair of lines $4xy + 2x + 6y + 3 = 0$ is:

In the circuit shown in the figure, what is the value of $I_1$ just after pressing the key $K$?