What is the molar solubility of $Ag_2CO_3$ $(K_{sp} = 4 \times 10^{-13})$ in $0.1 \ M \ Na_2CO_3$ solution?

In a fission reaction ${}_{92}^{236}U \to {}^{117}X + {}^{117}Y + n + n,$ the binding energy per nucleon of $X$ and $Y$ is $8.5\, MeV$ whereas that of ${}^{236}U$ is $7.6\, MeV$. The total energy liberated will be about:

The $IUPAC$ name of the following compound is

The major product in the following reaction is:

The pressure and density of a diatomic gas $\left(\gamma = \frac{7}{5}\right)$ change adiabatically from $(P, d)$ to $(P^{\prime}, d^{\prime})$. If $\frac{d^{\prime}}{d} = 32$,then $\frac{P^{\prime}}{P}$ is

Two stones of masses $m$ and $3m$ are whirled in horizontal circles,the heavier one in a radius $\left(\frac{r}{3}\right)$ and the lighter one in a radius $r$. The tangential speed of the lighter stone is '$n$' times the value of the heavier stone. When the magnitude of the centripetal force becomes equal,the value of $n$ is: