For any $y \in R$,let $\cot ^{-1}(y) \in (0, \pi)$ and $\tan ^{-1}(y) \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$. Then the sum of all the solutions of the equation $\tan ^{-1}\left(\frac{6 y}{9-y^2}\right)+\cot ^{-1}\left(\frac{9-y^2}{6 y}\right)=\frac{2 \pi}{3}$ for $0 < |y| < 3$,is equal to

Vapour pressure in $mm \ Hg$ of $0.1 \ mole$ of urea in $180 \ g$ of water at $25^{\circ} C$ is (The vapour pressure of water at $25^{\circ} C$ is $24 \ mm \ Hg$)

Which gas is released when $Na_2CO_3$ is heated?

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 ............. $K$.

$_6 C^{12}$ and $_1 T^3$ are formed in nature due to the nuclear reaction of a neutron with:

During the electrolytic reduction of alumina,the reaction at cathode is