If $u=e^{x^2-y^2}$, then

Two identical parallel plate air capacitors are connected in series to a battery of emf $V$. If one of the capacitors is inserted in a liquid of dielectric constant $K$,then the potential difference of the other capacitor will become:

The molar heat of formation of $NH_4NO_{3(s)}$ is $-367.54 \ kJ$ and those of $N_2O_{(g)}$ and $H_2O_{(l)}$ are $+81.46 \ kJ$ and $-285.78 \ kJ$ respectively at $25 \ ^oC$ and $1.0 \ atm$ pressure. Calculate $\Delta U$ at $25 \ ^oC$ for the reaction:
$NH_4NO_{3(s)} \to N_2O_{(g)} + 2H_2O_{(l)}$ (in $kJ$)

In the circuit shown in the given figure,the resistances $R_1$ and $R_2$ are respectively:

$A$ nucleus ruptures into two nuclear parts which have their velocity ratio equal to $2:1$. What will be the ratio of their nuclear size (nuclear radius)?

$A$ plano-convex lens is made of glass with a refractive index of $1.5$. The radius of curvature of its convex surface is $R$. What is its focal length?