If $\frac{dy}{dx} = \frac{xy + y}{xy + x}$,then the solution of the differential equation is

If the rate of disappearance of $N_2O_5$ in the following reaction is $1.2 \times 10^{-5} \ mol \ L^{-1} \ s^{-1}$,the rate of production of $NO_2$ in $mol \ L^{-1} \ s^{-1}$ is:
$2 \ N_2O_{5(g)} \longrightarrow 4 \ NO_{2(g)} + O_{2(g)}$

In a series resonant $LCR$ circuit,the voltage across $R$ is $100\,V$ and $R = 1\,k\Omega$ with $C = 2\,\mu F$. The resonant frequency $\omega$ is $200\,rad/s$. At resonance,the voltage across $L$ is:

Bird flu is caused by

$A$ proton, a deuteron, and an $\alpha$-particle having the same momentum enter a region of uniform electric field between the parallel plates of a capacitor. The electric field is perpendicular to the initial path of the particles. Then the ratio of deflections suffered by them is

If $\cos ^{-1}\left(\frac{5}{13}\right)+\cos ^{-1}\left(\frac{3}{5}\right)=\cos ^{-1} x$,then $x$ is equal to