$A$ conducting sphere of radius $R$ carrying a charge $q$ is joined to a conducting sphere of radius $2R$ carrying a charge $-2q$. The charge flowing between them will be

$A$ mass $m$ hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass $m$ and radius $R$. Assuming the pulley to be a perfect uniform circular disc,the acceleration of the mass $m$,if the string does not slip on the pulley,is:

The ratio of specific heats of a gas is $\gamma$. The change in internal energy of one mole of the gas,when the volume changes from $V$ to $2 V$ at constant pressure $p$ is

The vector sum of two forces is perpendicular to their vector difference. In that case,the forces

The probability that an individual suffers a bad reaction from an injection is $0.001$. The probability that out of $2000$ individuals exactly three will suffer a bad reaction is:

The reaction $A \xrightarrow{k}$ Product is zero order,while the reaction $B \xrightarrow{k}$ Product is a first order reaction. For what initial concentration of $A$ are the half-lives of the two reactions equal?