$A$ 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

Olefins can be hydrogenated by

Let $C$ be the centre of the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$. The tangent at any point $P$ on this hyperbola meets the straight lines $bx - ay = 0$ and $bx + ay = 0$ at points $Q$ and $R$ respectively. Then $CQ \cdot CR = $

$\lim _{x \rightarrow \infty} \left(\frac{x+a}{x+b}\right)^{x}$ is equal to

Suppose the gravitational force varies inversely as the $n^{th}$ power of distance. Then the time period of a planet in circular orbit of radius $R$ around the sun will be proportional to

In the following circuit,$PN-$ junction diodes $D_1, D_2,$ and $D_3$ are ideal. For the following potentials of $A$ and $B,$ the correct increasing order of resistance between $A$ and $B$ will be:
$(i) -10 \ V, -5 \ V$
$(ii) -5 \ V, -10 \ V$
$(iii) -4 \ V, -12 \ V$