In an $ac$ circuit,the instantaneous values of e.m.f. and current are $e = 200 \sin(314t) \text{ V}$ and $i = \sin(314t + \frac{\pi}{3}) \text{ A}$. The average power consumed in watt is

In humans,at the end of the first meiotic division,the male germ cells differentiate into the

In the figure shown,for given values of $R_1$ and $R_2$,the balance point for the jockey is at $40\, cm$ from $A$. When $R_2$ is shunted by a resistance of $10\,\Omega$,the balance point shifts to $50\, cm$. Find $R_1$ and $R_2$ $(AB = 1\, m)$.

Consider the following gaseous equilibria with equilibrium constants $K_{1}$ and $K_{2}$ respectively.
$SO_{2(g)} + \frac{1}{2} O_{2(g)} \rightleftharpoons SO_{3(g)}$
$2 SO_{3(g)} \rightleftharpoons 2 SO_{2(g)} + O_{2(g)}$
The equilibrium constants are related as

The biquadratic equation,two of whose roots are $1+i$ and $1-\sqrt{2}$,is

The structural formula of $2$-methyl-$2$-butene is: