When an $AC$ source of $e.m.f. \ e = E_0 \sin(100t)$ is connected across a circuit,the phase difference between the $e.m.f. \ e$ and the current $i$ in the circuit is observed to be $\frac{\pi}{4}$ as shown in the diagram. If the circuit consists possibly only of $RC$,$RL$,or $LC$ in series,find the relationship between the two elements.

Opening of flowers in the cymose inflorescence is

The events $A$ and $B$ have probabilities $0.25$ and $0.50$,respectively. The probability that both $A$ and $B$ occur simultaneously is $0.14$. Then,the probability that neither $A$ nor $B$ occurs is:

How many $H$ atoms are present in $0.046 \, g$ of ethanol $(C_2H_5OH)$?

If $g$ is the acceleration due to gravity on the earth's surface,the gain in the potential energy of an object of mass $m$ raised from the surface of the earth to a height equal to the radius $R$ of the earth is