The wavelengths of light used in an optical instrument are ${\lambda _1 = 4000 \ \mathring{A}}$ and ${\lambda _2 = 5000 \ \mathring{A}}$. The ratio of their respective resolving powers (corresponding to ${\lambda _1}$ and ${\lambda _2}$) is:

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.

An open vessel at $300 \ K$ is heated until $2/5$ of the air in it has been expelled. Assuming the volume of the vessel remains constant,find the temperature to which the vessel has been heated in $K$.

$A$ balloon with mass $m$ is descending down with an acceleration $a$ (where $a < g$). How much mass should be removed from it so that it starts moving up with an acceleration $a$?

If $5x - 12y + 10 = 0$ and $12y - 5x + 16 = 0$ are two tangents to a circle,then the radius of the circle is

Which of the following is $NOT$ a stage of sexual reproduction in fungi?