The ratio of angular speeds of the minute hand and the hour hand of a watch is:

Arrange the following set of compounds in order of their decreasing relative reactivity with an electrophile,$E^{+}$:
$(a)$ Chlorobenzene,$2,4-$dinitrochlorobenzene,$p-$nitrochlorobenzene
$(b)$ Toluene,$p-CH_3-C_6H_4-NO_2$,$p-O_2N-C_6H_4-NO_2$

An increase in equivalent conductance of a strong electrolyte with dilution is mainly due to

Match the following (Take the relative strength of the strongest fundamental forces in nature as $1$):
| List-$I$ (Fundamental forces in nature) | List-$II$ (Relative strength) |
| :--- | :--- |
| $(A)$ Strong nuclear force | $(e)$ $10^{-2}$ |
| $(B)$ Weak nuclear force | $(f)$ $1$ |
| $(C)$ Electromagnetic force | $(g)$ $10^{10}$ |
| $(D)$ Gravitational force | $(h)$ $10^{-13}$ |
| | $(i)$ $10^{-39}$ |
The correct match is:

$A$ man measures the period of a simple pendulum inside a stationary lift and finds it to be $T \ s$. If the lift accelerates upwards with an acceleration $g/4$,then the period of the pendulum will be

The number of ways of choosing $10$ objects out of $31$ objects,of which $10$ are identical and the remaining $21$ are distinct,is