$A$ body is projected from the ground at an angle of $\tan ^{-1}(\sqrt{7})$ with the horizontal. At half of the maximum height, the speed of the body is '$n$' times the speed of projection. The value of '$n$' is

$A$ nucleus ruptures into two nuclear parts which have their velocity ratio equal to $2:1$. What will be the ratio of their nuclear size (nuclear radius)?

Determine the correct configuration of the following molecule:

Solution $X$ contains $Na_2CO_3$ and $NaHCO_3$. $20 \ mL$ of $X$ when titrated using methyl orange indicator consumed $60 \ mL$ of $0.1 \ M$ $HCl$ solution. In another experiment,$20 \ mL$ of $X$ solution when titrated using phenolphthalein consumed $20 \ mL$ of $0.1 \ M$ $HCl$ solution. The concentrations (in $mol \ L^{-1}$) of $Na_2CO_3$ and $NaHCO_3$ in $X$ are respectively:

$A$ capacitor $C = 100 \ \mu F$ is connected to three resistors,each of resistance $1 \ k\Omega$,and a battery of emf $9 \ V$. The switch $S$ has been closed for a long time to charge the capacitor. When switch $S$ is opened,the capacitor discharges with a time constant of.....$ms$.

The presence of diversity at the junction of territories of two different habitats is known as