The radius of gyration of a disc of mass $50\,g$ and radius $2.5\,cm$,about an axis passing through its centre of gravity and perpendicular to the plane,is ....... $cm$.

The tension of a stretched string is increased by $69\%$. In order to keep its frequency of vibration constant,its length must be increased by ..... $\%$

Consider the following reaction: $N_{2(g)} + 3H_{2(g)} \longrightarrow 2NH_{3(g)}$. The rate of this reaction in terms of $N_2$ at $T \ K$ is $-\frac{d[N_2]}{dt} = 0.02 \ mol \ L^{-1} \ s^{-1}$. What is the value of $-\frac{d[H_2]}{dt}$ (in units of $mol \ L^{-1} \ s^{-1}$) at the same temperature?

The resistance of a bulb filament is $100\, \Omega$ at a temperature of $100\, ^oC$. If its temperature coefficient of resistance is $0.005\, (^oC)^{-1}$,at what temperature will its resistance become $200\, \Omega$?

Consider the following reaction,
$C_2H_5Cl + AgCN \xrightarrow{EtOH / H_2O} \underline{X} \text{ (major)}$
Which one of the following statements is true for $\underline{X}$?
$(I)$ It gives propionic acid on hydrolysis
$(II)$ It has an ester functional group
$(III)$ It has a nitrogen linked to ethyl carbon
$(IV)$ It has a cyanide group

Select the correct statement from the ones given below: