$A$ nucleus of mass number $189$ splits into two nuclei having mass numbers $125$ and $64$. The ratio of the radii of the two daughter nuclei is:

In the nuclear reaction: $X(n, \alpha) {_3Li^7}$,the term $X$ will be

Consider the following statements ($X$ and $Y$ stand for two different elements):
$(I)$ ${ }_{32}^{65} X$ and ${ }_{33}^{65} Y$ are isotopes.
$(II)$ ${ }_{42}^{86} X$ and ${ }_{42}^{85} Y$ are isotopes.
$(III)$ ${ }_{85}^{174} X$ and ${ }_{88}^{177} Y$ have the same number of neutrons.
$(IV)$ ${ }_{92}^{235} X$ and ${ }_{94}^{235} Y$ are isobars.
Which of the above statements are correct?

The order of magnitude of the density of a uranium nucleus is: (Given: ${m_p} = 1.67 \times 10^{-27} \ kg$)

Define $Z$,$A$,and $N$ by describing the structure of an atom.

$A$ 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)?