The radius of a nucleus of mass number $64$ is $4.8 \text{ fermi}$. Then the mass number of another nucleus having radius of $4 \text{ fermi}$ is $\frac{1000}{x}$,where $x$ is . . . . . . .

Consider the following statements:
$I$. All isotopes of an element have the same number of neutrons.
$II$. Only one isotope of an element can be stable and non-radioactive.
$III$. All elements have isotopes.
$IV$. All isotopes of carbon can form chemical compounds with oxygen-$16$.
Choose the correct option regarding an isotope.

The radius of a Germanium $(Ge)$ nucleus is twice the radius of a $^9_4Be$ nucleus. The number of nucleons in $Ge$ is ......

It is now believed that protons and neutrons (which constitute nuclei of ordinary matter) are themselves built out of more elementary units called quarks. $A$ proton and a neutron consist of three quarks each. Two types of quarks,the so-called 'up' quark (denoted by $u$) of charge $+(2/3)e$,and the 'down' quark (denoted by $d$) of charge $-(1/3)e$ together with electrons build up ordinary matter. Suggest a possible quark composition of a proton and neutron.

Consider the following two statements,$A$ and $B$ and identify the correct answer given below:
$A$. Nuclear density is same for all nuclei.
$B$. Radius of the nucleus $R$ and its mass number $A$ are related as $\sqrt{A} \propto R^{1 / 6}$.

Ratio of specific charge of $\alpha$-particle to that of proton is