In a nuclear fission process,a nucleus $A$ divides into two nuclei $B$ and $C$. If their binding energies are ${E_a}$,${E_b}$,and ${E_c}$ respectively,which of the following relations is correct?

Degenerate electron pressure will not be sufficient to prevent the core collapse of a white dwarf if its mass becomes $n$ times the solar mass. The value of $n$ is:

What is mass defect? Write down its formula.

What does the binding energy per nucleon show?

$A$ nucleus with mass number $242$ and binding energy per nucleon as $7.6\,MeV$ breaks into two fragments,each with mass number $121$. If each fragment nucleus has a binding energy per nucleon of $8.1\,MeV$,the total gain in binding energy is $........MeV$.

The binding energy of nucleons in a nucleus can be affected by the pairwise Coulomb repulsion. Assume that all nucleons are uniformly distributed inside the nucleus. Let the binding energy of a proton be $E_b^p$ and the binding energy of a neutron be $E_b^n$ in the nucleus. Which of the following statement(s) is(are) correct?
$(A)$ $E_b^p - E_b^n$ is proportional to $Z(Z-1)$ where $Z$ is the atomic number of the nucleus.
$(B)$ $E_b^p - E_b^n$ is proportional to $A^{-1/3}$ where $A$ is the mass number of the nucleus.
$(C)$ $E_b^p - E_b^n$ is positive.
$(D)$ $E_b^p$ increases if the nucleus undergoes a beta decay emitting a positron.