Let's analyze each of the given statements to determine which ones are correct:

(A) The angular momentum of an electron in $n^{\text{th}}$ orbit is an integral multiple of $\hbar$.

This statement reflects Bohr's quantization rule for angular momentum in the Bohr model of the hydrogen atom. According to this rule, the angular momentum of an electron in a stationary orbit is quantized and given by:

where $n$ is a principal quantum number (which can be any positive integer), and $\hbar$ is the reduced Planck's constant. Therefore, this statement (A) is correct.

(B) Nuclear forces do not obey inverse square law.

Nuclear forces, specifically strong nuclear forces, do act over short ranges within the nucleus but do not obey the inverse square law, which is characteristic of the electromagnetic and gravitational forces. Thus, statement (B) is correct.

(C) Nuclear forces are spin dependent.

The strength of the nuclear force can depend on the spin alignment of the nucleons. This is why some isotopes are more stable than others depending on spin-related factors. Thus, statement (C) is correct.

(D) Nuclear forces are central and charge independent.

The strong nuclear force is indeed charge independent, meaning it is the same regardless of the types of nucleons involved (neutrons or protons). However, nuclear forces are not always central; they can be tensor forces too, which involve more complex interactions that are not purely central. Therefore, the entirety of statement (D) is not correct; the statement should specify that nuclear forces are charge independent but may not always be central.

(E) Stability of nucleus is inversely proportional to the value of packing fraction.

This statement (E) is correct.

Based on the above explanations, the correct statements are (A), (B), (C) and (E). Hence, the correct answer is: