1. Statement (A): Primary amines do not give diazonium salts when treated with $\mathrm{NaNO_2}$ in acidic condition.

   This statement is false.

   • Aromatic primary amines react with nitrous acid (generated from $\mathrm{NaNO_2 + HCl}$) at low temperature to form diazonium salts.
   • Example: $\mathrm{C_6H_5NH_2 + NaNO_2 + 2HCl \rightarrow C_6H_5N_2^+Cl^- + NaCl + 2H_2O}$

   Hence, primary amines can give diazonium salts (especially aromatic primary amines).

2. Statement (B): Aliphatic and aromatic primary amines on heating with $\mathrm{CHCl_3}$ and ethanolic KOH form carbylamines.

   This statement is true.

   This is the carbylamine test: $\mathrm{RNH_2 + CHCl_3 + 3KOH \rightarrow RNC + 3KCl + 3H_2O}$

   Both aliphatic and aromatic primary amines give this test.

3. Statement (C): Secondary and tertiary amines also give carbylamine test.

   This statement is false.

   Only primary amines respond to the carbylamine test. Secondary and tertiary amines do not form isocyanides.

4. Statement (D): Benzenesulfonyl chloride is known as Hinsberg's reagent.

   This statement is true.

   Benzenesulfonyl chloride is indeed called Hinsberg's reagent and is used to distinguish primary, secondary, and tertiary amines.

5. Statement (E): Tertiary amines reacts with benzenesulfonyl chloride very easily.

   This statement is false.

   Tertiary amines do not react readily with benzenesulfonyl chloride because they do not have a replaceable hydrogen attached to nitrogen.

Correct statements

The true statements are: $\boxed{(B) \text{ and } (D)}$

So the correct option is: $\boxed{\text{D}}$

Comparison with stored answer

Stored correct answer: D

My derived answer: D

They agree.