To identify the correct statements from the options given, let's analyze each one:
(A) Primary amines do not give diazonium salts when treated with \({NaNO}_2\) in acidic condition.
This statement is incorrect. Primary aromatic amines react with sodium nitrite \(({NaNO}_2)\) in acidic conditions to form diazonium salts. Therefore, this statement is false.
(B) Aliphatic and aromatic primary amines on heating with \({CHCl}_3\) and ethanolic \({KOH}\) form carbylamines.
This statement is correct. The reaction mentioned is the carbylamine reaction (or isocyanide test), which is a test for primary amines, especially aliphatic and aromatic ones.
(C) Secondary and tertiary amines also give carbylamine test.
This statement is incorrect. Only primary amines respond to the carbylamine test to form isocyanides; secondary and tertiary amines do not give this reaction.
(D) Benzenesulfonyl chloride is known as Hinsberg’s reagent.
This statement is correct. Benzenesulfonyl chloride is used in the Hinsberg test to distinguish between primary, secondary, and tertiary amines.
(E) Tertiary amines react with benzenesulfonyl chloride very easily.
This statement is incorrect. Tertiary amines do not react with benzenesulfonyl chloride under mild conditions like primary and secondary amines do.
Based on this analysis, the correct statements are:
(B) and (D) only


In the following \(p\text{–}V\) diagram, the equation of state along the curved path is given by \[ (V-2)^2 = 4ap, \] where \(a\) is a constant. The total work done in the closed path is: 
Let \( ABC \) be a triangle. Consider four points \( p_1, p_2, p_3, p_4 \) on the side \( AB \), five points \( p_5, p_6, p_7, p_8, p_9 \) on the side \( BC \), and four points \( p_{10}, p_{11}, p_{12}, p_{13} \) on the side \( AC \). None of these points is a vertex of the triangle \( ABC \). Then the total number of pentagons that can be formed by taking all the vertices from the points \( p_1, p_2, \ldots, p_{13} \) is ___________.
Consider the following two reactions A and B: 
The numerical value of [molar mass of $x$ + molar mass of $y$] is ___.