Step 1: Understanding carbenes.
Carbenes are highly reactive species with a neutral carbon atom bonded to two substituents and having two electrons in an empty \( p \)-orbital. They are generally intermediates in reactions and can be formed by the reaction of amines with nitrous acid. They can insert into both \( \sigma \)- and \( \pi \)-bonds, forming new bonds.
Step 2: Analyzing the options.
(A) Carbene is a neutral species: Correct — Carbenes are neutral species with a carbon atom in a divalent state.
(B) Carbene is an intermediate in the Curtius rearrangement: Incorrect — the key intermediates in the Curtius rearrangement are an acyl azide, a nitrene.
(C) Carbene can insert into both \( \sigma \) and \( \pi \)-bonds: Correct — Carbenes are capable of inserting into both \( \sigma \) and \( \pi \)-bonds to form new compounds.
(D) Carbene is generated from amines on reaction with nitrous acid: Incorrect — While carbenes are generated from diazo compounds in some reactions, nitrous acid primarily forms diazonium salts, not directly carbenes from amines.
Step 3: Conclusion.
The correct answers are (A) and (C).
The reaction sequence given below is carried out with 16 moles of X. The yield of the major product in each step is given below the product in parentheses. The amount (in grams) of S produced is ____. 
Use: Atomic mass (in amu): H = 1, C = 12, O = 16, Br = 80
One mole of a monoatomic ideal gas starting from state A, goes through B and C to state D, as shown in the figure. Total change in entropy (in J K\(^{-1}\)) during this process is ............... 
The number of chiral carbon centers in the following molecule is ............... 
A tube fitted with a semipermeable membrane is dipped into 0.001 M NaCl solution at 300 K as shown in the figure. Assume density of the solvent and solution are the same. At equilibrium, the height of the liquid column \( h \) (in cm) is ......... 
An electron at rest is accelerated through 10 kV potential. The de Broglie wavelength (in A) of the electron is .............