What is X in the following sequence of reactions?     

$X+Na\to Y, Y+NaOH+CaO\to C{H}_4$ 

Given data: To find the reactants X for the preparation of methane

Detailed solution:  

Given reaction sequence involves reaction of a carboxylic acid with sodium produces sodium carboxylate salts, which was decarboxylated to give methane gas with lose of one carbon atom.  

Methanoic acid have only one carbon atom, if it loses carbon via carbon dioxide it  cannot able to produce methane gas. So option A is wrong.

Ethanoic acid react with sodium produces sodium ethanoate salts, which was  

decarboxylated to give methane gas with lose of one carbon atom.

The sodium metal does not react with alkanes unless it is a radical reaction, so option 

(C) and (D) are wrong. 

$C{H}_{3}COOH+Na\to C{H}_{3}COONa+NaOH+CaO\to C{H}_4+C{O}_2$

Hence the correct option is (B)