Through which of the following reactions number of carbon atoms can be increased in the chain?

The major product formed in the following reaction is:

In the reaction sequence

The major product X and Y, respectively, are

$\mathrm{P} \stackrel{{\mathrm{H}}_2/\mathrm{Pd}-{\mathrm{BaSO}}_4}{\to } \mathrm{Q} \underset{\left(\mathrm{ii}\right) \mathrm{dil}. \mathrm{HCl}}{\overset{\left(\mathrm{i}\right) \mathrm{conc}. \mathrm{NaOH}}{\to }} \mathrm{R}+\mathrm{S}$

$\mathrm{R}$ and $\mathrm{S}$ form benzyl benzoate when treated with each other. Hence, $\mathrm{P}$ is

In the following reactions, products $\mathrm{A}$ and $\mathrm{B}$ are:

The major product obtained in the following reaction is:

Consider the reactions:

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Identify $\mathrm{A},\mathrm{ }\mathrm{X},\mathrm{ }\mathrm{Y}$ and $\mathrm{Z}$.