Step 1: Oxidation of X
Compound X is oxidized by $K_{2}Cr_{2}O_{7}$ to form a product that reacts with phenyl hydrazine. This indicates the product is a carbonyl compound (aldehyde or ketone).
Step 2: Negative Tollen's Test
The product fails the silver mirror test, meaning it is a ketone, not an aldehyde.
Step 3: Precursor Identification
Ketones are produced by the oxidation of secondary alcohols. Among the options, $(CH_{3})_{2}CHOH$ (isopropyl alcohol) is the secondary alcohol.
Final Answer: (c)