The best reagent to convert pent-3-en-2-ol into pent-3-en-2-one is

The substrate is $$\mathrm{CH_3{-}C(OH){-}CH{=}CH{-}CH_3}$$, an allylic (-OH is on the carbon next to the C=C bond) secondary alcohol. We merely want to raise the oxidation state of the carbon bearing -OH from $$+1$$ to $$+2$$, i.e. convert the alcohol into a ketone, but we must leave the C=C bond intact.

Step 1 - Analyse each option
• Acidic $$\mathrm{KMnO_4}$$ (Option A) is a very strong oxidising agent. In acidic medium it attacks double bonds in addition to oxidising -OH groups, producing 1,2-diols or even cleaving the C=C to carboxylic acids. Hence it is not selective here.
• Acidic $$\mathrm{K_2Cr_2O_7}$$ (Option B) is also a strong, aqueous oxidant. It oxidises alcohols but, in the presence of water and acid, it can add across or cleave the C=C bond of an allylic system. Selectivity is poor.
• Pyridinium chloro-chromate, PCC (Option D), is a milder anhydrous Cr(VI) reagent. Although PCC normally stops at the carbonyl stage, with allylic alcohols it can promote allylic rearrangements and, in some cases, over-oxidation. Text-book syntheses of α,β-unsaturated ketones generally prefer another reagent (see below) for better yields.
• Chromic anhydride in glacial acetic acid, $$\mathrm{CrO_3/HOAc}$$ (Option C), is known as the Jones-Oppenauer or simply the “chromic anhydride-acetic acid” reagent. It is used specifically for the selective oxidation of allylic and benzylic alcohols to the corresponding enones or aryl ketones, leaving the C=C bond untouched. The medium is non-aqueous (glacial acetic acid), so unwanted hydration of the C=C cannot occur.

Step 2 - Predict the reaction with the best reagent
Using $$\mathrm{CrO_3/HOAc}$$, the allylic secondary alcohol undergoes two-electron oxidation:

$$\mathrm{CH_3{-}C(OH){-}CH{=}CH{-}CH_3} \;\xrightarrow[\text{glacial HOAc}]{CrO_3}\; \mathrm{CH_3{-}CO{-}CH{=}CH{-}CH_3}$$

The double bond between C-3 and C-4 remains exactly where it was, giving the required product pent-3-en-2-one.

Step 3 - Conclusion
Among the given reagents, only chromic anhydride in glacial acetic acid delivers clean, high-yield oxidation of an allylic secondary alcohol to the corresponding α,β-unsaturated ketone without disturbing the C=C bond.

Hence, the best reagent is:
Option C which is: Chromic anhydride in glacial acetic acid.