Which of the following statements is correct?

The sugar $$\text{glucose}$$ has the molecular formula $$\mathrm{C_6H_{12}O_6}$$ and in its open-chain (acyclic) form it possesses

$$\mathrm{\;CHO\!-\![CH(OH)]_4\!-\!CH_2OH}$$

i.e. an aldehydic group $$-CHO$$ at carbon 1 and a primary alcoholic group $$-CH_2OH$$ at carbon 6, the remaining four carbons each bearing a secondary $$-OH$$ group.

When only the aldehydic carbon is oxidised, we replace $$-CHO$$ by the carboxylic group $$-COOH$$ while leaving the alcohol at carbon 6 untouched. The reaction therefore becomes

$$$\mathrm{CHO\!-\![CH(OH)]_4\!-\!CH_2OH \;\xrightarrow[\text{mild}]{[O]} \;COOH\!-\![CH(OH)]_4\!-\!CH_2OH}$$$

The product so obtained is called gluconic acid. Because only one of the two possible oxidisable groups is converted into $$-COOH$$, the process is termed partial oxidation. Gluconic acid is therefore a monocarboxylic acid, not a dicarboxylic one.

Let us now examine each given statement.

Statement A: "Gluconic acid can form cyclic (acetal/hemiacetal) structure." A cyclic acetal (or hemiacetal) in carbohydrates originates from an intramolecular reaction between the aldehydic carbon 1 and an $$-OH$$ group on carbon 4 or carbon 5. Gluconic acid no longer contains an aldehyde; carbon 1 is already oxidised to the acid group $$-COOH$$. Hence such an intramolecular acetal formation is impossible. So statement A is false.

Statement B: "Gluconic acid is a dicarboxylic acid." As written above, gluconic acid possesses only one $$-COOH$$ group (at carbon 1). Carbon 6 still retains $$-CH_2OH$$. Therefore gluconic acid is monocarboxylic, not di-carboxylic. Statement B is false.

Statement C: "Gluconic acid is a partial oxidation product of glucose." We have just shown that mild oxidising agents such as $$\mathrm{Br_2/H_2O}$$ convert only the aldehyde of glucose to the acid without affecting the primary alcohol. Because the molecule is oxidised only in part, the term "partial oxidation product" is fully appropriate. Statement C is therefore true.

Statement D: "Gluconic acid is obtained by oxidation of glucose with $$\mathrm{HNO_3}$$." Nitric acid is a strong oxidising agent; it converts both the aldehyde at carbon 1 and the primary alcohol at carbon 6 into carboxylic groups, giving the dicarboxylic acid $$\mathrm{HOOC\!-\![CH(OH)]_4\!-\!COOH}$$ (called glucaric or saccharic acid). Hence oxidation with $$\mathrm{HNO_3}$$ does not yield gluconic acid. Statement D is false.

Among the four alternatives, only statement C satisfies the chemical facts.

Hence, the correct answer is Option C.