Identify what gluconic acid is

Glucose is an aldohexose, so it contains:

• one aldehyde group at $C_1$
• one primary alcohol group at $C_6$

On mild oxidation of glucose, only the aldehyde group gets oxidized to a carboxylic acid.

Thus: $\text{Glucose} \xrightarrow[\text{mild oxidation}]{} \text{Gluconic acid}$

So gluconic acid is: $\text{HOCH}_2(\text{CHOH})_4\text{COOH}$

Check each option

Option A: "Gluconic acid can form cyclic (acetal/hemiacetal) structure"

For a hemiacetal/cyclic hemiacetal, a molecule needs an aldehyde or ketone group to react intramolecularly with an alcohol group.

In gluconic acid, the aldehyde group of glucose has already been oxidized to $-COOH$. Therefore, it cannot form a cyclic hemiacetal/acetal like glucose.

So, A is incorrect.

Option B: "Gluconic acid is a partial oxidation product of glucose"

This is true because only the aldehyde group is oxidized, while the terminal $-CH_2OH$ group remains unchanged.

Hence, gluconic acid is indeed a partial oxidation product of glucose.

So, B is correct.

Option C: "Gluconic acid is obtained by oxidation of glucose with $HNO_3$"

Oxidation with nitric acid is a strong oxidation. It oxidizes both:

• the aldehyde group at $C_1$ to $-COOH$
• the primary alcohol group at $C_6$ to $-COOH$

This gives saccharic acid (glucaric acid), not gluconic acid.

So, C is incorrect.

Option D: "Gluconic acid is a dicarboxylic acid"

Gluconic acid contains only one carboxylic acid group. Therefore, it is not a dicarboxylic acid.

So, D is incorrect.

Final answer

The only correct statement is: $\boxed{\text{B}}$