Step 1: Identify the compound:
The structure is \( CH_3COCH_2COOC_2H_5 \), which is ethyl acetoacetate. It has a ketone group and an ester group, with a \( CH_2 \) group in between.
Step 2: Key idea:
The hydrogens on the middle \( CH_2 \) are acidic because two C=O groups pull electrons from it. This lets the compound move between a keto form and an enol form. The enol form has an -OH group and a C=C bond.
Step 3: Check statement (A):
Because of the acidic \( CH_2 \) group, the two forms exist together in equilibrium. This is keto-enol tautomerism. So (A) is TRUE.
Step 4: Check statement (B):
The enol form has an -OH group, so it reacts with sodium and releases hydrogen gas. The statement says it does not react, so (B) is FALSE.
Step 5: Check statement (C):
An enol gives a coloured complex with neutral ferric chloride. Ethyl acetoacetate gives a reddish violet colour. So (C) is TRUE.
Step 6: Check statement (D):
The ketone C=O reacts with 2,4-dinitrophenylhydrazine to form a yellow-orange hydrazone that settles as a precipitate. So (D) is TRUE.
Final Answer:
Statements (A), (C) and (D) are correct. \[ \boxed{\text{(A), (C) and (D)}} \]