Tautomerism is not exhibited by :

Options

A.
B.
C.
D.

Explanation

To determine which compound does not exhibit tautomerism, we need to understand the requirements for tautomerism to occur. Tautomerism typically involves the interconversion between a keto form and an enol form of a compound. For this process to happen, the following conditions must be met:

1. The compound must have at least one alpha hydrogen (a hydrogen atom attached to the carbon adjacent to the carbonyl group).
2. The alpha carbon must be sp³ hybridized.

Now, let's analyze the options provided in the question step by step:

### Step 1: Identify the compounds
We have four compounds to analyze. We will check each compound to see if it has an alpha hydrogen and if the alpha carbon is sp³ hybridized.

### Step 2: Analyze each compound

**Option A: RCOCH3**
- This compound has a keto group (C=O) and a methyl group (CH3) adjacent to it.
- The carbon adjacent to the carbonyl (the alpha carbon) is sp³ hybridized and has three hydrogens (CH3).
- Therefore, tautomerism is possible.

**Option B: RCOC=C**
- This compound has a keto group, but the adjacent carbon is part of a double bond (C=C).
- The carbon adjacent to the carbonyl (the alpha carbon) is sp² hybridized and does not have any hydrogen atoms.
- Therefore, tautomerism is **not possible**.

**Option C: RCOCH2CH3**
- This compound has a keto group and an ethyl group (CH2CH3) adjacent to it.
- The alpha carbon (the one adjacent to the carbonyl) is sp³ hybridized and has two hydrogens (CH2).
- Therefore, tautomerism is possible.

**Option D: RCOC(CH3)2**
- This compound has a keto group and a carbon that is bonded to two methyl groups (C(CH3)2) adjacent to it.
- The alpha carbon is sp³ hybridized and has three hydrogens (CH3).
- Therefore, tautomerism is possible.

### Conclusion
After analyzing all the options, we find that **Option B** is the only compound that does not exhibit tautomerism because the alpha carbon is sp² hybridized and lacks alpha hydrogen.

### Final Answer
Tautomerism is not exhibited by **Option B**.

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