Most transition metals:
(I) Form sets of compounds which display different oxidation states of the metal.
(II) form coloured ion in solution
(III)burn vigorously in oxygen
(IV) form complex compound of these

Options

A. I,II,III are correct
B. II,III,IV are correct
C. I,II are correct
D. all the correct

Explanation

To solve the question regarding the properties of transition metals, we will analyze each statement provided and determine their validity step by step.

### Step 1: Analyze the First Statement
**Statement (I)**: "Form sets of compounds which display different oxidation states of the metal."

**Analysis**: This statement is true. Transition metals are known for their ability to exhibit multiple oxidation states due to the relatively small energy difference between their 3d and 4s orbitals. For example, chromium can exist in oxidation states such as +2, +3, +6, etc.

### Step 2: Analyze the Second Statement
**Statement (II)**: "Form colored ions in solution."

**Analysis**: This statement is also true. Transition metals often form colored ions in solution due to d-d transitions, where electrons in the d-orbitals absorb visible light to move to higher energy levels. The presence of unpaired electrons in the d-orbitals contributes to this color. Even transition metals without unpaired electrons can show color due to ligand-to-metal charge transfer.

### Step 3: Analyze the Third Statement
**Statement (III)**: "Burn vigorously in oxygen."

**Analysis**: This statement is true as well. Many transition metals can react vigorously with oxygen to form metal oxides. For instance, metals like iron and chromium can burn in oxygen to produce various oxides.

### Step 4: Analyze the Fourth Statement
**Statement (IV)**: "Form complex compounds."

**Analysis**: This statement is true. Transition metals can form complex compounds due to their ability to accommodate multiple oxidation states and the presence of vacant d-orbitals, allowing them to coordinate with ligands.

### Conclusion
After analyzing all four statements, we find that all of them are true regarding the properties of transition metals. Therefore, the correct answer to the question is that all statements (I, II, III, and IV) are correct.

### Final Answer
All four statements about transition metals are correct.

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