STATEMENT-1 Oxidation state of carbon in its compound is always +4.
STATEMENT-2 : An element can show variable oxidation numbers.

Answer

To analyze the statements provided in the question, we will evaluate each statement one by one.

### Step 1: Evaluate Statement 1
**Statement 1:** The oxidation state of carbon in its compound is always +4.

To determine the validity of this statement, we need to consider examples of carbon compounds.

- **Example 1: Carbon Dioxide (CO₂)**
- Let the oxidation state of carbon be \( x \).
- The oxidation state of oxygen is -2.
- The formula for CO₂ is:
\[ x + 2(-2) = 0 \]
\[ x - 4 = 0 \implies x = +4 \]
- In CO₂, the oxidation state of carbon is +4.

- **Example 2: Carbon Monoxide (CO)**
- Let the oxidation state of carbon be \( x \).
- The oxidation state of oxygen is -2.
- The formula for CO is:
\[ x + (-2) = 0 \]
\[ x - 2 = 0 \implies x = +2 \]
- In CO, the oxidation state of carbon is +2.

From these examples, we can see that carbon can have different oxidation states in different compounds. Therefore, Statement 1 is **false**.

### Step 2: Evaluate Statement 2
**Statement 2:** An element can show variable oxidation numbers.

This statement is generally true. Many elements, especially transition metals and nonmetals, can exhibit multiple oxidation states due to their ability to lose different numbers of electrons.

- For example, carbon can have oxidation states of +4 (as in CO₂), +2 (as in CO), and even -4 (as in CH₄).
- Other elements like iron can have oxidation states of +2 and +3.

Thus, Statement 2 is **true**.

### Conclusion
- **Statement 1** is **false**.
- **Statement 2** is **true**.

### Final Answer
- Statement 1 is false because carbon does not always have an oxidation state of +4; it can vary.
- Statement 2 is true because many elements, including carbon, can show variable oxidation states.

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