Choose the wrong statement. Option 1 All quantities may be represented dimensionally in terms of the base quantities Option 2 A base quantity cannot be represented in terms of the rest of the base quantity Option 3 The dimension of a base quantity in other base quantities is always zero Option 4 The dimension of a derived quantities is never seen in any base quantity

Options

A. All quantities may be represented dimensionally in terms of the base quantities
B. A base quantity cannot be represented in terms of the rest of the base quantity
C. The dimension of a base quantity in other base quantities is always zero
D. The dimension of a derived quantities is never seen in any base quantity

Explanation

To solve the question, we need to analyze each of the provided options and determine which one is incorrect based on our understanding of dimensional analysis and the definitions of base and derived quantities.

### Step-by-Step Solution:

1. **Understanding Base and Derived Quantities**:
- Base quantities are fundamental physical quantities that cannot be expressed in terms of other quantities. Examples include mass (M), length (L), and time (T).
- Derived quantities are those that can be expressed in terms of base quantities. For example, velocity is derived from length and time (L/T).

2. **Analyzing Option 1**:
- **Statement**: "All quantities may be represented dimensionally in terms of the base quantities."
- This statement is **correct** because all physical quantities, whether base or derived, can be expressed in terms of the base quantities.

3. **Analyzing Option 2**:
- **Statement**: "A base quantity cannot be represented in terms of the rest of the base quantity."
- This statement is **correct** as base quantities are independent and cannot be expressed in terms of each other.

4. **Analyzing Option 3**:
- **Statement**: "The dimension of a base quantity in other base quantities is always zero."
- This statement is **correct** because a base quantity, when expressed in terms of itself, has a dimension of 1, and when expressed in terms of other base quantities, it has a dimension of 0.

5. **Analyzing Option 4**:
- **Statement**: "The dimension of a derived quantity is never seen in any base quantity."
- This statement is **incorrect**. Derived quantities are defined in terms of base quantities. For example, velocity (a derived quantity) has dimensions of length (L) divided by time (T), which means it is directly related to the base quantities.

### Conclusion:
The wrong statement is **Option 4**. Therefore, the answer to the question is:

**Option 4**.

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