(A) : Greater is the height of T.V. transmitting antenna, greater is its range.
(R) : The range of T.V. transmitting antenna is proportional to square root of its height.

Options

A. Both 'A' and 'R' are true and 'R' is the correct explanation of 'A'.
B. Both 'A' and 'R' are true and 'R' is not the correct explanation of 'A'.
C. A' is true abd 'R' false
D. A' is false and 'R' is false

Answer

To solve the question, we need to analyze both the assertion (A) and the reason (R) provided.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that "Greater is the height of the T.V. transmitting antenna, greater is its range."
- This implies that there is a direct relationship between the height of the antenna and its range. If the height increases, the range also increases.

2. **Understanding the Reason (R)**:
- The reason states that "The range of T.V. transmitting antenna is proportional to the square root of its height."
- This means that if we denote the height of the antenna as \( H_T \), the range \( D \) can be expressed as:
\[ D \propto \sqrt{H_T} \]
- This indicates that the range increases with the square root of the height.

3. **Mathematical Relationship**:
- The relationship between the range and height can be derived from the formula:
\[ D = \sqrt{2R \cdot H_T} \]
- Squaring both sides gives:
\[ D^2 = 2R \cdot H_T \]
- This shows that \( D^2 \) is directly proportional to \( H_T \), which implies that if the height increases, the range also increases.

4. **Evaluating the Truth of A and R**:
- Since the assertion (A) states that greater height leads to greater range, and we have established that this is true based on the mathematical relationship, we conclude that A is true.
- The reason (R) also holds true because it correctly describes the relationship between range and height as being proportional to the square root of the height.

5. **Conclusion**:
- Both the assertion (A) and the reason (R) are true, and R correctly explains A. Therefore, the correct answer is:
- Both A and R are true, and R is the correct explanation of A.

### Final Answer:
Both A and R are true, and R is the correct explanation of A.