(A) : The area to be covered for T.V. telecast is doubled, then the height of trans - mitting antenna will have to be doubled
(R) : For T.V. signal propulation covered is equal to product of population density abd area covered

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 analyze the statements given in the question, we will break down each statement (A) and (R) and evaluate their validity step by step.

### Step 1: Understanding Statement (A)
Statement (A) claims that if the area to be covered for TV telecast is doubled, then the height of the transmitting antenna will have to be doubled.

**Analysis:**
- The coverage area (A) of a TV signal is related to the height (h) of the transmitting antenna. The relationship can be expressed as:
\[ A \propto h^2 \]
- This means that if the area is doubled, we can express it as:
\[ 2A \propto h'^2 \]
where \( h' \) is the new height of the antenna.
- From the proportionality, we can derive that:
\[ 2h^2 = h'^2 \]
Taking the square root of both sides gives:
\[ h' = h\sqrt{2} \]
- Therefore, the height of the antenna does not need to be doubled; it needs to be increased by a factor of \( \sqrt{2} \).

**Conclusion for (A):** Statement (A) is **False**.

### Step 2: Understanding Statement (R)
Statement (R) states that for TV signal propagation, the coverage is equal to the product of population density and area covered.

**Analysis:**
- The population covered can be expressed as:
\[ \text{Population Covered} = \text{Population Density} \times \text{Area Covered} \]
- This statement is a valid representation of how many people are covered by the signal based on the area it covers and the density of the population in that area.

**Conclusion for (R):** Statement (R) is **True**.

### Final Conclusion
- Statement (A) is **False**.
- Statement (R) is **True**.
- Therefore, (A) is not a correct explanation for (R).