Assertion. Audio signal of frequencuy 10 KHz cannot be transmitted over long distance without modulation.
Reason. Length of the antenna required `lambda//4`. Should have practical value.

Options

A. If both Assertion and Reason are true and Reason is correct explanation of Assertion.
B. If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
C. If Assertion is true but Reason is false.
D. If both Assertion and Reason are false.

Answer

To solve the problem, we need to analyze the assertion and the reason provided in the question step by step.

### Step 1: Understanding the Assertion
The assertion states that an audio signal of frequency 10 kHz cannot be transmitted over long distances without modulation. This implies that modulation is necessary to effectively transmit signals at this frequency over long distances.

### Step 2: Understanding the Reason
The reason provided is that the length of the antenna required for this frequency should be λ/4 (where λ is the wavelength) and that this length should have a practical value.

### Step 3: Calculating the Wavelength (λ)
The wavelength (λ) can be calculated using the formula:
\[ \lambda = \frac{c}{f} \]
where:
- \(c\) is the speed of light (approximately \(3 \times 10^8\) m/s),
- \(f\) is the frequency (10 kHz = \(10 \times 10^3\) Hz = \(10^4\) Hz).

Substituting the values:
\[ \lambda = \frac{3 \times 10^8 \text{ m/s}}{10^4 \text{ Hz}} = 3 \times 10^4 \text{ m} = 30000 \text{ m} \]

### Step 4: Calculating the Antenna Length
The length of the antenna required for transmission is given by:
\[ \text{Length of antenna} = \frac{\lambda}{4} \]
Substituting the calculated wavelength:
\[ \text{Length of antenna} = \frac{30000 \text{ m}}{4} = 7500 \text{ m} \]

### Step 5: Analyzing the Practicality
The calculated antenna length is 7500 meters (or 7.5 km). This length is impractically long for a standard antenna, making it difficult to construct and use for transmission.

### Conclusion
Since the assertion is true (an audio signal of 10 kHz cannot be transmitted over long distances without modulation) and the reason is also true (the required antenna length is impractically long), we conclude that both the assertion and reason are correct, and the reason provides a correct explanation for the assertion.

### Final Answer
Both the assertion and reason are true, and the reason is the correct explanation for the assertion.

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