(A) : In a communication system based on amplitude modulation the modulation index is kept less than 1
(R) : If modulation index is less than 1, there is minimum distortion of signal

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 in the context of amplitude modulation in communication systems.

### Step-by-Step Solution:

1. **Understanding Amplitude Modulation (AM)**:
- Amplitude modulation is a technique used in electronic communication, most commonly for transmitting information via a radio carrier wave. In AM, the amplitude of the carrier wave is varied in proportion to the waveform being sent.

2. **Defining Modulation Index**:
- The modulation index (m) in amplitude modulation is defined as the ratio of the amplitude of the message signal (A_m) to the amplitude of the carrier signal (A_c):
\[ m = \frac{A_m}{A_c} \]

3. **Condition for Modulation Index**:
- The assertion states that the modulation index is kept less than 1 (m < 1). This is a standard practice in AM systems.

4. **Reason for Keeping Modulation Index Less than 1**:
- The reason states that if the modulation index is less than 1, there is minimum distortion of the signal. This is true because:
- If m < 1, the amplitude of the message signal does not exceed the amplitude of the carrier signal. This ensures that the carrier wave can adequately carry the information without distortion.
- If m were to exceed 1, the message signal would cause the carrier signal to be over-modulated, leading to distortion and loss of information.

5. **Conclusion**:
- Both the assertion (A) and the reason (R) are true. The reason (R) correctly explains the assertion (A), as keeping the modulation index less than 1 minimizes distortion in the transmitted signal.

### Final Answer:
- (A) is true, and (R) is true; (R) is the correct explanation of (A).