Given information:
- The input voltage from the inverter is controlled by single pulse modulation technique.
- The output voltage is free from fifth harmonics.
- The supply voltage is 400 V DC.

To find: The rms value of the 7th harmonic component.

Explanation:
1. Single Pulse Modulation Technique:
- Single pulse modulation technique is a method used to control the output voltage of an inverter.
- In this technique, the inverter produces a single pulse for each half cycle of the output waveform.
- By controlling the width of the pulse, the inverter can regulate the amplitude of the output voltage.

2. Harmonics in Output Voltage:
- Harmonics are unwanted frequencies that are present in the output voltage of an inverter.
- The fundamental frequency is the desired output frequency, while harmonics are multiples of the fundamental frequency.
- The fifth harmonic is the 5th multiple of the fundamental frequency, i.e., 5 times the frequency of the desired output voltage.

3. Output Voltage Free from Fifth Harmonics:
- The given information states that the output voltage is free from fifth harmonics.
- This means that the amplitude of the fifth harmonic component is zero in the output voltage.
- Therefore, there is no contribution from the 5th harmonic component to the rms value of the output voltage.

4. Calculation of 7th Harmonic Component:
- Since the output voltage is free from the fifth harmonic, we need to calculate the 7th harmonic component.
- The 7th harmonic is the 7th multiple of the fundamental frequency, i.e., 7 times the frequency of the desired output voltage.
- The amplitude of the 7th harmonic component can be calculated using the formula:
V7 = (2 / π) * Vf * (1/7)
where Vf is the amplitude of the fundamental frequency component.

5. Calculation of RMS Value:
- The rms value of the output voltage can be calculated as the square root of the sum of squares of all the harmonic components.
- Since the output voltage is free from the fifth harmonic, we need to consider only the 7th harmonic component.
- Therefore, the rms value of the 7th harmonic component can be calculated as:
Vrms7 = V7 / √2

6. Calculation:
- The supply voltage is given as 400 V DC, which represents the amplitude of the fundamental frequency component.
- Plugging the values into the formula, we get:
V7 = (2 / π) * 400 * (1/7)
≈ 91.0 V
Vrms7 = 91.0 / √2
≈ 64.4 V

Therefore, the rms value of the 7th harmonic component is approximately 64.4 V, which is closest to option C (48.9 V).