What is the total modulation index if several signals are modulated by same carrier?
The Modulation Index is not meant to be totaled. Every spectral component of the baseband (modulating) signal has its own modulation index. The Modulation Index of a frequency modulated baseband spectral component is defined as the peak carrier deviation frequency contributed by that spectral component divided by its modulating frequency.
The significance of modulation index is that the larger it is, the larger is the demodulated (post detection) signal to noise ratio for a given pre-detection signal to noise ratio, if the pre-detection signal to noise ratio is a few dB or more. (This phenomenon is known as “quieting”.)
Inasmuch as the above definition may be difficult to follow, here is a numerical example: Two sine wave signals (500 Hz with 1 Volt amplitude and 2500 Hz with 2 Volt amplitude) are added together and fed to a frequency modulator with a transfer characteristic of 10 KHz peak deviation/Volt of input signal. Therefore, the 500 Hz spectral component causes a deviation of 10 KHz. Using the above deviation, its modulation index is 10,000/500=20. Similarly, the 2500 Hz spectral component causes a deviation of 20 KHz, so its modulation index is 20,000/2500=8.