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Consider the frequency modulated signal 10cos[2π×10⁵t + 5sin(2π×1500t) + 7.5sin(2π×1000t)] with carrier frequency of 10⁵ Hz. The modulation index is

1. 12.5
2. 10
3. 7.5
4. 5

Correct answer: 12.5

Solution

The modulation index in frequency modulation is determined by the ratio of the peak frequency deviation to the modulation frequency. In this case, the peak frequency deviation is given by the sum of the amplitudes of the modulating signals (5 + 7.5 = 12.5), and since the carrier frequency is 10⁵ Hz, the modulation index is calculated as 12.5.

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