Correct Answer - Option 1 : 11.11%

**Concept:**

The standard equation of AM is

\(y\left( t \right) = {A_c}\cos 2\pi {f_c}t(1 + μ \cos 2\pi {f_m}t)\) -----(1)

The modulation efficiency of the AM signal is given as:

\(η = \frac{{{μ ^2}}}{{2 + {μ ^2}}} \times 100\)

Where, μ = Modulation index.

For under modulation : μ < 1

For critical modulation : μ = 1

For over modulation : μ > 1

__Calculation__:

Given:

[A + 0.5Acosωmt]cosωct

Compare it with equation (1)

μ = 0.5

The modulation efficiency of the AM signal is given as:

\(η = \frac{{{0.5^2}}}{{2 + {0.5^2}}} \times 100\)

η = 11.11%