An AM - signal is given as
`x_(AM) (t) = 100[ p (t) + 0.5g (t) ] cos omega_c t` in interval `0 le t lt 1 `. One set of possible values of the modulating signal and modulation index would be

Options

A. `t,0.5`
B. `t,1.0`
C. `t,1.5`
D. `t^(2), 2.0`

Explanation

To solve the problem, we need to analyze the given AM signal and determine the modulating signal and the modulation index.

### Step-by-Step Solution:

1. **Identify the Given AM Signal:**
The AM signal is given as:
\[ x_{AM}(t) = 100 \left[ p(t) + 0.5 g(t) \right] \cos(\omega_c t) \]
This is valid in the interval \(0 \leq t < 1\).

2. **Understand the Components of the AM Signal:**
In the general form of an AM signal:
\[ x_{AM}(t) = E_c \left[ 1 + m_a \cdot m(t) \right] \cos(\omega_c t) \]
where:
- \(E_c\) is the carrier amplitude,
- \(m_a\) is the modulation index,
- \(m(t)\) is the modulating signal.

3. **Compare the Given Signal with the General Form:**
From the given signal, we can identify:
- \(E_c = 100\)
- The term \(0.5 g(t)\) suggests that the modulating signal is \(m(t) = p(t) + 0.5 g(t)\).
- The modulation index \(m_a\) is \(0.5\).

4. **Determine the Modulating Signal:**
We can choose a simple form for \(p(t)\) and \(g(t)\). For instance, let:
- \(p(t) = 1\) (a constant signal),
- \(g(t) = t\) (a linear signal).

Thus, we can express the modulating signal as:
\[ m(t) = 1 + 0.5t \]

5. **Identify the Modulation Index:**
The modulation index \(m_a\) is already identified as \(0.5\).

### Final Answer:
One set of possible values of the modulating signal and modulation index would be:
- Modulating Signal: \(m(t) = 1 + 0.5t\)
- Modulation Index: \(m_a = 0.5\)