There are three routes: air, rail and road for going from Chennai to Hyderabad. But from Hyderabad to Vikarabad, there are two routes, rail and road. The number of routes from Chennai to Vikarabad via Hyderabad is:

Options

A. (a) `4`
B. (b) `5`
C. (c) `6`
D. (d) `7`

Answer

To solve the problem of finding the number of routes from Chennai to Vikarabad via Hyderabad, we can break it down into steps:

### Step 1: Identify Routes from Chennai to Hyderabad
We are given that there are three routes available from Chennai to Hyderabad:
1. Air
2. Rail
3. Road

### Step 2: Identify Routes from Hyderabad to Vikarabad
Next, we note that there are two routes available from Hyderabad to Vikarabad:
1. Rail
2. Road

### Step 3: Calculate Total Routes from Chennai to Vikarabad
To find the total number of routes from Chennai to Vikarabad via Hyderabad, we can use the principle of multiplication. For each route from Chennai to Hyderabad, there are two possible routes from Hyderabad to Vikarabad.

- For the Air route from Chennai to Hyderabad, we can take either Rail or Road to Vikarabad (2 options).
- For the Rail route from Chennai to Hyderabad, we can again take either Rail or Road to Vikarabad (2 options).
- For the Road route from Chennai to Hyderabad, we can again take either Rail or Road to Vikarabad (2 options).

Thus, the total number of routes can be calculated as follows:
\[ \text{Total Routes} = (\text{Routes from Chennai to Hyderabad}) \times (\text{Routes from Hyderabad to Vikarabad}) = 3 \times 2 = 6 \]

### Conclusion
Therefore, the total number of routes from Chennai to Vikarabad via Hyderabad is **6**.

### Answer
The correct option is C (6).

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