Step-by-step Solution:

1. Alphanumeric Series

Step 1: Analyze the given series for patterns

The given series is: 1, 10, 7, 20, 13, 30, 19, ...
This series can be broken down into two alternating sub-series:

• Sub-series 1 (odd positions): \(1, 7, 13, 19, \ldots\)
• Sub-series 2 (even positions): \(10, 20, 30, \ldots\)

Step 2: Determine the pattern in Sub-series 1

In Sub-series 1 (\(1, 7, 13, 19, \ldots\)), the difference between consecutive terms is constant:

• \(7 - 1 = 6\)
• \(13 - 7 = 6\)
• \(19 - 13 = 6\)

So, the next term in this sub-series would be: \(19 + 6 = 25\).

Step 3: Determine the pattern in Sub-series 2

In Sub-series 2 (\(10, 20, 30, \ldots\)), the difference between consecutive terms is constant:

• \(20 - 10 = 10\)
• \(30 - 20 = 10\)

So, the next term in this sub-series would be: \(30 + 10 = 40\).

Step 4: Combine the next terms to find the pair

The original series alternates between the two sub-series.
Therefore, the next pair is: \(\mathbf{40, 25}\).

Answer:

The correct option is: (C) 40 25