Series: 22, 24, 28, ?, 52, 84

To find the missing number in the given series, let's analyze the pattern and apply logical reasoning.

Pattern Analysis:
Looking at the given series, we can observe the following patterns:

1. The difference between the consecutive terms is not constant.
2. The difference between the consecutive terms alternates between 2 and 4.

Based on these patterns, we can infer that the series follows a pattern where the difference between consecutive terms increases by 2, then 4, and so on.

Calculating the missing number:
Let's calculate the difference between each pair of consecutive terms in the series:

24 - 22 = 2
28 - 24 = 4
? - 28 = 6
52 - ? = 8
84 - 52 = 32

From the pattern analysis, we know that the difference between consecutive terms alternates between 2 and 4. So, the missing number should be 28 + 6 = 34.

However, this does not match any of the given options (a) 36, (b) 38, (c) 42, (d) 46. Therefore, none of the options seem to be correct based on the pattern analysis.

Conclusion:
Based on the given series and the pattern analysis, it is not possible to determine the missing number with certainty. The correct answer might be outside the given options or there might be an error in the series itself. Hence, none of the provided options are correct.