A series is given with one number missing. Choose the correct alternative from the given options that will complete the series: 49, 64, ?, 100, 121

Introduction / Context:
This problem tests recognition of perfect squares in a simple number series. Many verbal reasoning questions use well known patterns such as square numbers of consecutive integers. The series is 49, 64, ?, 100, 121, and we must identify the missing term that preserves this structure.

Given Data / Assumptions:
- Series terms: 49, 64, ?, 100, 121.- Exactly one number is missing in the central position.- The other four terms are assumed to be correct and to follow a common pattern.- All values are positive integers and reasonably small, which is typical for square or cube patterns.

Concept / Approach:
The key observation is that 49, 64, 100 and 121 are familiar square numbers. If we express each term as n^2, we can see whether they correspond to consecutive values of n. Once we detect that, the missing number should simply be the square that belongs between the known consecutive squares.

Step-by-Step Solution:
- 49 = 7^2.- 64 = 8^2.- 100 = 10^2.- 121 = 11^2.- The sequence of bases is 7, 8, ?, 10, 11, which clearly should be consecutive integers 7, 8, 9, 10, 11.- Therefore, the missing base is 9, and the missing term is 9^2.- Compute 9^2 = 81.- So the completed series is 49, 64, 81, 100, 121.

Verification / Alternative check:
- Consecutive squares from 7 to 11 are: 7^2 = 49, 8^2 = 64, 9^2 = 81, 10^2 = 100, 11^2 = 121.- This matches the given pattern exactly once 81 is inserted in the missing position.- No other integer placed in the middle would preserve the idea of consecutive square numbers.

Why Other Options Are Wrong:
- 74, 75, 80 and 96 are not perfect squares, so they break the consecutive square structure.- In particular, none of these values can be written as n^2 with n an integer between 7 and 11.

Common Pitfalls:
- Some candidates focus on the differences (15, ?, 19, 21) and try to find a pattern in them, which is less natural here.- Forgetting standard square values, especially 9^2 = 81, can cause confusion.- Overcomplicating the series with advanced formulas is unnecessary for this straightforward square pattern.

Final Answer:
The series lists consecutive perfect squares from 7^2 to 11^2, so the missing term is 81.