What will come in place of question mark (?) in the given number series?
11 ? 83 299 811 1811

Options

A. 21
B. 12
C. 18
D. 19

Answer

To find the missing number in the series: 11, ?, 83, 299, 811, 1811, we need to identify a pattern in the numbers.

### Step-by-Step Solution:

1. **Identify the Numbers**: The series given is 11, ?, 83, 299, 811, 1811.

2. **Look for Patterns**: We can start by examining the differences between the numbers we do know:
- From 83 to 299: 299 - 83 = 216
- From 299 to 811: 811 - 299 = 512
- From 811 to 1811: 1811 - 811 = 1000

3. **Recognize the Differences**: The differences we calculated are:
- 216 = 6^3
- 512 = 8^3
- 1000 = 10^3

This suggests that the differences between the consecutive terms are cubes of even numbers (6, 8, 10).

4. **Find the Missing Difference**: The next even number before 6 is 4. The cube of 4 is:
- 4^3 = 64

5. **Calculate the Missing Number**: Now, we need to find the number that comes before 83 by subtracting the cube of 4 from 83:
- 83 - 64 = 19

6. **Final Series Check**: Now we can check the series with the missing number filled in:
- 11, 19, 83, 299, 811, 1811
- Differences:
- 19 - 11 = 8 (which is 2^3)
- 83 - 19 = 64 (which is 4^3)
- 299 - 83 = 216 (which is 6^3)
- 811 - 299 = 512 (which is 8^3)
- 1811 - 811 = 1000 (which is 10^3)

This confirms that the pattern holds true.

### Conclusion:
The number that will come in place of the question mark (?) is **19**.