What will come in place of question mark (? ) in the following number series ?
निम्नलिखित संख्या श्रंखला में प्रश्नवाचक चिन्ह (?) के स्थान पर क्या आयेगा ?
`4 " " 200 " "369" "513 " "634" "?`

Options

A. 788
B. 715
C. 734
D. 755

Answer

To solve the number series: `4, 200, 369, 513, 634, ?`, we will analyze the differences between the consecutive numbers and look for a pattern.

### Step-by-Step Solution:

1. **Identify the Numbers**:
The series is:
- 4
- 200
- 369
- 513
- 634
- ?

2. **Calculate the Differences**:
Let's find the differences between consecutive numbers:
- Difference between 200 and 4:
\( 200 - 4 = 196 \)
- Difference between 369 and 200:
\( 369 - 200 = 169 \)
- Difference between 513 and 369:
\( 513 - 369 = 144 \)
- Difference between 634 and 513:
\( 634 - 513 = 121 \)

So, the differences are:
- 196
- 169
- 144
- 121

3. **Identify the Pattern in Differences**:
The differences can be expressed as:
- \( 14^2 = 196 \)
- \( 13^2 = 169 \)
- \( 12^2 = 144 \)
- \( 11^2 = 121 \)

This indicates that the differences are perfect squares decreasing by 1 each time.

4. **Find the Next Difference**:
Following the pattern, the next difference should be \( 10^2 = 100 \).

5. **Calculate the Next Number**:
To find the next number in the series, we add this difference to the last number in the series:
\( 634 + 100 = 734 \)

6. **Conclusion**:
Therefore, the number that will come in place of the question mark (?) is **734**.