यदि संख्या 739142658 के दूसरे , चौथे तथा सातवें अंक से दो अंकों की विषम पूर्ण वर्ग संख्या बनाना संभव हो जबकि प्रत्येक अंक को केवल एक बार लिया जाता है तब उस दो अंकों की पूर्ण वर्ग संख्या का दूसरा अंक इनमे से कौन सा होगा ?

Options

A. 3
B. 4
C. 5
D. इनमे से कोई नहीं

Answer

**Step-by-Step Solution:**

1. **Identify the Digits:**
The given number is 739142658. We need to extract the second, fourth, and seventh digits from this number.
- Second digit: 3
- Fourth digit: 1
- Seventh digit: 6

2. **Form Two-Digit Combinations:**
We will create all possible two-digit combinations using the digits 3, 1, and 6. The combinations are:
- 31
- 36
- 13
- 16
- 63
- 61

3. **Check for Perfect Squares:**
We need to check which of these combinations are perfect squares. The perfect squares of two-digit numbers are:
- 16 (4^2)
- 25 (5^2)
- 36 (6^2)
- 49 (7^2)
- 64 (8^2)
- 81 (9^2)

From our combinations:
- 31: Not a perfect square
- 36: Perfect square (6^2)
- 13: Not a perfect square
- 16: Perfect square (4^2)
- 63: Not a perfect square
- 61: Not a perfect square

4. **Identify the Second Digit of Perfect Squares:**
The two-digit perfect squares we found are 36 and 16. Now we need to identify the second digit of these perfect squares:
- For 36, the second digit is 6.
- For 16, the second digit is 6.

5. **Conclusion:**
Since both perfect squares yield the same second digit, we conclude that the second digit of the two-digit perfect square formed from the given digits is **6**.

**Final Answer: 6**

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