In the given number '7392652182', if all the odd digits are first arranged in ascending order from left to right, followed by all the even digits arranged in ascending order, how many digits remain unchanged in their original positions?

The correct option is Two.

Step-by-step Explanation:

1. Identify the given number and its digit positions:
The given number is 7392652182.
Let us write down each digit along with its original position (1 through 10):
Position 1: 7
Position 2: 3
Position 3: 9
Position 4: 2
Position 5: 6
Position 6: 5
Position 7: 2
Position 8: 1
Position 9: 8
Position 10: 2

2. Separate and arrange the odd digits:
The odd digits present in the number are: 7, 3, 9, 5, 1.
Arranging all odd digits in ascending order (left to right):
1, 3, 5, 7, 9

3. Separate and arrange the even digits:
The even digits present in the number are: 2, 6, 2, 8, 2.
Arranging all even digits in ascending order (left to right):
2, 2, 2, 6, 8

4. Combine the arranged digits into a new sequence:
First all odd digits in ascending order, followed by all even digits in ascending order:
1 3 5 7 9 2 2 2 6 8

5. Compare original digit positions with new positions:
Position 1: Original = 7, New = 1 (Changed)
Position 2: Original = 3, New = 3 (Unchanged)
Position 3: Original = 9, New = 5 (Changed)
Position 4: Original = 2, New = 7 (Changed)
Position 5: Original = 6, New = 9 (Changed)
Position 6: Original = 5, New = 2 (Changed)
Position 7: Original = 2, New = 2 (Unchanged)
Position 8: Original = 1, New = 2 (Changed)
Position 9: Original = 8, New = 6 (Changed)
Position 10: Original = 2, New = 8 (Changed)

Conclusion:
Exactly 2 digits (digit 3 at position 2 and digit 2 at position 7) remain unchanged in their original positions.