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Previous Year Question (PYQs)

Consider an arbitrary number system with independent digits as 0,1 and A. If we generate first few numbers in sequence as 00, 01, 0A, 10, 11, 1A and if this process is continued to generate the numbers, then the position of 10A is ________




Solution

Custom Number System: Position of 10A

Given digits: 0, 1, A (base-3)

Convert 10A to base-10:

  • 1 → 1
  • 0 → 0
  • A → 2
  • 10A = 1×9 + 0×3 + 2 = 11

List of numbers in sequence:

  1. 00
  2. 01
  3. 0A
  4. 10
  5. 11
  6. 1A
  7. A0
  8. A1
  9. AA
  10. 100
  11. 101
  12. 10A

✅ Final Answer: 12


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