What should come at the place of question mark? 2, 5, 10, 17, 26, ?

Correct — C.
Rule: n² + 1 for n = 1, 2, 3 …

1² + 1 = 2, 2² + 1 = 5, 3² + 1 = 10
4² + 1 = 17, 5² + 1 = 26
Next: 6² + 1 = 37

Check with gaps: 3, 5, 7, 9, so the next gap is 11.
26 + 11 = 37 → option (c).

Why the others are wrong

• (a)
  35 — 35 adds the last gap of 9 again. The gaps climb by 2 each time, 3, 5, 7, 9, so the next is 11.
• (b)
  36 — 36 is 6² without the +1. Every term is one more than a square (26 = 5² + 1), so the sixth is 6² + 1.
• (d)
  38 — 38 needs a gap of 12. The gaps are the odd numbers 3, 5, 7, 9, so the next is 11, not 12.

Consecutive squares differ by consecutive odd numbers: 1, 4, 9, 16, 25, 36 have gaps 3, 5, 7, 9, 11. So a series whose gaps run 3, 5, 7, 9 is a square series shifted by a constant.

Here the shift is +1: 2, 5, 10, 17, 26 sit one above 1, 4, 9, 16, 25.

Key facts

• (n + 1)² − n² = 2n + 1, so consecutive squares differ by consecutive odd numbers.
• This series is n² + 1: 2, 5, 10, 17, 26, 37.

Common traps

• Stopping at 36 because it is a square and forgetting the +1.
• Repeating the last gap (26 + 9 = 35) instead of moving on to the next odd number.

No directly related past PYQ was found.