What should come at the place of question mark? 2, 5, 11, 23, 47, ?

Correct — A.
Rule: × 2, then + 1.

2 × 2 + 1 = 5
5 × 2 + 1 = 11
11 × 2 + 1 = 23
23 × 2 + 1 = 47

47 × 2 + 1 = 95 → option (a).

Why the others are wrong

• (b)
  97 — 97 is 47 × 2 + 3. The rule adds 1 after doubling at every step, so 47 gives 95.
• (c)
  93 — 93 is 47 × 2 − 1, subtracting where every earlier step adds: 2 → 5 is 2 × 2 + 1.
• (d)
  99 — 99 needs a jump of 52 from 47. The jumps 3, 6, 12, 24 double, so the next is 48, and 47 + 48 = 95.

When a series roughly doubles, test × 2 plus or minus a constant. Here 2 → 5 → 11 → 23 → 47, and each term is double the last plus 1.

The differences give an independent check: 3, 6, 12, 24 are themselves doubling, so the next difference is 48, and 47 + 48 = 95.

Key facts

• Each term is the previous term × 2 + 1.
• The differences 3, 6, 12, 24 double, so the next is 48.
• The terms are 3 × 2ⁿ − 1 for n = 0 to 5: 2, 5, 11, 23, 47, 95.

Common traps

• Doubling 47 to 94 and forgetting the + 1.
• Changing the added constant partway: the first step, 2 × 2 + 1 = 5, fixes it at 1.

No directly related past PYQ was found.