What should come at the place of question mark? : 4, 9, 19, 39, 79, ?

Correct — B.
Rule: × 2, then + 1.

4 × 2 + 1 = 9
9 × 2 + 1 = 19
19 × 2 + 1 = 39
39 × 2 + 1 = 79

79 × 2 + 1 = 159 → option (b).

Why the others are wrong

• (a)
  160 — 160 is 79 × 2 + 2. Every step adds 1 after doubling (4 → 9 is 4 × 2 + 1), so 79 gives 158 + 1 = 159.
• (c)
  161 — 161 is 79 × 2 + 3. The constant is fixed by the first step, 4 × 2 + 1 = 9, and never changes.
• (d)
  163 — 163 needs a jump of 84 from 79. The jumps 5, 10, 20, 40 double, so the next is 80, and 79 + 80 = 159.

When each term is roughly double the one before, test × 2 plus or minus a constant. Here 4 → 9 → 19 → 39 → 79, and each term is twice the last plus 1.

The differences give an independent check: 5, 10, 20, 40 double at every step, so the next difference is 80, and 79 + 80 = 159.

Key facts

• Each term is the previous term × 2 + 1.
• The differences 5, 10, 20, 40 double, so the next is 80.
• The terms are 5 × 2ⁿ − 1 for n = 0 to 5: 4, 9, 19, 39, 79, 159.

Common traps

• Doubling 79 to 158 and forgetting the + 1. 158 is not offered, which is the hint that a step is missing.
• Taking 160 as the round number after 79 × 2 without testing the constant against the first step.

No directly related past PYQ was found.