How many squares are present in the following figure?

Correct — A.
Rule: count by square size, then add.

The figure is a 3 × 3 grid with a small square inside each corner cell and the centre cell.

1 × 1 cells: 9
2 × 2 blocks: 4
Whole frame: 1
Small inner squares: 5

9 + 4 + 1 + 5 = 19 → option (a).

Why the others are wrong

• (b)
  21 — 21 needs two squares that are not there. Each inner square sits inside its cell without touching a grid line, so it forms nothing larger and counts once.
• (c)
  17 — 17 is two short. The grid alone gives 9 + 4 + 1 = 14, and the five inner squares, four corners and the centre, bring it to 19.
• (d)
  23 — 23 overshoots by four. A 2 × 2 block fits in just 4 places in a 3 × 3 grid, and no other lines close into a square.

Count squares by size, never by eye. Fix the smallest square, then ask how many positions each larger size can take.

In a 3 × 3 grid a 1 × 1 square fits in 9 places, a 2 × 2 in 4 and a 3 × 3 in 1, so the grid alone holds 14. A square drawn inside a cell adds exactly one, because its sides meet no other line.

Key facts

• A 3 × 3 grid holds 9 + 4 + 1 = 14 squares.
• An n × n grid holds 1² + 2² + … + n² squares, so a 4 × 4 grid holds 30.
• A square drawn inside a cell, touching none of its sides, adds exactly one.

Common traps

• Stopping at the nine cells and missing the four 2 × 2 blocks
• Forgetting that the outer frame is itself a square

No directly related past PYQ was found.