Question

Assertion (A): Number of rectangles on a chess board is $\,{}^4C_2 \times \,{}^4C_2$.
Reason (R): For a rectangle we needed to choose two horizontal lines & two vertical lines.

• A. Both (A) & (R) are individually true & (R) is correct explanation of (A).
• B. Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A).
• C. (A) is true but (R) is false.
• D. (A) is false but (R) is true.

Answer 1

Answer: (D)

$\because$ In a chess board, $9$ horizontal lines & $9$ vertical lines are there.
$\therefore $ Total number of rectangles of any size are $\,{}^9C_2 \times \,{}^9C_2$
$\therefore $ Assertion (A) is false.