Assertion (A): Number of rectangles on a chess board is 4C2 × 4C2. Reason (R): For a rectangle we needed to choose two horizontal lines two vertical lines.

Question

Assertion (A): Number of rectangles on a chess board is 4C2 × 4C2. 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.

Tardigrade Admin · Accepted Answer

∵ In a chess board, 9 horizontal lines 9 vertical lines are there. ∴ Total number of rectangles of any size are 9C2 × 9C2 ∴ Assertion (A) is false.

Q. Assertion (A): Number of rectangles on a chess board is $^{4} C_{2} \times^{4} C_{2}$ .
Reason (R): For a rectangle we needed to choose two horizontal lines & two vertical lines.

Both (A) & (R) are individually true & (R) is correct explanation of (A).

Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A).

(A) is true but (R) is false.

(A) is false but (R) is true.

$∵$ In a chess board, $9$ horizontal lines & $9$ vertical lines are there.
$∴$ Total number of rectangles of any size are $^{9} C_{2} \times^{9} C_{2}$
$∴$ Assertion (A) is false.

Q. Assertion (A): Number of rectangles on a chess board is 4C2​×4C2​. Reason (R): For a rectangle we needed to choose two horizontal lines & two vertical lines.