Assertion (A ): If a polygon has 66 diagonals, then its number of sides is 12. Reason (R ): Number of ways of selecting 2 points from n non collinear points is nC2.

Question

Assertion (A ): If a polygon has 66 diagonals, then its number of sides is 12. Reason (R ): Number of ways of selecting 2 points from n non collinear points is nC2. (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

Number of diagonals of n sided polygon = nC2 - n = 12C2 - 12 =66 - 12 = 54.

Q. Assertion (A ): If a polygon has $66$ diagonals, then its number of sides is $12$ .
Reason (R ): Number of ways of selecting $2$ points from $n$ non collinear points is $^{n} C_{2}$ .

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.

Number of diagonals of $n$ sided polygon $=^{n} C_{2} - n$
$=^{12} C_{2} - 12$
$= 66 - 12 = 54$ .

Q. Assertion (A ): If a polygon has 66 diagonals, then its number of sides is 12. Reason (R ): Number of ways of selecting 2 points from n non collinear points is nC2​.