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 $^nC_2$.

• 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)

Number of diagonals of $n$ sided polygon $= ^nC_2 - n$
$ = \,{}^{12}C_2 - 12$
$=66 - 12 = 54$.