UPSC NDA 2 2019 Mathematics Solved Paper

Concept:The number of diagonals in a polygon with $n$ sides is given by the formula $\frac{n(n-3)}{2}$ or equivalently ${}^{n}C_{2} - n$.Explanation:An octagon has $n = 8$ sides.A diagonal joins any two non-adjacent vertices.Total pairs of vertices are ${}^{8}C_{2} = 28$.Out of these, the 8 sides of the octagon are not diagonals.So subtract the sides: $28 - 8 = 20$.Alternatively, apply the formula directly: $\frac{8 \times (8-3)}{2} = \frac{8 \times 5}{2} = \frac{40}{2} = 20$.Answer:The correct option is D. 20.