NIMCET 2011 — Mathematics PYQ

1. The Formula:

The number of diagonals $D$ in a polygon with $n$ sides is given by:

2. Set up the Equation:

We are given that $D=44$. Plugging this into the formula, we get:

3. Solve for $n$:

Multiply both sides by 2:

Rearrange it into a quadratic equation:

4. Factorize the Equation:

We need two numbers that multiply to $-88$ and add up to $-3$. Those numbers are $-11$ and $+8$.

This gives us two possible values for $n$:

• $n-11=0\Rightarrow n=11$

• $n+8=0\Rightarrow n=-8$

Conclusion:

Since the number of sides of a polygon cannot be negative, we take $n=11$.

The correct option is (c) 11.