Let the quadratic equation $ax^2 + bx + c = 0$ where $a, b, c$ are obtained by rolling a dice thrice. What is the probability that the equation has equal roots?

**Solution:** For equal roots, discriminant $b^2 - 4ac = 0$. Each of $a, b, c$ can take values $1$ to $6$. Total outcomes = $6^3 = 216$. For given $a, c$, $b^2 = 4ac$ must be a perfect square $\le 36$. Possible $(a, c)$ pairs that make $b^2$ a perfect square: $(1,1),(1,4),(1,9),(1,16),(1,25),(1,36)$ within dice limit $(1,1)$, $(1,2)$, $(2,1)$, $(3,3)$, $(4,1)$ only valid → 6 cases out of 216. Hence probability = $\dfrac{6}{216} = \dfrac{1}{36}$. $\boxed{\text{Answer: (C) }\dfrac{1}{36}}$