KVPY 2019 SA Exam Previous Papers

For equal roots discriminant
$\mathit{D}=0\Rightarrow {\mathit{b}}^2-16\mathit{c}=0.$
${\mathit{b}}^2=4\times 4\times \mathit{c}$
$\Rightarrow \mathit{c}$ has to be perfect square.
Then, $\mathit{c}$ can be any perfect square numbers from the
given sets and the perfect square number in the set S
$=1,4,9,16,25,36,49,64,81,100$
$\therefore$ Number of ordered pair $\left(\mathit{b},\mathit{c}\right)$ will be 10
$\therefore$ Required probability
$=\frac{10}{100\times 100}=0.001$