JIPMAT (QA) PYQs

If $\sin (\alpha)$ and $\cos (\alpha)$ are the roots of the equation $a x^{2}+b x+c=0$, then $b^{2}$ is

The factors of polynomial $x^{3}-6 x^{2}+11 x-6$ are :

If highest common factor of $x^{2}-p x-q$ and $5 x^{2}-3 p x-15 q$ is $(x-3)$, then value of ( $\left.p, q\right)$ will be :