BMSAT Kozhikode (QA) PYQs

If $\sin\theta$ and $\cos\theta$ are the roots of the quadratic equation $px^2+qx+r=0$ $(p \neq 0)$, then which of the following relation holds good?

If one of the roots of the equation $x^2 + ax + 3a = 0$ is $1$, then its other root is

Say for positive quantities a, b, $a + b$ equals $a^2 + ab + b^2$. Choose the nearest value to b if a is given as 0.5.