CAT (QA) PYQs

The equations $3x^2 - 5x + p = 0$ and $2x^2 - 2x + q = 0$ have one common root. The sum of the other roots of these two equations is

Let $m$ and $n$ be positive integers, If $x^2 + mx + 2n = 0$ and $x^2 + 2nx + m = 0$ have real roots, then the smallest possible value of $m + n$ is

The roots $\alpha, \beta$ of the equation $3 x^{2}+\lambda x-1=0$, satisfy $\frac{1}{\alpha^{2}}+\frac{1}{\beta^{2}}=15$. The value of $\left(\alpha^{3}+\beta^{3}\right)^{2}$, is