CAT (QA) PYQs

The number of distinct real roots of the equation $(x + \frac{1}{x})^2 - 3(x + \frac{1}{x}) + 2 = 0$ equals

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

Suppose one of the roots of the equation $ax^2 - bx + c = 0$ is $2+\sqrt{3}$ where a, b and c are rational numbers and $a \neq 0$. If $b = c^3$ then $|a|$ equals