CAT (QA) PYQs

Let $f(x)$ be quadratic polynomial in $x$ such that $f(x) \geq 0$ for all real numbers $x$. if $f(2)=0$ and $f(4)=6$, then $f(-2)$ is equal to

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

If $x$ and $y$ are real numbers such that $4x^2 + 4y^2 - 4xy - 6y + 3 = 0$, then the value of $(4x + 5y)$ is