CAT (QA) PYQs

Let $A$ be a real number. Then the roots of the equation $x^2 - 4x - \log_2A = 0$ are real and distinct if and only if

Let $f(x)=x^{2}+a x+b$ and $g(x)=f(x+1)-f(x-1)$. If $f(x) \geq 0$ for all real $x$, and $g(20)=72$, then the smallest possible value of $b$ is

Let $\alpha$ and $\beta$ be the two distinct roots of the equation $2x^2 - 6x + k = 0$, such that $(\alpha + \beta)$ and $\alpha\beta$ are the distinct roots of the equation $x^2 + px + p = 0$. Then, the value of $8 (k - p)$ is