CAT (QA) PYQs

Let k be the largest integer such that the equation $(x - 1)^2 + 2kx + 11 = 0$ has no real roots. If y is a positive real number, then the least possible value of $k/4y + 9y$ is

The minimum possible value of the sum of the squares of the roots of the equation $x^{2}+(a+3) x-(a+5)=0$ is

What is the largest positive integer such that $\frac{n^2 + 7n + 12}{n^2 - n - 12}$ is also a positive integer?