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

Let $a_{1}, a_{2}, \ldots, a_{52}$ be positive integers such that $a_{1}<a_{2}<\ldots<a_{52}$. Suppose, their arithmetic mean is one less than the arithmetic mean of $a_{2}, a_{3}$, $\ldots, a_{52}$. If $a_{52}=100$, then the largest possible value of $a_{1}$ is

If $a,b,c$ and $d$ are integers such that their sum is 46, then the minimum possible value of $(a-b)^2 + (a-c)^2 + (a-d)^2$ is