CAT (QA) PYQs

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

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