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

Let $f(x) =$ min{$2x², 52-5x$}, where x is any positive real number. Then the maximum possible value of $f(x)$ is

If $x$ and $y$ are positive real numbers satisfying $x + y = 102$, then the minimum possible value of $2601(1+\frac{1}{x})(1+\frac{1}{y})$ is