CAT (QA) PYQs

If $x$ and $y$ are non-negative integers such that $x+9=z, y+1=z$ and $x+y<z+5$, then the maximum possible value of $2 x+y$ ?

Let $a, b, x, y$ be real number such $a² + b² = 25, x² + y² = 169$, and $ax + by = 65.$ If $k = ay - bx,$ then

Let $n$ be any natural number such that $5^{n-1} < 3^{n+1}$. Then, the least integer value of m that satisfies $3^{n+1} < 2^{n+m}$ for each such $n$, is