CAT (QA) PYQs

For some real numbers $a$ and $b$, the system of equations $x + y = 4$ and $(a + 5)x + (b^2 - 15)y = 8b$ has infinitely many solutions for $x$ and $y$. Then, the maximum possible value of $ab$ is

If certain amount of money is divided equally among n person, each one receives Rs $352$. However, if two persons receive Rs $506$ each and the remaining amount is divided equally among the other persons, each of them received less than or equal to Rs $330$. Then, the maximum possible value of $n$ is

A basket of $2$ apples, $4$ oranges and $6$ mangoes costs the same as a basket of $1$ apple, $4$ oranges and $8$ mangoes, or a basket of $8$ oranges and $7$ mangoes. Then the number of mangoes in a basket of mangoes that has the same cost as the other baskets is