CAT (QA) PYQs

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

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

A donation box can receive only cheques of Rs. $100$, Rs. $250$, and Rs. $500$. On one good day, the donation box was found to contain exactly $100$ cheques amounting to a total sum of Rs. $15250$. Then, the maximum possible number of cheques of Rs. $500$ that the donation box may have contained, is