CAT (QA) PYQs

While multiplying three real numbers, Ashok took one of the numbers as $73$ instead of $37$. As a result, the product went up by $720$. Then the minimum possible value of the sum of squares of the other two numbers is

The number of real-valued solutions of the equation $2^x + 2^{-x} = 2 - (x - 2)^2$ is

Among $100$ students, $x_{1}$ have birthdays in January, $x_{2}$ have birthday in February, and so on.

If $x_{0}=\max \left(x_{1}, x_{2}, \ldots , x_{12}\right)$, then the smallest possible value of $x_{0}$ is