CAT (QA) PYQs

In a group of $10$ students, the mean of the lowest $9$ scores is $42$ while the mean of the highest $9$ scores is $47$. For the entire group of $10$ students, the maximum possible mean exceeds the minimum possible mean by

A class consists of $20$ boys and $30$ girls. In the mid-semester examination, the average score of the girls was $5$ higher than that of the boys. In the final exam, however, the average score of the girls dropped by $3$ while the average score of the entire class increased by $2$. The increase in the average score of the boys is

The mean of all $4-$digit even natural numbers of the form $'aabb',$ where $a > 0,$ is