CAT (QA) PYQs

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

Ramesh and Gautam are among $22$ students who write an examination. Ramesh scores $82.5$. The average score of the $21$ students other than Gautam is $62$. The average score of all the $22$ students is one more than the average score of the $21$ students other than Ramesh. The score of Gautam is

Consider six distinct natural numbers such that the average of the two smallest numbers is $14$, and the average of the two largest numbers is $28$. Then, the maximum possible value of the average of these six numbers is