CAT (QA) PYQs

Brishti went on an 8-hour trip in a car. Before the trip, the car had travelled a total of x km till then, where x is a whole number and is palindromic, i.e., $x$ remains unchanged when its digits are reversed. At the end of the trip, the car had traveled a total of $26862 \mathrm{~km}$ till then, this number again being palindromic. If Brishti never drove at more than $110 \mathrm{~km} / \mathrm{hr}$, then the greatest possible average speed at which she drove during the trip, in km/hr, was

For a $4$-digit number, the sum of its digits in the thousands, hundreds and tens places is $14$, the sum of its digits in the hundreds, tens and units places is $15$, and the tens place digit is $4$ more than the units place digit. Then the highest possible $4$-digit number satisfying the above conditions is

For any natural number $n$, let $a_{n}$ be the largest integer not exceeding $\sqrt{n}$. Then the value of $a_{1}+a_{2}+\ldots .+a_{50}$ is