CAT (QA) PYQs

The number of integers $x$ such that $0.25 < 2^x < 200$, and $2^x + 2$ is perfectly divisible by either $3$ or $4$, is

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

How many three-digit numbers are greater than $100$ and increase by $198$ when the three digits are arranged in the reverse order?