Consider the first 100 natural numbers. How many of them are NOT divisible by any one of 2, 3, 5, 7 and 9?

9 is covered by 3. Numbers up to 100 divisible by 2, 3, 5 or 7 number 78 by inclusion-exclusion, so 100 - 78 = 22 (1 and the 21 primes from 11 to 97). (Answer as per the official UPSC answer key.)