Challenge Prelims V1.0 – Day 60 – CSAT Paper

1. A box contains 14 black balls, 20 blue balls, 26 green balls, 28 yellow balls, 38 red balls and 54 white balls. Consider the following statements:

1. The smallest number n such that any n balls drawn from the box randomly must contain one full group of at least one colour is 175.
2. The smallest number m such that any m balls drawn from the box randomly must contain at least one ball of each colour is 167.

Which of the above statements are correct? (UPSC 2023)

2. A question paper has 5 multiple choice questions. Each questions has 4 options to choose from. A candidate can either attempt the question or can leave it unattended. How many different sequences of answers are possible?

3. How many numbers are there from 100 to 1000 such that it has at least one 5 as a digit?

4. A 3 digit number ‘X’ is exactly divisible by 4. It is given that X can only have 2, 3, 4, 5 and 7 as digits and each digit is distinct. How many such numbers are there?

5. All the five letters of the word ‘INDIA’ are arranged to form different words without repeating any letter in one word. The words so formed are then arranged as in dictionary. What will be the position of word INDIA in that sequence?