CSAT 2022

Q. What is the number of numbers of the form 0.XY, where X and Y are distinct non-zero digits?

a. 72
b. 81
c. 90
d. 100
Correct Answer: a. 72

Question from UPSC Prelims 2022 CSAT Paper

Explanation :

Counting distinct non-zero digit combinations in the decimal form 0.XY

The number of numbers of the form 0.XY, where X and Y are distinct non-zero digits, can be found by counting the number of possibilities for X and Y, and then multiplying them together.

There are 9 choices for X (all digits except 0), and once X is chosen, there are 8 choices for Y (all digits except the chosen value of X).
Therefore, the total number of numbers of the form 0.XY is:
9 × 8 = 72

Therefore, the answer is (a) 72.

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