# 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.