A) 1024
B) 810
C) 2346
D) None of these
Correct Answer: B
Solution :
The total number between 10 and 1000 are 989 but we have to form the numbers by using numerals \[1,\ 2,........9,\ \ i.e.\]0 is not occuring so the numbers containing any ?0? would be excluded i.e., Required number of ways \[=989-\left\{ \begin{align} & 20,\ 30,\ 40,................100=9 \\ & 101,\ 102,...................200=19 \\ & 201,........................300=19 \\ & ............................................. \\ & ............................................. \\ & 901,..........................990=18 \\ \end{align} \right\}\] \[=989-(9+18+19\times 8)=810\]. Aliter: Between 10 and 1000, the numbers are of 2 digits and 3 digits. Since repetition is allowed, so each digit can be filled in 9 ways. Therefore number of 2 digit numbers \[=9\times 9=81\] and number of 3 digit numbers \[9\times 9\times 9=729\] Hence total ways\[=81+729=810\].
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