The arithmetic mean of the nine numbers in the given set ${9, 99, 999, 999999999}$ is a $9$ digit numbers $N$ , all whose digits are distinct. The number $N$ does not contain the digit

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Solution

$A . M = \frac{9 + 99 + 999 + 999999999}{9}$

$= 9 \frac{1 + 11 + 111 + 111111111}{9}$

$= 1 + 11 + 111 + 111111111$

$1 + 11 = 12$

$1 + 11 + 111 = 123$

$∴ 1 + 11 + 111 + 111111111 = 123456789$

$\Rightarrow A . M . = 123456789$

Hence A.M. does not contain 0 as one of its digit.

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The arithmetic mean of the nine numbers in the given set {9,99,999,999999999} is a 9 digit numbers N, all whose digits are distinct. The number N does not contain the digit

A.M=9+99+999+9999999999=91+11+111+1111111119=1+11+111+1111111111+11=121+11+111=123∴1+11+111+111111111=123456789⇒A.M.=123456789Hence A.M. does not contain 0 as one of its digit.

The arithmetic mean of the nine numbers in the given set ${9, 99, 999, 999999999}$ is a $9$ digit numbers $N$ , all whose digits are distinct. The number $N$ does not contain the digit

$A . M = \frac{9 + 99 + 999 + 999999999}{9}$

$= 9 \frac{1 + 11 + 111 + 111111111}{9}$

$= 1 + 11 + 111 + 111111111$

$1 + 11 = 12$

$1 + 11 + 111 = 123$

$∴ 1 + 11 + 111 + 111111111 = 123456789$

$\Rightarrow A . M . = 123456789$

Hence A.M. does not contain 0 as one of its digit.