Question

The sum of all $3-$digit numbers less than or equal to $500,$ that are formed without using the digit ${}^{\prime \prime }{1}^{\prime \prime }$ and they all are multiple of $11,$ is

Answer 1

The required numbers are $209,220,231,...,495$
This A.P. contains $27$ terms
Sum of this A.P. $=\frac{27}{2}[209+495]=9504$
Only $231,319,341,418$ and $451$ are not allowed in this sum.
So, required sum $=9504-1760=7744$