JEE Main 2022 Mathematics question
The number of 7-digit numbers which are multiples of 11 and are formed using all the digits 1, 2, 3, 4, 5, 7 and 9 is .
Answer: 576
Solution
The digits 1, 2, 3, 4, 5, 7, 9 have sum 31. For divisibility by 11, − must be a multiple of 11, and since + = 31 is odd the difference is odd, so it is (0 and are impossible). So the sums of the digits in the three even places and in the four odd places are either (10, 21)
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