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(A) number is divisible by $11$ if the difference between the sum of digits at odd places and the sum of digits at even places is either $0$ or a mult

Vedclass · Accepted Answer

$2$

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(A) number is divisible by $11$ if the difference between the sum of digits at odd places and the sum of digits at even places is either $0$ or a multiple of $11$.Let the missing digit be $x$.The number is $5x3457$.Sum of digits at odd places (from right) $= 7 + 4 + x = 11 + x$.Sum of digits at even places (from right) $= 5 + 3 + 5 = 13$.For the number to be divisible by $11$,the difference must be $0$ or a multiple of $11$.$(11 + x) - 13 = 0$ or $(11 + x) - 13 = 11$.Case $1$: $x - 2 = 0 \implies x = 2$.Case $2$: $x - 2 = 11 \implies x = 13$ (not possible as $x$ must be a single digit).Therefore,the least value is $2$.

The least value to be given to $$ so that the number $53457$ is divisible by $11$ is

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The least value to be given to $*$ so that the number $5*3457$ is divisible by $11$ is