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Question

The number of 6 digit numbers that can be formed using the digits 0,1,2,5,7 and 9 which are divisible by 11 and no digit is repeated, is:

A
36
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B
60
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C
48
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D
72
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Solution

The correct option is C 60
Sum of given digits 0,1,2,5,7,9 is 24.
Let the six digit number be abcdef and to be divisible by 11.
So |(s+c+e)(b+d+f)| is multiple of 11.
Hence only possibility is a+c+e=12=b+d+f
Case - I {a,c,e}={9,2,1}&{b,d,f}={7,5,0}
So, Number of numbers =3!×3!=36
Case - II {a,c,e}={7,5,0} and {b,d,f}={9,2,1}
So, Number of numbers 2×2!×3!=24
Total =60

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