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Question

If 540 is divided by 11, then remainder is α and if 22003 is divided by 17, then remainder is β. Then the value of (βα) is

A
3
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B
5
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C
7
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D
8
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Solution

The correct option is C 7
540=(52)20=(22+3)20=22λ+320,λN
Also, 320=(32)10=(112)10=11μ+210,μN
Now, 210=1024=11×93+1
Remainder =1 i.e., α=1

22003=2322000=8(24)500=8(16)500
=8(171)500=8(17v+1),vN
=8×17v+8
Remainder =8 i.e., β=8
βα=81=7

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