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Question

If (521)2n+1 and f = R –[[R], where [R]denotes the greatest integer less than or equal to R, then R(1f) =

A
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C
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Solution

The correct option is A
Let S=(521)2+1R+S=(5+21)2n+1+(521)2n+1=2[(2n+1)C052n+1+(2n+1)C25(2n1)21+= Even integer
[R]+ f +S = Even integer
0< 521<10<(521)2n+1< 10<S<1

f =R[R]0<f< 10f+S < 2f+S=11f=S

R (1f) = RS = (521)2n+1(521)2n+1=42n+1

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