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Question

R=(55+11)2n+1 and f=R[R], where [] denotes the greatest integer function. Then the value of Rf is


A
42n+1
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B
22n+1
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C
2n
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D
8n+1
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Solution

The correct option is A 42n+1
Here f=R[R] is the fractional part of R thus if I is the integral part of R Then
R=I+f=(55+11)2n+1 and 0<f<1Letf=(5511)2n+1.Then 0<f<1 (as 5511<1)
Now I+ff=(55+11)2n+1(5511)2n+1=2[2n+1C1(55)2n×11+2n+1C3(55)2n2×113+]
= an even integer 
ff must also be an integer
ff=0,(0<f<1,0<f<1,1<ff<1)
f=f
RF=RF=(55+11)2n+1(5511)2n+1=(125121)2n+1=42n+1
 

Mathematics

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