KVPY SX SB Exam 05-Nov-2017 Question Paper

Question : 5 of 120

Marks: +1, -0

The fractional part of a real number x is x –[x], where [x] is the greatest integer less than or equal to x. Let F

_1

and F

_2

be the fractional parts of

(44 -√2017 ) ^2017

and

(44 + √2017 ) ^2017

respectively. Then

F_1 + F_2

lies between the numbers

Solution:

I + F_2 = (√ 2017+44)^ 2017

F_2' = (√ 2017-44)^ 2017 ;0< F_2 ' < 1

I + F_2 -F_2'=2[^2017C_1(√2017)^2016(44)+...]

F_2 = F_2'

F_2 = (0.911)^2017

Now,

F_1 =(44-√2017)^2017=-(0.911)^2017

Fractional part can not –ve.
So,

F_1 = 1 -(0.911)^2017

So,

F_1 + F_2 = 1

1 lie Between 0.9 & 1.35

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