JEE Main 2017MathematicsFunctionsMediumMCQ

JEE Main 2017 — Functions Question with Solution

JEE Main 2017 (09 Apr Online)

Question

The function f :N→I defined by fx=x-5x5 , where N is the set of natural numbers and x denotes the greatest integer less than or equal to x, is:

Choose an option

Show full solutionCorrect option: C
Correct answer
Cneither one-one nor onto

Step-by-step explanation

Given, f( x )=x−5[ x 5 ]

Hence, f( x )=5( x 5 −[ x 5 ] )

=5{ x 5 }

Since, x is a natural number. 

Hence, x5=0,15,25,35,45

Hence, f( x )=0 , when x=5n, n∈N

=1 when x=5n+1, n∈N

=2 when x=5n+2, n∈N

=3 when x=5n+3, n∈N

=4 when x=5n+4, n∈N

Hence, fx is neither one-one nor onto.

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About this question

This is a previous-year question from JEE Main 2017, covering the Functions chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.