JEE Main 2022MathematicsFunctionsClassification Of FunctionsmediumMCQ

JEE Main 2022 — Functions Question with Solution

From: JEE Main 2022 (Online) 28th June Morning Shift

Question

Let a function f : N N be defined by

f(n) = \left[ {\matrix{ {2n,} & {n = 2,4,6,8,......} \cr {n - 1,} & {n = 3,7,11,15,......} \cr {{{n + 1} \over 2},} & {n = 1,5,9,13,......} \cr } } \right.

then, f is

Choose an option

Show full solutionCorrect option: D
Correct answer
Done-one and onto

Step-by-step explanation

When n = 1, 5, 9, 13 then will give all odd numbers.

When n = 3, 7, 11, 15 .....

n 1 will be even but not divisible by 4

When n = 2, 4, 6, 8 .....

Then 2n will give all multiples of 4

So range will be N.

And no two values of n give same y, so function is one-one and onto.

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About this question

This is a previous-year question from JEE Main 2022, 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.