Verified Solution • 2025–26 Session moderate

QJEEM22Ma72a8: JEE Main 2022 Mathematics - Class 11 JEEM22Ma72a8 Solution: Let a function f : N N be defined by f ( n ) = [ 2 n , n = 2 ,…

Let a function f : N →\to N be defined by

f(n)=[2n,n=2,4,6,8,......n−1,n=3,7,11,15,......n+12,n=1,5,9,13,......

then, f is

Multiple Choice Options

  • A one-one but not onto
  • B onto but not one-one
  • C neither one-one nor onto
  • D one-one and onto

Step-by-Step Verified Solution

When n = 1, 5, 9, 13 then n+12{{n + 1} \over 2} 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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