Sets, Relations and Function: Let A=\1,2,3,4\ and B=\1,4,9,16\ . Then the number of many-one… | JEE Main 2025

JEE Main 2025 (Online) 22nd January Evening ShiftQuestion 1

Let $A=\{1,2,3,4\}$ and $B=\{1,4,9,16\}$. Then the number of many-one functions $f:A\to B$ such that $1\in f(A)$ is equal to :

Sets, Relations and Function

$151$✓ Correct answer$139$$163$$127$

Solution

Functions with $1$ in the range: $4^4-3^4=175$; the $24$ bijections all contain $1$, so many-one ones number $175-24=151$.

Sets, Relations and Function - JEE Mathematics question (JEE Main 2025 (Online) 22nd January Evening Shift)