CAT 2024 Functions Question (Hard)

Question

Consider two sets and . Let be a function from to such that for every element in , there is at least one element in such that . Then, the total number of such functions is

Accepted Answer

Step 1 Set A has 6 elements A 6 Set B has 3 elements B 3 We need the number of functions f A B such that every element of B is used at least once These are total onto functions surjective functions Step 2 Number of onto functions from A to B total functions from A to B functions missing at least one

CAT 2024

Quantitative

Functions

Hard

Consider two sets $A=\{2,3,5,7,11,13\}$ and $B=\{1,8,27\}$ . Let $f$ be a function from $A$ to $B$ such that for every element $b$ in $B$ , there is at least one element $a$ in $A$ such that $f(a)=b$ . Then, the total number of such functions $f$ is

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