If the number of elements in the sets $G$ and $A$ are 3 and 4 respectively, then match the items of List I with those of List II
The correct match is A B C D

Question

If the number of elements in the sets $G$ and $A$ are 3 and 4 respectively, then match the items of List I with those of List II The correct match is A B C D

Aicharya · Accepted Answer

Given that, number of elements in the sets $G$ and $A$ are 3 and 4 respectively. (A) The number of non bijective function from $G \times G$ to $G=3^9=19683$

(B) $A$ to $A$

Here, $a$ has 4 choice, $b$ has $3, c$ has 2 and $d$ has 1 choice. So, number of bijective functions from $A$ to $A$ is $ =4 \times 3 \times 2 \times 1=24 $ (C) $G$ to $G \times A$

So, number of function from $G$ to $G \times A$ is $ =12^3=1728 $ (D) $A$ to $A \times A$ The number of surjective from $G$ to $G \times A$ i.e. 4 to 16 is 0 So, $\mathrm{A} \rightarrow \mathrm{V}, \mathrm{B} \rightarrow \mathrm{I}, \mathrm{C} \rightarrow \mathrm{III}, \mathrm{D} \rightarrow$ II

If the number of elements in the sets $G$ and $A$ are 3 and 4 respectively, then match the items of List I…

Solution