NIMCET 2010 — Mathematics PYQ

• Number of elements in Set $A$, $n(A)=m=3$

• Number of elements in Set $B$, $n(B)=n=4$

Step 2: Apply the formula for the number of injections

If $n\ge m$, the number of injective functions from $A$ to $B$ is given by the permutation formula:

Step 3: Perform the calculation

Substitute $n=4$ and $m=3$:

Logical Explanation:

• The first element of $A$ has $4$ choices in $B$.

• The second element of $A$ has $3$ choices remaining (since it must be distinct).

• The third element of $A$ has $2$ choices remaining.

• Total ways $=4\times 3\times 2=24$.

Conclusion:

The total number of injective functions is $24$.

Correct Option:

(c) $24$