Q54 / 160 · AP EAMCET 2021 (23 Aug Shift 1) · Mathematics

If a set $A$ has $m$ elements and set $B$ has $n$ elements and the number of injections from $A$ to $B$ is 2520 . Then, $m$ is equal to

  • A
    2
  • B
    7
  • C
    6
  • Correct answer
    D
    5

Solution

Given, $|A|=m$ and $|B|=n$ Total number of injective function from $A$ to $B$ is $\frac{n !}{(n-m) !}$ Given, $\frac{n !}{(n-m) !}=2520$ Total number of injections from $A$ to $B={ }^n P_m=2520$ $\begin{array}{ll} \Rightarrow & { }^n P_m=7 \times 6 \times 5 \times 4 \times 3={ }^7 P_5 \\ \Rightarrow & n=7, m=5 \end{array}$

Hence, the correct answer is option: 'D'.

More Sets and Relations Questions