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JEE Main
Exam
JEE Main
Subject
Mathematics
Chapter
Sets and Relations

JEE Main · Mathematics · Sets and Relations

If a set A has m elements and set B has n elements and the number...

If a set AA has mm elements and set BB has nn elements and the number of injections from AA to BB is 2520 . Then, mm is equal to

Options

  1. A2
  2. B7
  3. C6
  4. D5

Correct answer

D. 5

Step-by-step solution

Given, ∣A∣=mand|A|=m and|B|=nTotalnumberofinjectivefunctionfromTotal number of injective function fromAtotoBisis\frac{n !}{(n-m) !}Given,Given,\frac{n !}{(n-m) !}=2520TotalnumberofinjectionsfromTotal number of injections fromAtotoB={ }^n P_m=2520⇒nPm=7×6×5×4×3=7P5⇒n=7,m=5\begin{array}{ll} \Rightarrow& { }^n P_m=7 \times6 \times5 \times4 \times3={ }^7 P_5 \\ \Rightarrow & n=7, m=5 \end{array}
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