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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Basics of Mathematics

NDA 2022 · Mathematics · Basics of Mathematics

Let A=\ 7,8,9,10,11,12,13,14,15,16\ and let f: A arrow N be defined...

Let A={7,8,9,10,11,12,13,14,15,16}A=\{7,8,9,10,11,12,13,14,15,16\} and let f:A→Nf: A \rightarrow N be defined by f(x)=f(x)= the highest prime factor of xx. How many elements are there in the range of ff ?

Options

  1. A44
  2. B55
  3. C66
  4. D77

Correct answer

C. 66

Step-by-step solution

∴f(x)= the highest prime factor of x∴f(7)=7,f(8)=2,f(9)=3,f(10)=5,f(11)=11f(12)=3,f(14)=7,f(15)=5,f(16)=2,f(13)=13∴ Range ={2,3,5,7,11,13}\begin{aligned} & \therefore f(x)=\text{ the highest prime factor of } x \\ & \therefore f(7)=7, f(8)=2, f(9)=3, f(10)=5, f(11)=11 \\ & f(12)=3, f(14)=7, f(15)=5, f(16)=2, f(13)=13 \\ & \therefore \quad \text{ Range }=\{2,3,5,7,11,13\}\end{aligned}
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