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

NDA 2022 · Mathematics · Basics of Mathematics

Consider the following statements : 1. (n!)/(3!) is divisible by 6...

Consider the following statements : 1. n!3!\frac{n!}{3!} is divisible by 6 , where n>32.n!3!+3n > 3 2. \frac{n!}{3!}+3 is divisible by 7 , where n>3n > 3 Which of the above statements is/are correct?

Options

  1. A1 only
  2. B2 only
  3. CBoth 1 and 2
  4. DNeither 1 nor 2

Correct answer

D. Neither 1 nor 2

Step-by-step solution

Statement 1 Let n=4 ∴n!3!=4!3!=4\therefore \frac{\mathrm{n}!}{3!}=\frac{4!}{3!}=4 is not divisible by 6 Statement 2 Let n=5 ∴n!3!+3=5!3!+3=5.4+3=23\therefore \frac{\mathrm{n}!}{3!}+3=\frac{5!}{3!}+3=5.4+3=23 is not divisible by 7.
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