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AP EAMCET202418 May 2024Morning ShiftMathematicsBinomial TheoremActual

For all positive integers ' n ' if 3 (5^ 2 n +1 )+2^ 3 n +1 is divisible by k , then the number of prime numbers less than or equal to k is

Options

  1. A17
  2. B6
  3. C7
  4. D8

Correct answer

C. 7

Step-by-step solution

If n=13 (5^ 2 1+1 )+2^ 3 1+1 =3 125+16=391=17 23 So, 3 (5^ 2 n+1 )+2^ 3 n+1 is divisible by least prime number k=17 . So, the number of prime numbers less than or equal to 17 is 7 . The numbers are 2,3,5,7,11,13 and 17 .

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