AP EAMCET · Maths · Binomial Theorem
For all positive integers ' \(n\) ' if \(3\left(5^{2 \mathrm{n}+1}\right)+2^{3 \mathrm{n}+1}\) is divisible by \(k\), then the number of prime numbers less than or equal to \(k\) is
- A \(17\)
- B \(6\)
- C \(7\)
- D \(8\)
Answer & Solution
Correct Answer
(C) \(7\)
Step-by-step Solution
Detailed explanation
If \(n=1\) \(3\left(5^{2 \times 1+1}\right)+2^{3 \times 1+1}=3 \times 125+16=391=17 \times 23\) So, \(3\left(5^{2 n+1}\right)+2^{3 n+1}\) 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…
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