KCET · Maths · Basic of Mathematics
If \( P(n): " 2^{2 n-1} \) is divisible by \( k \) for all \( n \varepsilon N^{\prime \prime} \) is true, then the value of ' \( k \) ' is
- A \( 06 \)
- B \( 3 \)
- C \( 07 \)
- D \( 12 \)
Answer & Solution
Correct Answer
(B) \( 3 \)
Step-by-step Solution
Detailed explanation
Given that, \(P(n):\) " \(2^{2 n-1}\) is divisible by \(\mathrm{k}\) for all \(\mathrm{n} \mathrm{N}\) "
Thus
\(2^{2 n}-1=4^{n}-1=(3+1)^{n}-1=3 m\)
Therefore, the value of \(\mathrm{k}\) is 3 .
Thus
\(2^{2 n}-1=4^{n}-1=(3+1)^{n}-1=3 m\)
Therefore, the value of \(\mathrm{k}\) is 3 .
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