TS EAMCET · Maths · Basic of Mathematics
For any integer \(n \geq 1\), the number of positive divisors of \(n\) is denoted by \(d(n)\). Then, for a prime \(P, d\left(d\left(d(P)^7\right)\right)\) is equal to
- A \(1\)
- B \(2\)
- C \(3\)
- D \(P\)
Answer & Solution
Correct Answer
(C) \(3\)
Step-by-step Solution
Detailed explanation
Since, \(d(n)\) represents number of the divisors of \(n\). \(\begin{array}{rlrl} & d\left(P^7\right) =8 \\ & d(8)= d\left(2^3\right) =4 \\ & d(4)= d\left(2^2\right) =3 \\ \therefore & d\left(d\left(d\left(P^7\right)\right)\right) =3 \end{array}\)
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