Start Free Mock LoginAlready registered? Login here

Mathematics - Permutation & Combination Question with Solution | TestHub

MathematicsPermutation & CombinationnPr & nCrMedium2 minQB

MathematicsMediumsingle choice

Statement I: If a natural number $P$ has 105 positive divisors, then ${P} = 0$ . Statement II: $2^{2} \cdot 3^{4} \cdot 5^{6}$ is such a number.

Options:

Answer:

Solution:

This repeats Q32. Odd divisor count makes every prime exponent even, hence $P$ is a square; the example indeed has 105 divisors but alone does not prove I.

Stream:JEESubject:MathematicsTopic:Permutation & CombinationSubtopic:nPr & nCr

⏱ 2mℹ️ Source: QB

Doubts & Discussion

Loading discussions...