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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 ${P} = 0$ , where braces denote fractional part. Statement II: $2^{2} \cdot 3^{4} \cdot 5^{6}$ is such a number.

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Answer:

Solution:

Since 105 is odd, each prime exponent of $P$ is even, so $P$ is a square. The example has $(2 + 1) (4 + 1) (6 + 1) = 105$ divisors but does not prove the general claim.

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

⏱ 2mℹ️ Source: QB

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