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Mathematics - Permutation & Combination Question with Solution | TestHub

MathematicsPermutation & CombinationFundamental PrincipleMedium2 minQB

MathematicsMediumsingle choice

Total number of divisors of $3^{5} . 5^{7} . 7^{9}$ which are of the form $4 λ + 1, λ \geq 0$ , is

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Answer:

Solution:

Any positive integral power of 5 is of the form $4 λ + 1$ . Even power of 3 and 7 are of the form $4 λ + 1$ and odd powers of 3 and 7 are of the form $4 λ - 1$ . The required number $= 8 (3 \times 5 + 3 \times 5)$

Stream:JEESubject:MathematicsTopic:Permutation & CombinationSubtopic:Fundamental Principle

⏱ 2mℹ️ Source: QB

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