Total number of divisors of 3 5 ⋅ 5 7 ⋅ 7 9 which are of the form 4 λ + 1 , λ ≥ 0 , is (60) l then l is

Mathematics - Probability Question with Solution | TestHub

MathematicsProbabilityMiscellaneous/MixedMedium2 minQB

MathematicsMediuminteger

Total number of divisors of $3^{5} \cdot 5^{7} \cdot 7^{9}$ which are of the form $4 λ + 1, λ \geq 0$ , is (60) $l$ then $l$ is

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:ProbabilitySubtopic:Miscellaneous/Mixed

⏱ 2mℹ️ Source: QB

Doubts & Discussion

Loading discussions...