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Mathematics - Permutation & Combination Question with Solution | TestHub

MathematicsPermutation & CombinationFundamental PrincipleHard2 minQB

MathematicsHardsingle choice

Number of pairs of positive integers (p,q) whose LCM (Least common multiple) is 8100, is "K". Then number of ways of expressing K as a product of two coprime numbers is $____$

Options:

Answer:

Solution:

L.C.M $(p, q) = 2^{2} 3^{4} . 5^{2}$ $P = 2^{a_{4}} 3^{b_{1}} \cdot 5^{c_{1}} q = 2^{a_{2}} 3^{b_{2}} 5^{c_{2}} \Rightarrow max {a_{1}, a_{2}} = 2 \Rightarrow 5 ways$

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

⏱ 2mℹ️ Source: QB

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