The number of ordered pairs ( m , n ) , m , n ∈ { 1 , 2 , … ..50 } such that 6 n + 9 m is multiple of 5

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MathematicsPermutation & CombinationFundamental PrincipleMedium2 minQB

MathematicsMediumsingle choice

The number of ordered pairs $(m, n), m, n \in {1, 2, \dots ..50}$ such that $6^{n} + 9^{m}$ is multiple of 5

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Answer:

Solution:

All the numbers of the form $6^{n}$ will end with $6 9^{m}$ will end with 9, if m is odd, and will end with 1, if m is even so $6^{n} + 9^{m}$ will end with 5 if n is any number and m is odd. So ordered pairs will be $50 \times 25 = 1250$

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

⏱ 2mℹ️ Source: QB

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