Mathematics - Permutation & Combination Question with Solution | TestHub

MathematicsPermutation & CombinationFundamental PrincipleMedium2 minQB

MathematicsMediumsingle choice

Let the product of all the divisors of 1440 be P. If P is divisible by $2 4^{X}$ , then the maximum value of x is

Answer:

Solution:

Product of all divisions of $N = N^{\frac{TN D}{2}}$

$1440 = 2^{5} \cdot 3^{2} \cdot 5$

$TN D = 6 \cdot 3 \cdot 2 = 36$

$N^{\frac{TN D}{2}} = (2^{5} \cdot 3^{2} \cdot 5)^{\frac{36}{2}} = (2^{5} \cdot 3^{2} \cdot 5)^{18} = 2^{90} \cdot 3^{36} \cdot 5^{18}$

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

⏱ 2mℹ️ Source: QB

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