Mathematics - Permutation & Combination Question with Solution | TestHub

MathematicsPermutation & CombinationMiscellaneous/MixedMedium2 minQB

MathematicsMediumsingle choice

Passage / Comprehension

Let S be the set of the first 18 positive integers.

The number of ways of selecting two numbers form $S$ such that the sum of their cubes is divisible by 3 is

Answer:

Solution:

$a^{3} + b^{3}$ is divisible by 3 only if 3 divides $a + b$ .

∴ Required number $= 6 C_{1} \times 6 C_{1} + 6 C_{2} = 51$

Stream:JEESubject:MathematicsTopic:Permutation & CombinationSubtopic:Miscellaneous/Mixed

⏱ 2mℹ️ Source: QB

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