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Mathematics - Permutation & Combination Question with Solution | TestHub

MathematicsPermutation & CombinationDivision of Identical itemsMedium2 minQB

MathematicsMediummultiple choice

Let $a = i + j + k$ and let $r$ be a variable vector such that $r . i, r . j$ and $r . k$ are positive integers. If $r . a \leq 12$ then the number of values of $r$ is

Options:(select one or more)

Answer:

B, C

Solution:

If $r = x i + y j + z k$ then from the question $x, y, z$ are positive integers. Also $r . a \leq 12 \Rightarrow x + y + z \leq 12$ ∴ the number of values of $r =$ the number of positive integral solutions of $(x + y + z \leq 12)$ $= \sum_{n = 3}^{12}^{n - 1} C_{2} =^{2} C_{2} +^{3} C_{2} + \dots . +^{11} C_{2} =^{12} C_{3} =^{12} C_{9}$

Stream:JEESubject:MathematicsTopic:Permutation & CombinationSubtopic:Division of Identical items

⏱ 2mℹ️ Source: QB

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