Mathematics - Permutation & Combination Question with Solution | TestHub

MathematicsPermutation & CombinationnPr & nCrMedium2 minQB

MathematicsMediuminteger

Let P be the product of distances of any vertex of a regular decagon inscribed in a unit circle from the remaining vertices then the sum of digits occuring in P is

Answer:

Solution:

If $1, α_{1}, α_{2}, \dots, α_{9}$ are the 10 th roots of unity then $(1 - α_{1}) (1 - α_{2}) \dots (1 - α_{9}) = 10 \Rightarrow ∣ 1 - α_{1} ∣ ∣ 1 - α_{2} ∣ \dots ∣ 1 - α_{9} ∣ = 10$ .

So, $P = 10$ .

Stream:JEESubject:MathematicsTopic:Permutation & CombinationSubtopic:nPr & nCr

⏱ 2mℹ️ Source: QB

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