Binomial TheoremHard

Question

In the expansion of , n ∈ N, if the sum of the coefficients of x5 and x10 is 0, then n is :

Options

A.25
B.20
C.15
D.None of these

Solution


General term = (-1)n-r x5r-2n
If 5r - 2n = 5, then 5r = 2n + 5 ⇒ r = + 1
If 5r - 2n = 10, then 5r = 2n + 10 ⇒ r = + 2
Let n = 5k
Now  
⇒ = 0
⇒   k = 3  ⇒  n = 15

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