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Question
Select the correct answer from the given alternatives.
The term not containing x in expansion of `(1 - x)^2 (x + 1/x)^10` is
Options
11C5
10C5
10C4
10C7
Solution
11C5
Explanation;
`(1 - x)^2(x + 1/x)^10 = (1 - 2x + x^2)(x + 1/x)^10`
= `(1 - 2x + x^2) [""^10"C"_0 x^10 + ""^10"C"_1 x^9(1/x) + ""^10"C"_2 x^8(1/x)^2 + ""^10"C"_3 x^7(1/x)^3 + ""^10"C"_4 x^6(1/x)^4 + ""^10"C"_5 x^5(1/x)^5 + ""^10"C"_6 x^4(1/x)^6 + ...]`
=(1 – 2x + x2) [10C0 x10 + 10C1 x8 + 10C2 x6 + 10C3 x4 + 10C4 x2 + 10C5 + 10C6 x–2 + ...]
∴ term not containing x = 10C5 + 10C6 = 11C6 = 11C5
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