Maharashtra State BoardHSC Science (Electronics) 11th
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Select the correct answer from the given alternatives. The term not containing x in expansion of (1-x)2(x+1x)10 is - Mathematics and Statistics

MCQ

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

  • 11C

  • 10C5 

  • 10C

  • 10C

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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

Concept: General Term in Expansion of (a + b)n
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APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 4 Methods of Induction and Binomial Theorem
Miscellaneous Exercise 4 | Q I. (4) | Page 85
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