Maharashtra State BoardHSC Science (Electronics) 11th
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Find the constant term (term independent of x) in the expansion of (x2-1x)9 - Mathematics and Statistics

Sum

Find the constant term (term independent of x) in the expansion of `(x^2 - 1/x)^9`

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Solution

Here, a = x2, b = `(-1)/x`, n = 9

We have, tr+1 = nCr an–r .br 

= `""^9"C"_"r" (x^2)^(9 - "r") ((-1)/x)^"r"` 

= 9Cr x18–2r (–1)r .x–r

= 9Cr (–1)r x18–3r

To get the term independent of x, we must have

x18–3r  = x0

 ∴ 18 – 3r = 0

∴ r = 6

∴ the term independent of x = 9C6 (–1)6

= `(9!)/(6!3!) xx 1`

= `(9 xx 8 xx  7)/(3 xx 2 xx 1)`

= 84

∴ the term independent of x is 84.

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
Exercise 4.3 | Q 3. (iv) | Page 80
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