Maharashtra State BoardHSC Science (General) 11th
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Answer the following: x6 in the expansion of (3x2-13x)9 - Mathematics and Statistics

Sum

Answer the following:

x6 in the expansion of `(3x^2 - 1/(3x))^9`

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Solution

Let tr+1 contains x6 in the expansion of `(3x^2 - 1/(3x))^9`

We know that, in the expansion of (a+ b)n,

tr+1 = nCr an–r br 

Here a = 3x2, b = `-1/(3x)`, n = 9

∴ tr+1 = `""^9"C"_"r"(3x^2)^(9-"r")(-1/(3x))^"r"` 

= `""^9"C"_"r".3^(9 - "r").x^(18 - 2"r").(-1/3)^"r".x^(-"r")`

= `""^9"C"_"r".3^(9 - "r").(-1/3)^"r".x^(18 - 3"r")`

But tr+1 has x6

∴ power of x = 6

∴ 18 – 3r = 6

∴  r = 4

∴ coefficient of x6 = `""^9"C"_4.(3)^5(-1/3)^4`

= `(9 xx 8 xx 7 xx 6)/(1 xx 2 xx 3 xx 4) xx 3`

= 378

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 II. (9) (i) | Page 86
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