Maharashtra State BoardHSC Science (General) 11th
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In the following expansion, find the indicated term. (4x5-52x)9, 7th term - Mathematics and Statistics

Sum

In the following expansion, find the indicated term.

`((4x)/5 - 5/(2x))^9`, 7th term

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Solution

We know that the (r + 1)th term in the expansion of (a + b)n is

tr+1 = nCr an–r b

Hence a = `(4x)/5` b = `-5/(2x)`, n = 9 and for t7, r = 6

∴ 7th term in the expansion of `((4x)/5 - 5/(2x))^9`

= t7 =  `""^9"C"_6((4x)/5)^(9 - 6) (-5/(2x))^6`

= `""^9"C"_3((4x)/5)^3 (-5/(2x))^6`    ...[∵ nCr = nCn–r]

= `(9 xx 8 xx 7)/(1 xx 2 xx 3) xx (4^3.x^3)/5^3 xx 5^6/(2^6.x^6)`

= `84 xx 5^3 xx 1/x^3`

= `10500/x^3`

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 1. (iii) | Page 80
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