Maharashtra State BoardHSC Science (General) 11th
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In the following expansion, find the indicated term. (13+a2)12, 9th term - Mathematics and Statistics

Sum

In the following expansion, find the indicated term.

`(1/3 + "a"^2)^12`, 9th term

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Solution

Here, a = `1/3`, b = a2, n = 12

For 9th term, r = 8

We have, tr+1 = nCr an–r .br 

∴ t9 = `""^12"C"_8(1/3)^(12-8) ("a"^2)^8 = (12!)/(8!4!).(1/3)^4."a"^16`

= `(12 xx 11 xx 10 xx 9)/(4 xx 3 xx 2 xx 1) xx 1/81 xx "a"^16`

= `55/9"a"^16` 

∴ 9th term in the expansion of `(1/3 + "a"^2)^12` is `55/9"a"^16`

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. (iv) | Page 80
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