Maharashtra State BoardHSC Science (General) 11th
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In the following expansion, find the indicated term. (x2-4x3)11, 5th term - Mathematics and Statistics

Sum

In the following expansion, find the indicated term.

`(x^2 - 4/(x^3))^11`, 5th term

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Solution

Here, a = x2 , b = `-(4)/x^3`, n = 11

For 5th term, r = 4

We have, tr+1 = nCr . an–r.br

∴ t5 = `""^11"C"_4(x^2)^(11 - 4).(-(4)/x^3)^4`

= `(11!)/(4!7!)(x^2)^7.(-(4)/x^3)^4` 

= `(11 xx 10 xx 9 xx 8)/(4 xx 3 xx 2 xx 1) xx x^14 xx 256/x^12`

= 330 × 256 × x2

= 84480 x2

∴ 5th term in the expansion of `(x^2 - 4/x^3)^11` is 84480 x2

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. (ii) | Page 80
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