Maharashtra State BoardHSC Science (General) 11th
Advertisement Remove all ads

In the following expansion, find the indicated term. (3a+4a)13, 10th term - Mathematics and Statistics

Sum

In the following expansion, find the indicated term.

`(3"a" + 4/"a")^13`, 10th term

Advertisement Remove all ads

Solution

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

tr+1 = nCr pn–r qr 

Here p = 3a, q = `4/"a"`, n = 13 and for t10, r = 9.

∴ 10th term in the expansion of `(3"a" + 4/"a")^13` 

= t10 = `""^13"C"_9 (3"a")^(13-9).(4/"a")^9`

= `""^13"C"_4 (3"a")^4.(4/"a")^9`    ...[∵ nCr = nCn–r]

= `(13 xx 12 xx 11 xx 10)/(1 xx 2 xx 3 xx 4) xx 81"a"^4 xx 4^9/"a"^9`

= `715 xx 81 xx 262144 xx 1/"a"^5`

= `15182069760/"a"^5`

Concept: General Term in Expansion of (a + b)n
  Is there an error in this question or solution?
Advertisement Remove all ads

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. (v) | Page 80
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×