Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
Advertisement Remove all ads

Find the Middle Term in the Expansion Of: (Ii) ( a X + B X ) 12 - Mathematics

Find the middle term in the expansion of: 

(ii)  \[\left( \frac{a}{x} + bx \right)^{12}\]

 

Advertisement Remove all ads

Solution

(ii) Here,
n = 12 (Even number)
Therefore, the middle term is the 

\[\left( \frac{n}{2} + 1 \right)th\]   i.e. 7th term
 
\[Now, \]
\[ T_7 = T_{6 + 1} \]
\[ =^{12}{}{C}_6 \left( \frac{a}{x} \right)^{12 - 6} (bx )^6 \]
\[ = ^{12}{}{C}_6 a^6 b^6 \]
\[ = \frac{12 \times 11 \times 10 \times 9 \times 8 \times 7}{6 \times 5 \times 4 \times 3 \times 2} a^6 b^6 \]
\[ = 924 a^6 b^6\]

 

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 18 Binomial Theorem
Exercise 18.2 | Q 13.2 | Page 38
Advertisement Remove all ads

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×