Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  CBSE XI  >>  Math  >>  Binomial Theorem
0 votes

Find the coefficient of $x^5$ in the expansion of the product $(1+2x)^6(1-x)^7$

$\begin{array}{1 1}(A)\;181\\(B)\;161\\(C)\;151\\(D)\;171\end{array} $

Can you answer this question?

1 Answer

0 votes
  • $(a+b)^n=nC_0a^n+nC_1a^{n-1}b+nC_2a^{n-2}b^2+.........nC_ra^{n-r}b^r+......nC_nb^n$
$\Rightarrow 1+12x+60x^2+20\times 8x^3+15\times 16x^4+6\times 32x^6+64x^5$
$\Rightarrow 1+12x+60x^2+160x^3+240x^4+192x^5+64x^6$-----(1)
$\Rightarrow 1-7x+21x^2-35x^3+35x^4-21x^5+7x^6-x^7$-------(2)
Multiplying (1) and (2) and collecting the coefficient of $x^5$
$\therefore$ Coefficient of $x^5$ in the product $(1+2x)^6(1-x)^7$
$\Rightarrow 1\times (-21)+12\times 35+60\times (-35)+160\times 21+240\times (-7)+192\times 1$
$\Rightarrow -21+420-2100+3360-1680+192$
$\Rightarrow 171$
Hence (D) is the correct answer.
answered Jun 23, 2014 by sreemathi.v

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App