Ask Questions, Get Answers

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

Find a if the coefficients of $x^2$ and $x^3$ in the expansion of $(3+ax)^9$ are equal.

$\begin{array}{1 1}(A)\;\large\frac{9}{4}\\(B)\;\large\frac{9}{5}\\(C)\;\large\frac{9}{7}\\(D)\;\large\frac{9}{8}\end{array} $

Can you answer this question?

1 Answer

0 votes
  • General term =$T_{r+1}=nC_ra^{n-r}b^r$
  • $C(n,r)=\large\frac{n!}{r!(n-r)!}$
General term =$T_{r+1}=9C_r.3^{9-r}a^rx^r$
Putting $r=2$
Coefficient of $x^2=9C_23^{9-2}a^2$
$\Rightarrow \large\frac{9\times 8}{2}$$3^7a^2$
$\Rightarrow 4.3^9a^2$----(1)
Putting $r=3$
Coefficient of $x^3=9C_33^{9-3}a^3$
$\Rightarrow \large\frac{9\times 8\times 7\times 6!}{3\times 2\times 6!}$$\times 3^6....a^3$
$\Rightarrow 4\times 7\times 3^7.a^3$------(2)
Equating (1) and (2)
$4.3^9a^2=4\times 7\times 3^7a^3$
(Or) $3^2=7a$
Hence (C) is the correct answer.
answered Jun 23, 2014 by sreemathi.v

Related questions

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