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 $x^{15}$ in the expression of $(x-x^2)^{10}$

$\begin{array}{1 1}(A)\;252\\(B)\;-252\\(C)\;255\\(D)\;-255\end{array} $

Can you answer this question?

1 Answer

0 votes
  • The general term in the expansion of $(a-b)^n$
  • $T_{r+1}=(-1)^rnC_r a^{n-r}b^r$
$ T_{r+1}=(-1)^r 10C_r (x)^{10-r}(x^2)^r$
$\Rightarrow (-1)^r10C_r x^{10-r}x^{2r}$
$\Rightarrow (-1)^r10C_r x^{10-r+2r}$
$\Rightarrow $ Now for this is to contain $x^{15}$ we observe that
Thus the coefficient of $x^{15}$ is
$\Rightarrow (-1) \large\frac{10\times 9\times 8\times 7\times 5!}{5\times 4\times 3\times 2\times 5!}$
$\Rightarrow -252$
Hence (B) is the correct answer.
answered Jun 24, 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