MCQ
$(1-x)^{2008}\left(1+x+x^2\right)^{2007}$ ના વિસ્તરણમાં $x^{2012}$ નો સહગુણક........................છે.
- ✓$0$
- B$11$
- C$2$
- D$3$
$ (1-x)\left(1-x^3\right)^{2007} $
$ (1-x)\left({ }^{2007} C_0-{ }^{2007} C_1\left(x^3\right)+\ldots \ldots .\right)$
General term
$ (1-x)\left((-1)^r{ }^{2007} C_r x^{3 r}\right) $
$ (-1)^{r 2007} C_r x^{3 r}-(-1)^{r 2007} C_r x^{3 r+1} $
$ 3 r=2012 $
$ r \neq \frac{2012}{3} $
$ 3 r+1=2012 $
$ 3 r=2011 $
$ r \neq \frac{2011}{3}$
Hence there is no term containing $\mathrm{x}^{2012}$.
So coefficient of $x^{2012}=0$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.