The coefficient of 8th term in the expansion of(1+x)10 is

# The coefficient of ${8}^{th}$ term in the expansion of${\left(1+x\right)}^{10}$ is

1. A

120

2. B

7

3. C

${}^{10}{C}_{8}$

4. D

210

Fill Out the Form for Expert Academic Guidance!l

+91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)

### Solution:

Given  expansion of ${\left(1+x\right)}^{10}$ is

We have general term in the expansion ${\left(x+a\right)}^{n}$

$\left(\therefore \text{\hspace{0.17em}}\text{\hspace{0.17em}}{T}_{r+1}={\text{\hspace{0.17em}}}^{n}{\text{C}}_{r}\text{\hspace{0.17em}}{x}^{n-r}\text{\hspace{0.17em}}{\left(a\right)}^{r}\text{\hspace{0.17em}}$be the expansion of ${\left(x+a\right)}^{n}\right)$

${8}^{th}$ term:

$\text{\hspace{0.17em}}{T}_{r+1}={\text{\hspace{0.17em}}}^{n}{\text{C}}_{r}\text{\hspace{0.17em}}{x}^{n-r}\text{\hspace{0.17em}}{\left(a\right)}^{r}\text{\hspace{0.17em}}$

$\text{\hspace{0.17em}}{T}_{8}={T}_{7+1}\text{\hspace{0.17em}}={\text{\hspace{0.17em}}}^{10}{\text{C}}_{7}\text{\hspace{0.17em}}{\left(1\right)}^{10-7}\text{\hspace{0.17em}}{\left(x\right)}^{7}\text{\hspace{0.17em}}$

coefficient ${x}^{7}$ in  $\text{\hspace{0.17em}}{T}_{8}={T}_{7+1}\text{\hspace{0.17em}}={\text{\hspace{0.17em}}}^{10}{\text{C}}_{7}$  +91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)