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Find the co-efficient of x^{19} in the expansion of (1-x)(1+x^{3})^{12}

  • Option 1)

    924

  • Option 2)

    462

  • Option 3)

    -462

  • Option 4)

    -924

 

Answers (1)

As laernt in concept

General Term in the expansion of (x+a)^n -

T_{r+1}= ^{n}c_{r}\cdot x^{n-r}\cdot a^{r}
 

- wherein

Where r\geqslant 0 \, and \, r\leqslant n

r= 0,1,2,----n

 

 (1+x)(1+x^{3})^{12}

=(1+x^{3})^{12}- x(1+x^{3})^{12}

We get x^{19} in -x(1+x^{3})^{12}

We will find x^{18} in (1+x^{3})^{12}

=> ^{12}C_r(x^{3})^{r}, we get r=6

Thus

- ^\textrm{12}C_6= -924

 


Option 1)

924

Incorrect option

Option 2)

462

Incorrect option

Option 3)

-462

Incorrect option

Option 4)

-924

Correct option

Posted by

Vakul

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