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TS EAMCET 4-Aug-2021 Shift 1 Question Paper

Section: Mathematics

Question : 17 of 160

Marks: +1, -0

x^{4}

(1-x-x^{2}+x^{3})^{6}

Solution: 👈: Video Solution

(1-x-x^{2}+x^{3})^{6}=[(1-x)(1-x^{2})]^{6}

=(1-x)^{12}(1+x)^{6}

In the expansion of

(1-x)^{12}

, coefficient are of the form

(-1)^{r^{12}} C_{r}

and in

(1+x)^{12}

, coefficient are of the form

{}^{6}C_{r}

Coefficient of

x^{4}

in expansion of

(1-x-x^{2}+x^{3})^{6}

={}^{12}C_{0} \times {}^{6}C_{4}-{}^{12}C_{1} \times {}^{6}C_{3}+{}^{12}C_{2} \times {}^{6}C_{2}

-{}^{12}C_{3} \times {}^{6}C_{1}+{}^{12}C_{4} \times {}^{6}C_{0}

=15-240+990-1320+495=-60

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