In expansion of {(1 + x + {x^3} + {x^4})^{10}}, coefficient of {x^4} is

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7.Binomial Theorem

hard

In the expansion of ${(1 + x + {x^3} + {x^4})^{10}},$ the coefficient of ${x^4}$ is

A

$^{40}{C_4}$

B

$^{10}{C_4}$

C

$210$

D

$310$

Solution

(d) ${(1 + x + {x^3} + {x^4})^{10}} = {(1 + x)^{10}}\,{(1 + {x^3})^{10}}$

$ = (1 + {}^{10}{C_1}\,.\,x + {}^{10}{C_2}\,.\,{x^2} + …..)(1 + {}^{10}{C_1}\,.\,{x^3} + {}^{10}{C_2}\,.\,{x^6} + …..)$

$\therefore $ Coefficient of ${x^4}$

$ = \,{}^{10}{C_1}.{}^{10}{C_1} + {}^{10}{C_4} = 310$.

Standard 11

Mathematics

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