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7.Binomial Theorem
hard
${(1 + x + {x^3} + {x^4})^{10}},$ ના વિસ્તરણમાં ${x^4}$ નો સહગુણક મેળવો.
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
