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BITSAT 2019

Exam: BITSAT
Year: 2019
Subject: Mathematics
Chapter: Binomial Theorem

BITSAT 2019 · Mathematics · Binomial Theorem

In the expansion of (1 + x + x^ 3 + x^ 4 )10 , the coefficient of...

In the expansion of

\left(1 + x + x^{3} + x^{4}\right)10

, the coefficient of

x^{4}

is

Options

A $235$
B $310$
C $285$
D $325$

Correct answer

B. $310$

Step-by-step solution

$\left(1 + x + x^{3} + x^{4}\right)10 = \left[\left(1 + x\right)\left(1 + x^{3}\right)\right]10$

$= \left(1 + x\right)10\left(1 + x^{3}\right)10$

$= \left(1 + C1 10 x + C2 10 x^{2} + C3 10 x^{3} + C4 10 x^{4} \ldots\right)\times \left(1 + C1 10 x^{3} + C2 10 x^{6} + \ldots.\right)$

$∴$ Coefficient of $x^{4} = \left(C1 10\right)\left(C1 10\right) +$ C4 10 $</p><p>$ = 100 + 210 = 310 $</p>$

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