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AP EAMCET Engineering 23 Apr 2019 Shift 1 Paper

Section: Mathematics

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Question : 19 of 160

Marks: +1, -0

The coefficient of

x^4

in the expansion of

\frac{1}{(1-x)(1-2x)(1-3x)}

is

602
301
$\frac{601}{2}$
302

Solution:

Consider the expression,

\frac{1}{(1-x)(1-2x)(1-3x)}

=(1-x)^{-1}(1-2x)^{-1}(1-3x)^{-1}

=(1+x+x^2+x^3+x^4)

(1+2x+4x^2+8x^3+16x^4)

(1+3x+9x^2+27x^3+81x^4)

The coefficient of

x^4

is required so expand up to

x^4

,

(1-ax)^{-n}=1+ax+a^2x^2+a^3x^3+.

So, coefficient of

x^4

is,

81+54+36+24+16+27+18

+12+8+9+4+3+2+1=301

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