KVPY SX SB Exam 2012 Question Paper

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Question : 82 of 120

Marks: +1, -0

The coefficient of

x^2012

in

{1+x}/{(1+x^2)(1-x)}

is

2010
2011
2012
2013
None of the above

Solution:

Coeff. of

x^2012

(1+x)^2/{(1+x^2)(1-x^2)}

=(1+x)^2(1-x^4)^{-1}

=(1+2x+x^2)(1-x^4)^{-1}

Coeff. of

x^2012

+ 2Coeff of

x^2011

+ Coeff of

x^2010

in the expansion of

(1- x^4)^{–1} x^2011

and

x^2010

not possible in

(1 - x^4)^{–1}

= only coeff. of

x^2012

in the expassion of

(1- x^4)^{–1}

^{1 + 503-1}C_503 = 1

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