The coefficient of x59 in the expansion of 1-x40x-120 isA- 59B- 0C- -20D- 20

The correct option is D 20 nbsp; nbsp;(1+x)^40(x 1)^20= (1 x^2)^20(1+x)^20 nbsp; So,the coefficient of x^59 in the expansion of (1+x)^40(x 1)^20 = ^20C_2 ...

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Standard XII

Mathematics

Combination

The coefficie...

Question

The coefficient of $x^{59}$ in the expansion of $(1 + x)^{40} (x - 1)^{20}$ is

0

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- 20

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20

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59

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Solution

The correct option is C $20$
$(1 + x)^{40} (x - 1)^{20} = (1 - x^{2})^{20} (1 + x)^{20}$
So,the coefficient of $x^{59}$ in the expansion of $(1 + x)^{40} (x - 1)^{20}$
$=^{20} C_{20} \times^{20} C_{19} = 20$

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The coefficient of x59 in the expansion of (1+x)40(x−1)20 is

The correct option is C 20 (1+x)40(x−1)20=(1−x2)20(1+x)20 So,the coefficient of x59 in the expansion of (1+x)40(x−1)20 =20C20×20C19=20

The coefficient of $x^{59}$ in the expansion of $(1 + x)^{40} (x - 1)^{20}$ is

The correct option is C $20$
$(1 + x)^{40} (x - 1)^{20} = (1 - x^{2})^{20} (1 + x)^{20}$
So,the coefficient of $x^{59}$ in the expansion of $(1 + x)^{40} (x - 1)^{20}$
$=^{20} C_{20} \times^{20} C_{19} = 20$