The coefficient of x 16 in the expansion of 2- x 20 isA- 20 C 4B- 20 -16 C 4C- 16 -20 C 16D- 20 C 16

The correct option is C 16 ×^20C_16 nbsp;General term of nbsp;(2 x)^20 nbsp; is ^20C_r2^20 r( x)^r For x^16 term r=16 So, coefficient of x^16 is ^20C_162 ...

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Standard XII

Mathematics

Binomial Coefficients

The coefficie...

Question

The coefficient of $x^{16}$ in the expansion of $(2 - x)^{20}$ is

^{20} C_{4}

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20 \times^{16} C_{4}

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16 \times^{20} C_{16}

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^{20} C_{16}

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Solution

The correct option is C $16 \times^{20} C_{16}$
General term of $(2 - x)^{20}$ is $^{20} C_{r} 2^{20 - r} (- x)^{r}$
For $x^{16}$ term
$r = 16$
So, coefficient of $x^{16}$ is $^{20} C_{16} 2^{4} = 16 \times^{20} C_{16}$

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The coefficient of x16 in the expansion of (2−x)20 is

The correct option is C 16×20C16 General term of (2−x)20 is 20Cr220−r(−x)r For x16 term r=16 So, coefficient of x16 is 20C1624=16×20C16

The coefficient of $x^{16}$ in the expansion of $(2 - x)^{20}$ is

The correct option is C $16 \times^{20} C_{16}$
General term of $(2 - x)^{20}$ is $^{20} C_{r} 2^{20 - r} (- x)^{r}$
For $x^{16}$ term
$r = 16$
So, coefficient of $x^{16}$ is $^{20} C_{16} 2^{4} = 16 \times^{20} C_{16}$