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General Term of Binomial Expansion

Coefficient o...

Question

Coefficient of $x^{16}$ in $(1 + x + x^{2}) (1 - x)^{15}$

A

16

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B

-14

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C

14

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D

-16

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Solution

The correct option is C 14
$(1 + x + x^{2}) (1 - x)^{15}$
$= (1 + x + x^{2}) (1 - 15 x +^{15} C_{2} x^{2} -^{15} C_{3} x^{3} . . . -^{15} C_{15} x^{15})$
Hence coefficient of $x^{16}$ will be.
$-^{15} C_{15} x . x^{15} +^{15} C_{14} x^{2} . x^{14}$
Hence coefficient will be.
$= - 1 + 15$
$= 14$

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Similar questions

f (x) = 1 - x + x^{2} - x^{3} + \dots \dots - x^{15} + x^{16} - x^{17}

, then the coefficient of

x^{2}

f (x - 1)

f (x) = 1 - x + x^{2} - x^{3} + . . . . - x^{15} + x^{16} + x^{17}

, then the coefficient of

x^{2}

f (x - 1)

f (x) = 1 - x + x^{2} - x^{3} + \dots - x^{15} + x^{16} - x^{17},

then the coefficient of

x^{2}

f (x - 1)

f (x) = 1 + x^{2} - x^{3} + . . . - x^{15} + x^{16} - x^{17}

, then the coefficient of

x^{2}

f (x - 1)

Q. The ratio of coefficient of

x^{15}

to the term independent of

x

in the expansion of

{(x^{2} + \frac{1}{2 x})}^{15}

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