In the expansion of ( a x + b x ) 12 , the coefficient of x − 10 will be Options: A . &nbsp 12 a 11 B . &nbsp 12 b 11 a C . &nbsp 12 a 11 b D . &nbsp 12 a 11 b 11

Answer: Option C : C T r + 1 = 12 c r ( a x ) 12 − r ( b x ) r = 12 c r . a 12 − r . b r . x 2 r − 12 ∴ 2 x − 12 = − 10 ⇒ r = 1 ∴ coefficient = 12. a 11 . b

In the expansion of ( ax+bx)12, the coefficient of x−10 will be

Discussion Forum : Binomial Theorem

Question -

In the expansion of ( $\frac{a}{x} + b x)^{12}$ , the coefficient of $x^{- 10}$ will be

Options:

A .

12 a^{11}

B .

12 b^{11} a

C .

12 a^{11} b

D .

12 a^{11} b^{11}

Answer: Option C
:
C

$T_{r + 1} = 12_{c_{r}} {(\frac{a}{x})}^{12 - r} {(b x)}^{r} = 12_{c_{r}} . a^{12 - r} . b^{r} . x^{2 r - 12} ∴ 2 x - 12 = - 10 \Rightarrow r = 1 ∴ coefficient = 12. a^{11} . b$

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