In the expansion of ( a x + b x ) 12 , the coefficient of x − 10 will be Options: A . &nbsp12a11 B . &nbsp12b11a C . &nbsp12a11b D . &nbsp12a11b11

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

Question

In the expansion of (

\frac{a}{x} + b x)^{12}

, the coefficient of

x^{- 10}

will be

Options:

A . 12a11

B . 12b11a

C . 12a11b

D . 12a11b11

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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