The coefficient of x6- y-2 in the expansion of x2-y-y-x12

The correct option is C T_r+1=^12C_r(x^2/y )^12 r( y/x )^r =^12C_r x^24 3r.y^2r 12( 1)^r ∴ Coefficient of x^6 y^ 2 is obtained, 24 3r=6 and r 12 = 2 ⇒ r=6 a ...

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Standard XII

Mathematics

Middle Terms

The coefficie...

Question

The coefficient of $x^{6} . y^{- 2}$ in the expansion of ${(\frac{x^{2}}{y} - \frac{y}{x})}^{12}$ is

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Solution

The correct option is C
$T_{r + 1} =^{12} C_{r} {(\frac{x^{2}}{y})}^{12 - r} {(- \frac{y}{x})}^{r} =^{12} C_{r} x^{24 - 3 r} . y^{2 r - 12} (- 1)^{r} ∴ C o e f f i c i e n t o f x^{6} y^{- 2} i s o b t a i n e d, 24 - 3 r = 6 a n d r - 12 = - 2 \Rightarrow r = 6 a n d r = 5 w h i c h i s n o t p o s s i b l e$

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The coefficient of x6.y−2 in the expansion of (x2y−yx)12 is

The correct option is C Tr+1=12Cr(x2y)12−r(−yx)r=12Crx24−3r.y2r−12(−1)r∴ Coefficient of x6 y−2 is obtained, 24−3r=6 and r−12 =−2⇒r=6 and r=5 which is not possible

The coefficient of $x^{6} . y^{- 2}$ in the expansion of ${(\frac{x^{2}}{y} - \frac{y}{x})}^{12}$ is