The 6^{th} term in the expansion of left( 2x^ | vedclass

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(B) The general term in the expansion of $(x + a)^n$ is given by $T_{r+1} = {^n}C_r x^{n-r} a^r$.For the $6^{th}$ term,we set $r+1 = 6$,which implies

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$-\frac{896}{27}$

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(B) The general term in the expansion of $(x + a)^n$ is given by $T_{r+1} = {^n}C_r x^{n-r} a^r$.For the $6^{th}$ term,we set $r+1 = 6$,which implies $r = 5$.Here,$n = 10$,$x = 2x^2$,and $a = -\frac{1}{3x^2}$.$T_6 = {^{10}}C_5 (2x^2)^{10-5} \left( -\frac{1}{3x^2} ight)^5$$T_6 = {^{10}}C_5 (2x^2)^5 \left( -\frac{1}{3x^2} ight)^5$$T_6 = \frac{10 	imes 9 	imes 8 	imes 7 	imes 6}{5 	imes 4 	imes 3 	imes 2 	imes 1} 	imes (32x^{10}) 	imes \left( -\frac{1}{243x^{10}} ight)$$T_6 = 252 	imes 32 	imes \left( -\frac{1}{243} ight)$$T_6 = -\frac{252 	imes 32}{243} = -\frac{8064}{243} = -\frac{896}{27}$

The $6^{th}$ term in the expansion of $\left( 2x^2 - \frac{1}{3x^2} \right)^{10}$ is

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