The term independent of x in -x-2-x18 is

The correct option is A T_r+1=^18C_r ( √(x) )^18 r ( 2/x )^r=^18C_rx^9 r/2( 2)^ r If T_r+1 is independent of x, then 9 r/2 r=0⇒ r=6 So term independent of x=T ...

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Standard XII

Mathematics

Geometric Progression

The term inde...

Question

The term independent of x in ${(\sqrt{x} - \frac{2}{x})}^{18}$ is

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Solution

The correct option is A
$T_{r + 1} =^{18} C_{r} {(\sqrt{x})}^{18 - r} {(- \frac{2}{x})}^{r} =^{18} C_{r} x^{9 - \frac{r}{2}} (- 2)^{- r}$
If $T_{r + 1}$ is independent of x, then $9 - \frac{r}{2} - r = 0 \Rightarrow r = 6$
So term independent of $x = T_{7} =^{18} C_{6} 2^{6}$

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The term independent of x in (√x−2x)18 is

The correct option is A Tr+1=18Cr(√x)18−r(−2x)r=18Crx9−r2(−2)−r If Tr+1 is independent of x, then 9−r2−r=0⇒r=6 So term independent of x=T7=18C626

The term independent of x in ${(\sqrt{x} - \frac{2}{x})}^{18}$ is

The correct option is A
$T_{r + 1} =^{18} C_{r} {(\sqrt{x})}^{18 - r} {(- \frac{2}{x})}^{r} =^{18} C_{r} x^{9 - \frac{r}{2}} (- 2)^{- r}$
If $T_{r + 1}$ is independent of x, then $9 - \frac{r}{2} - r = 0 \Rightarrow r = 6$
So term independent of $x = T_{7} =^{18} C_{6} 2^{6}$