If the term independent of x in the expansion of -x - kx210 is 405- then the values of k can be

T_r+1 = ^10C_r (√(x))^10 r( kx^2)^r = ^10C_r x^(10 r/2 2r) ( k)^r nbsp; For this to be independent of x, 10 r2 2r=0⇒ r=2 ∴ ^10C_2( k)^2 = 405 nbsp; ⇒ k ...

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Standard XII

Mathematics

Term Independent of x

If the term i...

Question

If the term independent of $x$ in the expansion of ${(\sqrt{x} - \frac{k}{x^{2}})}^{10}$ is $405$ , then the value(s) of $k$ can be

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Solution

The correct option is C $3$
$T_{r + 1} =^{10} C_{r} {(\sqrt{x})}^{10 - r} {(\frac{- k}{x^{2}})}^{r} =^{10} C_{r} x^{(\frac{10 - r}{2} - 2 r)} (- k)^{r}$
For this to be independent of $x$ , $\frac{10 - r}{2} - 2 r = 0 \Rightarrow r = 2$

$∴^{10} C_{2} (- k)^{2} = 405 \Rightarrow k = \pm 3$

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Term Independent of x

Standard XII Mathematics

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If the term independent of x in the expansion of (√x−kx2)10 is 405, then the value(s) of k can be

The correct option is C 3Tr+1= 10Cr(√x)10−r(−kx2)r= 10Crx(10−r2−2r)(−k)r For this to be independent of x, 10−r2−2r=0⇒r=2 ∴ 10C2(−k)2=405⇒k=±3

If the term independent of $x$ in the expansion of ${(\sqrt{x} - \frac{k}{x^{2}})}^{10}$ is $405$ , then the value(s) of $k$ can be

The correct option is C $3$
$T_{r + 1} =^{10} C_{r} {(\sqrt{x})}^{10 - r} {(\frac{- k}{x^{2}})}^{r} =^{10} C_{r} x^{(\frac{10 - r}{2} - 2 r)} (- k)^{r}$
For this to be independent of $x$ , $\frac{10 - r}{2} - 2 r = 0 \Rightarrow r = 2$

$∴^{10} C_{2} (- k)^{2} = 405 \Rightarrow k = \pm 3$