If the term independent of x in the - x - k - x 210 is 405 - then the values of k can beA- -3B- -2C- 3D- 2

The correct options are A 3 C 3T_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 ∴ ...

You visited us 3 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Term Independent of x

If the term i...

Question

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

- 3

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

- 2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct options are
A $- 3$
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 $x$ , $\frac{10 - r}{2} - 2 r = 0 \Rightarrow r = 2$

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

Suggest Corrections

Similar questions

Q. If the term independent of

x

in the expansion of

{(\sqrt{x} - \frac{k}{x^{2}})}^{10}

405

, then the value(s) of

k

can be

Q. If the term independent of

x

in the

{(\sqrt{x} - \frac{k}{x^{2}})}^{10}

is 405, then

k

equals

Q. If the term independent of

x

in the expansion of

{(\sqrt{x} - \frac{k}{x^{2}})}^{10}

405

, then

k

equals:

Q. Find the real value of

k

if the term independent of

x

in the expansion of

{(\sqrt{x} + \frac{k}{x^{2}})}^{10}

405

If the absolute term (independent of x) in the expansion of ${(\sqrt{x} - \frac{k}{x^{2}})}^{10}$ is 405 then k =

Join BYJU'S Learning Program

Explore more

Term Independent of x

Standard XII Mathematics

Join BYJU'S Learning Program

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

The correct options are A −3 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 ${(\sqrt{x} - \frac{k}{x^{2}})}^{10}$ is $405$ , then the value(s) of $k$ can be