The coefficient of the term independent of x in -x-3-3-2 x2-10 isA- 1 B- 10 C1C- 5-12D- None of these

The correct option is D T_r+1=^10C_r (√(x/3) )^10 r(√(3/2x^2) )^r =^10C_r (1/√(3) )^10 r(√(3/2) )^r x^5 r/2 r Let T_r+1 be the term independent of x. ∴ 5 r/2 ...

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Byju's Answer

Standard XII

Mathematics

Middle Terms

The coefficie...

Question

The coefficient of the term independent of x in ${[\sqrt{\frac{x}{3}} + \sqrt{\frac{3}{2 x^{2}}}]}^{10}$ is

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Solution

The correct option is D
$T_{r + 1} =^{10} C_{r} {(\sqrt{\frac{x}{3}})}^{10 - r} {(\sqrt{\frac{3}{2 x^{2}}})}^{r} =^{10} C_{r} {(\frac{1}{\sqrt{3}})}^{10 - r} {(\sqrt{\frac{3}{2}})}^{r} x^{5 - \frac{r}{2} - r} L e t T_{r + 1} b e t h e t e r m i n d e p e n d e n t o f x . ∴ 5 - \frac{r}{2} - r = 0 \Rightarrow \frac{3 r}{2} = 5 \Rightarrow r = \frac{10}{3} ∴ r i s n o t a w h o l e n u m b e r . ∴ G i v e n e x p r e s s i o n d o e s n o t h a v e t e r m i n d e p e n d e n t o f x .$

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The coefficient of the term independent of x in [√x3+√32x2]10 is

The correct option is D Tr+1=10Cr(√x3)10−r(√32x2)r=10Cr(1√3)10−r(√32)rx5−r2−rLet Tr+1 be the term independent of x.∴5−r2−r=0⇒3r2=5⇒r=103∴r is not a whole number.∴ Given expression does not have term independent of x.

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