The coefficient of x 3 in - x 5-3-x36 isA- 120B- 420C- 540D- 0

The correct option is C 540T_r+1= ^6C_r (x^5/2 )^6 r(3/x^3/2 )^r = ^6C_r 3^rx^15 5r/2 3r/2=^6C_r 3^r x^15 4r ∴ 15 4r=3 or r=3 ∴ T_r+1= T_3+1^6C_3(3)^3x^15 ...

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Byju's Answer

Standard XI

Mathematics

Coefficients of Terms Equidistant from Beginning and End

The coefficie...

Question

The coefficient of $x^{3} i n {(\sqrt{x^{5}} + \frac{3}{\sqrt{x^{3}}})}^{6} i s$

120

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420

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540

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Solution

The correct option is C 540
$T_{r + 1} =^{6} C_{r} {(x^{\frac{5}{2}})}^{6 - r} {(\frac{3}{x^{\frac{3}{2}}})}^{r} =^{6} C_{r} 3^{r} x^{15 - \frac{5 r}{2} - \frac{3 r}{2}} =^{6} C_{r} 3^{r} x^{15 - 4 r} ∴ 15 - 4 r = 3 o r r = 3 ∴ T_{r + 1} = T_{3 + 1}^{6} C_{3} (3)^{3} x^{15 - 4 (3)} = 20 \times 27 \times + x^{3} = 540 x^{3} ∴ c o e f f i c i e n t o f x^{3} = 540$

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The coefficient of x3 in (√x5+3√x3)6 is

The correct option is C 540Tr+1=6Cr(x52)6−r(3x32)r=6Cr 3rx15−5r2−3r2=6Cr3rx15−4r∴15−4r=3 or r=3∴Tr+1=T63+1C3(3)3x15−4(3)=20×27×+x3=540x3∴ coefficient ofx3=540

The coefficient of $x^{3} i n {(\sqrt{x^{5}} + \frac{3}{\sqrt{x^{3}}})}^{6} i s$