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Binomial Theorem — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsBinomial Theorem1 Mark
MCQ
The coefficient of $x^3$ in $\Big(\sqrt{\text{x}^5}+\frac{3}{\sqrt{\text{x}^{3}}}\Big)^5$ is:
  • A
    $0$
  • B
    $120$
  • C
    $420$
  • ✓
    $540$
✓

Answer

Correct option: D.
$540$
$\text{r}=\frac{6\times\frac{5}{2}-3}{\frac{5}{2}+\frac{3}{2}}=\frac{15-3}{4}=3$
$\therefore$ Coefficient of $x^3$ is ${ }^6 \mathrm{C}_3 3^3$
$=\frac{6\times5\times4}{3\times2\times1}\cdot27$
$= 5 \times 4 \times 27$
$= 540$

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