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Binomial Theorem — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSBinomial Theorem1 Mark
MCQ
The coefficient of x3 in $\Big(\sqrt{\text{x}^5}+\frac{3}{\sqrt{\text{x}^{3}}}\Big)^5$ is:
    • A
      0
    • B
      120
    • C
      420
    • D
      540
    ✓

    Answer

    1. 540

    Solution:

    $\text{r}=\frac{6\times\frac{5}{2}-3}{\frac{5}{2}+\frac{3}{2}}=\frac{15-3}{4}=3$

    $\therefore$ Coefficient of x3 is 6C3​33

    $=\frac{6\times5\times4}{3\times2\times1}\cdot27$

    = 5 × 4 × 27 = 540

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