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BITSAT 2011
Exam
BITSAT
Year
2011
Subject
Mathematics
Chapter
Binomial Theorem

BITSAT 2011 · Mathematics · Binomial Theorem

The term independent of x in the expansion of ( ( 9 x- 1 3 x )^ 18...

The term independent of xx in the expansion of (\left(9 \mathrm{x}-\frac{1}{3 \sqrt{\mathrm{x}}}\right)^{18}, \mathrm{x} \gt0), is a times the corresponding binomial coefficient. Then a is

Options

  1. A3
  2. B1/31 / 3
  3. C−1/3-1 / 3
  4. DNone of these

Correct answer

D. None of these

Step-by-step solution

(Tr+1=18Cr(9x)18−r(−13x)r=(−r)r18Cr918−3r2\mathrmx18−3r2\begin{aligned} \mathrm{T}_{\mathrm{r}+1}& ={ }^{18} \mathrm{C}_{\mathrm{r}}(9 \mathrm{x})^{18-\mathrm{r}}\left(-\frac{1}{3 \sqrt{\mathrm{x}}}\right)^{\mathrm{r}}\\ & =(-\mathrm{r})^{\mathrm{r}}{ }^{18} \mathrm{C}_{\mathrm{r}}9^{18-\frac{3 \mathrm{r}}{2}} \mathrmx^{18-\frac{3 \mathrm{r}}{2}} \end{aligned}isindependentofis independent of\mathrm{x}providedprovided(\mathrm{r}=12)andthen12) and then(\mathrm{a}=$1).
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