For the binomial expansion 32x2−13x9, which of the following is (are) true

Tr+1=9Cr32x29−r−13xrThe power of x is 2(9−r)−r=0. ∴ r=6∴ T7= term independent of x=9C632x23−13x6=9.8.712.3⋅3323⋅136=718

For the binomial expansion 32x2−13x9, which of the following is (are) true

Tr+1=9Cr32x29−r−13xrThe power of x is 2(9−r)−r=0. ∴ r=6∴ T7= term independent of x=9C632x23−13x6=9.8.712.3⋅3323⋅136=718

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For the binomial expansion ${(\frac{3}{2} x^{2} - \frac{1}{3 x})}^{9}$ , which of the following is (are) true

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The highest power of $x$ in the expansion is 18.

The Value of the term independent of x is $\frac{7}{18}$

The seventh term does not depend on x.

No independent term

answer is A, B, C.

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$T_{r + 1} =^{9} C_{r} {(\frac{3}{2} x^{2})}^{9 - r} {(- \frac{1}{3 x})}^{r}$

The power of $x$ is $2 (9 - r) - r = 0 . ∴ r = 6$

$∴ T_{7} =$ term independent of $x$

$\begin{aligned} =^{9} C_{6} {(\frac{3}{2} x^{2})}^{3} {(- \frac{1}{3 x})}^{6} \\ = \frac{9.8.7}{12.3} \cdot \frac{3^{3}}{2^{3}} \cdot \frac{1}{3^{6}} = \frac{7}{18} \end{aligned}$

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For the binomial expansion 32x2−13x9, which of the following is (are) true

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For the binomial expansion ${(\frac{3}{2} x^{2} - \frac{1}{3 x})}^{9}$ , which of the following is (are) true