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lf the term independent of x in the expansion of ${(\frac{3}{2} x^{2} - \frac{1}{3 x})}^{9}$ is k, then 18k is equal to

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a

5

b

7

c

9

d

11

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detailed solution

Correct option is B

given binomial is 32x2−13x9So the general term,Tr+1=9Cr32x29−r−13xr=9Cr329−r−13rx18−3rlf the term is independent of x, then 18−3r=0⇒r=6∴(r+1) th term =7th term is independent of xNow, as T6+1=k⇒ 9C6323−136=k⇒ 9×8×73×2×127×8=k⇒k=718⇒18k=7Hence, option (b) is correct.

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lf some three consecutive coefficients in the binomial expansion of (x + 1)ⁿ in powers of x are in the ratio 2 : 15 : 70, then the average of these three coefficients is

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