The term that is independent of x- in the expansion of 3-2 x2-1-3 x9 i A- 9 C43-24-1-35B- 9 C63-25-1-34C- 9 C61-65D- 9 C63-26-1-36

The correct option is C (3/xx^2 1/3x )^9 = ∑_r=0^9 ^9C_r (3/2x^2 )^9 r( 1/3x )^r For the term that is independent of x, we must have, 18 2r r=0⇒ r ...

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Byju's Answer

Standard XI

Mathematics

Term Independent of X

The term that...

Question

The term that is independent of x, in the expansion of ${(\frac{3}{2} x^{2} - \frac{1}{3 x})}^{9}$ is

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Solution

The correct option is B
${(\frac{3}{x} x^{2} - \frac{1}{3 x})}^{9} = \sum_{r = 0}^{9}^{9} C_{r} {(\frac{3}{2} x^{2})}^{9 - r} {(- \frac{1}{3 x})}^{r} F o r t h e t e r m t h a t i s i n d e p e n d e n t o f x, w e m u s t h a v e, 18 - 2 r - r = 0 \Rightarrow r = 6 T h u s, r e q u i r e d t e r m =^{9} C_{6} {(\frac{3}{2} x^{2})}^{3} {(- \frac{1}{3 x})}^{6} i . e,^{9} C_{6} {(\frac{3}{2})}^{3} {(\frac{1}{3})}^{6}$

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Similar questions

Find the term independent of x in the expansion of $(1 + x + 2 x^{3}) {(\frac{3}{2} x^{2} - \frac{1}{3 x})}^{9}$

Q. The coefficient of the term independent of x in the expansion of

(1 + x + 2 x^{3}) {(\frac{3}{2} x^{2} - \frac{1}{3 x})}^{9}

Q. Find the term independent of

x

in the expansion of the expression,

(1 + x + 2 x^{3}) {(\frac{3}{2} x^{2} - \frac{1}{3 x})}^{9}

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^{'} x^{'}

in the expansion of the expression ,

(1 + x + 2 x^{3}) {(\frac{3}{2} x^{2} - \frac{1}{3 x})}^{9}

Q. If the term independent of

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{(\frac{3}{2} x^{2} - \frac{1}{3 x})}^{9}

k

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is equal to:

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The term that is independent of x, in the expansion of (32x2−13x)9 is

The correct option is B (3xx2−13x)9=∑9r=0 9Cr(32x2)9−r(−13x)rFor the term that is independent of x, we must have,18−2r−r=0⇒r=6Thus, required term=9C6(32x2)3(−13x)6i.e, 9C6(32)3 (13)6

The term that is independent of x, in the expansion of ${(\frac{3}{2} x^{2} - \frac{1}{3 x})}^{9}$ is