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Find the coefficient of x^7 in the expan...

Find the coefficient of `x^7` in the expansion of `(x-1/(x^2))^(40)`.

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Suppose `x^{7}` occurs at the `(r+1)` th term in the given expression.
Then, we have:
`T_{r+1}=\ ^{40} C_{r} x^{40-r}(frac{-1}{x^{2}})^{r} `
`=(-1)^{r 40} C_{r} x^{40-r-2 r}`
For this term to contain `x^{7}`, we must have:
`40-3 r=7`
`Rightarrow 3 r=40-7=33 `
`Rightarrow r=11 `
...
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RD SHARMA-BINOMIAL THEOREM-Solved Examples And Exercises
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  2. Find the coefficient of x^(10) in the expansion of (2x^2-1/x)^(20).

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  3. Find the coefficient of x^7 in the expansion of (x-1/(x^2))^(40).

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  4. Find the coefficient of : x^(-15) in the expansion of (3x^2-a/(3x^3))^...

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  5. Find the coefficient of x^9 in the expansion of (x^2-1/(3x))^9.

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  6. Find the coefficient of \ x^m in the expansion of (x+1/x)^ndot

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  7. The co-efficient of x in the expansion of (1-2x^3+3x^5)(1+1/x)^8 is:

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  8. Find the coefficient of a^5b^7 in (a-2b)^(12)

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  9. Find the coefficient of x in the expansion of (1-3x+7x^2)(1-x)^(16).

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  10. Does the expansion of (2x^2-1/x)^(20) contain any term involving x^9?

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  11. Show that the expansion of (x^2+1/x)^12 does not contain any term invo...

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  12. Find the middle term in the expansion of ((2x)/3-3/(2x))^(20)

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  13. Find the middle term in the expansion of : (x^2-2/x)^(10)

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  14. Find the middle term in the expansion of : (a/x+\ b x)^(12)

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  15. Find the middle term in the expansion of : (x/a-a/x)^(10)

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  16. Find the middle term in the expansionansion of (3x-x^3/6)^9.

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  17. Find the middle term in the expansion of : \ (3x-2/(x^2))^(15)

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  18. Find the middle term in the expansion of (2x^2-1/x)^7

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  19. Find the middle term in the expansion of : (x^4-1/(x^3))^(11)

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  20. Find the middle term in the expansion of : \ (x-1/x)^(10)

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