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Find the middle term in the expansion of : `(1+3x+3x^2+x^3)^(2n)`

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To find the middle term in the expansion of \((1 + 3x + 3x^2 + x^3)^{2n}\), we can follow these steps: ### Step 1: Identify the expression We start with the expression: \[ (1 + 3x + 3x^2 + x^3)^{2n} \] ...
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RD SHARMA-BINOMIAL THEOREM-Solved Examples And Exercises
  1. Find the middle term in the expansion of : (x^4-1/(x^3))^(11)

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

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  3. Find the middle term in the expansion of : (1+3x+3x^2+x^3)^(2n)

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  4. Find the middle term in the expansion of : (1-2x+x^2)^n

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  5. Find the middle term in the expansion of : (2x-(x^2)/4)^9

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  6. The middle term of (x-1/x)^(2n+1) is

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  7. Find the middle terms in the expansion (3x-(x^3)/6)^7 .

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  8. Find the middle term in the expansion of : (p/x+x/p)^9

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  9. Find the middle term in the expansion of :\ (x/3+9y)^(10)

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  10. Find the middle term in the expansion of : (2a x-b/(x^2))^(12)

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

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  12. Term independent of x in the expansion of (3x^2-1/(3x))^9.

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  13. Find the term independent of x in the expansion of (a) (sqrt(x)/(3)+3/...

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  14. Find the term independent of x in the expansion of (a) (sqrt(x/3)+sqrt...

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  15. Find the term independent o f x in the expansion of the following expr...

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  16. Find the term independent of x in the expansion off the following expr...

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  17. Find the term independent of x in the expansion off the following expr...

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  18. Find the term independent of x in the expansion off the following expr...

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  19. Find the term independent of x in the expansion off the following expr...

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  20. Find the term independent of x in the expansion of [(3x^2/2)-(1/3x)]^9

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