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Show that the coefficient of the middle...

Show that the coefficient of the middle term in the expansion of `(1+x)^(2n)`is equal to the sum of the coefficients of two middle terms in the expansion of `(1+x)^(2n-1)`.

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MODERN PUBLICATION-BINOMIAL THEOREM-EXERCISE 8 (B)(LONG ANSWER TYPE QUESTION-I)
  1. Find the middle in the expansion of : (i) (x/3 + 9y)^10 (ii) (...

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  2. Show that the coefficient of the middle term in the expansion of (1+x...

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  3. Write and simplify the term involving x^5 in the expansion of (x- 1/x)...

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  4. Determine the term involving x^3 in ( 5 - 2x)^6

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  5. Find the coefficient of x^10 in the expansion of (2x^2 - 3/x)^11 , x ...

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  6. Find the coefficient of x^40 in the expansion of (1+2x+x^2)^54

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  7. Which term contains x^8 in the expansion of (x^2 - 1/x)^10? Also , fin...

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  8. If the coefficients of a^(m) and a^(n) in the expansion of (1+a)^(m+n)...

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  9. Find a if the coefficient of x^2 and x^3 in the expansion of (3+ax)^9 ...

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  10. Find the coefficient of a^4in the product (1+2a)^4(2-a)^5using binomi...

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  11. In the binomial expansion of (a+b)^n , coefficients of the fourth and ...

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  12. In the expansion of (1+a)^(34) , if the cofficient of (r-5)^(th) and (...

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  13. Which term is independent of 'x' in the expansion of (2x^2 + 1/x)^12 ...

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  14. Write and simplify the term independent of 'x' in the expansion of (x^...

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  15. Find the term independent of x in the expansion of: (x-1/x)^(12) .

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  16. Find the term independent of x in the expression (x-1/x)^(14)

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  17. Find the term independent of x in the expansion of (3/2x^2-1/(3x))^6.

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  18. Find the term independent of 'x' , x ne 0 in the expansion of (x^2 ...

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  19. Find the term independent of 'x' , x ne 0 in the expansion of (3 - (...

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  20. Write and simplify the coefficient of the term independent of 'x' in t...

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