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prove that the coefficient of x^n in the...

prove that the coefficient of `x^n` in the expansion of `(1+x)^(2n)` is twice the coefficient of `x^n` in the expansion of `(1+x)^(2n-1)`

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NAGEEN PRAKASHAN-BINOMIAL THEOREM-Exercise 8C
  1. Find the coefficient of x^(2).y^(7) in the expansion of (x+2y)^(9)

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  2. Prove that the ratio of the coefficient of x^10 in (1 - x^2)^10 & the ...

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  3. Prove that the greatest coefficient in the expansion of (1+x)^(2n) is...

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  4. Find a positive value of m for which the coefficient of x^2 in the ex...

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  5. The sum of the coefficients of x^(32) and x^(-17) in (x^4- 1/(x^3))^15...

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  6. If the coefficient of x^7 in (ax^2+1/(bx))^11 is equal to the coeffici...

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

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  8. Find the coefficient of x^(10) in the expansion of (1-x^(2))^(10)

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  9. The coefficient of x^(-17) in the expansion of (x^4-1/x^3)^(15) is

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  10. Find the coefficient of x^(40) in the expansion of (1+2x+x^2)^(27)dot

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  11. If 'n' is a positive integer then prove that the coefficient fox^(m) i...

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  12. Find the term independent of x (constant term) in the following expans...

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  13. Prove that the term independent of x in the expansion of (x +1/x)^(2n)...

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

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  15. Find the coefficient of x^(2).y^(7) in the expansion of (x+2y)^(9)

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  16. Prove that the ratio of the coefficient of x^10 in (1 - x^2)^10 & the ...

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  17. prove that the coefficient of x^n in the expansion of (1+x)^(2n) is tw...

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  18. Find a positive value of m for which the coefficient of x^2 in the ex...

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  19. The sum of the coefficients of x^(32) and x^(-17) in (x^4- 1/(x^3))^15...

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  20. Find the coefficients of x^7 in (a x^2+1/(b x))^(11)a n dx^(-7)in(a x^...

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