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If x^p occurs in the expansion of (x^2+1...

If `x^p` occurs in the expansion of `(x^2+1//x)^(2n)` , prove that its coefficient is `((2n)!)/([1/3(4n-p)]![1/3(2n+p)]!)` .

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RD SHARMA ENGLISH-BINOMIAL THEOREM-All Questions
  1. If the fourth term in the expansion of (a x+1/x)^n \ is \ 5/2,\ then ...

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  2. The sum of the coefficients of first three term in the expansion of (x...

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  3. If x^p occurs in the expansion of (x^2+1//x)^(2n) , prove that its coe...

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  4. The coefficient of x^m in (1+x)^m +(1+m)^(m+1) +...+(1+x)^n ,m≤n is

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  5. If in the expansion of (1-x)^(2n-1) ardenotes the coefficient of x^r t...

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  6. If 3rd, 4th, 5th terms in the expansion of (x+a)^n be 84, 280 and 560,...

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  7. Find the number of terms which are free from radical signs in the e...

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  8. Find the 11th term form the beginning and the 11th term form the end...

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  9. Find the 7th term in the expansion of (3x^2-1/(x^3))^(10)dot

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  10. Find the 5th term from the end in the expansion of (3x-1/(x^2))^(10)do...

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  11. Find the 7th term in the expansion of ((4x)/5+5/(2x))^8dot

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  12. Find the 4th term from the beginning and 4^(th) term from the end in ...

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  13. Find the 4th term from the end in the expansion of ((4x)/5-5/(2x))^9do...

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  14. Find the 7th term from the end in the expansion of (2x^2-3/(2x))^8dot

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  15. Find the coefficient of x^(10) in the expansion of (2x^2-1/x)^(20).

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

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

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

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

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  20. The co-efficient of x in the expansion of (1-2x^(3) + 3x^(5)) (1+1/x)^...

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