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Find the coefficients of x^(50) in the e...

Find the coefficients of `x^(50)` in the expression `(1+x)^(1000)+2x(1+x)^(999)+3x^2(1+x)^(998)++1001 x^(1000)` .

A

`""^(1000)C_(50)`

B

`""^(1000)C_(50)`

C

`""^(1002)C_(50)`

D

`""^(1000)C_(51)`

Text Solution

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The correct Answer is:
C
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OBJECTIVE RD SHARMA ENGLISH-BINOMIAL THEOREM AND ITS APPLCIATIONS -Exercise
  1. if the coefficients of x^(5)" and "x^(15) in the expansion of (x^(2)+(...

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  2. If n is a positive integer and C(k)=""^(n)C(k), then the value of sum(...

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  3. Find the coefficients of x^(50) in the expression (1+x)^(1000)+2x(1+x)...

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  4. about to only mathematics

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  5. The coefficient of x^(n) in the expansion of (1)/((1-x)(3 -x)), is

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  6. The coefficient of x^(n) in the expansion of ((1+x)^(2))/((1 - x)^(3))...

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  7. If (r+1)t h term is the first negative term in the expansion of (1+x)^...

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  8. The coefficient of x^(6) in the expansion of (1 + x + x^(2))^(-3) is

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  9. The coefficient of x^n in the expansion of (1 + x+x^2+...........)^-...

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  10. If the binomial expansion of (a +b x)^-2 is 1/4-3x+......., then (a, ...

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  11. If C(r) = ""^(n)C(r) and (C(0) + C(1)) (C(1) + C(2)) … (C(n-1) + C(n))...

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  12. If the third term in the expansion of (1+x)^mi s-1/8x^2, then find the...

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  13. If p is nearly equal to q and n gt 1 , such that ((n+1) p+(n-1)q)/(...

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  14. If y=3 x + 6 x^(2) + 10 x^(3) +… then x =

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  15. If y = (1)/(3) + (1*3)/(3 *6) + (1 * 3*5)/(3*6*9) +… then the value ...

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  16. If (1+2x+x^2)^n=sum(r=0)^(2n)ar x^r ,then ar is a.(.^nC2)^2 b. .^n ...

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  17. In the expansion of (sqrt(x^5)+3/(sqrt(x^3)))^6 coefficient of x^3 is ...

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  18. Find the number of nonzero terms in the expansion of (1+3sqrt(2)x)^9+(...

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  19. The coefficient of y in the expansion of (y^(2) + c//y)^(5) is

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  20. The greatest coefficient in the expansion of (1 + x)^(10), is

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