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If sum(r=0)^n((r^3+2r^2+3r+2)/(r+1)) ^...

If `sum_(r=0)^n((r^3+2r^2+3r+2)/(r+1)) ^nC_r=(2^4+2^3+2^2-2)/3`

A

2

B

`2^(2)`

C

`2^(3)`

D

`2^(4)`

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The correct Answer is:
A
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VIKAS GUPTA (BLACK BOOK)-BIONMIAL THEOREM-Exercise-4 : Subjective Type Problems
  1. If sum(r=0)^n((r^3+2r^2+3r+2)/(r+1)) ^nCr=(2^4+2^3+2^2-2)/3

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  2. The sum of series 3*""^(2007)C(0)-8*""^(2007)C(1)+13*""^(2007)C(2)-18...

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  3. In the polynomial function f(x)=(x-1)(x^(2)-2)(x^(3)-3)……..(x^(11)-11...

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  4. If sum(r=0)^(3n)a(r)(x-4)^(r )=sum(r=0)^(3n)A(r)(x-5)^(r ) and a( k)=1...

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  5. If 3^(101)-2^(100) is divided by 11, the remainder is

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  6. Find the hundred's digit in the co-efficient of x^(17) in the expansio...

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  7. Let n in N, Sn=sum(r=0)^(3n)^(3n)Cr and Tn=sum(r=0)^n^(3n)C(3r), then ...

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  8. Find the sum of possible real values of x for which the sixth term of ...

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  9. Let q be a positive with q le 50. If the sum ""^(98)C(30)+2" "^(97)C...

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  10. The remainder when (sum(k=1)^(5) ""^(20)C(2k-1))^(6) is divided by 11,...

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  11. Let a=3^(1/223) +1 and for all n ge 3 let f(n) = C(n,0) a^(n-1) - C(n,...

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  12. In the polynomial (x-1)(x^(2)-2)(x^(3)-3)…(x^(11)-11), the coefficient...

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  13. Let the sum of all divisiors of the form 2^(p)*3^(q) (with p, q posit...

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  14. Find the sum of possible real values of x for which the sixth term of ...

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  15. Let 1+ sum(r=1)^10 (3^r C(10,r) + r C(10,r))=2^10 (alpha 4^5+beta) whe...

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  16. if Sn = C0C1 + C1C2 +...+ C(n-1)Cn and S(n+1)/Sn = 15/4 then n is

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