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sum(r=0)^(m)( n+r )C(n)=...

`sum_(r=0)^(m)( n+r )C_(n)=`

A

1: `100 C_(51) `

B

2: `100 C_(52) `

C

3: `-100 C_(53) `

D

4 : `100 C_(54) `

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Verified by Experts

The correct Answer is:
C
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HIMALAYA PUBLICATION-BINOMIAL THEOREM-QUESTION BANK
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  2. The term independent of x in the expansion of (x^(2)-(1)/(x))^(6) ...

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  3. sum(r=0)^(m)( n+r )C(n)=

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  4. If (1+2 x+x^(2))^(n)=sum(r=0)^(2 n) a(r) x^(r), then a(r) =

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  5. (C(0))/(1)-(C(1))/(2)+(C(2))/(3)+.. . .+((-1)^(n))/(n+1). C(n) =

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  6. The value of C(1)+4C(2)+7C(3)+ . . .+(2n-2)C(n) is

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  7. If T, denotes the r^(th) term in the expansion of (x+(1)/(y))^(23)...

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  8. If C(0), C(2), C(4).. . are the binomial coefficients in the expansi...

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  9. The largest term in the expansion of (3+2x)^(50) where x=1/5 is:

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  10. If (1+x+x^(2))^(n) = sum(r=0)^(2 n) a(r). x^(r) then a(1)-2 a(2)+3 a...

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  11. If C(n) is the coefficient of x^(n) in the expansion of (1+x)^(n) ...

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  12. Term independent of x in (2 x^(2)+(3)/(x^(3)))^(15) is

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  13. The coefficients of the middle term in the expansion of (1+x)^(40) is

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  14. The term independent of x in the expansion of (x^(2)-(1)/(x))^(6) ...

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  15. The coefficients of x^(-n) in (1+x)^(n)(1+(1)/(x))^(n) is

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  16. The sum of the coefficients in the expansion of (1+x-3 x^(2))^(171) i...

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  17. If (1+x)^(n) = C(0)+C(1).x+C(2). x^(2)+..+C(n). x^(n) then C(0)+2. ...

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  18. In the expansion of (1+x)^(n) the coefficients of pth and (p+1)^(t...

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  19. The coefficient of x^(5) in the expansion of (x^(2)-x-2)^(5) is

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  20. The first three terms in the expansion of (1+a x)^(n ne 0) are 1,6 x...

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