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The sum of the series sum(r=0)^(10)""^(2...

The sum of the series `sum_(r=0)^(10)""^(20)C_(r)` is `2^(19)+""^(20)C_(10)`.

A

`2^(20)`

B

`2^(19)`

C

` 2^(19) + (1)/(2) ""^(20)C_(10)`

D

`2^(19)- (1)/(2) ""^(20)C_(10)`

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. Given positive integers r >1,n >2 and that the coefficient of (3r d)t ...

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  2. Find the number of terms in the expansions of the following: (1+sqrt(2...

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  3. The sum of the series sum(r=0)^(10)""^(20)C(r) is 2^(19)+""^(20)C(10).

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  4. The coefficient of x^(-10) in (x^2-1/x^3)^10, is

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  5. If the coefficients of rth, (r+1)t h ,a n d(r+2)t h terms in the expan...

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  6. If C(r) stands for .^(r)C(r), then the sum of the first (n+1) terms o ...

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  7. If (1 + x + x^2)^n = (C0 + C1x + C2 x^2 + ............) then the value...

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  8. If the coefficients of 2nd, 3rd and the 4th terms in the expansion of ...

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  9. If the coefficient of 2nd, 3rd and 4th terms in the expansion of (1...

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  10. If the 6th term in the expansion of(1/(x^(8/3))+x^2(log)(10)x)^8 is 56...

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  11. Find the term in(3sqrt(((a)/(sqrt(b))) + (sqrt((b)/ ^3sqrt(a))))^(21) ...

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  12. If the coefficients of 2nd, 3rd and 4th terms in the expansion of (1+...

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  13. Find the coefficient of x^4 in the expansion of (1+x+x^2+x^3)^(11)dot

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  14. If (1 + x - 2 x^(2))^(6) = 1 + C(1) x + C(2) x^(2) + C(3) x^(3) + …+ C...

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  15. If the coefficient of the middle of term in the expansion of (1+x)^(2n...

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  16. If a1,a2, a3, a4 be the coefficient of four consecutive terms in the e...

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  17. The coefficient of x^r[0lt=rlt=(n-1)] in the expansion of (x+3)^(n-1)+...

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  18. If (1-x+x^2)^n=a0+a1x+a2x^2+ .........+a(2n)x^(2n),\ find the value o...

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

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  20. the coefficient of x^(7) in (ax - b^(-1) x^(-2))^(11) is

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