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The sum (1)/(2)""^(10)C(0)-""^(10)C(1)+2...

The sum `(1)/(2)""^(10)C_(0)-""^(10)C_(1)+2.""^(10)C_(2)-2^(2)*""^(10)C_(3)+ . . .+2^(9)*""^(10)C_(10)` equals:

A

`(1)/(2) `

B

0

C

`(1)/(2). 3^(10) `

D

`(1)/(2). 2^(10) `

Text Solution

Verified by Experts

The correct Answer is:
A
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The sum of series: ""^(20)C_(0)-""^(20)C_(1)+""^(20)C_(2)-""^(20)C_(3)+ . . . +""^(20)C_(10) is:

The value of ""^(10) C_(2) + ""^(10) C_(3) + … + ""^(10) C_(9) is

The value of ""^(16)C_(9)+""^(16)C_(10)-""^(16)C_(6)-""^(16)C_(7) is

C_(0)-C_(1)+C_(2)-C_(3)+ . . .+(-1)^(n)C_(n) is equal to

Value of 2C_(0)+(2^(2))/(2)C_(1)+(2^(3))/(3)C_(2)+ . . .+(2^(11))/(11)C_(10) is:

20 C_(0)+20 C_(1)+20 C_(2)+.. .+20 C_(10) =

The value of sum_(r=1)^(10)r(n C_(r))/(n C_(r-1)) =

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The solution set "^10C_(x-1)>2 . "^10C_x is

HIMALAYA PUBLICATION-BINOMIAL THEOREM-QUESTION BANK
  1. If the coefficients of 2nd, 3rd and 4th terms in the expansion of (1+x...

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  2. If the rth term is the middle term in the expansion of (x^(2)-(1)/(2x)...

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  3. The sum (1)/(2)""^(10)C(0)-""^(10)C(1)+2.""^(10)C(2)-2^(2)*""^(10)C(3)...

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  4. The value of: ""^(15)C(0)^(2)-""^(15)C(1)^(2)+""^(15)C(2)^(2)- . . ....

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  5. If the expansion of (x^(2)+(2)/(x))^(n) for positive integer n has 13t...

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  6. The fourth term in the binomial expansion of (x^(2)+(2)/(x^(2)))^(n)...

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  7. Sum to (n+1) terms of the series: (C(0))/(2)-(C(1))/(3)+(C(2))/(4)-(C(...

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  8. Value of 2C(0)+(2^(2))/(2)C(1)+(2^(3))/(3)C(2)+ . . .+(2^(11))/(11)C(1...

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  9. 20 C(0)+20 C(1)+20 C(2)+.. .+20 C(10) =

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  10. If the coefficients of x^(7) and x^(8) in (2+(x)/(3))^(n) are equal, t...

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  11. The coefficient of x^(5) in (1+x^(2))^(5)(1+x)^(4) is

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  12. In the expansion of (x^(2)+(2)/(x))^(n) for positive integer n has a t...

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  13. If the r^(th) term in the expansion of ((x)/(3)-(2)/(x^(2)))^(16) co...

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  14. The sum of the coefficients in the expansion of (a x^(2)-2 x+1)^(35) i...

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  15. If the coefficient of 4^(th) term in the expansion of (x+(alpha)/(2...

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  16. If the rth term is the middle term in the expansion of (x^(2)-(1)/(2x)...

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  17. The coefficient of x^(13) in the expansion of (1-x)^(5)(1+x+x^(2)+x...

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  18. The coefficient of (1)/(y^(2)) in (y+(c^(3))/(y^(2)))^(10) is

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  19. If the r^(th) term in the expansion of ((x)/(3)-(2)/(x^(2)))^(10) con...

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  20. The 7^(th) term in ((1)/(y)+y^(2))^(10) , when expanded in descendin...

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