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sum(r=1)^(n) r.""^(2n)C(r )=...

`sum_(r=1)^(n) r.""^(2n)C_(r )=`

A

`n.2^(2n-1)`

B

`2^(2n-1)`

C

`2^(n-1)+1`

D

none

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The correct Answer is:
a
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ML KHANNA-BINOMIAL THEOREM AND MATHEMATICAL INDUCTION -Problem Set (4) (MULTIPLE CHOICE QUESTIONS)
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  2. If (1+x)^(n) =C(0) +C(1)x +C(2)x^(2) +…+C(n)x^(n), then C(0) +3C(1) +...

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  3. sum(r=1)^(n) r.""^(2n)C(r )=

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  4. ""^(16)C(1)-2""^(16)C(2)+3""^(16)C(3)…. - 16""^(16)C(16)=

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  5. (1)/(n!) +(1)/(2!(n-2)!) +(1)/(4!(n-4)!) +... is equal to

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  6. sum(r=1)^(n//2) (1)/((2r-1)! (n+1-2r)!)=

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  7. The value of ""^(14)C(1) +""^(14)C(3) +""^(14)C(5) + …+""^(14)C(11) is

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  8. If A=C(0) -C(2) +C(4)… and B=C(1)-C(3)+C(5)… then (B)/(A)=

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  9. In the expansion of ( 1+ x)^(50), the sum of the coefficient of odd po...

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  10. Find the sum of the coefficients of all the integral powers of x in th...

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  11. The value of ""^(13)C(2) +""^(13)C(3) +""^(13)C(4) +…+""^(13)C(13) is

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  12. The sum of last ten coefficients in the expansion of (1+x)^(19) when ...

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  13. If S=(1)/(2) ""^(10)C(0) -""^(10)C(1) +2""^(10)C(2)-2^(2)" "^(10)C(3)…...

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  14. If (1 + x)^(n) = sum(r=0)^(n) C(r) x^(r),(1 + (C(1))/(C(0))) (1 + (C(...

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  15. Let (1 + x)^(n) = sum(r=0)^(n) C(r) x^(r) and , (C(1))/(C(0)) + 2 (...

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  16. The value of sum(r=1)^(10) r. (""^(n)C(r))/(""^(n)C(r-1) is equal to

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  17. If P(n) denotes the product of the binomial coefficients in the expan...

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  18. If C(0), C(1), C(2), ..., C(n) denote the binomial cefficients in t...

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  19. If C(0), C(1), C(2), …. C(n) denote the coefficients in the expansion ...

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  20. Statement-1: sum(r =0)^(n) (r +1)""^(n)C(r) = (n +2) 2^(n-1) Stat...

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