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If (1+x)^(15)=C0+C1x+C2x^2++C(15)x^(15),...

If `(1+x)^(15)=C_0+C_1x+C_2x^2++C_(15)x^(15),` then find the su of `C_1+2C_3+3C_4++14 C_(15)dot`

A

64329

B

212993

C

503146

D

none

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The correct Answer is:
b
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ML KHANNA-BINOMIAL THEOREM AND MATHEMATICAL INDUCTION -Problem Set (4) (MULTIPLE CHOICE QUESTIONS)
  1. If n is ann integer greater than 1, then a-^(n)C(1)(a-1)+.^(n)C(2)(a...

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  2. C(0) -(C(1))/(2)+(C(2))/(3) -(C(3))/(4) + ….=

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  3. If (1+x)^(15)=C0+C1x+C2x^2++C(15)x^(15), then find the su of C1+2C3+3C...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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