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If Ck is the coefficient of x^k in the e...

If `C_k` is the coefficient of `x^k` in the expansion of `(1 + x)^2005` and if a,d are real numbers then `sum_(k = 0)^(2005) (a + kd).C_k` =

A

`(2a + 2005d)2^2004`

B

`(2a + 2005d)2^2005`

C

`(2a + 2004d)2^2005`

D

`(2a + 2004d)2^2005`

Text Solution

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The correct Answer is:
A
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AAKASH SERIES-BINOMIAL THEOREM-EXERCISE - II
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  2. ""^(n) C(r+1)+2""^(n)C(r) +""^(n)C(r-1)=

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  3. If Ck is the coefficient of x^k in the expansion of (1 + x)^2005 and i...

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  4. The sum of the series ""^20C0 - ""^20C1 + ""^20C2 - ""^20C3 +…….""^20C...

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  5. If S(n) = underset (r=0) overset( n) sum (1) /(""^(n) C(r)) and T...

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  6. C0 - [C1 -2.C2+ 3.C3-……..+(-1)^(n-1).n.Cn] =

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  7. C0+4. C1 + 7. C2+…...(n+1) terms =

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  8. 2. C2 + 6. C3 + 12. C4 +….. + n (n-1) . Cn=

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  9. Sum of last 8 coefficients in (1 + x)^16 is

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  10. C0 + (C1)/(2) (4) + (C2)/(3) (16) + …………..+(Cn)/(n + 1) (2^(2n))

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  11. (1 +x)^15 = a0 + a1x +…..+a15 x^15 rArr sum(r = 1)^15 r (ar)/(a(r - 1)...

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  12. The value of sum(r = 1)^15 r^2 ((""^15Cr)/(""^15C(r - 1)) ) of is equa...

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  13. If ak is the coefficient of x^k in the expansion of (1 +x+x^2)^n for k...

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  14. Find the sum of the following (""^(15)C(1))/(""^(15)C(0))+2(""^(15)C...

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  15. If a0, a1 , a2 …..an are binomial coefficients then (1 + a1/a0)(1 +a2/...

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  16. ((C0 + C1)(C1 + C2)(C2 + C3)………(C(n-1) + Cn) )/(C0C1C2…Cn)

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  17. If (1+x)(1+x+x^2)(1+x+x^2+x^3)……(1+x+x^2+……+x^(n-1)) = a0 + a1x + a2x^...

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  18. If (1 -x + x^2)^n = a0 +a1x + a2x^2+….+a(2n)x^(2n) then a0 + a2 +a4 +...

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  19. If (1)/(1!(n-1)!) + (1)/(3!(n-3)!) + (1)/(5!(n-5)!) +…. =

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  20. C0 + C1 + 2.C2(3) + 3.C3(3^2)+ 4.C4(3^3) + ……+n.Cn 3^(n-1) =

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