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The value of sum(r = 1)^15 r^2 ((""^15Cr...

The value of `sum_(r = 1)^15 r^2 ((""^15C_r)/(""^15C_(r - 1)) )` of is equal to

A

1240

B

560

C

1085

D

680

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Verified by Experts

The correct Answer is:
D
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AAKASH SERIES-BINOMIAL THEOREM-EXERCISE - II
  1. C0 + (C1)/(2) (4) + (C2)/(3) (16) + …………..+(Cn)/(n + 1) (2^(2n))

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  2. (1 +x)^15 = a0 + a1x +…..+a15 x^15 rArr sum(r = 1)^15 r (ar)/(a(r - 1)...

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

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

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

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

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

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

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

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

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  12. (1 + x+x^2)^8 = a0 + a1x +…….+a16 x^16 then a0 - a2 + a4 - a6 + ……..+a...

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  13. If ar is the coefficient x^r in the expansion of (1+x+x^2)^n then a1 -...

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  14. If (1+2x +3x^2)^10 = a0 +a1x +a2x^2 + ……+a20x^20 then a2/a1 =

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  15. ""^15C2 + 2.""^15C3 + 3. ""^15C4 + …..+ 14.""^15C15 =

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  16. ""^20C10.""^15C0 + ""^20C9.""^15C1 + ""^20C8.""^15C2 + …..+""^20C0.""^...

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  17. ""^10C1 . ""^9C5 + ""^10C2. ""^9C4 + ""^10C3. ""^9C3 + ""^10C4. ""^9C2...

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  18. sum(r=1)^(10) r. (""^nCr)/(""^nC(r-1)) =

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  19. sum(r = 0)^(n-1) (Cr)/(Cr + C(r+1)) =

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  20. The sum of the coefficients in the binomial expansion of (1/x + 2x)^n ...

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