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If n > 3, then x y C0-(x-1)(y-1)C1+(x-2...

If `n > 3,` then `x y C_0-(x-1)(y-1)C_1+(x-2)(y-2)C_2-(x-3)(y-3)C_3+..............+(-1)^n(x-n)(y-n)C_n,` equals

A

xyz

B

`x+y+z`

C

`xy+yz+zx`

D

0

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The correct Answer is:
D
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VK JAISWAL-BIONMIAL THEOREM-Exercise-4 : Subjective Type Problems
  1. If n > 3, then x y C0-(x-1)(y-1)C1+(x-2)(y-2)C2-(x-3)(y-3)C3+...........

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  2. The sum of series 3*""^(2007)C(0)-8*""^(2007)C(1)+13*""^(2007)C(2)-18...

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  3. In the polynomial function f(x)=(x-1)(x^(2)-2)(x^(3)-3)……..(x^(11)-11...

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  4. If sum(r=0)^(3n)a(r)(x-4)^(r )=sum(r=0)^(3n)A(r)(x-5)^(r ) and a( k)=1...

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  5. If 3^(101)-2^(100) is divided by 11, the remainder is

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  6. Find the hundred's digit in the co-efficient of x^(17) in the expansio...

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  7. Let n in N, Sn=sum(r=0)^(3n)^(3n)Cr and Tn=sum(r=0)^n^(3n)C(3r), then ...

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  8. Find the sum of possible real values of x for which the sixth term of ...

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  9. Let q be a positive with q le 50. If the sum ""^(98)C(30)+2" "^(97)C...

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  10. The remainder when (sum(k=1)^(5) ""^(20)C(2k-1))^(6) is divided by 11,...

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  11. Let a=3^(1/(223))+1 and for all geq3,l e tf(n)=^n C0dota^(n-1)-^n C1do...

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  12. In the polynomial function f(x)=(x-1)(x^(2)-2)(x^(3)-3)……..(x^(11)-11...

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  13. Let the sum of all divisiors of the form 2^(p)*3^(q) (with p, q posit...

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  14. For what value of x is the ninth term in the expansion of (3^(log3 sqr...

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  15. Let 1+ sum(r=1)^10 (3^r C(10,r) + r C(10,r))=2^10 (alpha 4^5+beta) whe...

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  16. Let S(n)=""^(n)C(0)""^(n)C(1)+""^(n)C(1)""^(n)C(2)+…..+""^(n)C(n-1)""^...

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