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If n gt 3, then xyz^(n)C(0)-(x-1)(y-1)(z...

If `n gt 3`, then `xyz^(n)C_(0)-(x-1)(y-1)(z-1)""^(n)C_(1)+(x-2)(y-2)(z-2)""^(n)C_(2)-`
`(x-3)(y-3)(z-3)""^(n)C_(3)+…..+(-1)^(n)(x-n)(y-n)(z-n)""^(n)C_(n)` equals :

A

xyz

B

0

C

#REF!

D

None of these

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The correct Answer is:
B
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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

""^(n)C_(n-r)+3.""^(n)C_(n-r+1)+3.""^(n)C_(n-r+2)+""^(n)C_(n-r+3)=""^(x)C_(r)

The value of ""(n)C_(1). X(1 - x )^(n-1) + 2 . ""^(n)C_(2) x^(2) (1 - x)^(n-2) + 3. ""^(n)C_(3) x^(3) (1 - x)^(n-3) + ….+ n ""^(n)C_(n) x^(n) , n in N is

If "^(n)C_(0)-^(n)C_(1)+^(n)C_(2)-^(n)C_(3)+...+(-1)^(r )*^(n)C_(r )=28 , then n is equal to ……

if (1+a)^(n)=.^(n)C_(0)+.^(n)C_(1)a++.^(n)C_(2)a^(2)+ . . .+.^(n)C_(n)a^(n) , then prove that (.^(n)C_(1))/(.^(n)C_(0))+(2(.^(n)C_(2)))/(.^(n)C_(1))+(3(.^(n)C_(3)))/(.^(n)C_(2))+. . . +(n(.^(n)C_(n)))/(.^(n)C_(n-1))= Sum of first n natural numbers.

The coefficient of x^(n) in the polynomial (x+""^(2n+1)C_(0))(X+""^(2n+1)C_(1)) (x+""^(2n+1)C_(2))……(X+""^(2n+1)C_(n)) is

Prove that .^(n)C_(1) + 2 xx .^(n)C_(2) + 3 xx .^(n)C_(3) + "…." + n xx .^(n)C_(n) = n2^(n-1) . Hence, prove that .^(n)C_(1).(.^(n)C_(2))^(2).(.^(n)C_(3))^(3)"......."(.^(n)C_(n))^(n) le ((2^(n))/(n+1))^(.^(n+1)C_(2)) AA n in N .

Prove that .^(n)C_(0) + (.^(n)C_(1))/(2) + (.^(n)C_(2))/(3) + "……" +(. ^(n)C_(n))/(n+1) = (2^(n+1)-1)/(n+1) .

(1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+….+C_(n)x^(n) then C_(0)C_(2)+C_(1)C_(3)+C_(2)C_(4)+…..+C_(n-2)C_(n) is equal to :

VMC MODULES ENGLISH-BINOMIAL THEOREM-LEVEL 2
  1. If (1 + x)^(n) = C(0) = C(1) x + C(2) x^(2) + …+ C(n) x^(n) , find...

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  2. If (1+x)^(n)=C(0)+C(1)x+C(2)x^(2)+….+C(n)x^(n), then the value of sums...

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  3. Prove that sum(r=0)^ssum(s=1)^n^n Cs^n Cr=3^n-1.

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  4. The value of underset(r=0)overset(20)sum(-1)^(r )(.^(50)C(r))/(r+2) is...

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  5. The value of ""^(n)C(n)+""^(n+1)C(n)+""^(n+2)C(n)+….+""^(n+k)C(n) :

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  6. The value of sum(r=0)^50 (.^(100)Cr.^(200)C(150+r)) is equal to

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  7. The value of sum(r=0)^(2n)(-1)^(r)*(""^(2n)C(r))^(2) is equal to :

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  8. Find the sum sum(i=0)^r.^(n1)C(r-i) .^(n2)Ci .

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  9. If a(n) = sum(r=0)^(n) (1)/(""^(n)C(r)) , find the value of sum(...

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  10. sum(r=0)^n (-1)^r .^nCr (1+rln10)/(1+ln10^n)^r

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  11. If R = (sqrt(2) + 1)^(2n+1) and f = R - [R], where [ ] denote the ...

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  12. Let ( 5 + 2 sqrt(6))^(n) = I + f , where n, I in N and 0 lt f lt ...

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  13. If x= (7 + 4 sqrt(3))^(2n) = [x] + f , where n in N and 0 le f lt...

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  14. If n gt 3, then xyz^(n)C(0)-(x-1)(y-1)(z-1)""^(n)C(1)+(x-2)(y-2)(z-2)"...

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  15. about to only mathematics

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  16. If n gt 3, then xyz^(n)C(0)-(x-1)(y-1)(z-1)""^(n)C(1)+(x-2)(y-2)(z-2)"...

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  17. Let n be positive integer such that, (1+x+x^(2))^(n)=a(0)+a(1)x+a(2)x^...

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  18. Find the value of underset(0leiltjlen)(sumsum)(.^(n)C(i)+.^(n)C(j)).

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  19. If (1+x+x^(2))^(n) = a(0) + a(1)x+ a(2)x^(2) + "……" a(2n)x^(2n), find...

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  20. Find the value of 1/(81^n)-(10)/(81^n)^(2n)C1+(10^2)/(81^n)^(2n)C2-(10...

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