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If (1+x)^(n)=underset(r=0)overset(n)sumC...

If `(1+x)^(n)=underset(r=0)overset(n)sumC_(r).x^(r)`, then
`(1+(C_(1))/(C_(0)))(1+(C_(2))/(C_(1))) . . . .(1+(C_(n))/(C_(n-1)))=`

A

`(n^(n-1))/((n+1)!)`

B

`((n+1)^(n+1))/((n+1)!)`

C

`((n+1)^(n))/(n!)`

D

`((n+1)^(n+1))/(n!)`

Text Solution

Verified by Experts

The correct Answer is:
C
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AAKASH INSTITUTE-BINOMIAL THEOREM-Assignment (section-B)
  1. In the expansion of (y^(1//5)+x^(1//10))^55, the number of terms free ...

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  2. Consider the following statements S(1): The total of terms in (x^(2)...

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  3. If (1+x)^(n)=underset(r=0)overset(n)sumC(r).x^(r), then (1+(C(1))/(C...

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  4. (C(1))/(C(0))+(2.C(2))/(C(1))+(3.C(3))/(C(2))+ . . .+(20.C(20))/(C(19)...

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  5. Find the term independent of x in the expansion of (1+x+2x^3)[(3x^2//2...

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  6. If in the expansion of (1+x)^m (1-x)^n, the coefficients of x and x^2 ...

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  7. the value of x , for which the 6th term in the expansions of[2^log2sqr...

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  8. If (1-x^(3))^(n)=underset(r=0)overset(n)(sum)a(r)x^(r)(1-x)^(3n-2r), t...

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  9. Let (1+x^2)^2*(1+x)^n=sum(k=0)^(n+4)ak*x^k If a1, a2 and a3 are iun ...

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  10. The coefficient of x^1007 in the expansion (1+x)^(2006)+x(1+x)^(2005)+...

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  11. underset(r=0)overset(n)(sum)(-1)^(r).^(n)C(r)[(1)/(2^(r))+(3^(r))/(2^(...

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  12. In the expansion of (x +a)^(n) the sum of even terms is E and that ...

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  13. The sum of the last eight coefficients in the expansion of (1 + x)^16 ...

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  14. Find the coefficient of x^3y^4z^5 in the expansion of (xy+yz+zx)^6

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  15. In the expansion of (3x+2y-z)^(8), the coefficients of x^(2)y^(3)z^(3)...

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  16. If n is ann integer greater than 1, then a-^(n)C(1)(a-1)+.^(n)C(2)(a...

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  17. (C(0))/(1)+(C(1))/(2)+(C(2))/(3)+ . . . .+(C(100))/(101) equals

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  18. 2C0+2^2/2 C1+2^3/3 C2+.............+2^11/11 C10 =?

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  19. The coefficient of x^(n) in the polynomial (x+""^(2n+1)C(0))(X+""^(2n+...

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  20. If C(r) stands for .^(n)C(r)=(n!)/(r!n-r!) and underset(r=1)overset(n)...

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