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The term independent of x in the expansi...

The term independent of x in the expansion of `(1+x)^(n)(1-(1)/(x))^(n)` is:

A

`C_(0)^(2)+2C_(1)^(2)+ . . .+(n+1)C_(n)^(2)`

B

`(C_(0)+C_(1)+ . . .+C_(n))^(2)`

C

`C_(0)^(2)+C_(1)^(2)+ . . .+C_(n)^(2)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
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MODERN PUBLICATION-BINOMIAL THEOREM-MCQ.s (LEVEL-II)
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  2. If in the expansion of (2a-(a^(2))/(4))^(9), the sum of middle terms i...

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  3. The term independent of x in the expansion of (1+x)^(n)(1-(1)/(x))^(n)...

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  4. The greatest value of the term independent of x in the expansion of (x...

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  5. If the largest interval to which x belongs so that the greatest term i...

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  7. If the coefficients of the middle term of (1+x)^(2n+2) is p and the co...

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  8. sum(r=1)^(n)(sum(p=0)^(r-1)""^(n)C(r)""^(r)C(p)2^(p)) is equal to:

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  9. The term independent of x in the expression of (1+x+2x^(3))((3)/(2)x^(...

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  10. If (1)/(1!11!)+(1)/(3!9!)+(1)/(5!7!)=(2^(p))/(q!) and f(x+y)=f(x).f(y)...

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  11. If (1+x)^(n)=sum(r=0)^(n)a(r)x^(r) and b(r)=1+(a(r))/(a(r-1)), and pro...

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  12. Find the coefficient of x^(6) y^(3) in the expansion of ( x+ 2y ) ^(...

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  13. If C(r) stands for ""^(n)C(r) and sum(r=1)^(n)(r*C(r))/(C(r-1))=210, t...

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  14. For a positive integer n, let a(n)=1+(1)/(2)+(1)/(3)+(1)/(4)+ . . .+...

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  15. In the binomial expansion of (a-b)^(n),nge5, the sum of the 5th and 6t...

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  16. The value of ((30),(0))((30),(10))+((30),(1))((30),(11))+((30),(2))(...

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  17. For natural number m, n if (1-y)^(m)(1+y)^(n)=1+a(1)y+a(2)y^(2)+ . . ....

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  18. In the binomial expansion of (a-b)^(n),nge5, the sum of 5th and 6th te...

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  19. If a(1),a(2),a(3),a(4) are coefficients of any four consecutive terms ...

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  20. If n is a positive integer and C(k)=""^(n)C(k), then the value of sum(...

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