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sum(r=1)^(n) (-1)^(r-1) ""^nCr(a - r) =...

`sum_(r=1)^(n) (-1)^(r-1) ""^nC_r(a - r) = `

A

a

B

`-a`

C

2a

D

3a

Text Solution

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The correct Answer is:
A
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AAKASH SERIES-BINOMIAL THEOREM-PRACTICE EXERCISE
  1. (1+x+x^2 + ……+x^p)^n = a0 + a1x + a2 x^2 + ….+a(np) x^(np) rArr a1 + 2...

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  2. C1 + 4.C2 +7.C3 +…….+(3n-2).Cn=

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  3. sum(r=1)^(n) (-1)^(r-1) ""^nCr(a - r) =

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  4. 2.C0 + (2^2)/(2).C1 + (2^3)/(3).C2 + ……+(2^11)/(11).C10 =

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  5. ""^11C0^2 - ""^11C1^2 + ""^11C2^2 - ""^11C3^2 + ……- "^11C11^2 =

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  6. (C0)/(1) + (C2)/(3) + (C4)/(5) + ……+(C16)/(17) =

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  7. (C1)/(2) + (C3)/(4) + …….+(C15)/(16)=

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  8. The coefficient of x^3 in (1-4x)^(1//2) is

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  9. The range of x for which the expansion of (1-3/x)^(-3//4) is valid is

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  10. The range of x of which the expansion of (2-3x^2)^(-11/2)is valid is

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  11. The fifth term of (1 - (2x)/(3))^(3//4) is

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  12. For |x| lt 1, the (r + 1)^(th) term in the expansion of sqrt(1 - x) is

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  13. The general term of (2a - 3b)^(-1//2) is

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  14. In the expansion of (1+x+x^2+x^3+…..oo)^3, coefficient of x^3 is

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  15. In the expansion of (1-2x+3x^2 -4x^3+…."to")^4 coefficient of x^2 is

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  16. The coefficient of x^24 in (1+3x+6x^2 + 10x^3 + ……oo)^(2//3) is

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  17. The coefficient of x^10 in (1-2x + 3x^2)/(1-x) is

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  18. The coefficient of x^9 in the expansion of (1-5x)/(1+x) is

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  19. The coefficient of x^4 in the expansion of ((1 -3x)^2)/((1 - 2x)) is

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  20. For |x| lt 1, the coefficient of x^r in the expansion of ((1+x)^2)/((1...

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