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The coefficient of x^(n) in the expansi...

The coefficient of `x^(n)` in the expansion of `(1)/((1-x)(3 -x))`, is

A

`(3^(n+1)-1)/(2.3^(n+1))`

B

`(3^(n+1)-1)/(3^(n+1))`

C

`2((3^(n+1)-1)/(3^(n+1)))`

D

none of these

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The correct Answer is:
A
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OBJECTIVE RD SHARMA-BINOMIAL THEOREM AND ITS APPLCIATIONS -Exercise
  1. Find the coefficients of x^(50) in the expression (1+x)^(1000)+2x(1+x)...

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  2. If Cr stands for .^nCr, then the sum of the series (2(n/2)!(n/2)!)/...

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  3. The coefficient of x^(n) in the expansion of (1)/((1-x)(3 -x)), is

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

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  5. Coefficient of x^n in the expansion of (1-2x+3x^2-4x^3+....oo)^2 is

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  6. If (r+1)t h term is the first negative term in the expansion of (1+x)^...

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  7. The coefficient of x^6 in the expansion of (1+x+x^2)^(-3), is

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  8. The coefficient of x^n in the expansion of (1 + x+x^2+...........)^-...

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  9. If the binomial expansion of (a +b x)^-2 is 1/4-3x+......., then (a, ...

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  10. If C(r) = ""^(n)C(r) and (C(0) + C(1)) (C(1) + C(2)) … (C(n-1) + C(n))...

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  11. If the third term in the expansion of (1+x)^mi s-1/8x^2, then find the...

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  12. If p is nearly equal to q and n gt 1 , such that ((n+1) p+(n-1)q)/(...

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  13. If y=3 x + 6 x^(2) + 10 x^(3) +… then x =

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  14. If y = (1)/(3) + (1*3)/(3 *6) + (1 * 3*5)/(3*6*9) +… then the value ...

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  15. If (1+2x+x^2)^n=sum(r=0)^(2n)ar x^r ,t h e na= (^n C2)^2 b. ^n Crdot^...

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  16. In the expansion of (sqrt(x^5)+3/(sqrt(x^3)))^6 coefficient of x^3 is ...

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  17. Find the number of nonzero terms in the expansion of (1+3sqrt(2)x)^9+(...

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  18. The coefficient of y in the expansion of (y^(2) + c//y)^(5) is

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  19. The greatest coefficient in the expansion of (1 + x)^(10), is

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  20. The approximate value of (7.995)^(1//3) correct to four decimal pla...

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