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If (1)/((1 - 2x)(1 + 3x)) is to tbe expa...

If `(1)/((1 - 2x)(1 + 3x))` is to tbe expanded as a power series of x, then

A

`|x| lt 1//2`

B

`|x| lt 1//6`

C

`-1//3 lt x lt 1//2`

D

`|x| lt 1//3`

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The correct Answer is:
D
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AAKASH SERIES-BINOMIAL THEOREM-EXERCISE - II
  1. sum(r = 0)^(n-1) (Cr)/(Cr + C(r+1)) =

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  2. The sum of the coefficients in the binomial expansion of (1/x + 2x)^n ...

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  3. If (1)/((1 - 2x)(1 + 3x)) is to tbe expanded as a power series of x, t...

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  4. 1 + ""^2C1x + ""^3C2 + ""^4C3 x^3 + ….. to oo terms can be summed up ...

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  5. If Sn denotes the sum of first n natural number then S1 + S2x + S3 x^2...

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  6. ""^4C1 + ""^5C2.(1/2) + ""^6C3.(1/2)^2+….. to oo terms :

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  7. If |x| lt 1 , then the coefficient of x^n in expansion of (1+x+x^2 + x...

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  8. If the expansion in powers of x of the function (1)/((1-ax)(1-bx)) is ...

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  9. The coefficient of x^24 in the expansion of (1+x^2)^(12) (1+x^12)(1+x^...

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  10. If 0 lt x lt 1, the first negative term in the expansion of (1+x)^(27/...

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  11. Find the coefficient of x^(10) in the expansion of (1+2x)/((1-2x)^(2))...

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  12. The first negative term in the expansion of (1+x)^(3//4) is

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  13. If T(r +1) is the first negative term in the expansion of (1+x)^(7//2)...

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  14. If x^3, x^4, x^5 …….can be neglected then sqrt(x^2 + 16 ) - sqrt(x^2 +...

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  15. If 'c' is small in comparison with l then ((l)/(l+c))^(1//2) + ((l)/(l...

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  16. If x is numerically so small so that x^2 and higher powers of x can be...

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  17. If x is small so that x^2 and higher powers can be neglected, then the...

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  18. 1+(2)/(4) + (2.5)/(4.8)+(2.5.8)/(4.8.12)+(2.5.8.11)/(4.8.12.16)+…..=

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  19. (3)/(4.8)+(3.5)/(4.8.12)+(3.5.7)/(4.8.12.16)+….=

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  20. Observe the following statements : Statement -I : In the expansion...

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