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If (1+x)(1+x+x^2)(1+x+x^2+x^3)……(1+x+x^2...

If `(1+x)(1+x+x^2)(1+x+x^2+x^3)……(1+x+x^2+……+x^(n-1))` = `a_0 + a_1x + a_2x^2 +…….+a_m x^m ` then `a_0 +a_1 + …..+ a_m = `

A

n!

B

2n!

C

3n!

D

4n!

Text Solution

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The correct Answer is:
A
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AAKASH SERIES-BINOMIAL THEOREM-EXERCISE - II
  1. If a0, a1 , a2 …..an are binomial coefficients then (1 + a1/a0)(1 +a2/...

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  2. ((C0 + C1)(C1 + C2)(C2 + C3)………(C(n-1) + Cn) )/(C0C1C2…Cn)

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  3. If (1+x)(1+x+x^2)(1+x+x^2+x^3)……(1+x+x^2+……+x^(n-1)) = a0 + a1x + a2x^...

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  4. If (1 -x + x^2)^n = a0 +a1x + a2x^2+….+a(2n)x^(2n) then a0 + a2 +a4 +...

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  5. If (1)/(1!(n-1)!) + (1)/(3!(n-3)!) + (1)/(5!(n-5)!) +…. =

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  6. C0 + C1 + 2.C2(3) + 3.C3(3^2)+ 4.C4(3^3) + ……+n.Cn 3^(n-1) =

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  7. (1 + x+x^2)^8 = a0 + a1x +…….+a16 x^16 then a0 - a2 + a4 - a6 + ……..+a...

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  8. If ar is the coefficient x^r in the expansion of (1+x+x^2)^n then a1 -...

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  9. If (1+2x +3x^2)^10 = a0 +a1x +a2x^2 + ……+a20x^20 then a2/a1 =

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  10. ""^15C2 + 2.""^15C3 + 3. ""^15C4 + …..+ 14.""^15C15 =

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  11. ""^20C10.""^15C0 + ""^20C9.""^15C1 + ""^20C8.""^15C2 + …..+""^20C0.""^...

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  12. ""^10C1 . ""^9C5 + ""^10C2. ""^9C4 + ""^10C3. ""^9C3 + ""^10C4. ""^9C2...

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  13. sum(r=1)^(10) r. (""^nCr)/(""^nC(r-1)) =

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  14. sum(r = 0)^(n-1) (Cr)/(Cr + C(r+1)) =

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

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

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  17. 1 + ""^2C1x + ""^3C2 + ""^4C3 x^3 + ….. to oo terms can be summed up ...

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

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  19. ""^4C1 + ""^5C2.(1/2) + ""^6C3.(1/2)^2+….. to oo terms :

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

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