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Coefficient of x^(2009) in (1+x+x^(2)+x^...

Coefficient of `x^(2009)` in `(1+x+x^(2)+x^(3)+x^(4))^(1001) (1-x)^(1002)` is

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The correct Answer is:
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`E = (1+x+x^(2)+x^(3)+x^(4))^(199) (x-1)^(201)`
`= ((1-x^(5))/(1-x))^(199)(x-1)^(201)`
`= - (1-x)^(2)(1-x^(5))^(199)`
`= - 1(1-2x+x^(2))(1-.^(199)C_(1)x^(5)+.^(199)C_(2)x^(10)-"…..")`
`:.` Coefficient `x^(103)` in `E = 0`
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CENGAGE-BINOMIAL THEOREM-Exercise (Numerical)
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  2. Let a and b be the coefficients of x^3 in (1+x+2x^2+3x^3)^4a n d(1+x+2...

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  3. If R is remainder when 6^(83)+8^(83) is divided by 49, then the value ...

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  4. The remainder, if 1+2+2^2++2^(1999) is divided by 5 is.

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  5. Given (1-2x+5x^2-10 x^3)(1+x)^n=1+a1x+a2x^2+ and thata1 2=2a2 then the...

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  6. The largest real value of x such that sum(k=0)^4((3^(4-k))/((4-k)!))((...

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  7. Coefficient of x^(2009) in (1+x+x^(2)+x^(3)+x^(4))^(1001) (1-x)^(1002)...

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  8. The total number of different terms in the product (.^(101)C(0) - .^(1...

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  9. The constant term in the expansion of (x -2/x^(2))^(9) is

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  10. The value of sum(r=0)^(3) ""^(8)C(r)(""^(5)C(r+1)-""^(4)C(r)) is "".

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  11. The value of (.^(21)C(1) - .^(10)C(1)) + (.^(21)C(2) - .^(10)C(2)) + (...

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  12. Let a=3^(1/(223))+1 and for all geq3,let f(n)=^n C0dota^(n-1)-^n C1do...

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  13. Let 1+sum(r=1)^(10)(3^rdot(10)Cr+rdot(10)Cr)=2^(10)(alpha. 4^5+beta)w ...

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  14. The value of (lim)(nvecoo)sum(r=1)^(r-1)(sum(t=0)^(r-1)1/(5^n)dot^n Cr...

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  15. If sum(r=0)^(10)((r+2)/(r+1))^^n Cr=(2^8-1)/6 , then n is 8 b. 4 c. 6 ...

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  16. If S(n) = (.^(n)C(0))^(2) + (.^(n)C(1))^(2) + (.^(n)C(n))^(n), then ma...

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  17. The value of .^(40)C(0) xx .^(100)C(40) - .^(40)C(1) xx .^(99)C(40) + ...

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  18. The value of sum(0leiltjle5) sum(""^(5)C(j))(""^(j)C(i)) is equal to "...

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  19. If (1-x-x^(2))^(20) = sum(r=0)^(40)a(r).x^(r ), then value of a(1) + 3...

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  20. The value of sum(r=1)^(11)tan^(2)((r pi)/(24)) is

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