Compare the coefficients

Algebra Level 3

Suppose the polynomials P1(x)P_1(x) and P2(x)P_2(x) are obtained by expanding and simplifying the following algebraic expressions

P1(1)=(1+x2x5)2000P2(x)=(1x2+x5)2000.P_1(1) = (1 + x^2 - x^5)^{2000} \\ P_2(x) = (1 - x^2 + x^5)^{2000}.

Let C1C_1 and C2C_2 be the coefficient of x800x^{800} in the polynomials P1(x)P_1(x) and P2(x)P_2(x) respectively. Which of the given option is true?

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