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The coefficient of \(x^{301}\) in \((1+x)^{500}+x(1+x)^{499}\) \(+x^2(1+x)^{498}+\ldots+x^{500}\) is: [JEE Main 2023, 30…

Q1

The coefficient of \(x^{301}\) in \((1+x)^{500}+x(1+x)^{499}\) \(+x^2(1+x)^{498}+\ldots+x^{500}\) is:

[JEE Main 2023, 30 Jan (Shift 1)]

a

\({ }^{501} C _{302}\)

b

\({ }^{500} C _{301}\)

c

\({ }^{500} C _{300}\)

d

\({ }^{501} C _{200}\)

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