jee-main 2022 Q65

jee-main · India · session1_25jun_shift2 Binomial Theorem (positive integer n) Find a Specific Coefficient in a Product of Binomial/Polynomial Expressions

The coefficient of $x^{101}$ in the expression $(5 + x)^{500} + x(5 + x)^{499} + x^2(5 + x)^{498} + \ldots + x^{500}$, $x > 0$ is
(1) ${}^{501}C_{101} \times 5^{399}$
(2) ${}^{501}C_{101} \times 5^{400}$
(3) ${}^{501}C_{100} \times 5^{400}$
(4) ${}^{500}C_{101} \times 5^{399}$

The coefficient of $x^{101}$ in the expression
$(5 + x)^{500} + x(5 + x)^{499} + x^2(5 + x)^{498} + \ldots + x^{500}$, $x > 0$ is\\
(1) ${}^{501}C_{101} \times 5^{399}$\\
(2) ${}^{501}C_{101} \times 5^{400}$\\
(3) ${}^{501}C_{100} \times 5^{400}$\\
(4) ${}^{500}C_{101} \times 5^{399}$

Paper Questions

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