jee-main 2017 Q65

jee-main · India · 02apr Binomial Theorem (positive integer n) Evaluate a Summation Involving Binomial Coefficients
The value of ${}^{21}C_1 - {}^{10}C_1 + {}^{21}C_2 - {}^{10}C_2 + {}^{21}C_3 - {}^{10}C_3 + {}^{21}C_4 - {}^{10}C_4 + \ldots + {}^{21}C_{10} - {}^{10}C_{10}$ is
(1) $2^{21} - 2^{11}$
(2) $2^{21} - 2^{10}$
(3) $2^{20} - 2^{9}$
(4) $2^{20} - 2^{10}$ 
The value of ${}^{21}C_1 - {}^{10}C_1 + {}^{21}C_2 - {}^{10}C_2 + {}^{21}C_3 - {}^{10}C_3 + {}^{21}C_4 - {}^{10}C_4 + \ldots + {}^{21}C_{10} - {}^{10}C_{10}$ is\\
(1) $2^{21} - 2^{11}$\\
(2) $2^{21} - 2^{10}$\\
(3) $2^{20} - 2^{9}$\\
(4) $2^{20} - 2^{10}$
Paper Questions
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