jee-main 2023 Q65

jee-main · India · session2_06apr_shift2 Number Theory GCD, LCM, and Coprimality

If $\operatorname{gcd}(m, n) = 1$ and $1^{2} - 2^{2} + 3^{2} - 4^{2} + \ldots + (2021)^{2} - (2022)^{2} + (2023)^{2} = 1012m^{2}n$ then $m^{2} - n^{2}$ is equal to
(1) 240
(2) 200
(3) 220
(4) 180

If $\operatorname{gcd}(m, n) = 1$ and $1^{2} - 2^{2} + 3^{2} - 4^{2} + \ldots + (2021)^{2} - (2022)^{2} + (2023)^{2} = 1012m^{2}n$ then $m^{2} - n^{2}$ is equal to\\
(1) 240\\
(2) 200\\
(3) 220\\
(4) 180

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