jee-main 2023 Q66

jee-main · India · session1_30jan_shift2 Proof True/False Justification

Let $x = (8\sqrt{3} + 13)^{13}$ and $y = (7\sqrt{2} + 9)^{9}$. If $[t]$ denotes the greatest integer $\leq t$, then
(1) $[x] + [y]$ is even
(2) $[x]$ is odd but $[y]$ is even
(3) $[x]$ is even but $[y]$ is odd
(4) $[x]$ and $[y]$ are both odd

Let $x = (8\sqrt{3} + 13)^{13}$ and $y = (7\sqrt{2} + 9)^{9}$. If $[t]$ denotes the greatest integer $\leq t$, then\\
(1) $[x] + [y]$ is even\\
(2) $[x]$ is odd but $[y]$ is even\\
(3) $[x]$ is even but $[y]$ is odd\\
(4) $[x]$ and $[y]$ are both odd

Paper Questions

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