Medium MCQ +4 / -1 PYQ · JEE Mains 2023

Let $x=(8 \sqrt{3}+13)^{13}$ and $y=(7 \sqrt{2}+9)^9$. If $[t]$ denotes the greatest integer $\leq t$, then :

A $[x]$ is odd but $[y]$ is even
B $[x]$ and $[y]$ are both odd
C $[x]+[y]$ is even Correct answer
D $[x]$ is even but $[y]$ is odd

Solution

If ${I_1} + f = {(8\sqrt 3 + 13)^{13}},f' = {(8\sqrt 3 - 13)^{13}}$ ${I_1} + f - f'=$ Even ${I_1} =$ Even ${I_2} + f - f' = {(7\sqrt 2 + 9)^9} + {(7\sqrt 2 - 9)^9}$ = Even ${I_2} =$ Even

About this question

Subject: Mathematics · Chapter: Binomial Theorem · Topic: Binomial Expansion

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Let $x=(8 \sqrt{3}+13)^{13}$ and $y=(7 \sqrt{2}+9)^9$. If $[t]$ denotes the greatest integer $\leq t$, then :

Solution

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