JEE Mains · Maths · STD 11 - 7. binomial theoram
Let \(x=(8 \sqrt{3}+13)^{13}\) and \(y=(7 \sqrt{2}+9)^9\). If \([t]\) denotes the greatest integer \(\leq t\), then
- A \([x]+[y]\) is even
- B \([x]\) is odd but \([y]\) is even
- C \([x]\) is even but \([y]\) is odd
- D \([x]\) and \([y]\) are both odd
Answer & Solution
Correct Answer
(A) \([x]+[y]\) is even
Step-by-step Solution
Detailed explanation
Sol. \(x=(8 \sqrt{3}+13)={ }^{13} C_0 \cdot(8 \sqrt{3})^{13}+{ }^{13} C_1(8 \sqrt{3})^{12}(13)^1+\ldots\) \(x ^{\prime}=(8 \sqrt{3}-13)^{13}={ }^{13} C _0(8 \sqrt{3})^{13}-{ }^{13} C _1(8 \sqrt{3})^{12}(13)^1+\ldots\)…
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