JEE Mains · Maths · STD 11 - 7. binomial theoram
Among the statements: \((S1):\) \(2023^{2022}-1999^{2022}\) is divisible by \(8.\) \((S2)\) : \(13(13)^{ n }-11 n -13\) is divisible by \(144\) for infinitely many \(n \in N\).
- A both \((S1)\) and \((S2)\) are incorrect
- B only \((S2)\) is correct
- C both \((S1)\) and \((S2)\) are correct
- D only \((S1)\) is correct
Answer & Solution
Correct Answer
(C) both \((S1)\) and \((S2)\) are correct
Step-by-step Solution
Detailed explanation
\(\text { l. } S _1=(1999+24)^{2022}-(1999)^{2022}\) \(\Rightarrow{ }^{2022} C _1(1999)^{2021}(24)+{ }^{2022} C _2(1999)^{2020}(24)^2+\ldots \text { so on }\) \(S _1\) is divisible by \(8\) \(S _2: 13\left(13^{ n }\right)-11 n -13\)…
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