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JEE Advanced 2024 Paper 1

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Question : 5

Total: 51

Let S={a+b√2:a,b∈ℤ},T1={(−1+√2)n:n∈ℕ} and T2={(1+√2)n:n∈ℕ}. Then which of the following statements is (are) TRUE?

[JEE Adv 2024 P1]

ℤ∪T1∪T2⊂S
T1∩(0,‌
1
2024
)=ϕ, where ϕ denotes the empty set
T2∩(2024,∞)≠ϕ
For any given a,b∈ℤ,cos(π(a+b√2))+isin‌(π(a+b√2))∈ℤ if and only if b=0, where i=√−1

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