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Mathematics · 2021

JEE Main · 25 July 2021, Shift 1 · Q87

Let S={n ∈ N (0, i; 1, 0)^n (a, b; c, d) = (a, b; c, d) ∀ a., b, c, d ∈ R}, where i=√ -1. Then the number of 2-digit numbers in the set S is \ \ \ \.

Let $\displaystyle S=\left\{n \in N \left\lvert\,\left(\begin{array}{ll}0 & i \\ 1 & 0\end{array}\right)^n\left(\begin{array}{ll}a & b \\ c & d\end{array}\right)=\left(\begin{array}{ll}a & b \\ c & d\end{array}\right) \forall a\right., b, c, d \in R\right\}$, where $\displaystyle i=\sqrt{-1}$. Then the number of $\displaystyle 2$-digit numbers in the set $\displaystyle S$ is \_\_\_\_.
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JEE Main 2021 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.