Class JEE Mathematics Statistics and Probability Q #992
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4 Marks 2025 JEE Main 2025 (Online) 28th January Morning Shift MCQ SINGLE
Two number $k_1$ and $k_2$ are randomly chosen from the set of natural numbers. Then, the probability that the value of $i^{k_1} + i^{k_2}$, ($i = \sqrt{-1}$) is non-zero, equals
(A) $\frac{3}{4}$
(B) $\frac{1}{2}$
(C) $\frac{1}{4}$
(D) $\frac{2}{3}$
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Correct Answer: A
Explanation
$i^{k_1} + i^{k_2} \ne 0 \Rightarrow i^{k_1} \rightarrow 4$ option for $i, -1, -i, 1$
Total cases $ \Rightarrow 4 \times 4 = 16$
Unfovourble cases $ \Rightarrow i^{k_1} + i^{k_2} = 0$
$ \{\begin{array}{c}1, -1 \\ -1, 1 \\ i, -i \\ -i, i\end{array}\}$
4 Cases $\Rightarrow$ Probability $ = \frac{16-4}{16} = \frac{3}{4}$

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