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CSAT 2024

Q17 2024, Number System: Unit Digit

30³⁰ 3= 10³⁰ * 3³⁰
Any power to 10 will have zeros in the end. Hence, the question basically simplifies to “What is the unit digit in the value of 330?”
Repetition Cyclicity:
The cyclicity of the unit digit 3 is 4, resulting in the unit digit of the number being 3, 9, 7 and 1.
The pattern repeats every 4 powers.
31 = 3
32 = 9
33 = 27 (unit digit 7)
34 = 81 (unit digit 1)
.
.
And so on.
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Now, 30 = 28 + 2. Hence, the answer will be 9.
Therefore, option (d) is the correct answer.

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