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Unit digit of a power, or of a sum, difference or product of powers (cycles of 4)

This type of question, asked 8 times: CDS 2 2016, CDS 1 2019, CDS 2 2019, CDS 2 2020, CDS 1 2021, CDS 1 2023, CDS 2 2025, CDS 1 2026. All 8 questions below, oldest first.

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  1. Question 1

    CDS 2 2016

    33
    What is the unit digit of 71397^{139} ?

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  2. Question 2

    CDS 1 2019

    87
    What is the digit in the unit's place of the number represented by 398−3893^{98} - 3^{89} ?

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  3. Question 3

    CDS 2 2019

    19
    What is the unit place digit in the expansion of 7737^{73} ?

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  4. Question 4

    CDS 2 2020

    8
    What is the digit in the unit place of 3993^{99} ?

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  5. Question 5

    CDS 1 2021

    9
    What is the unit digit in the expansion of 673267^{32}?

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  6. Question 6

    CDS 1 2023

    38
    What is the last digit of the sum S=927+279S = 9^{27} + 27^9 ?

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  7. Question 7

    CDS 2 2025

    83
    A Question is given followed by two Statements I and II. Consider the Question and the Statements. Question : The last digit in the expansion of the number (54D)100(54D)^{100} is 1. What is the value of the digit DD? Statement-I : D>5D > 5 Statement-II : DD is a multiple of 3. Which one of the following is correct in respect of the above Question and the Statements?

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  8. Question 8

    CDS 1 2026

    30
    What is the digit in the unit place of the number 11×33×55×77×991^1 \times 3^3 \times 5^5 \times 7^7 \times 9^9 ?

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