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    ​The digit in the unit's place of  2302^{30}230​ is: ​​
    Question

    ​The digit in the unit's place of  2302^{30}​ is: ​​

    A.

    8

    B.

    6

    C.

    4

    D.

    2

    Correct option is C

    Given:

    We are to find the unit digit of 230 2^{30}​​

    Concept Used:
    The unit digit of powers of 2 follows a cyclic pattern of 4:

    22=4,23=8,24=6,25=2,and so on...\quad 2^2 = 4,\quad 2^3 = 8,\quad 2^4 = 6,\quad 2^5 = 2,\quad \text{and so on...}​​

    Cycle: 2, 4, 8, 6 → Repeats every 4 terms.

    So,  Divide the power by 4 and write the remainder at the place of power. 

    Solution:

    304\frac{30}{4} = 2 (Remainder)

    Therefore, (2)2= 4

    So, the unit digit is 4

    Thus, the correct option is (c) 4

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