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Q1) What is the units digit of $\left (39^{11} – 32^{11} \right)$?

    (a)(b) 5

    (c)(d) 8

Q2) What will be in the unit place of $45^8 + 19^{11} – 62^{18}$?

    (a)(b) 2

    (c)(d) 7

1 Answer

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In these type of questions, i.e. when you raise a number to some power, find the pattern of unit digit and then solve.

(1) $39^{11} - 32^{11}$

For $39^{11}$ : Unit digit of 39 is 9, and thus unit digits of its powers will be 9,1,9,1,... So $39^{11}$ ends in 9.

For $32^{11}$ : Unit digit of 32 is 2, and thus unit digits of its powers will be 2,4,8,6,2 (and then pattern continues). So $32^{11}$ ends in 8.

So unit digit of $39^{11} - 32^{11} = 9-8 = 1$

Solve second question similarly and we get 5 + 9 - 4 = 0 for unit digit.

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