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This mock test of Finding Unit Digit - MCQ Test for UPSC helps you for every UPSC entrance exam.
This contains 5 Multiple Choice Questions for UPSC Finding Unit Digit - MCQ Test (mcq) to study with solutions a complete question bank.
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QUESTION: 1

Find the unit digit of (7493^{263})x(151^{29})

Solution:

**Answer:** c)7

Solution:

The given product is (7493^{263})x(151^{29})

Required unit digit = the unit digit of(3^{263})x(1^{29}) ...(1)

In the value of 3 to the power 4, we have the unit digit as 1.

so, we can rewrite (3^{263}) = [3^{(4x65 + 3)}] = [(3^{4})^{65}] x (3^{3})

Then from eqn(1),

The unit digit of(3^{263})x(1^{29}) = The unit digit of[(3^{4})^{65}] x (3^{3}) x 1^{29}

= The unit digit of[1^{65}] x 27 x 1

= The unit digit of 1 x 7 x 1 = 7

Hence, the answer is 7.

QUESTION: 2

Find the unit digit of 634^{262} + 634^{263}

Solution:

Given that 634^{262} + 634^{263}

= 634^{262}(1 + 634)

= (634^{262}) x 635

The unit digit of (634^{262}) x 635 = the unit digit of (4^{262} x 5)

We know that, the unit digit of 4 to the power of any odd number is 4 and the unit digit of 4 to the power of any even number is 6.

Then the unit digit of (4^{262} x 5) = unit digit of(6 x 5) = 0

QUESTION: 3

The digit in the unit place of the number represented by (7^{95} * 3^{58}) is

Solution:

QUESTION: 4

What is the units digit of 57^{45}?

Solution:

QUESTION: 5

What is the units digit of 39^{61}?

Solution:

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