The unit digit in 7105 is:

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answer is C.

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Detailed Solution

Concept- To solve this question, first we will need to find a pattern or sequence among the unit’s digit of the exponents of 7. Then, using this sequence, we will have to calculate the last digit of our given exponent of 7 to obtain our desired answer.
We know that,

and so on, i.e.,
The pattern of the unit digit can be observed to be 7,9,3,1 and then back to 7 .
So, starting from

which is the first term, every fifth term will have its unit digit as 7 , or,
If we divide the exponents of 7 into sets of 4 , the first number of every set will have 7 as its unit digit. Now, since 105 is divisible by 5 [Due to the last digit being 5 , it is divisible by 5 as the divisibility of 5 rule says any number whose last digits are 0 or 5 are divisible by 5 ]

, i.e.,
After 21 sets of 4 terms,

will be the first term of the next set, Hence, the unit digit of

will be 7 .
Hence, the correct answer is option 3.

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