the last digit of 2137^754 is.....

a) 1

b)3

c)7

d) 9

Dear mihir
2137^754=(2130+7)^754
on binomial expansion,we find that the first teram is not divisible by 10 while others are divisible by 10..
SO only first term will contribute to last digit..
the first term is 7^754
the last digit of this will be the last digit of given question.'
now observe the last digit in following arguments.
7^1=7,
7^2=49,
7^3=513
7^4=last digit being 1
and then the last digits repeat
the last digits are 7,9,3,1,7,9,3,1,
SO 7^(4n+1)---last digit is 7
7^(4n+2)---- last digit is 9
so on dividing 754 by 4 we get 2 as remainder...
so the last digit will be 9...
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Sahil Arora
IIT Delhi

Since we can see the 7^1=7 7^2=49 7^3=343=7^4has it`s unit digit 1 so now see for 752 the unit digit=1 now for 753unitdigit=7 754unit digit =9