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the last digit of 2137^754 is..... a) 1 b)3 c)7 d) 9

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


a) 1

b)3

c)7

d) 9

Grade:12

5 Answers

sahil malhotra
21 Points
11 years ago

8

mihir mehan
16 Points
11 years ago

bhaiya yeh toh option hi nahi hai !!!!!!!!!  please also explain how you reached that answer whenever you post a reply.

Askiitians Expert Sahil Arora - IITD
19 Points
11 years ago
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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Regards,
Askiitians Experts
Sahil Arora
IIT Delhi
RAJESH
12 Points
6 years ago
units of 7754=7377*72​​                                                                                                                          therefore 72=49 and the units digit of it is 9
Aakash Yadav
36 Points
4 years ago
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

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