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

sahil malhotra
21 Points
```										8
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7 years ago
mihir mehan
16 Points
```										bhaiya yeh toh option hi nahi hai !!!!!!!!!  please also explain how you reached that answer whenever you post a reply.
```
7 years ago
Askiitians Expert Sahil Arora - IITD
19 Points
```										Dear mihir2137^754=(2130+7)^754on 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 7^754the 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=5137^4=last digit being 1and then the last digits repeatthe last digits are 7,9,3,1,7,9,3,1,SO 7^(4n+1)---last digit is 77^(4n+2)---- last digit is 9so on dividing 754 by 4 we get 2 as remainder...so the last digit will be 9...Please feel free to post as many doubts on our discussion forum as you can. If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation. All the best mihir !!!Regards,Askiitians ExpertsSahil AroraIIT Delhi
```
7 years ago
RAJESH
12 Points
```										units of 7754=7377*72​​                                                                                                                          therefore 72=49 and the units digit of it is 9
```
2 years ago
36 Points
```										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
```
11 months ago
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