NixonDutt wrote:

Can someone please answer the question.

As per me,we should get the answer from multiple of 7 .

In which, all of the options are answer.

Hi

power \(x^2\) means x multiplied two times x*xSo \(57^n\) means 57*57*57...n times

Each digit

has a cyclicity when multiplied x timesSo 7 has cyclicity which repeats after every 4th term

7^1=7..7^2=7*7=9....7^3=7*7*7=9*7=3...7^4=7*7*7*7=3*7=1

So cyclicity is 7,9,3,1,7....

Also it is multiple of odd, so all even are out..

5 as units digit requires 5 as a multiple but here we have 7..

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Some useful Theory.

1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048

2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825

3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html

4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html

5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html