N is a positive integer

quantity A - Remainder when 2^N is divided by 10

quantity B - remainder when 7^N is divided by 5

N is a positive integer

quantity A - Remainder when 2^N is divided by 10

quantity B - remainder when 7^N is divided by 5

Write down 7 as 2+5

Now, in the binomial expansion of (2+5)^N, you get 2^N + 5^N + (other terms which have both 5 and 2)

Take for example (2+5)^2 = 2^2 + 5^2 + 2.5.2

Now, in the expansion, you can see that except for the first term, all other terms are perfectly divisible by 5 (because they contain at least one factor of 5), so the only reminder you’ll get will be because of 2^N/5, so that simplifies the option B, now you can easily compare.

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sir , I was unable to understand. is there any other way to solve this .

You can try by choosing numbers

N = 1,2,3,4,5,6…

2^N = 2,4,8,16,32,64

Quantity A = 2,4,8,6,2,4…

7^N = 7,49,343,2401,16807,117649,…

Quantity B = 2,4,3,1,2,4…

Compare A and B

2 = 2

4 = 4

8 > 3

6 > 1

2 = 2

4 = 4

…

…

Answer would be D

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