Doubt from permutation and combination

Question 30

I am trying to solve your problem...

YES Sir please solve this problem.

@ujwal_2020 is option D correct ?

Yes it is the correct answer what was your approach . Share it.

Actual solution is merely of 3 lines , here i have just explained each step with example for clear understanding

Once you have understood the problem , this is all it takes to solve this question

Can you pls explain the process where you calculated the product of divisors of N

I have solved in details for can be solved without showing the actual terms and thus it get shortened.

@ujwal_2020 for example a number is 2²5³7² then to get the number of divisors of it , we do the following

Any divisor of this number will have ether
No 2 or one 2 or two 2 so for selecting 2 there are 3 options
Then we have
No 5 or one 5 or two 5 or three 5 so we have 4 options
Similarly for 7 we have 3 options
So total number of divisors = 334 = 36
Similarly you can get the number of divisors of K in the above solution