Directions for question (12): Read the direction given below and solve the questions based on it. Following method of representation of the digits is given: XXXXXXXXXX = N XXXXXXXXXX = N1M...

Directions for question (12): Read the direction given below and solve the questions based on it. Following method of representation of the digits is given: (11) 10 = N2 (10) 10 = N1M1 (101) 10 and (110) 10 are represented as N2M1. As it can be seen above, 1 is represented by N and 0 is represented by M. Further, number of times the digits occur is written with the help of numerals. As obvious, digit 0 cannot come as the left most digit (like 0101 is not possible) as this will be same as 101. So what matters is how many times 1 and 0 are coming and not the order of their occurrences. Total number of 1 coming is written after N and total number of 0 is coming is written after M. So, N3M2 can be written in following possible ways: 11100, or, 10101, or 11001, or 10010 and so on. 12. When P = MxNy (a natural number), where x and y can take only whole number values, is divided by Q (a natural number). For which of the following values of Q, remainder obtained can never be equal to 0 for any value of x and y? (a) 37 (b) 213 (c) 412 (d) 589 (e) None of these