Latest self Aptitude Question SOLUTION: let set M={M1,M2,M3,...,M10},where all 10 elements are distinct.if sets are formed which contain 1 or more elements of set M,with subscript of each elements in a specific set being

The question can be analysed base on the smallest subscript preesent in the set.

Let a possible set has the smallest subscript as (M1). Now let us consider all the possibilities with the given condition
Here M2 can be included ar excluded; M3 can be included or excluded; same is the case with M4,M5,....M10.
Note that as the smallest subscript is M1, there is no need to certainly exclude any element, because every number is a multiple of 1

So, for selecting M2, there are two possibilities(yes or No)same is the case with M3(yes or no).......same for M10(yes or no)

Total possibilities with M1 as the lowest subscript is 2*2*2*....9times = 2^9= 512 possible sets

Now lets consider the case of M2 as the lowest possible subscript, the definete elements that must be excluded from this set are M3,M5,M7,M9

M4 can be included or excluded(two ways) same is the case with M6 andM8 and M10, so total possibilities is 2*2*2*2= 16 ways
Similarly the number of possible sets with

M3 as lowest element is 2*2=4; only M6 and M9 are considered
M4 as the lowest element is 2; only M8 is considered
M5 as the lowest element is 2; only M10 is considered
M6 as the lowest element is only one set
Only one set each with M7,M8,M9,M10 as lowest element

So, total sets is 512(M1)+16(M2)+4(M3)+2(M4)+2(M5)+1(M6)+1(M7)+1(M8)+1(M9)+1(M10)

Answer is 541 sets