The correct option is C {m:m is a multiple of 10} & {n:n is a multiple of 5}
A set is a subset of another set if each and every element of the set is an element of the second set.
Using this let's take the examples one by one.
A.{p,q,r} & {a,p,b,q,c,r}
Here, the first set has elements p,q,r which are also the elements of the second set.
This means the first set is a subset of the second set.
B.{x:x is an isoceles triangle in x−y plane} & {y:y is a triangle in x−y plane}
Here, the first set contains all isoceles triangles in the x−y plane.
And the second set contains all triangles in the x−y plane.
Clearly, this means the first set is the subset of the second set.
C.{m:m is a multiple of 10} & {n:n is a multiple of 5}
In roster form we can write the sets as:
{10,20,30,...} & {5,10,15,20,25,...}
Here, also all the elements of the first set will be an element of the second set.
This means first set will be the subset of the second set.
D.{b:b is a vowel in the word TEA} & {c:c is a vowel in the word CAT}
In roster form we can write the sets as:
{E,A} & {A}
Clearly, E∉{A}
This means the first set is not the subset of the second case.