Suppose, $A_1, A_2, \ldots, A_{30}$ are thirty sets each having 5 elements and $B_1, B_2, B_n$ are $n$ sets each with 3 elements, let $\bigcup_\limits{i=1}^{30} A_i=\bigcup_\limits{j=1}^n B_j=S$ and each element of $S$ belongs to exactly 10 of the $A_i{ }^{\prime}$ 's and exactly 9 of the $B_j$ 's. Then, $n$ is equal to

Two finite sets have $m$ and $n$ elements. The number of subsets of the first set is 112 more than that of the second set. The values of $m$ and $n$ are, respectively

The set $\left(A \cap B^{\prime}\right)^{\prime} \cup(B \cap C)$ is equal to

Let $F_1$ be the set of parallelograms, $F_2$ the set of rectangles, $F_3$ the set of rhombuses, $F_4$ the set of squares and $F_5$ the set of trapeziums in a plane. Then, $F_1$ may be equal to

Let $S=$ set of points inside the square, $T=$ set of points inside the triangle and $C=$ set of points inside the circle. If the triangle and circle intersect each other and are contained in a square. Then,