NIMCET 2019 Question Paper with solutions

Suppose ${\mathit{A}}_1$, ${\mathit{A}}_2$,..., ${\mathit{A}}_{30}$ are thirty sets each having 5 elements with no common element across the sets and ${\mathit{B}}_1,\mathit{B}2$,... ${\mathit{B}}_{\mathit{n}}$ are n sets each having 3 elements with no common element across the sets. Let $\underset{\mathit{i}=1}{\overset{30}{\cup }}{\mathit{A}}_{\mathit{i}}$ = $\underset{\mathit{j}=1}{\overset{30}{\cup }}{\mathit{B}}_{\mathit{j}}$ = S and each element of S belong toexactly 10 of ${\mathit{A}}_{\mathit{i}}$’s and exactly 9 of ${\mathit{B}}_{\mathit{j}}$’s. The value of n is equal to