QJEEM20Ma5285: JEE Main 2020 Mathematics - Class 11 JEEM20Ma5285 Solution: Let ∪ i = 1 50 ⁡ X i = ∪ i = 1 n ⁡ Y i = T where each X i…

$$\underset{i=1}{\overset{50}{\cup }}{X}_i=$$ X₁, X₂,....., X₅₀ = 50 sets. Given each sets having 10 elements.

So total elements = 50 $$\times$$ 10

$$\underset{i=1}{\overset{n}{\cup }}{Y}_i=$$ $$ Y₁, Y₂,....., Y_n = n sets. Given each sets having 5 elements.

So total elements = 5 $$\times$$ n

Now each element of set T contains exactly 20 of sets X_i.

So number of effective elements in set T = $$\frac{50\times 10}{20}$$

Also each element of set T contains exactly 6 of sets Y_i.

So number of effective elements in set T = $$\frac{50\times 10}{20}$$

$$\therefore$$ $$\frac{50\times 10}{20}$$ = $$\frac{5\times n}{20}$$

$$\Rightarrow$$ n = 30