JEE PYQ: Sets And Relations Question 9
Question 9 - 2020 (04 Sep Shift 2)
Let $\bigcup_{i=1}^{50} X_i = \bigcup_{i=1}^{n} Y_i = T$, where each $X_i$ contains 10 elements and each $Y_i$ contains 5 elements. If each element of the set $T$ is an element of exactly 20 of sets $X_i$’s and exactly 6 of sets $Y_i$’s, then $n$ is equal to
(1) 15
(2) 50
(3) 45
(4) 30
Show Answer
Answer: (4)
Solution
$\bigcup_{i=1}^{50} X_i = \bigcup_{i=1}^{n} Y_i = T$
$\because n(X_i) = 10, n(Y_i) = 5$
So, $\bigcup_{i=1}^{50} X_i = 500, \bigcup_{i=1}^{n} Y_i = 5n$
$\Rightarrow \frac{500}{20} = \frac{5n}{6} \Rightarrow n = 30$
BETA
