Suppose A_1, A_2, A_3, dots, A_{30} are 30 se | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let $|S|$ be the number of elements in the set $S$.Given that each of the $30$ sets $A_i$ has $5$ elements,the sum of the number of elements in al

Vedclass · Accepted Answer

$45$

Vedclass · Answer

(C) Let $|S|$ be the number of elements in the set $S$.Given that each of the $30$ sets $A_i$ has $5$ elements,the sum of the number of elements in all $A_i$ is $30 	imes 5 = 150$.Since each element of $S$ belongs to exactly $10$ of the $A_i$'s,we have $|S| 	imes 10 = 150$,which implies $|S| = 15$.Similarly,for the sets $B_j$,each of the $n$ sets has $3$ elements,so the sum of the number of elements in all $B_j$ is $n 	imes 3 = 3n$.Since each element of $S$ belongs to exactly $9$ of the $B_j$'s,we have $|S| 	imes 9 = 3n$.Substituting $|S| = 15$,we get $15 	imes 9 = 3n$.$135 = 3n \Rightarrow n = 45$.

Similar Questions

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 the sets $X_{i}$ and exactly $6$ of the sets $Y_{i}$,then $n$ is equal to:

$A$ certain $12$-hour digital clock displays the hour and the minute of a day. Due to a defect in the clock,whenever the digit $1$ is supposed to be displayed,it displays $7$. What fraction of the day will the clock show the correct time?

If a set $A$ has $2n + 1$ elements,then how many subsets of $A$ contain at least $n$ elements?

In a group of $65$ people,$40$ like cricket and $10$ like both cricket and tennis. How many like tennis only and not cricket? How many like tennis?

Let $A = \{x : x \in R, |x| < 1\};$ $B = \{x : x \in R, |x - 1| \ge 1\}$ and $A \cup B = R - D,$ then the set $D$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module