Subject Experts Solutions for Chapter: Set Theory, Exercise 2: PRACTICE QUESTIONS (COMPETITION WING)

In a class of $50$ students, each student passed Maths or English. If $10$ students passed both Maths and English and $30$ students passed Maths, then find the number of students who passed English.

If $A=\left\{x/x is a factor of 4\right\}, B=\left\{x/x is a factor of 8\right\} and C=\left\{x/x is a factor of 10\right\}$, then which of the following statement is true?

Given that $X=\left\{Natural numbers less than 100 divisible by 6\right\}, Y=\left\{Natural numbers less than 100 divisible by 8\right\}, Z=\left\{Natural numbers less than 100 divisible by 18\right\}$

Find $n\left(X\cap Y\cap Z\right)$

The strength of a class is $96$. In it, $56$ students like cricket and $40$ students like football. Which of the following can be concluded?

In an office, the ratio of the percentage of employees who like only tea, percentage of employees who like only coffee, percentage of employees who like both the drinks and percentage of employees who like neither of the drinks is $8 : 7 : 6 : 4$. Find the percentage of employees who like neither of the drinks

In an office, the ratio of the percentage of employees who like only tea, percentage of employees who like only coffee, percentage of employees who like both the drinks and percentage of employees who like neither of the drinks is $8 : 7 : 6 : 4$. If the number of employees in the office is $150$, then find the number of employees who like only tea.

A class of $20$ students went to picnic. Each of those students played at least one of the games "Green Glass Doors" and "Clap and Catch". Twelve students played "Green Glass Doors" and $13$ students played "Clap and Catch". How many students played "Clap and Catch" but not "Green Glass Doors" 

The number of non-empty proper subsets of a set $A$ is $510$. Find the number of elements of the set $A$