In a certain town $25\%$ families own a phone and $15\%$ own a car, $65\%$ families own neither a phone nor a car. $2000$ families own both a car and a phone. Consider the following statements in this regard:
$1$. $10\%$ families own both a car and a phone
$2$. $35\%$ families own either a car or a phone
$3$. $40,000$ families live in the town
Which of the above statements are correct
$1$ and $2$
$1$ and $3$
$2$ and $3$
$1, 2$ and $3$
In a class of $55$ students, the number of students studying different subjects are $23$ in Mathematics, $24$ in Physics, $19$ in Chemistry, $12$ in Mathematics and Physics, $9$ in Mathematics and Chemistry, $7$ in Physics and Chemistry and $4$ in all the three subjects. The total numbers of students who have taken exactly one subject is
In a survey of $220$ students of a higher secondary school, it was found that at least $125$ and at most $130$ students studied Mathematics; at least $85$ and at most $95$ studied Physics; at least $75$ and at most $90$ studied Chemistry; $30$ studied both Physics and Chemistry; $50$ studied both Chemistry and Mathematics; $40$ studied both Mathematics and Physics and $10$ studied none of these subjects. Let $\mathrm{m}$ and $\mathrm{n}$ respectively be the least and the most number of students who studied all the three subjects. Then $\mathrm{m}+\mathrm{n}$ is equal to .............................
In a group of $70$ people, $37$ like coffee, $52$ like tea and each person likes at least one of the two drinks. How many people like both coffee and tea?
Let $X = \{ $ Ram ,Geeta, Akbar $\} $ be the set of students of Class $\mathrm{XI}$, who are in school hockey team. Let $Y = \{ {\rm{ }}$ Geeta, David, Ashok $\} $ be the set of students from Class $\mathrm{XI}$ who are in the school football team. Find $X \cup Y$ and interpret the set.
Of the members of three athletic teams in a school $21$ are in the cricket team, $26$ are in the hockey team and $29$ are in the football team. Among them, $14$ play hockey and cricket, $15$ play hockey and football, and $12$ play football and cricket. Eight play all the three games. The total number of members in the three athletic teams is