Exercise 1.4
Page no - 1.55
Question 1
If $A$ and $B$ are two sets such that $n(A \cup B)=50, n(A)=28$ and $n(B)=32$, find $n(A \cap B)$.
Question 2
If $A$ and $B$ are two sets such that $A \cup B$ has 18 elements, $A$ has 8 elements and $B$ has 15 elements, how many elements does $A \cap B$ have ?
Question 3
In a school there are 20 teachers who teach mathematics or physics. Of these, 12 teach mathematics and 4 teach physics and mathematics. How many teach physics ?
Question 4
If $S$ and $T$ are two sets such that $S$ has 21 elements, $T$ has 32 elements and $S \cap T$ has 11 elements, how many elements does $S \cup T$ have ?
Question 5
In a group of 50 people, 35 speak Hindi, 25 speak both English and Hindi and all the people speak at least one of the two languages. How many people speak only English and not Hindi ? How many people speak English ?
Question 6
In a group of 400 people, 250 can speak Hindi and 200 can speak English. How many can speak both Hindi and English ?
Question 7
If $X$ and $Y$ are two sets such that $X$ has 40 elements, $X \cup Y$ has 60 elements and $X \cap Y$ has 10 elements, how many elements does $Y$ have ?
Question 8
In a committee 50 people speak French, 20 speak Spanish and 10 speak both Spanish and French. How many speak at least one of these two languages ?
Question 9
In a group of 65 people, 40 like cricket, 10 like both cricket and tennis. How many like tennis only and not cricket ? How many like tennis ?
Question 10
In a group of people, 50 speak both English and Hindi and 30 people speak English but not Hindi. All the people speak at least one of the two languages. How many people speak English ?
Question 11
If $45 \%$ of the students of a class have offered Mathematics and $85 \%$ of them Biology, find the percentage of students who offered Biology only ?
Question 12
In a group, every member knows at least one of the languages-Hindi and Urdu. 100 members know Hindi, 50 know Urdu and 25 of them both Hindi and Urdu. How many members are there in the group ?
Question 13
In a survey of 600 students in a school, 150 students were found to be drinking Tea and 225 drinking Coffee, 100 were drinking both Tea and Coffee. Find how many students were drinking neither Tea nor Coffee?
Question 14
In a class of 35 students, 17 have taken Mathematics, 10 have taken mathematics but not physics. Find the number of students who have taken both mathematics and physics and the number of students who have taken physics but not mathematics. It is given that each student has taken either mathematics or physics or both.
Question 15
Out of 500 car owners investigated, 400 owned car $A$ and 200 owned car $B$. 50 owned both cars $A$ and $B$. Is this data correct?
Question 16
In a group of 45 students, 22 can speak Hindi only, 12 can speak English only. How many can speak both Hindi and English?
Question 17
In a town with population 5000,2800 read the Times of India, 2300 read Indian Express and 400 read both. How many read neither?
Page no - 1.56
Question 18
An investigator interviewed 100 students to determine their preferences for the three drinks : Milk $(M)$, Coffee $(C)$ and Tea $(T)$. He reported the following : 10 students had all the three drinks $M, C, T, 20$ had $M$ and $C, 30$ had $C$ and $T$ : 25 had $M$ and $T ; 12$ had $M$ only, 5 had $C$ only; 8 had $T$ only. Using a Venn diagram, find how many did not take any of the three drinks?
Question 19
In a survey of 25 students, it was found that 15 had taken mathematics, 12 had taken physics and 11 had taken chemistry, 5 had taken mathematics and chemistry, 9 had taken mathematics and physics, 4 had taken physics and chemistry and 3 had taken all the three subjects. Find the number of students who had taken (i) only chemistry (ii) only mathematics (iii) only physics (iv) physics and chemistry but not mathematics (v) mathematics and physics but not chemistry (vi) only one of the subjects (vii) at least one of the three subjects (viii) none of three subjects.
Question 20
In a survey of 100 persons it was found that 28 read magazine $A, 30$ read magazine $B, 42$ read magazine $C, 8$ read magazines $A$ and $B, 10$ read magazines $A$ and $C, 5$ read magazines $B$ and $C$ and 3 read all the three magazines. Find :
(i) How many read none of the three magazines ?
(ii) How many read magazine $C$ only ?
Question 21
In a survey it was found that 21 people liked product $A, 26$ liked product $B$ and 29 liked product $C$. If 14 people liked products $A$ and $B ; 12$ pcople liked products $C$ and $A ; 14$ people liked products $B$ and $C$ and 8 liked all the three products. Find how many liked product $C$ only.
Question 22
In a survey of 60 people, it was found that 25 people read Newspaper $H, 26$ read Newspaper $T, 26$ read Newspaper $I, 9$ read both $H$ and $I, 11$ read both $H$ and $T, 8$ read both $T$ and $I, 3$ read all the three newspapers. Find :
(i) the number of people who read at least one of the newspapers
(ii) the number of people who read exactly one newspaper.
Question 23
In a survey of 100 students, the number of students studying the various languages were found to be : English only 18, English but not Hindi 23 , English and Sanskrit 8, English 26, Sanskrit 48, Sanskrit and Hindi 8 , no language 24. Find :
(i) How many students were studying Hindi ?
(ii) How many students were studying English and Hindi ?
Question 24
In a group of children, 35 play football out of which 20 play football only, 22 play hockey, 25 play cricket out of which 11 play cricket only. Out of these 7 play cricket and football but not hockey, 3 play football and hockey but not cricket and 12 play football and cricket both. How many play all the three games ? How many play cricket and hockey but not football, how many play hockey only ? What is the total number of children in the group ?
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