NCERT Class 11-Math's Exemplar Chapter 1 Sets CBSE Board Problems
Glide to success with Doorsteptutor material for CBSE : fully solved questions with step-by-step explanation- practice your way to success.
Long Answer Type
Question 23:
Let A, B and C be sets. Then show that
Answer:
Given: A, B and C are three given sets
To prove:
Let
Let
We know:
and
From (i) and (ii):
Hence Proved
Question 24:
Out of students; passed in English, passed in Mathematics, in Science, in English and Mathematics, 7 in Mathematics and Science; 4 in English and Science; 4 in all the three. Find how many passed
(i) in English and Mathematics but not in Science
(ii) in Mathematics and Science but not in English
(iii) in Mathematics only
(iv) in more than one subject only
Answer:
(i) 2
(ii) 3
(iii) 3
(iv) 9
Question 25:
In a class of 60 students, 25 students play cricket and 20 students play tennis, and 10 students play both the games. Find the number of students who play neither?
Answer:
Given:
Total number of students are
Students who play cricket and tennis are and respectively
Students who play both the games are
To find: number of students who play neither
Let be the total number of students, C and T be the number of students who play cricket and tennis respectively
Number of students who play either of them
Number of student who play neither
Hence, there are 25 students who play neither cricket nor tennis.
Question 26:
In a survey of 200 students of a school, it was found that 120 study Mathematics, 90 study Physics and 70 study Chemistry, 40 study Mathematics and Physics, 30 study Physics and Chemistry, 50 study Chemistry and Mathematics and 20 none of these subjects. Find the number of students who study all the three subjects.
Answer:
Given:
Total number of students
Number of students study Mathematics
Number of students study Physics
Number of students study Chemistry
Number of students study Mathematics and Physics
Number of students study Mathematics and Chemistry
Number of students study Physics and Chemistry
Number of students study none of them
Let U be the total number of students, P, M and C be the number of students study Physics, Mathematics and Chemistry respectively
To find: number of students who study all the three subjects
Number of students who play either of them
Number of students who play either of them
From (i) and (ii):
Hence, there are 20 students who study all three subjects.