NCERT Class 11-Math's Exemplar Chapter 1 Sets CBSE Board Problems

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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.