## NCERT Solutions for Class 11 Maths Chapter 1

### Class 11 Maths Chapter 1 Sets Solutions

Class: | 11 |

Subject: | Mathematics |

Chapter 1: | Sets |

### 11th Maths Chapter 1 Solutions

NCERT Solutions for Class 11 Maths Chapter 1 Sets in English Medium is given below to free download. These solutions and Offline apps 2021-22 are based on latest NCERT Books 2021-22 for all students who are following CBSE Syllabus 2021-22.

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#### Important Questions on Sets

1. In a survey of 450 people, it was found that 110 play cricket, 160 play tennis and 70 play both cricket as well as tennis. How many play neither cricket nor tennis? [Answer: 23]

2. In a town of 10,000 families it was found that 40% families buy newspaper A, 20% families buy newspaper B and 10% families by newspaper C. 5% families buy A and B, 3%, buy B and C and 4% buy A and C. If 2% families buy all the three newspapers, find the no of families which buy(1) A only (2) B only (3) none of A, B and C (4) exactly two newspapers (5) exactly one newspaper (6) A and C but not B (7) at least one of A,B, C. [Answer: {2, 3, 5}]

3. Two finite sets have m and n elements. The total number of subsets of first set is 56 more than the total number of subsets of the second set. Find the value of m and n. [Answer: m = 6 and n = 3]

##### Class 11 Maths Chapter 1 Important Questions for Practice

1. In a group of 84 persons, each plays at least one game out of three viz. tennis, badminton and cricket. 28 of them play cricket, 40 play tennis and 48 play badminton. If 6 play both cricket and badminton and 4 play tennis and badminton and no one plays all the three games, find the number of persons who play cricket but not tennis.

2. In a class, 18 students took Physics, 23 students took Chemistry and 24 students took Mathematics of these 13 took both Chemistry and Mathematics, 12 took both Physics and Chemistry and 11 took both Physics and Mathematics. If 6 students offered all the three subjects, find: (1) The total number of students. (2) How many took Maths but not Chemistry. (3) How many took exactly one of the three subjects.

### Important Questions on 11th Maths Chapter 1

##### Write the following sets in the set-builder form: (3, 6, 9, 12).

Set builder form of {3, 6, 9, 12} = {x: x = 3n, n∈ N and 1 ≤ n ≤ 4}

##### List all the elements of the following set: A = {x: x is an odd natural number}.

A = {x: x is an odd natural number} = {1, 3, 5, 7, 9 …}

##### Write down all the subsets of the following set: {1, 2, 3}.

The subsets of {1, 2, 3} are Φ, {1}, {2}, {3}, {1, 2}, {2, 3}, {1, 3} {1, 2, 3}

##### Let A = {a, b}, B = {a, b, c}. Is A ⊂ B? What is A ∪ B?

Here, A = {a, b} and B = {a, b, c} Yes, A ⊂ B. A ∪ B = {a, b, c} = B

##### In a group of 400 people, 250 can speak Hindi and 200 can speak English. How many people can speak both Hindi and English?

Let H be the set of people who speak Hindi, and E be the set of people who speak English ∴ n(H ∪ E) = 400, n(H) = 250, n(E) = 200 n(H ∩ E) = ? We know that: n(H ∪ E) = n(H) + n(E) – n(H ∩ E) ∴ 400 = 250 + 200 – n(H ∩ E) ⇒ 400 = 450 – n(H ∩ E) ⇒ n(H ∩ E) = 450 – 400 ∴ n(H ∩ E) = 50 Thus, 50 people can speak both Hindi and English.

##### If S and T are two sets such that S has 21 elements, T has 32 elements and S ∩ T has 11 elements, how many elements does S ∪ T have?

It is given that: n(S) = 21, n(T) = 32, n(S ∩ T) = 11 We know that: n (S ∪ T) = n (S) + n (T) – n (S ∩ T) ∴ n (S ∪ T) = 21 + 32 – 11 = 42 Thus, the set (S ∪ T) has 42 elements.

##### If X and Y are two sets such that X has 40 elements, X ∪Y has 60 elements and X ∩Y has 10 elements, how many elements does Y have?

It is given that: n(X) = 40, n(X ∪ Y) = 60, n(X ∩ Y) = 10 We know that: n(X ∪ Y) = n(X) + n(Y) – n(X ∩ Y) ∴ 60 = 40 + n(Y) – 10 ∴ n(Y) = 60 – (40 – 10) = 30 Thus, the set Y has 30 elements.

##### 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 C denote the set of people who like coffee, and T denote the set of people who like tea n(C ∪ T) = 70, n(C) = 37, n(T) = 52 We know that: n(C ∪ T) = n(C) + n(T) – n(C ∩ T) ∴ 70 = 37 + 52 – n(C ∩ T) ⇒ 70 = 89 – n(C ∩ T) ⇒ n(C ∩ T) = 89 – 70 = 19 Thus, 19 people like both coffee and tea.

##### 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?

Let C denote the set of people who like cricket, and T denote the set of people who like tennis ∴ n(C ∪ T) = 65, n(C) = 40, n(C ∩ T) = 10 We know that: n(C ∪ T) = n(C) + n(T) – n(C ∩ T) ∴ 65 = 40 + n(T) – 10 ⇒ 65 = 30 + n(T) ⇒ n(T) = 65 – 30 = 35 Therefore, 35 people like tennis. Now, (T – C) ∪ (T ∩ C) = T Also, (T – C) ∩ (T ∩ C) = Φ ∴ n (T) = n (T – C) + n (T ∩ C) ⇒ 35 = n (T – C) + 10 ⇒ n (T – C) = 35 – 10 = 25 Thus, 25 people like only tennis.

##### 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?

Let F be the set of people in the committee who speak French and S be the set of people in the committee who speak Spanish ∴ n(F) = 50, n(S) = 20, n(S ∩ F) = 10 We know that: n(S ∪ F) = n(S) + n(F) – n(S ∩ F) = 20 + 50 – 10 = 70 – 10 = 60 Thus, 60 people in the committee speak at least one of the two languages.

##### In a survey of 600 students in a school, 150 students were found to be taking tea and 225 taking coffee, 100 were taking both tea and coffee. Find how many students were taking neither tea nor coffee?

Let U be the set of all students who took part in the survey. Let T be the set of students taking tea. Let C be the set of students taking coffee. Accordingly, n(U) = 600, n(T) = 150, n(C) = 225, n(T ∩ C) = 100 To find: Number of student taking neither tea nor coffee i.e., we have to find n(T’ ∩ C’). n(T’ ∩ C’) = n(T ∪ C)’ = n(U) – n(T ∪ C) = n(U) – [n(T) + n(C) – n(T ∩ C)] = 600 – [150 + 225 – 100] = 600 – 275 = 325 Hence, 325 students were taking neither tea nor coffee.

##### In a group of students 100 students know Hindi, 50 know English and 25 know both. Each of the students knows either Hindi or English. How many students are there in the group?

Let U be the set of all students in the group. Let E be the set of all students who know English. Let H be the set of all students who know Hindi. ∴ H ∪ E = U Accordingly, n(H) = 100 and n(E) = 50 n( H U E ) = n(H) + n(E) – n(H ∩ E) = 100 + 50 – 25 = 125 Hence, there are 125 students in the group.

##### How many exercises, questions, and examples are there in class 11 Maths Chapter 1?

There are seven exercises in class 11 Maths Chapter 1 (Sets).

In the first exercise (Ex 1.1), there are six questions.

In the second exercise (Ex 1.2), there are six questions.

In the third exercise (Ex 1.3), there are 9 questions.

In the fourth exercise (Ex 1.4), there are 12 questions.

In the fifth exercise (Ex 1.5), there are seven questions.

In the sixth exercise (Ex 1.6), there are eight questions.

In the last exercise (Miscellaneous), there are 16 questions.

So, there are in all 64 questions in class 11 Maths Chapter 1.

There are in all 34 examples in class 11 Maths Chapter 1.

- Examples 1, 2, 3, 4, 5 are in Ex 1.1.
- Examples 6, 7, 8 are in Ex 1.2.
- Examples 9, 10, 11 are in Ex 1.3.
- Examples 12, 13, 14, 15, 16, 17, 18, 19 are based on Ex 1.4.
- Examples 20, 21, 22 are in Ex 1.5.
- Examples 23, 24, 25, 26, 27 are in Ex 1.6.
- Examples 28, 29, 30, 31, 32, 33, 34 are based on Miscellaneous exercise.

##### Which problems of chapter 1 of class 11th Maths are most important for the first term exams?

Problems of chapter 1 of class 11th Maths that are most important for the exams are:

1. Questions 2, 3, 4, and 5 of exercise 1.1.

2. Questions 1 and 6 of exercise 1.2.

3. Questions 1, 3, 4, 5, 6, 7, and 9 of exercise 1.3.

4. Questions 3, 4, 5, 9, and 12 of exercise 1.4.

5. Questions 1, 3, 4, 5, and 7 of exercise 1.5.

6. Questions 2, 7, and 8 of exercise 1.6.

7. Questions 2, 4, 5, 6, 7, 8, 9, 11, 12, 13, 15, 16 of miscellaneous exercise on chapter 1.

8. Examples 5, 6, 9, 11, 13, 18, 22, 24, 25, 27, 29, 30, 31, 32, 33, 34.

Yes, there are some books other than NCERT from which students can practice extra questions of chapter 1 of class 11th Maths. The names of these books are NCERT Exemplar, R.L. Arora, R.D. Sharma, R.S. Aggarwal. These books are the best books after NCERT and NCERT Exemplar. The languages of these books are students friendly. Students can easily prepare chapter 1 of class 11th Maths from these books. Students can also see the previous year’s question papers.

##### Is chapter 1 of class 11 Maths easy to solve?

Chapter 1 of class 11th mathematics is not easy and not complicated. It lies in the middle of easy and hard because some examples and questions of this chapter are easy, and some are difficult. But difficulty level of any chapter varies from student to student. So, Chapter 1 of class 11th mathematics is easy or not depends on students also. Some students find it complex, some find it simple, and some find it in the middle of simple and complex.