Miscellaneous exercise class 11 chapter 1

Question11: Let A and B be sets. If A ∩ X = B ∩ X = φ and A ∪ X = B ∪ X for some set X, show that A = B Solution: A = A ∩ (A ∪ X) //absorption law A = A ∩ (B ∪ X) //given that A ∩ X = B ∩ X = (A ∩ B) ∪ (A ∩ X) //distributive law = (A ∩ B) ∪ φ //given that A ∩ X = φ A = (A ∩ B) …(1) Repeating above process by taking B = B ∩ (B ∪ X) We get B = (A ∩ B) …(2) from (1) and (2) A = B Question12: Find sets A, B and C such that A ∩ B, B ∩ C and A ∩ C are non-empty sets and A ∩ B ∩ C = φ Solution: (A ∩ B) should be non-empty means atleast one element is common in between them … same for (B ∩ C) & (A ∩ C) A ∩ B ∩ C = φ means there should not be any element common in all the three sets A, B and C Let A = and A ∩ B ∩ C = φ Question13: 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? Solution: There are total 600 students Let A and B represents sets of students taking tea and coffee respectively n(A) = 150 n(B) = 225 Students taking both tea and coffee = n(A ∩ B) = 100 Students taking either tea or coffee = n(A ∪ B) = ? By principle of inclusion-exclusion, n(A ∪ B) = n(A) + n(B) – n(A ∩ B) = 150 + 225 – 100 = 275 Now, Number of students who neither take tea nor coffee = total students – Number of Students who either take tea or coffee = 600 – 275 = 325 There are 325 students who neither take tea nor coffee Question 14: In a group of stu...

Sets Class 11NCERT PDF material comes handy for all the students of Class 11. The solution material can be essential for last-minute revision. Download it and get accustomed to the critical techniques to solve questions related to Sets. The best part is that you can avail it free of cost. Every learner needs to get familiar with all the concepts of the chapter as it will help in studying other Maths topics like Probability, Sequences and Geometry. Although this is relatively an easy chapter, you still need to devote a considerable amount of time and practice for the same. Set Class 11 NCERT SolutionsPDF by Vedantu is prepared for your assistance. Points To Remember Before Solving Exercises: 1. Set: A set is called a well-defined collection of objects. 2. Representation of Sets: There are 2 methods to represent a set • Roster or Tabular Form: In this form, we list all the members of the set within braces , then A will be the subset of B since elements of A are also present in set B. 5. Power Set: The collection of all of the subsets of a set A is known as the power set of A. Generally this is denoted by P(A). If the no of elements in A i.e. n(A) = n, then the no of elements in P(A) = 2 n . 6. Universal Set: A set which contains all sets in a given context is defined as the universal set. 7. Venn-Diagrams: Venn diagrams are diagrams that show the relationship between two sets. The universal set U is represented by a point inside a rectangle, and its subsets are represented b...

NCERT Solutions for Class 11 Maths Chapter 1 Sets Miscellaneous Examples Free PDF download of NCERT Solutions for Class 11 Maths Chapter 1 miscellaneous prepared by expert Mathematics teacher at Mathongo.com as per CBSE (NCERT) books guidelines. Download our Class 11 Maths Chapter 1 Sets miscellaneous Questions with Solutions to help you to revise complete Syllabus and Score More marks in your exams. FREE PDF • • • • • • • •

CBSE Study Material • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Miscellaneous Exercise * According to the CBSE Syllabus 2023-24, this chapter has been renumbered as Chapter 10. NCERT Solutions for Class 11 Maths are provided here to help the students in understanding the steps to solve mathematical problems that are in the Class 11 Maths NCERT textbook. Chapter 11 Conic Sections of Class 11 Maths is categorised under the CBSE Syllabus for the session 2023-24. The Miscellaneous Exercise of • Sections of a Cone • Circle • Parabola • Ellipse • Hyperbola Each question of the exercise has been carefully solved for the students to understand, keeping the examination in mind. The Download PDF carouselExampleControls112 Previous Next Solutions for Class 11 Maths Chapter 11 – Miscellaneous Exercise 1. If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus. Solution: We know that the origin of the coordinate plane is taken at the vertex of the parabolic reflector, ...

NCERT Solutions for Class 11 Maths Chapter 1 Sets Miscellaneous Exercise Get Free NCERT Solutions for Class 11 Maths Chapter 1 Sets Miscellaneous Exercise PDF in Hindi and English Medium. Sets Class 11 Maths NCERT Solutions are extremely helpful while doing your homework. Sets Miscellaneous Exercise Class 11 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the questions in Chapter 1 Class 11 Sets Miscellaneous Exercise provided in NCERT Textbook. • • • • • • • • • • • • • • • • • • Chapter 1: • अध्याय 1: Free download NCERT Solutions for Class 11 Maths Chapter 1 Sets Miscellaneous Exercise PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCERT Books based on updated CBSE Syllabus for the session 2019-20. Solution 1: Solution 2: Solution 3: Solution 4: Solution 5: Solution 6: Solution 7: Solution 8: Solution 9: Solution 10: Solution 11: Solution 12: Solution 13: Solution 14: Solution 15: Solution 16: प्रश्न 3. मान लीजिए A, B और Cऐसे समुच्चय हैं कि A ∪ B = A ∪ C तथा A ∩ B = A ∩ C, तो दर्शाइए कि B = C हल: दिया है: A ∪ B = A ∪ C (A ∪ B) ∩ C = (A ∪ C) ∩ C = C [(A ∪ C) ∩ C = C ] (A ∩ C) ∩ (B ∩ C) = C (A ∩ B) ∪ (B ∩ C) = C ….(i) [A ∩ C = A ∩ B = दिया है।] A ∪ B = A ∪ C (A ∪ B) ∩ B = (A ∪ C) ∩ B B = (A ∪C) ∩ B = (A ∩ B) ∪ (C ∩ B) या (A ∩ ) ∪ (B ∩ C) = B ……(ii) (i) और (ii) से B = C प्राप्त होता है। प्रश्न 4. दिखाइए कि निम्नलि...

Balbharti Maharashtra State Board 11th Maths Solutions Chapter 1 Angle and its Measurement Miscellaneous Exercise 1 I. Select the correct option from the given alternatives. Question 1. \(\left(\frac\) cm Question 11. The angles of a quadrilateral are in A.P. and the greatest angle is double the least. Find angles of the quadrilateral in radians. Solution: Let the measures of the angles of the quadrilateral in degrees be a – 3d, a – d, a + d, a + 3d, where a > d > 0 ∴ (a – 3d) + (a – d) + (a + d) + (a + 3d) = 360° … [Sum of the angles of a quadrilateral is 360°] ∴ 4a = 360° ∴ a = 90° According to the given condition, the greatest angle is double the least, ∴ a + 3d = 2.(a – 3d) ∴ 90° + 3d = 2.(90° – 3d) ∴ 90° + 3d = 180° – 6d 9d = 90° ∴ d = 10° ∴ The measures of the angles in degrees are a – 3d = 90° – 3(10°) = 90° – 30° = 60°, a – d = 90° – 10° = 80°, a + d = 90°+ 10°= 100°, a + 3d = 90° + 3(10°) = 90° + 30° = 120° Categories Post navigation

NCERT Solutions for Class 11 Maths Chapter 1 - Sets NCERT Solutions for Class 11 Maths Chapter 1 Sets are prepared by our expert faculty at BYJU’S according to the latest update on the CBSE Syllabus for 2023-24. These Sets are used to define the concepts of functions and relations, some of which are covered in Chapter 1 of the NCERT textbook. The Class 11 Maths Chapter 1 of NCERT, categorised under the CBSE syllabus, also has some basic definitions and operations involving the sets. It is necessary to get fundamental knowledge on Sets since the study of sequences, geometry, and probability requires it. However, this is an easy chapter among all the chapters of NCERT Class 11 Maths, to score maximum marks in the board examination. These Access Answers to NCERT Class 11 Maths Chapter 1 – Sets Download PDF carouselExampleControls112 Previous Next Also Access NCERT Solutions for Class 11 Maths Chapter 1 – Sets Exercise 1.1 page: 4 1. Which of the following are sets? Justify your answer. (i) The collection of all months of a year beginning with the letter J. (ii) The collection of ten most talented writers of India. (iii) A team of eleven best-cricket batsmen of the world. (iv) The collection of all boys in your class. (v) The collection of all natural numbers less than 100. (vi) A collection of novels written by the writer Munshi Prem Chand. (vii) The collection of all even integers. (viii) The collection of questions in this Chapter. (ix) A collection of most d...