Prove that root 5 is an irrational number Solution:- Let us assume that on the contrary that √5 is a rational number. Then there exist positive integers ‘a’ and ‘ b’ such that ⇒ Where and are coprime i.e. there HCF is 1 Squaring both side ⇒ ⇒ is divisible by 5 then also divisible by … Read more
Class 10 chapter 1(Real number) Case based: 3 Raman is hosting the new year party for his friends. He wants to purchase some eatables like patties and buns for making burgers, some towels and some shining papers and glitter papers for decorting his house. When he reaches the store, he … Read more
Class 10 chapter 1(Real number) Case based: 2 The school Principal wants to address the students of classes eighth to tenth on the importance of personal hygiene. He asks the teacher in charge of the school to arrange all the students of eighth, ninth and tenth classes in a single hall. There … Read more
Case based:1 A seminar is being conducted by an educational organisation, where the participants will be educators of different subjects. The number of participants in Hindi, English and Mathematics are 60, 84 and 108 respectively. (A) In each room the same number of participants are to be seated and all of them being … Read more
Question 2: Check whether the relation R in R defined as R={(a, b): a ≤ b³} is reflexive, symmetric or transitive. Solution:- Reflexive:- , since is not reflexive. Symmetric:- R is not symmetric. Transitive:- is not transitive. is neither reflexive nor symmetric nor transitive. Other question:- R= {(a, b): a ≤ b²} is neither reflexive … Read more
Question 1:- Show that the relation R on the set R of real numbers, defined as R= {(a, b): a ≤ b²} is neither reflexive nor symmetric nor transitive. Solution: We have, where a, b ∈ R Reflexivity:- Obiviously, is a real number and is not true. Therefore, R is not reflexive. Symmetric:- Let the … Read more
Exercise 8.2(Application of Integrals) Chapter 8 Exercise 8.2 ncert math solution class 12 Question 1: Find the area of the circle which is interior to the parabola . Solution : The required area is represented by the shaded area OBCDO. Solving the given equation of circle , and parabola , Whent then we obtain the … Read more
Exercise 8.1(Application of Integrals) Chapter 8 Exercise 8.1 ncert math solution class 12 Question1: Find the area of the region bounded by the curve and the lines and the x-axis. Solution : The area of the region bounded by the curve, , the lines, and , and the -axis is the area . Area of … Read more
Chapter 7 ( Miscellaneous Exercise) Chapter 7 Miscellaneous Ncert math solution class 11 Question 1: How many words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER? Solution: The word DAUGHTER has 3 vowels, A, E, U and 5 consonants D, G, H, … Read more
EXERCISE 7.4(Permutations and Combinations) Exercise 7.4 ncert solutions maths class 11 Question 1: If , find . Solution: Given that We know that if then either or If On rearranging we get Now, Question 2: Determine if (i) (ii) Solution: (i) Given that: Substituting the formula we get On multiplying we get (ii) Given that: … Read more