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 in … Read more
Question 2: Check whether the relation R in R defined as R={(a, b): a ≤ b³} is reflexive, symmetric or transitive. Solution:- R defined as R={(a, b): a ≤ b³} is reflexive, symmetric or transitive. Reflexive:- , since is not reflexive. Symmetric:- R is not symmetric. Transitive:- is not transitive. is neither reflexive nor symmetric … 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: R of real numbers, defined as R= {(a, b): a ≤ b²} is neither reflexive nor symmetric nor transitive. where a, b ∈ R Reflexivity:- Obiviously, … Read more
Exercise 8.2(Application of Integrals) 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 B Point of intersection as and . Area Area … 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, x = 1 and x = 4, and the X-axis is … 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 r=p or r=n-p 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) … Read more
Exercise 7.3(Permutations and Combinations) Chapter 7 Exercise 7.3 ncert solutions maths class 11 Question 1: How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated? Solution: Total number of digit n=9 Number of places where the digit can fill If repetition of digit not allowed, Then … Read more
Exercise 7.2(Permutations and Combinations) Exercise 7.2 ncert solutions maths class 11 Question 1: Evaluate (i) 8! (ii) 4! – 3! Solution: (i) Given 8! We know that 8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 40320 (ii) Given 4!-3! 4! – 3! = (4 × 3!) … Read more
Exercise 7.1(Permutations and Combinations) Ncert math solution(Exercise 7.1 ncert solutions maths class-11) Question 1: How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5, assuming that (i) Repetition of the digits is allowed? (ii) Repetition of the digits is not allowed? Solution: 3-digit numbers can be formed from the … Read more