Team Gmath 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 r = 3 If repetition of digit … 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 × … 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
Chapter 6(Miscellaneous Exercise) Class 11 Math Solve the inequalities in Exercises 1 to 6.I(Chapter 6 Miscellaneous ncert math solution class 11) Question 1: 2 ≤ 3x – 4 ≤ 5 Solution: Given that, 2 ≤ 3x – 4 ≤ 5 ⇒ 2 ≤ 3x – 4 ≤ 5 ⇒ 2 + 4 ≤ 3x – 4 + … Read more
Exercise 6.3(Linear Inequalities) Solve the following system of inequalities graphically:(Ex 6.3 Linear Inequalities ncert math solution class 11) Question 1: x ≥ 3, y ≥ 2 Solution : Given that, x ≥ 3 …..(i) y ≥ 2…….(ii) The graph of the lines x = 3 and y = 2 are drawn in the figure below. … Read more