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
Exercise 6.2(Linear Inequalities ) Solve the following inequalities graphically in two-dimensional plane:(Ex 6.2 Linear Inequalities ncert math solution class 11) Question 1: x + y < 5 Solution: Given that x 0 5 y 5 0 Now, draw a dotted line x + y = 5 in the graph Now, consider x + y < … Read more
Exercise 6.1 (Linear Inequalities) Ex 6.1 Linear Inequalities ncert math solution class 11 Question 1: Solve , when (i) is a natural number. (ii) is an integer. Solution: Given that: (i) is a natural number. Hence, in this case, the solution set . (ii) is an integer. The integers less than are …-3, . Hence, … Read more
Chapter – 5(Miscellaneous Exercise) Complex Numbers and Quadratic Equations Chapter 5 Miscellaneous ncert math solution class 11 Question 1: Evaluate: Solution : Given Question 2: For any two complex numbers and , prove that: Solution: Let and Therefore, Now Question 3: Reduce to the standard form. Solution :Given that Question 4: If prove that Solution … Read more
Question:- A and B throw a die alternatively till one of them gets ‘6’ and win the game. Find their respective probabilities of winning, If A starts first Solution: Let S denote the success(getting a ‘6’) and F denote the failure(Not getting a ‘6’). Thus, P(A wins in the … Read more