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
Question:- Two balls are drawn at random one by one with replacement from an urn containing equal number of red balls and green balls. Find the probability distribution of number of red balls. Also, find the mean of the random variable. Solution:- Let X represent the number of red balls Possible value of X = … Read more
Question:- Find the equations of the diagonals of the parallelogram PQRS whose vertices are P(4, 2, -6), Q(5, -3, 1), R(12, 4, 5) and S(11, 9, -2). Use these equations to find the point of intersection of diagonals. Solution:- Vertices of parallelogram PQRS are P(4, 2, -6), Q(5, -3, 1), R(12, 4, 5) and S(11, … Read more
Question: A line l passes through point (-1,3,-2) and is perpendicular to both the lines and . Find the vector equation of the line l. Hence, obtain its distance from origin. Solution: Point (-1, 3, -2) Equation of lines Let dr’s of the line l are (a, b, c) Equation of line passes through the … Read more
![A function f:[-4,4] → [0,4] is given by f(x) = √16 - x²](https://gmath.in/wp-content/uploads/2023/03/one-one.png)
Question: A function f:[-4,4] → [0,4] is given by f(x) = √16 – x². show that f is an onto function but not a one-one function. Further, find all possible values of ‘a’ for which f(a) = √7. Solution:- A function is given that One-one :- Let are lies in Therefore, But Thus the given … Read more
Question:- Recent studies suggest that roughly 12 % of the world population is left handed. Depending upon the parents, the chances of having a left handed child are as follows : A : When both father and mother are left handed : Chances of left handed child is 24 % … Read more