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
Question: Engine displacement is the measure of the cylinder volume swept by all the pistons of a piston engine. The piston moves inside the cylinder bore. The cylinder bore in the form circular cylinder open at the top is to be made from a metal sheet of area 75 π cm². Based … Read more
Question: The use of electric vehicle will curb air pollution in the long run. The use of electric vehicles is increasing every year and estimated electric vehicles in use at any time t is given by the function V: Where t represents the time and t = 1, 2, 3 . . . corresponds to … Read more
Exercise 5.3(Complex Numbers and Quadratic Equations) Solve each of the following equations:(Exercise 5.3 complex no. ncert math solution class 11) Question 1: . Solution : The given quadratic equation is . Question 2: . Solution: The given quadratic equation is . On comparing the given equation with , we obtain , and Therefore, the discriminant … Read more
Exercise 5.2 (Complex number) Find the modulus and the arguments of each of the complex numbers in Exercises 1 to 2.(Exercise 5.2 complex no. ncert math solution class 11) Question 1: Solution : Let Comparing the real and imaginary parts, we have Squaring and adding equation (1) and (2), we have Therefore, modulus Now, dividing … Read more
Exercise 5.1(Complex Number) Express each of the complex number given in the Exercises 1 to 10 in the form a + ib.(Exercise 5.1 complex no. ncert math solution class 11) Question 1: Solution: Question 2: Solution: Question 3: Solution: Question 4: Solution: Question 5: Solution: Question 6: Solution: Question 7: Solution: Question 8: Solution: Question … Read more
Chapter 4:(Principle Of Mathematical Induction) Prove the following by using the principle of mathematical induction for all n ∈ N (Exercise 4.1 ncert math solution class 11) Question 1:- Solution: Let be the given statement For , Assume that is true for some positive integer , such that We will now prove that is also … Read more