Team Gmath 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 – – – (i) – – – (ii) Let dr’s of the line l are … Read more
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 f:[-4, 4] → [0, 4] is given that One-one :- Let are lies in … 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 on the above … 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