Class 11 maths ch 5 miscellaneous exercise solutions

The chapterComplex Number and Quadratic Equation Class 11consists of several mathematical concepts, theorems, and formulas that are fundamental for solving sums of algebra. In this regard,NCERT Solutions for Class 11 Maths Chapter 5,prove to be extremely beneficial, as it provides step-wise solutions to all sums given in the exercises of this chapter. The NCERT Solutions for Chapter 5 Maths Class 11is available in a free downloadable PDF version on Vedantu. These solutions are curated by senior mathematics teachers at Vedantu as per the CBSE guidelines. Download Vedantu NCERT Book Solution to get a better understanding of all the exercises questions. Exercise 5.1: This exercise consists of 13 questions and is focused on finding the roots of quadratic equations. The questions are based on various concepts, such as the quadratic formula, the discriminant of a quadratic equation, and finding the nature of roots. Students will learn how to find the roots of quadratic equations and analyze the nature of these roots based on the values of the discriminant. Exercise 5.2: This exercise consists of 10 questions and is focused on solving problems related to the relationship between roots and coefficients of a quadratic equation. The questions are based on various concepts such as Vieta's formulas, the sum and product of roots, and finding the quadratic equation given its roots. Students will learn how to apply these formulas to solve problems related to quadratic equations. Exercise...

Miscellaneous Exercise 1. Find the values of K for which the line is: (a) parallel to the axis (b) parallel to the axis (c) passing through the origin. Ans. Given: Equation of line (a) If the line parallel to axis, then (b) If the line parallel to axis, then (c) If the line passes through origin then K = 1 or K = 6 2. Find the values of and if the equation is the normal form of the line Ans. Given: Dividing both sides by , we have Putting and , Equation of line in normal form Comparing with and 3. Find the equations of the lines which cut-off intercepts on the axes whose sum and product are 1 and respectively. Ans. Let equation of line be and it is given that and Now, solving and , Now, solving and Therefore, the required line And 4. What are the points on the axis whose distance from the line is 4 units? Ans. Given: Equation of line and let point on axis be Perpendicular distance from point to this line = = According to question Taking Taking Therefore, required points are and 5. Find the perpendicular distance from the origin of the line joining the points and Ans. Equation of the line joining points and Now, perpendicular distance from (0, 0) to this line, = = = = = = 6. Find the equation of the line parallel to axis and drawn through the point of intersection of the lines and Ans. Solving and , we have and Point of intersection of lines are and But the required line is parallel to axis, therefore the equation of required line is . 7. Find the equation of a line drawn p...

Updated for new NCERT Book - 2023-24. Learn Chapter 10 Conic Sections of Class 11 free with solutions of all NCERT Questions, Examples and Miscellaneous exercises. All solutions are provided with step-by-step explanation for your reference. Let's see what conic section is. We learned In this chapter, we talk about Conic Sections, that is, sections of the cone Specifically, we talk about Circles, Ellipse, Parabola and Hyperbola So, the topics of the chapter include • Circles - How to find equation of circle, center of circle • Parabola - Equation of parabola, its directrix, eccentricity and focus • Ellipse - Equation of ellipse, its directrix, eccentricity, focus and vertices • Hyperbola - Equation of hyperbola, its directrix, eccentricity, focus and vertices • Other questions like mirror problem , Triangle in parabola problem, Beam problem, Locus, Path traced problems Click on an exercise to start with answers of the questions, or the topic to learn the concepts with the questions