# Higher Algebra Hall & Knight Miscellaneous Equations (Chapter 10) Solutions

Hall and Knight Higher Algebra Chapter 10 ‘Miscellaneous Equations’ comprises all the essential topics of the chapter that are essential for Class 12 board exams and competitive exams preparation. These solutions will help in forming a stronger command over simultaneous solutions of an equation, division of equations, successions and combinations. They also cover vital ideas regarding equations in fractional format and equations with rational and irrational values. We have included detailed theoretical explanations along with solutions to help you form a better understanding of the chapter. You will also learn about the concepts of homogeneous equations, cross multiplication and indeterminate equations from these solutions.

Higher Algebra by Hall and Knight Miscellaneous Equations solutions include 4 exercises with 129 questions. There are different kinds of questions revolving around the numerous concepts from the chapter in the exercise. Once you solve these questions you will learn to solve problems which deal with simultaneous solving of equations, variable derivation, reciprocating values and substitution. These exercise questions are based on the latest JEE exam pattern. They will make you aware of all the possible questions that can be framed from the topics of the chapter.

Instasolv’s Elementary Algebra & Higher Algebra by Hall and Knight Miscellaneous Equations solutions have been prepared to make sure that you can find instant solutions for your doubts. Our subject matter experts always adhere to the latest syllabus for competitive exams and ensure that you have 100% accurate solutions every time.

## Important Topics for Hall and Knight Higher Algebra Solutions Chapter 10: Miscellaneous Equations

**Different Kinds of Equations **

As the name of the chapter already suggests, here you will get to deal with numerous equations which are of multiple types. There are simple quadratic equations, equations based on formula, fraction based equations and equations which deal with roots and cube roots. You will also learn about different rules which are utilized in the course of solving these equations and methods like reciprocating of values, substitution, breaking the equation, consolidating of terms, simultaneous solution and cross multiplication

**Indeterminate Equations**

In this chapter, you will learn about the term “indeterminate equations”. In cases when the number of unknown quantities in an equation is relatively more than the number of independent equations, the numbers of solutions become unlimited and such kinds of equations are termed as the indeterminate equations. In this chapter, you will not get to deal with complex indeterminate equations however the equations that you will study will revolve around positive integral values of the unknown quantities, smaller coefficients and coefficients of unity

### Exercise Discussions of Higher Algebra by Hall and Knight Solutions Chapter 10: Miscellaneous Equations

**Example X a **

**The exercise has a total of 51 questions.**- The entire exercise has equations containing fractions, roots, and variables, rational and irrational values.
- It begins with simple power-based equations and further covers complex problems with coefficients of roots and fractions
- You will be required to use the method of inspection, equidistant term and reciprocal execution to solve these questions.

**Example X b **

**The exercise has 41 questions in total.**- It begins with questions where you are provided with two expressions and you are required to solve them simultaneously.
- There is another exercise where the equation is present in the form of a2+b2+ 2ab and a2+b2-2ab with different variables.
- Some of the questions are even presented in the form of fractions
- There are certain questions where you will also encounter problems where the equations are present with roots and root fractions.
- Overall the exercise contains different types of equations which are required to be solved by different methods that have been discussed in the chapter.

**Example X c **

- There are a total of 16 questions in this exercise.
- The exercise contains equations which include three or more unknown quantities.
- You are required to implement the cross multiplication and division method to solve these equations and derive the value of all the three variables.

**Example X d **

- The exercise has a total of 21 questions.
- It begins with questions where you are provided with equations and you are required to solve them in positive integers.
- There are some questions where you are required to find the general solutions of the equations along with the least values of the variables
- The exercise also has questions where you will have to implement the unitary method with respect to the information that has been shared in the questions. The last section of the exercise contains such word problems.

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