NCERT Class 11 Maths Solutions: The transition of a student from class 10th to class 11th is one of the most challenging academic periods. The drastic expansion of the course material has already got them by their heels and arrested their average pace of studies. The exponential rise in the intellectual level of the studies, on the other hand, also makes it difficult for them. To ease this transition and help the students with their new and increased workload, Aakash provides them CBSE NCERT Solutions for Class 11th maths. Experts and Senior Faculty prepare the NCERT solutions for class 11. The solutions prepared are done, keeping in mind the recent transition of students from class 10th to class 11th. Thus, the solutions for them are explained thoroughly. The key aim is to help them to understand with their 10th standard intellect and help them with exams as well.
In the Aakash NCERT solutions for class 11th mathematics, we have taken into consideration every chapter and provided a solution for all the problems in the 16 chapters as per NCERT maths. Each solution is done in a stepbystep scenario and has followthrough with an indepth question analysis. The analysis is provided to help the students understand the core concept of the questions and how to approach these questions in 23 different ways. The language being used in the solutions is extremely easy, which makes it easy for the students to grasp the solution.
Aakash has also provided the PDF of NCERT Solutions for class 11th All Subjects apart from the NCERT solutions.
Aakash has covered everything in the NCERT solutions for class 11th maths, and there is nothing left to practise. We all know that Mathematics is the subject of concepts and solutions, and we have created the perfect pathways in our stepbystep solution which not only help the student to reach the answer but also gets the core concepts cleared. The solutions give an idea to the student about the pattern and formulas that the question follows and the basic concepts are inculcated into the student in our practice sessions which come together and form the consolidated approach towards mathematics. The Aakash NCERT solutions for class 11th PDF for maths is the ideal help that a student needs to not only score marks and learn but also ease the difficult transition of 11th standard from a pretty easy class 10th syllabus.
The very first chapter in NCERT class 11th deals with the concepts of set, their definition, and their representation. The chapter introduces the students to the Set Theory and covers the topics of Subsets, Power Sets and Universal sets. It also introduces the various types of sets which include the finite set, infinite set, empty set. The chapter also covers the concept of the Venn diagrams, which form the visual representation of union and intersection operations. The difference of sets, the complement of a set also find a place in the chapter, and their properties are also covered.
The chapter forms a base for a lot of subsequent concepts, and the students cover Ordered pair, Cartesian product of sets, the definition of relation, the range of a function, and the domain and codomain of a relation. The pictorial diagram of a relation and the number of elements in the cartesian product of sets is also covered in the chapter. The chapter also teaches about the functions being exceptional cases of relation, pictorial forms of a function, types of functions, the range, domain, and codomain of these functions. The graphs of the various functions are also covered in this topic, and students will learn to form relations between two sets.
The chapter deals in the angles, the positivity, and negativity of the angles. The chapter also covers the measuring of the angles in radians along with degrees. The conversion method from one form to another is also one of the topics of this chapter. The chapter uses a circle to define these trigonometric functions. The chapter deals with the graphs, signs, domain, and range of these trigonometric functions. The chapter goes further and covers the addition and subtraction of the trigonometric angles. The equations of sin, cos, and tan with the function value of 2x and 3x in simpler terms are also covered in the chapter.
The chapter covers the process of proving a theorem or a function for every number in its domain. It is a proving technique, and the chapter covers the principle along with the simplistic application of the method.
The chapter deals with the need for complex numbers to solve certain types of quadratic equations. The chapter covers the algebraic aspect of the complex number along with the cartesian and the polar form of the complex numbers. The fundamental operations of algebra are all taught with context to the complex numbers, and the solutions of quadratic equations with complex number systems are the topics in this chapter. The square roots of the complex numbers are also discussed in the chapter.
The chapter deals in operation when inequality is introduced in the linear equations. The representation of the inequality in a single variable on a number line and double variable on a graph along with the graphical method to find the solution of these inequalities is covered in this chapter.
The art and concept of picking out things and arranging them in a specific order are taught in this chapter. Permutation defines the arrangement of objects in a definitive order, and the combination does not care for arrangement in order. The chapter deals in factorial, concepts of counting, derivation of formulae, alphabetical arrangement, and other simple applications.
The chapter covers the Binomial theorem for the positive integers. The chapter discusses the use of this theorem to solve the complex calculations that would have taken much time to solve via repetitive multiplication. The chapter also covers the history, development, proof of the binomial theorem. Furthermore, Pascal’s triangle, along with the general and middle term of the binomial theorem along with the simple applications of this theorem, is also covered by the chapter.
The ordered list of numbers is termed as a sequence, and the chapter deals with the definition and operation of these sequences and series. The Arithmetic Progression (A.P.), Geometric Progression (G.P.) along with their mean values, are covered by the chapter. The chapter also teaches the students to find the nth of the series and the sum of the series. There is also a section of a combination of arithmetic and geometric progression.
The chapter helps the students revisit the concepts of coordinate geometry. The origin shifting, the slope of the line, various forms of equations of a line which include the twopoint form, slopeintercept form, one point, and slope form, intercept form, and finally the parallel to axis form are covered in this chapter. The chapter also deals in the intersection of these lines and the family of lines along with the general equation of the line.
The chapter serves as the continuation of the coordinate concepts but builds upon the intricacies. The conic section is formed by the intersection of the surface of the cone with a plane. The topics that are covered in the section are circle, parabola, hyperbola, and ellipse along with a straight line, pair of intersecting lines, and a point as a degenerate scenario of the conic section. The general equations, along with the particular case equation of each of the conic section is taught in the chapter.
The chapter deals in the general space by introducing a third coordinate and a Zaxis. It deals in the placing of the earlier covered basic concepts in a 3D space. The chapter contains planes, lines, points, the distance between these points, planes. The chapter also covers the general equation of these lines, planes, and application of the distance and section formula.
The chapter deals in the existence of the limits and derivative. This chapter serves as an introduction of calculus which will form a significant aspect of mathematics in time to come for the student. The chapter deals with proving the derivative or limit exists along with finding the value of these limits and derivatives.
The chapter forms the basis of computers and modern physics. The chapter covers the fundamental deductive reasoning with operators such as “if”, “only if”, “implies”, “and/or” etc. The chapter teaches to check the validity of statements.
The chapter deals with the handling of data and usage of the given data for a specific task. The chapter covers concepts of dispersion, methods of calculation for grouped and ungrouped data. Terms such as mean, median, variance, mean deviation, standard deviation are introduced in the chapter and study is done on the grouped/ungrouped data given.
The chapter deals with finding out the chance of some specific event happening during a general event. The concepts of favourable events, sample space, occurrences, exclusive, exhaustive events are explained to the students. The chapter also revisits the concept of “and” and “or” introduced in the chapter of Permutation and Combination.
The Aakash NCERT Solutions for Mathematics have the following highlights:
Q. Why are NCERT solutions for class 11th maths essential?
A. The sudden change in the level of mathematics from class 10th to class 11th is huge and cannot be bridged by just the tutorial sessions. The basic concepts nodoubt need to be taught but armed just with the basic concepts, if a student embarks upon solving the questions himself/herself, then much time would be wasted, and there is a lot to cover in other subjects as well. Aakash NCERT solutions for class 11th, on the other hand, not only consolidate the concept by applying those in the questions but also save time.
Q. Where to find and download NCERT solutions for class 11th maths?
A. Aakash provides all the solutions of NCERT for class 11th in mathematics, and it is available on the Aakash website. The solutions are in order and chapterwise. They are consolidated in just one PDF file.
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