Class 11th is the beginning stage of one’s technical career. The students can get the assistance of the best faculty of mathematics. The faculties have years of experience in a teaching career. The NCERT solutions for class 11 maths is prepared as per the latest syllabus. The very idea of preparing this study material is to ensure that students do not miss anything.
This NCERT solution for class 11 maths is prepared some very experienced teachers. If students are stuck at any topic, they right away consult our experts. Since class 11th maths is considered to a grade of advance level, so students need to learn it accordingly. Our team has segregated NCERT solutions for class 11 maths on the basis of chapters. This solution is arranged in a systematic manner, which helps students.
The NCERT solution to each and every sum is provided in a very judicious manner. Special care has been taken on difficult topics. The team has taken efforts to break down the most typical numerical as well into simpler type. We have also provided students with more practical based questions in NCERT solutions for class 11 maths, which help them enhance their thinking horizon. All we want from students is un-deviated attention and perseverance.
Students can also find simple tips and tricks to solve critical numerical. The NCERT solutions for class 11 maths can also help students to prepare for their competitive examinations. This NCERT solutions for class 11 maths can be utilised by students to strengthen their foundation of concepts. The holistic and diversified approach adopted by us helps students to learn various topics without missing any of them.
The study material comprises of various competitive level questions as well which helps in understanding competitive examinations. The very speciality of NCERT solutions for class 11 maths provided by Physics Wallah is easy to read. The NCERT solutions for class 11 maths has been very effective for students when revising just before the examination. All the questions are chosen very selectively.
A set is a well-defined collection of distinct objects. Well-defined collection means that there exists a rule with the help of which it is possible to tell whether a given object belongs or does not belong to given collection. Generally sets are denoted by capital letters A, B, C, X, Y, Z etc.
REPRESENTATION OF A SET-Usually, sets are represented in the following ways
ROASTER FORM OR TABULAR FORM-In this form, we list all the member of the set within braces (curly brackets) and separate these by commas. For example, the set of all even numbers less than 10 and greater than 0 in the roster form is written as: A = {2,4, 6,8}
SET BUILDER FORM OR RULE FORM-In this form, we write a variable (say x) representing any member of the set followed by a property satisfied by each member of the set. A = {x| x < 5, x < N} the symbol ‘|’ stands for the words” such that”.
Function can be classified into two categories:
Each of above category comprises entire gamut of function. Thus if a function is not one-one, it has to be many-one and vice-versa.
Similarly if function is into then it cannot be onto and converse.
Based on above two categories of function, we can classify functions into four type
Literally, the word 'trigonometry' means the study of the properties of triangles. This involves the measurement of angles and lengths. An angle is defined as the amount of rotation of a revolving line with respect to a fixed line. If the rotation is in anticlockwise sense, the angle is taken to be positive, otherwise negative. Basically, we use two types of systems to measure an angle, viz., the sexagesimal system (or English system) and the circular system. In the former, a right angle is divided into 90 equal parts and each part is called one degree (1°). So, a straight angle is 180° and complete angle is 360°. Each degree is further divided into 60 equal parts and each part is called one minute (1'). Each minute again has 60 equal parts, each part being called one second (1).
Very often we come across many equations involving several powers of one variable. If the indices of all these powers are integers then the equation is called a polynomial equation. If the highest index of a polynomial equation in one variable is two, then it is a quadratic equation. A quadratic equation is a second degree polynomial in x usually equated to zero. In other ‘words, for an equation to be a quadratic, the coefficient of x2 should not be zero and the coefficients of any higher power of x should be 0.
Roots of the equation-Just as a first degree equation in x has one value of x satisfying the equation, a quadratic equation in x has two values of x that satisfy the equation. The values of x that satisfy the equation are called the ROOTS of the equation. These roots may be real or complex.
In earlier classes, we have studied equations in one variable and two variables and also solved some statement problems by translating them in the form of equations. Now a natural question arises: ‘Is it always possible to translate a statement problem in the form of an equation? For example, the height of all the students in your class is less than 160 cm. Your classroom can occupy atmost 60 tables or chairs or both. Here we get certain statements involving a sign ‘<’ (less than), ‘>’ (greater than), (less than or equal) and (greater than or equal) which are known as inequalities. In this Chapter, we will study linear inequalities in one and two variables. The study of inequalities is very useful in solving problems in the field of science, mathematics, statistics, optimisation problems, economics, psychology, etc.
In real life we are often encountered with problems of counting. Many a times the number of ways of happening of an event is so large that we can not count it on our hands. Permutation and Combinations are techniques to simplify the process of counting and are very useful when the number of ways of happening of some event are very large.
THE SUM RULE-Suppose a work A can occur in m ways and B can occur in n ways and both cannot occur simultaneously. Then A or B (at least one of them) can occur in (m + n) ways. This rule is also applicable for two or more exclusive events. THE PRODUCT RULE-Suppose there are two works A and B. Let A can occur in m ways and B in n ways. Suppose that the ways for A and B are not related in the sense that B occur in n ways regardless the outcome of A. Then both A and B can occur in mn ways. For example, let there be two questions A and B which can be solved by two methods and 3 methods respectively. Then both A and B can occur in 2 3 = 6 ways. The above rules are very useful and many problems of this chapter can be solved by using these fundamental concepts without using any formula.
Binomial Theorem was introduced by Newton for the purpose of calculating or approximating expansion of two terms raised to any power.
A sequence is a set of terms in a definite order. The sequence which obey a definite rule and its general term is always expressible in terms ofn, is called progression.
Important Formulas
The idea of limits is one of the basic concepts that distinguishes calculus from the remaining branches of mathematics. Limits are used to check the behaviour of functions close to certain points. This use paves the way to define continuity and differentiability of functions which are extremely important concepts to analyse functions. We also introduce derivatives in this lesson and discuss their geometrical significance. Problems involving the concepts of limit, continuity and differentiability simultaneously are very common, which are explained elaborately in this lesson. Limit and continuity of a function, limit and continuity of the sum, difference, product and quotient of two functions, L’Hospital rule of evaluation of limits of functions, continuity of composite functions, intermediate value property of continuous functions.
One of the most important objectives of statistical analysis is to get one single value that describes the characteristics of entire mass of unwieldy data Such a value is called central value or the average. It is a single value, which represents a group of values.
Classification of Data:
TYPES OF AVERAGES
(a)Mean
(b)Median
(c)Mode
RANDOM EXPERIMENT-An experiment, whose all possible outcomes are known in advance but the outcome of any specific performance can not predicted before the completion of the experiment, is known as random experiment.
Sample space and Sample Point-A set of all possible outcomes associated with same random experiment is called sample space and is usually denoted by ‘S’. Each element of a sample space is called a sample point.
The team has totally removed the un-necessary studying part from the study material. We wish students have sharp question-solving skills for examination. Students referring NCERT solutions for class 11 maths have an extra cutting edge over the rest students. These NCERT solutions for class 11 maths are helpful for a student looking to score maximum marks. The complete study material has been prepared after extensive research of previous year question papers.
Students don’t need to study all the textbook, rather they can refer NCERT solutions for class 11 maths. We have been always the topmost preference of toppers. We provide students with a special strategy to score maximum marks and minimise mistakes.
The complete study material is available for free. Students can access these NCERT solutions for class 11 maths with a single click. Students looking for expert guidance can contact our team. This NCERT solutions for class 11 maths can be accessed on multiple devices.
NCERT solutions for class 11 Maths is prepared by expert of Physics Wallah to gives you errorless and accurate solutions of all questions given in the NCERT.
Q-1. How to score full marks in class 11 Maths with the help of NCERT solutions of class 11 Maths ?
Ans- To score good marks in class 1 Maths you need to have good foundation of concepts and its application in the numerical. Conceptual celerity can be develop by reading and understanding the theory part given in the chapter of NCERT and application can be understood through solved examples and questions given in Exercise.
Q-2. What are the most important chapters of class 11 Maths ?
Ans- In unit test and final exam of class 11 maths all most all chapters are covered and questions are asked form all chapters. Few topics are needed to be solved more frequently like Trigonometric Functions, Modulus and Conjugate of a Complex Number, Binomial Theorem, Permutations and Combinations, Linear Inequalities.
Q-3. What are the tips and trick to do final revision for class 11 Maths ?
Ans- class 11 Maths consist of 16 chapters so make sure you have prepared a detail notes of all 16 chapters which consist of all important points and formulas used. These notes are to be prepared form NCERT text book and having all bullet points which are needed to solve the questions. Notes prepared by you is highly helpful for the final revision of class 11 Maths. Do solve few sample papers of class 11 Maths which help you to find out the mistake you do in the exam and work on these mistakes.
Q-4. Should we use some additional book apart form NCERT text book of class 11 Maths ?
Ans- If you are preparing for class 11 Maths than no need to follow any reference book NCERT class 11 Maths is sufficient for class 11 Maths. But if you are preparing for competitive entrance exam than you must follow few additional book of Maths and solve MCQ based questions for class 11 Maths.
Q-5. Solving Exercise question by the help of NCERT solutions for class 11 Maths is good practice ?
Ans- No, NCERT solutions for class 11 maths is only for reference one shouldn’t use it as helping guide. Use these solutions only for the numerical which you can’t solve despite of several attempts.
