NCERT Solutions for Class 12 Maths: We can’t live without mathematics in our everyday life; hence learning mathematics is of great importance. Mathematics also is of importance in any career. It’s a core subject hence you need to pass. NCERT Solutions have offered a step-by-step way of solving questions giving the students an easier time. Furthermore, after every chapter, the student will get practice questions.
NCERT Solutions for Class 12 Maths chapter wise
Chapter 1: Relations & Functions
Here the student will learn relation types, functions types, functions composition & invertible function, and binary operations. Other topics include reflexive, transitive, symmetric, and equivalence plus one-to-one & onto functions. The student will also find miscellaneous examples. For further practice, the student will find an exercise solution.
Chapter 2: Inverse Trigonometric of a Function
Here the learner will learn basic concepts about inverse trigonometric functions, inverse trigonometric-functions properties, and graphical representations. The concepts are well explained using examples and the student will have exercises about the chapter. The two exercises will teach the students the behavior of functions, elementary properties, and their graphical representations.
Chapter 3: Matrix
Chapter three will take the student via properties of matrices which are the most significant tools of Maths. Here the students study the basic concepts of Matrices & Matrix Algebra. Moreover, the students will also study matrix notations, equality, order, & types. They’ll also study zero matrix, identity matrix, symmetric & skew-symmetric matrix. They will study the method of finding matrix transpose & operations including multiplication, addition & scalar multiplication.
This chapter has a total of 62 exercise questions which will help the student have a deeper understanding of matrix algebra and basic concepts of a matrix.
Chapter 4: Determinants
This chapter is a continuation of chapter three. This chapter explains the Matrix concept known as Determinants. Chapter 4 deals with determinants of orders of up to 3, & their inverses & cofactors. Chapter 4 also explains determinants applications, like calculating an area of triangles, set of linear-equations consistency, and adjoint of matrices.
Chapter 5: Continuity & Differentiability
Chapter 5 will help the student learn about continuity, continuous function algebra, meaning & definition of differentiability, composite functions derivatives, implicit functions derivatives, the inverse of trigonometric-functions derivatives, exponential & logarithmic functions, functions derivatives in parametric forms, logarithmic differentiation, second-order derivatives, mean-value theorem.
Chapter 6: Applications of Derivatives
In this chapter, the student will learn how to get derivatives of composite functions, implicit functions, inverse trigonometric functions, logarithmic functions, and exponential functions. The student will also learn tangents & normal curves, rate of change to some quantities, and increasing & decreasing functions.
Furthermore, the student will learn maxima & minima and simple questions which are based on these concepts. This chapter has exercises to allow the student to practice in detail the concepts.
Chapter 7: Integrals
This chapter explains the definition of indefinite integral, integration being an inverse procedure of differentiation, indefinite integral interpretation, indefinite integral properties, comparison in between differentiation & integration, integration methods like integration through substitution, integration through partial fractions, integration through parts, trigonometric identities integration, integral functions integration, definite integrals definition & meaning, definite integral as sum limit, basic calculus theorem, definite integrals evaluation by substitution, definite integrals properties.
Chapter 8: Application of Integrals
Chapter 8 deals with applications of integrations in finding the area in a simple curve, parabolas, ellipses, and lines. The student will have exercises explaining this chapter’s concepts.
Chapter 9: Differential Equations
Here the student will learn some basic concepts which are related to differential equations, general & particular solutions of differential equations, differential equations formation, and several ways to solve question-based on first-degree equations of differential & other differential equations applications in various places.
Chapter 10: Vector Algebra
In this chapter, the student will learn about vector quantities, that’s, the quantities which have both magnitude & direction. This chapter covers the way one finds position vector, basic vector algebra concepts, direction cosines, vectors types including zero vector, collinear vector, unit vector, negative of a vector, equal vector, vectors addition, vector addition properties, scalar multiplication of a vector, vector components, vector joining 2-points, section formula, a product of 2-vectors, dot or scalar product of 2 vectors, scalar product properties, vector on a line projection, vector or cross-product of 2 vectors
Chapter 11: 3D Geometry
In this chapter, the student will study the direction cosines & direction-ratios of line combining two points, equations of lines & planes at space under various conditions. Furthermore, the student will also understand the angle between 2 lines, two planes, a line & a plane, the shortest distance between 2 skew lines & the distance from a point to a plane.
Chapter 12: Linear Programming
The concepts highlighted in this chapter includes problem about linear programming, mathematical formulation of a problem, graphical way of solving linear-programming questions, and various kinds of linear programming question.
Chapter 13: Probability
Chapter 13 will help the student revise topics like conditional probability, Bayes’-theorem, & total probability theorem. Along with that, the student will also study the binomial distribution concept which will help him/her solve questions related to probability. Other topics covered here include properties of conditional probability, probability of more than 2 events multiplication rule, multiplication-theorem on probability, independent events, sample space partition, random variables & probability distributions, random variable probability distribution, random variable mean, random variable variance, binomial distribution, and Bernoulli trials.
