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11.1 Introduction In Class XI, while studying Analytical Geometry in two dimensions, and the introduction to three dimensional geometry, we confined to the Cartesian methods only. In the previous chapter of this book, we have studied some basic concepts of vectors. We…

NCERT Class 12 Maths Relations and Functions

1.1 Introduction Recall that the notion of relations and functions, domain, co-domain and range have been introduced in Class XI along with different types of specific real valued functions and their graphs. The concept of the term ‘relation’ in …

NCERT Class 12 Maths Probability

13.1 Introduction In earlier Classes, we have studied the probability as a measure of uncertainty of events in a random experiment. We discussed the axiomatic approach formulated by Russian Mathematician, A.N. Kolmogorov (1903-1987) and treated…

NCERT Class 12 Maths Matrices

3.1 Introduction The knowledge of matrices is necessary in various branches of mathematics. Matrices are one of the most powerful tools in mathematics. This mathematical tool simplifies our work to a great extent when compared with other straight forward…

NCERT Class 12 Maths Linear Programming

12.1 Introduction In earlier classes, we have discussed systems of linear equations and their applications in day to day problems. In Class XI, we have studied linear inequalities and systems of linear inequalities in two variables and their solutions by graphical…

NCERT Class 12 Maths Inverse Trigonometric Functions

2.1 Introduction In Chapter 1, we have studied that the inverse of a function f, denoted by f –1, exists if f is one-one and onto. There are many functions which are not one-one, onto or both and hence we can not talk of their inverses. In Class XI, we…

NCERT Class 12 Maths Integrals

7.1 Introduction Differential Calculus is centred on the concept of the derivative. The original motivation for the derivative was the problem of defining tangent lines to the graphs of functions and calculating the slope of such lines. Integral Calculus is motivated…

NCERT Class 12 Maths Differential Equations

9.1 Introduction In Class XI and in Chapter 5 of the present book, we discussed how to differentiate a given function f with respect to an independent variable, i.e., how to find f (x) for a given function f at each x in its domain of definition. Further, in the…

NCERT Class 12 Maths Determinants

and is called the determinant of A or det A. Determinants have wide applications in Engineering, Science, Economics, Social Science, etc. In this chapter, we shall study determinants up to order three only with real entries. Also, we will study various properties of…

NCERT Class 12 Maths Continuity and Differentiability

5.1 Introduction This chapter is essentially a continuation of our study of differentiation of functions in Class XI. We had learnt to differentiate certain functions like polynomial functions and trigonometric functions. In this chapter, we introduce…