424
M ATHEMATICS
Chapter
10
VECTOR ALGEBRA
In most sciences one generation tears down what another has built and what
one has established another undoes. In Mathematics alone each generation
builds a new story to the old structure. HERMAN HANKEL
10.1 Intr

PROBABILITY
Chapter
531
13
PROBABILITY
The theory of probabilities is simply the Science of logic
quantitatively treated. C.S. PEIRCE
13.1 Introduction
In earlier Classes, we have studied the probability as a
measure of uncertainty of events in a random e

INTEGRALS
Chapter
287
7
INTEGRALS
Just as a mountaineer climbs a mountain because it is there, so
a good mathematics student studies new material because
it is there. JAMES B. BRISTOL
7.1 Introduction
Differential Calculus is centred on the concept of the

D IFFERENTIAL EQUATIONS
Chapter
379
9
DIFFERENTIAL EQUATIONS
He who seeks for methods without having a definite problem in mind
seeks for the most part in vain. D. HILBERT
9.1 Introduction
In Class XI and in Chapter 5 of the present book, we
discussed how

5 04
MATHEMATICS
Chapter
12
LINEAR PROGRAMMING
The mathematical experience of the student is incomplete if he never had
the opportunity to solve a problem invented by himself. G. POLYA
12.1 Introduction
In earlier classes, we have discussed systems of lin

APPLICATION OF INTEGRALS
Chapter
359
8
APPLICATION OF INTEGRALS
One should study Mathematics because it is only through Mathematics that
nature can be conceived in harmonious form. BIRKHOFF
8.1 Introduction
In geometry, we have learnt formulae to calculat

THREE DIMENSIONAL GEOMETRY
Chapter
463
11
THREE DIMENSIONAL GEOMETRY
L The moving power of mathematical invention is not
reasoning but imagination. A. DEMORGAN L
11.1 Introduction
In Class XI, while studying Analytical Geometry in two
dimensions, and the

Chapter
1
RELATIONS AND FUNCTIONS
There is no permanent place in the world for ugly mathematics . . It may
be very hard to define mathematical beauty but that is just as true of
beauty of any kind, we may not know quite what we mean by a
beautiful poem, b

56
MATHEMATICS
Chapter
3
MATRICES
The essence of Mathematics lies in its freedom. CANTOR
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 mathemati

Chapter
2
INVERSE TRIGONOMETRIC
FUNCTIONS
Mathematics, in general, is fundamentally the science of
self-evident things. FELIX KLEIN
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

Chapter
4
DETERMINANTS
All Mathematical truths are relative and conditional. C.P. STEINMETZ
4.1 Introduction
In the previous chapter, we have studied about matrices
and algebra of matrices. We have also learnt that a system
of algebraic equations can be e

Chapter
5
CONTINUITY AND
DIFFERENTIABILITY
The whole of science is nothing more than a refinement
of everyday thinking. ALBERT EINSTEIN
5.1 Introduction
This chapter is essentially a continuation of our study of
differentiation of functions in Class XI. W

194
M ATHEMATICS
Chapter
6
APPLICATION OF
DERIVATIVES
With the Calculus as a key, Mathematics can be successfully applied
to the explanation of the course of Nature. WHITEHEAD
6.1 Introduction
In Chapter 5, we have learnt how to find derivative of composi

2 56
MATHEMATICS
Appendix
2
MATHEMATICAL MODELLING
A.2.1 Introduction
In class XI, we have learnt about mathematical modelling as an attempt to study some
part (or form) of some real-life problems in mathematical terms, i.e., the conversion of
a physical

268
M ATHEMATICS
ANSWERS
EXERCISE 1.1
1. (i)
(ii)
(iii)
(iv)
(v)
3.
5.
9.
13.
15.
Neither reflexive nor symmetric nor transitive.
Neither reflexive nor symmetric nor transitive.
Reflexive and transitive but not symmetric.
Reflexive, symmetric and transiti