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
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 probabil
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
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
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 Introducti
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 Introd
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 s
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
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
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
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 al
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 o
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 Chap
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
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 transiti