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Paper-III Mathematics

1. Algebra:Concept of a set, Union and Intersection of sets, Complement of a set, Null set, Universal

set and Power set, Venn diagrams and simple applications. Cartesian product of two sets,

relation and mapping examples, Binar operation on a set examples.!epresentation of real num"ers on a line Complex num"ers# $odulus, %rgument,

%lge"raic operations on complex num"ers Cu"e roots of unit. Binar sstem of

num"ers, Conversion of a decimal num"er to a "inar num"er and vice versa. %rit&metic,'eometric and (armonic Progressions. )ummation of series involving %.P., '.P., and

(.P... *uadratic e+uations wit& real coefficients *uadratic expressions# extreme values.

Permutation and com"ination, Binomial t&eorem and its applications. $atrices and

-eterminants# pes of matrices, e+ualit, matrix addition and scalar multiplication properties. $atrix multiplication noncommutative and distri"utive propert over

addition. ranspose of a matrix, -eterminant of a matrix. $inors and Cofactors.

Properties of determinants. )ingular and nonsingular matrices. %d/oin and Inverse of a

s+uarematrix, )olution of a sstem of linear e+uations in two and t&ree varia"leselimination met&od, Cramers rule and $atrix inversion met&od 0$atrices wit& m rows

and n columns w&ere m, n to 2 are to "e considered3. Idea of a 'roup, 4rder of a'roup, %"elian group. Identiti and inverse elements Illustration " simple examples.

5. Trigonometry:%ddition and su"traction formulae, multiple and su"multiple angles. Product and

factoring formulae. Inverse trigonometric functions -omains, !anges and 'rap&s.

-e$oivre6s t&eorem, expansion of )in n7 and Cos n7 in a series of multiples of )ines and

Cosines. )olution of simple trigonometric e+uations. %pplications# (eig&ts and -istance.

2. Analytic Geometry (two dimensions3# !ectangular Cartesian. Coordinate sstem,distance "etween two points, e+uation of a straig&t line in various forms, angle "etweentwo lines, and distance of a point from a line. ransformation of axes. Pair of straig&t

lines, general e+uation of second degree in x and condition to represent a pair of

straig&t lines, point of intersection, angle "etween two lines. 8+uation of a circle instandard and in general form, e+uations of tangent and normal at a point, ort&ogonall of

two circles. )tandard e+uations of para"ola, ellipse and &per"ola parametric

e+uations, e+uations of tangent and normal at a point in "ot& Cartesian and parametric

forms.

9. Dierential !alc"l"s# Concept of a real valued function domain, range and grap&.

Composite functions one to one, onto and inverse functions, alge"ra of real functionsexamples of polnomial, rational, trigonometric, exponential and logarit&mic functions.

Notion of limit, )tandard limits examples. Continuit of functions examples, alge"raic

operations on continuous functions. -erivative of a function at a point, geometrical andp&sical interpretation of a derivative applications. -erivative of sum, product and

+uotient of functions, derivative of a function wit& respect to anot&er function, derivative

of a composite function, c&ain rule. )econd order derivatives. !ole:s t&eorem 0statement

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onl3, increasing and decreasing functions. %pplication of derivatives in pro"lems of

maxima, minima, greatest and least values of a function.

;. Integral !alc"l"s and Dierential e#"ations# Integral Calculus# Integration as

inverse of differential, integration " su"stitution and " parts, standard integrals

involving alge"raic expression, trigonometric, exponential and &per"olic functions.8valuation of definite integralsdetermination of areas of plane regions "ounded " curves

applications. -ifferential e+uations # -efinition of order and degree of a differential

e+uation, formation of a differential e+uation " examples. 'eneral and particularsolution of a differential e+uation, solution of first order and first degree differential

e+uation of various tpes examples. )olution of second order &omogeneous differential

e+uation wit& constant coefficient.

simple pro"lems. %rea of a triangle, parallelogram and

pro"lems of plane geometr and trigonometr using vector met&ods. ?or@ done " a

force and moment of a force.

A. %tatistics and probability# )tatistics# re+uenc distri"ution, cumulative fre+uenc

distri"ution examples. 'rap&ical representation (istogram, fre+uenc polgon

examples. $easure of central tendenc mean, median and mode. Variance and standarddeviation determination and comparison. Correlation and regression. Pro"a"ilit#

!andom experiment, outcomes and associated sample space, events, mutuall exclusive

and ex&austive events, impossi"le and certain events. Union and Intersection of events.Complementar, elementar and composite events. -efinition of pro"a"ilit# classical

and statistical examples. 8lementar t&eorems on pro"a"ilit simple pro"lems

conditionals pro"a"ilit, Baes6 t&eorem simple pro"lems. !andom varia"le as functionon a sample space. Binomial distri"ution, examples of random experiments giving rise to

Binomial distri"ution. Personalit est 8ac& candidate will "e interviewed " a Board

w&o will &ave "efore t&em a record of &is career "ot& academic and extramural. &e

will "e as@ed +uestions on matters of general interest. )pecial attention will "e paid toassessing t&eir potential +ualities of leaders&ip, initiative and intellectual curiosit, tact

and ot&er social +ualities, mental and p&sical energ, power of practical application and

integrit of c&aracter.