Most Possible Areas or Units of Selection of Questions in II p

8/3/2019 Most Possible Areas or Units of Selection of Questions in II p

1/68

MOSTPOSSIBLE

AREAS ORUNITS OF

SELECTION OFQUESTIONS IN

II P.U.ANNUALEXAMINATION


2/68

- OF

KARNATAKA,

INDIAALGEBRAELEME

NTS OF NUMBER

THEORY:

a)


3/68

Properties of

Divisibility and

congruences

b)Use of property of

congruence to findtheunitdigit and

remainder


4/68

. Solving linearcongruence,c)

finding thenumber and

sum ofdivisorsd)Findi

ng GCD of two


5/68

numbers andrepresentation

of two as alinear

combination ofl and m and

showing l


6/68

andm are notunique.(

ESSAY TYPE)

STRESS

MORE: on


7/68

finding GCD ,last

digit,remainder, number and

sum of divisorsof number.

MATRICES ANDDETERMINANTS


8/68

:

a). Solving thesimultaneous

linear equationsbyCramers

Rule b).


9/68

Solving the

simultaneous

equations by

matrixmethod.c). Finding the

Inverse, adjointof a matrix.d).

Finding


10/68

characteristicequation,

roots,e).Finding the inverse

and verificationusing Caley

Hamilton

Theorem..


11/68

f).Properties ofDeterminants and

problemsusingproperties

(definite possiblequestion)


12/68

STRESSMORE : On

solvingequations

bymatrixmethod,

cramers rule,


13/68

finding inverseanddeterminant

s usingproperties.

GROUPS:a).


14/68

Proving a set

(given) forms an

Abelian group

.b).

Questionsregarding

Properties of


15/68

groups,Theorems&problems

on subgroups,

STRESSMORE: On

proving a given


16/68

set formsagroup under

given binaryoperation.

VECTORS:a). Questions

on vector


17/68

product, Crossproduct,

Vector tripleproduct, Scalar

triple product.APPLICATONOF

VECTORS


18/68

like sine rule,projection rule,

cosinerule ,proofs of

compoundangle formulae,

angle in


19/68

asemicircle isright angle,

diagonals ofparallelogram b

isect eachother, medians


20/68

of a traingle areconcureent.

STRESS

MORE: Onapplication of

vectors, proble


21/68

ms on vectortriple product,

cross product.Vector triple

product


22/68

TIPS:CONCENTR

ATE MORE ON

CHAPTERS

:MATRICESAND

DETERMINA

NTS.ANDVECTOR


23/68


24/68

Any derivation on

circles.concentrate

more on Derivation

of equationof tangent,

condition oforthoganality,

length of atangent,

radical axis is


25/68

perpendicular to line

of centers, condition

for the line y=mx+c

to be tangenttocircle and point of

contact.b). Frequently

questions on


26/68

circles isasking on

findingthe equationof circle by finding

g, f&c

; and alsoonorthogonal

circles.


27/68

STRESS

MORE: Onfinding

constants g, fand cusing

given


28/68

conditions andproblems on

orthogonalcircles

CONIC SECTION:a).


29/68

Any(13) derivation

on conic section.

(Definite

)Concentrate more

on Derivation ofParabola,ellipse,

Hyperbola,condition for the


30/68

line y=mx+c tobe

tangent to parabola,

ellipse, Hyperbola,

Equationof tangentand normal to

parabola,ellipse,Hyperbola at

(x1,

y


31/68

1

).b). Finding the

properties ofstandard forms

andother formsof conics i.e.

finding


32/68

vertex,focus,directrix,etcc).

Finding theconics by using

the propertiesof conics.(Dete


33/68

rmination ofconics)

STRESS

MORE : OnDerivation

(total 13)


34/68

andFinding theproperties of

conics from thegivenequations

ofconicCONCEN

TRATE MORE


35/68

ON: CONICSECTION

TRIGNOMETRY:INVERSE

TRIGNOMETRIC

FUNCTIONS:Problems using the

concept of tan-


36/68

x

tan-1

y, sin-1

x

sin


37/68

-1

y etcFinding thevalue of x or solve

for x .STRESS

MORE: Onproblems using

properties


38/68

of Inversefuntions.

GENERALSOLUTION OF

TRIG.

EQUATIONS:General solution of

problems of a cosx+ b sinx =c ,and


39/68

solving trig

equations using

transformationform

ulae(product intosum or sum into

product),COMPLEX NUMBERS:

a).


40/68

Finding the cube

roots and fourth

roots of

complexnumbersand representing

them inarganddiagram.or

finding the


41/68

continued product

of roots .

b). Statement

and proving

Demoivrestheorem

and problemsusing


42/68

demoivrestheorem.CONC

ENTRATEMORE ON:

COMPLEXNUMBERS.

CALCULUS:DIFFERENTIATION:


43/68

a).Finding thederivatives of

trigonometricfunctions,exponenti

al functions,logarithmic

functions,Inversetrigonometri


44/68

c functions,

Derivatives of

sinax,

cosax,tanax.secax,cosecax, cotax,

sec2x.cos2x, etc.Sin2

x,cos2


45/68

x, log ax, etc by first

principles

method.(Definite)

b). Problemson second

order

Differentiation.c).


46/68

sub tangent,

subnormal, length

of the

subtangentandsubnormal,

Question onMaxima and

Minima or


47/68

Derivative asarate measure ,

Angle ofIntersection of

two curves.


48/68

STRESSMORE : On

finding thederivative

fromfirstprinciples, and

using Implicit,


49/68

Parametricdifferentiation.

Second orderderivatives,

Derivative asarate measure,


50/68

maxima andminima

INTEGRATION:c). One

question onProblems on


51/68

Integrals oftheform

(Particular forms)1

a

bcosx


52/68

,

1

a

bsinx,

1


53/68

acosx

bsinx

c

1a


54/68

cos2

x

bcos2x


55/68

c

1

a

2


56/68

x2

1

x2

a


57/68

2

1x

x2

a


58/68

2

1a2

x2

1


59/68

x2

a2

a2


60/68

x2

,

x

2


61/68

a2

,

px

qax2


62/68

bx

c,

px

q


63/68

ax2

bx


64/68

c,

pcosx

qsinxacosx

bsinx


65/68

, ex

[f(x)+f'(x)]

Integrationbysubstitution

and by parts,Integration by


66/68

partialfractions, b).

Evaluating thedefinite Integral

using

theproperties.c).Finding the area

bounded by the twocurves orcurve and


67/68

line, finding the area

of the circle, ellipse

byintegration

methodc).

Solving theDifferential

equation by themethod


68/68

of separation of

variables and

equation reducible

tovariable seperableform

STRESS MORE:

units a) and b

Documents

Most Possible Areas or Units of Selection of Questions in II p