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;;amrhg fhk& u.ska fokq ,ef'

P ys O%ejl LKavdxl o" ldiSh

LKavdxl hehso .;ag

f,i ,efnk nj myod fokak'

Ydjg tall ffoYslh

nj w: olajkak'

O

ksmqK;dugu


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3' jD; a;hl p,kh jk

wxY =jl m %f.h iy

;ajrKh fidhhs'

nj o" nj o , l g

,n nj o fmkajkak'

P jD;a;hl p,kh jk w;r

OP = a( ksh;hls)

tg

nj myod fokak'

P wxY+f m%f.h = iy

;ajrKh hkm%;sM,

jrKh lrkak'

m%f.h ;ajrKh

m%f.h(

iamYlh Tiafia l%shd lrk nj o

;ajrKh(

1. flakah foig ixrplh nj o

2. iamYlfha Ydjg ixrplhnj o myod fokak'

ksmqK;dugu


O

O O

QKhkaf.a

c ftlHh .kq ,nk nj meye,slrkak'

wkql, Nd;fhkamy; i`oykam%;sM, ,nd

.kak'

1' flakafha fldaKhla wdmd;kh

lrk wrh jQ taldldr jD;a; pdmhl

.=re;aj flakah iu;sl wlaIh u;"

flakafha isg rlskamsysgk

nj fmkajkak'

2' flakafha fld aKhla wdmd;kh

lrk wrh jQtaldldr jD;a; LKavhl

.=re;aj flakah iu;sl wlaIh u;"

flakafha isg rlska msysgk

nj fmkajkak'

3' wrh jQ>k wO f.da,hl .=re;aj

flakah iu;sl wlaIh u; flakafhaa

isg rlskamsysgk nj fmkajkak'

06

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2' mN%uKfhka cks; jk

jia;=jl .=re;aj flakah

fidhhs'

ixhqla; >k jia;=jl" >k

jia;=jlska b;s jQ fldgil

.=re;aj flakah fidhhs'

4' wrh jQ l=yr wO f.da,hl .=re;aj

flakah" wdOdrlfha" flakafha isg

iu;sl wlaIh u; rlskamsysgk

nj fmkajkak'

5' Wi h jQ taldldr >k iDcq jD;a;

fla;=jl .=re;aj flakah" wdOdrlhaisg

rlska iu;sl wlaIh u; msysgk

nj fmkajkak'

6' Wi h jQtaldldr iDcq l=yr fla;=jl

.=re;aj flakah wdOdrlfha isg

rlska iu;sl wlaIh u; msysgk nj

fmkajkak'

jl%hl fldgila h wlaIhla jgd

mN%uKh fuka iEfok >k jia;=jl

.=re;aj flakafha msysu idlPd lrkak'

ksoiqk( jl%h wlaIh jgdmN%uKh fuka iEfok

iy w;r jQ >k jia;=f

.=re;aj flakah fidhkak'

ksoiqka u.ska meye,s lr O .eg

iùg isiqkafhduq lrkak'

jia;=jla .=re;aj flakah yd nr okakd

fldgia follskafyda Bg je .KklskaiE we;s g" ixhqla; jia;=f nr ta ta

fldgiaj, nfrysim%hqla;fhka ,efnk

nj;atys.=re;aj flakah fiu iòyd >QK

uQ,Ou Nd; lrk wdldrh;a meye,s

lrkak'

ixhqla; jia;+kaf.a .eg idlPd lrkak'

tf,iu jia;=jl fldgila bj;a l< g

b;s jQ fldgil .=re;aj flakah ,nd .;

yels nj o ksoiqka u.ska fmkajd fokak'.eg iù iòyd isiqka fhduqlrkak'

04

ksmqK;dugu bf.kq M,

Ih lreKq lrf.k hdu iòyd w;aje,la ld,fo.Kk

2'13

2'14

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iu;=,s; jia;+kaf.a ia:dhs;dj

meyeos,slrhs'

1' t,a,d ; sfnk jia;=jl ia:dhs;dj

idlPd lrkak'

jia;=j u; n, folla muKla l%shdlrk ksid tu n, fol iudk m%;sreoaO

j l%shd l< hq;= nj fmkajd fokak'

tk" T = W iy AG isria nj

fmkajkak'

2. wdk; ;,hla u; ksYap, j we;s

jia;=jl ia:dhs;dj idlPd lrkak'

jia;=j u; my; iòykan, l%shd lrk nj

myokak'

(i) jia;=f nr

(ii) A ydB ,laIHj, l%shd lrk

wNs,n m%;sl%shd jk RAiy RB.(iii) A ydB ys >IK n,

iu;=,s;;dj iòyd .=re;aj flakah isriaj

A, B ,laIH w;r msysh hq;=nj fmkajd

fokak'

.=re;aj flakah Tiafia G isria j AB g

msg;skamsysgkafkak tu.skaN%uKhlawe;s

jk nj; a tg ji a; =j fmr, Sfuka

iu;=,s;;dj fòk nj;a idlPd lrkak'

ksoiqka u.ska meyeos,s lr tjeks .eg,qiùg isiqka fhduq lrkak'

04

G

T

W

A.

FA

A

B

G

W

FB

RA

RB

>

>

ksmqK;dugu


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1' iiNd mlaIK ia;r

lrhs'

2' k she wjldYh w:

olajhs'

3' isoahlaw:l:kh lrhs'

4' isoa wjldYh meye, s

lrhs'

5' ir, ^iq.u& i so a iy

ixhqla; iso a meye,s

lrhs'

iNd;df fm!rdKsl w:oelau yd tysiSud ls m%ldY

lrhs'

iNd;dj

iiNd mlaIKhlahkql=ulaoehsidlPd

lrkak'

h mlaIKhl ,eh yelsish u m%;sM,

we;=

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ksmqK;dugu


4'3

2' iNd;df iajisoauh

w: oelau m%ldY lrhs'

3' iajiso auh w: oelau

Nd;fhka iNd;d

m%fhhkaidOkh lr tu

m%fhhka Nd; lr

.eg iòhs'

1' wiNdjH iNd;djw: olajhs'

(ii) kshe wjldYh wm; jk g by;

iQ;%h j,x.= fkdf'

iiNd mlaIKhl kshe wjldYhg

wkqrEm isoa wjldYh hehs .ksuq'

my; iòyka wjYH;d ;Dm a; lrk

Y%s;hlg iNd;d Y%s;hla

hehs lshkq,ef'

(i) kE u iòyd

(ii)(iii) A

1, A

2wfkHdkH jYfhka nysIaldr

isoakafolla k"

my; iòyka m%fhhka idOkh lrkak'

(i)

(ii)

(iii)

(iv)

(v) k

ksoiqka bm;a lr .eg iùg isiqka

fhduq lrkak'

A yd B hkqiiNd mlaIKhl kshe

wjldYh yd ix>; isoa follahehs.ksuq'

A isoah is we;ehs we;s g B isoah

is f wiNdjH iNd;dj P(BA)

u.ska wxlkh lrkq ,nk w;r"

f,i w: olajkak'

fuysP(A) > 0 f'

ksoiqka u.ska meye,s lrkak'

.eg iùg isiqkafhduq lrkak'

06

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ksmqK;dugu


4'4

4'5

2' wiNjH iNd;d

m%fhhka idOkh lrhs'

3' .=Kk kS;sh iòykalrhs'

iajdh;a; isoaka w: olajhs'

1' kshe wjldYhl

Nd.kh w: olajhs'

2' uq iNd;d m%fhh

m%ldY lrhs'

my; oelafjk m%fhhkaidOkh lrkak'

(i) P(A) > 0 k

(ii) iy P(A) > 0 k

(iii) k

m%fhhka Nd;fhka.eg iùg isiqka

fhduq lrkak'

isoakafolla iòyd .=Kk kS;sh

f,i m%ldY lrkak'

isoa ;=klaiòyd .=Kk kS;sh m%ldY lrkak'

A1iy A

2hkq wjldYfhaisoakafolla

hehs o A1iy A

2 iajdh;a; hehs o .ksuq'

f,i w:

olajkak'

iajdh;a; isoaka ;=kla iòyd fuh meye,s

lrkak'

B1, B

2,...B

hkq iiNd mlaIKhl

kshe wjldYh yd ix>; isoa wjldYfha

jQisoaka hehs.ksuq'

(i)

(ii) k

{B1, B

2,...B

} hkq ys Nd.khla

hehs lshkq ,nk nj m%ldY lrkak'

{B1, B

2,...B

} hkq kshe wjldYh yd

ix>; isoa wjldYfha jQ Nd.khla

hehs .ksuq'

06

06

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ksmqK;dugu


3' fiaf.am%fhh m%ldY lr

.eg i`u i`oyd Nd;

lrhs'

A hkq isoa wjldYfhajQ kE u isoahla

k tg" nj

fmkajkak'

fuys f'


fhduq lrkak'

{B1, B

2,...B

} hkq isoa wjldYfha jQ

Nd.khla hehs .kak' A hkq isoa

wjldYfha jQkEu isoahla k tg"

nj fmkajkak'


fhduq lrkak'

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;=kajk jdrh;=kajk jdrh;=kajk jdrh;=kajk jdrh;=kajk jdrh

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ixhqla; .Ks;hixhqla; .Ks;hixhqla; .Ks;hixhqla; .Ks;hixhqla; .Ks;h I (I (I (I (I (;=kajk jdrh;=kajk jdrh;=kajk jdrh;=kajk jdrh;=kajk jdrh)))))

1' meial,a;%sfldaKh meyeos,slrhs'

2' oamo m%idrKh m%ldY lridOkh lrhs'

3' o amo ix.=Klhka ydm%idrKfha ix.=Klhkaw;r fjki meye,slrhs'

10.1oamo m%idrKh

11 2 1

1 3 3 11 4 6 4 1

wka;j, ixLHd yereKq g wfkla kEuixLHdjlaby; fma

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4' oamo m%idrKfha ,laIKmeye,s lrhs'

oamo m%idrKfhaje;u moh;aje;u ix.=Klh;a fidhhs'

1' w;d;a;al tallh ydw;d; a; a l ixLH djy`kd .kshs'

2' ixlSK ixLHd w: olajhs'

3' ixlSK ixLHd folliudk;dj iòyd wjYH;d

m%ldY lrhs'

4' ixl SK ixLHdjlm%;snoaOh w: olajhs'

ixlSK ixLHd iòyd h luw: olajhs'

.

m%idrKh Nd;fhka oamo m%idrKfha,laIK ,nd .kak'

tu ,laIK Nd;fhka.eg iùg isiqkafhduqlrkak'

oamo m%idrKfha je;u moh;a je;uix.=Klh;afidhk whqre idlPd lrkak'

ksoiqka u.ska meye,s lr .eg iùgisiqkafhduq lrkak'

ixlSK ixLHd

jk m i w;d;a;al tallh

y`kajkak'

iy jk ai wdldrfha ixLHdyqfolaw;a;d;al ixLHd f,i y`kajk nj

m%ldY lrkak' , idlPd lrkak'

iy g"

ixlSK ixLHdjlaf,i y`kajk nj m%ldYlrkak'

a, ixlSK ixLHdf ;d;a;al fldgi

hehs lshkq ,nk w;r th u.ska

wxlkh lrk nj;a b, ixlSK ixLHdfw;d;a;al fldgi hehs lshkq ,nk w;r

th u.skawxlkh lrk nj;am%ldY

lrkak'

iy f,i .kak'

iy nj m%ldY

lrkak'

k z ixlSK ixLHdfm%;snoaOh u.ska wxlkh lrk w;r th

f,i w: olajk nj m%ldY

lrkak'

, iy f,i.kak'

06

02

02

10.2

14.1

14.2

ksmqK;dugu


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14.3

tg"

(i)

(ii)

(iii)

(iv)

(v)

ixlSK ixLHd l=,lh by; lu hgf;aixjD; nj m%ldY lrkak'

iy

;d;a;al ixLHd nj fmkajkak'.eg i`ug isiqka fhduq lrkak'

wd.kaa igyk ixlSK ;,h& y`kajkak'ixlSK ixLHdjla wd.ka igyfkys

,laIHhlska ksrEmKh l< yelsnj myodfokak'

g wd.ka igyfka

,laIHh u.skaz ixlSK ixLHdj ksrEmKhlrkak'

z ixlSK ixLHdf udmdxlh u.ska

wxlkh lrkak'

nj m%ldY lrkak'

031' ixl SK ixLHdjl awd.ka igykl

ksrEmKh lrhs'

2' ixl SK ixLHdjludmdxlh w: olajhs'

O

P.

ksmqK;dugu


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3' ksYaY=kH jQixlSK

ixLHdjla

wdldrhg olajhs'

4' ixl SK ixLHdjlia:drh y`kajhs'

5' wd.ka igykl

ixlSK ixLHd ksrEmKh

lrk ,laIH ksudKh

lrhs'

hkqksYaY=kH jQixlSK ixLHdjla

hehs.kak' tg

fuys

iy f'

z hkqksYaY=kH ixlSK ixLHdjla f,i.kak' ;Dma; lrk

ia:drh f,i y`kajkak.

z ixlSK ixLHdf ia:drh ia:dz u.ska

wxlkh lrkak'

ia:d z = argz

z ysm%Odk ia:drh ia:d (z)= Ar gz u.ska

wxlkh lrkak'

Arg z = k tg nj m%ldY

lrkak'

z ixlSK ixLHdj we;s g my; iòyka

,laIH wd.ka igyfka ksrEmKh lsug

wdrNl ksudK bm;a lrkak'

(i) (ii) ;

yd ixlSK ixLHd we;s g my;

oelafjk ,laIH wd.ka igyfkaksrEmKh

lsug cHd;sl ksudK bm;a lrkak'

(i) (ii)

(iii) fuys

iòyd

nj idOkh lr wd.ka igyk u.ska

cHd;slj myokak'

nj wfmdaykh lrkak'

ksoiqkau.skameye,slr .eg iùg isiqkafhduq lrkak'

ksmqK;dugu


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14.4

14.5

1' ixl SK ixLHdjl

udmdxlh yd ia:drh

fidhhs'

2' iy ixlSK

ixLHd wd.ka igyfkaksrEmKh lsug ksudKbm;a lrhs'

ixlSK ;,fha m: fidhhs'

yd

k"

nj;a

nj;afmkajkak'

iy wd.ka igyfka ksudKh

lr olajkak'

z we;s g fok

ixlSK ixLHdj ksrEmKh lrkak'

ksoiqka u.ska meye,slrkak'

iy ixlSK ixLHd ms

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12.1 1' kHdihlaw: olajhs'

2' kHdij, iudk;dj w:olajhs'

3' kHdi wdl,kh w:olajhs'

kHdi

kHdihla hkq iDcqfldaKdi%ixLHd je,la

nj;a kHdi A, B, C.. wd bx.%Sis lemsg,awl=rej,ska wxlkh lrk nj;a m%ldY

lrkak'

fma

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0412.2

4' kHdihla wYhlska .=Klsu w: olajhs'

5' kHdihl fmru w:olajhs'

kHdij, fY aI wji a:dmeyeos,slrhs'

kHdi wdl,kh

(i) ixjD; nj

(ii) kHdfoaY nj(iii) >gkh jk nj

myod fokak'

k ish

, i`oyd

nj m%ldY lrkak'

g

= .

A kHdihl fmru AT u.ska wxlkh

lrk nj;a k ,

fuysish i`oyd nj;a m%ldY

lrkak'

iy

(i)

(ii)

nj i;Hdmkh lrkak'

.Kh jQ A kHdihl g Aiup;=ri%kHdihlaf,i w: olajkak'

kdhl m%Odk& lKh

f,i y`kajkak'

A iup;=ri%kHdifhys

o kA tall kHdihla f,i y`kajd

th In u.ska wxlkh lrkak'

ksmqK;dugu


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12.3 1' kHdi .=Ks;h w: olajhs'

2' .eg iù iòydm%fhhka Nd; lrhs'

A iup;=ri% kHdihl ish

iòyd k th lK kHdihla

f,i w: olajkak'

A iup;=ri% kHdihl kA iu;sl kHdihla f,i w:olajkak'

A iup;=ri% kHdihl kA l=l iu;sl kHdihla f,i w:olajkak'

A iup;=ri%kHdihl g

k A Wv;a;%sfldaKsl kHdihlaf,iw: olajkak'

A iup;=ri%kHdihl g

k A hg;a;%sfldaKsl kHdihla f,iy`kajkak'

by; tl tlla ksoiqka u.ska meye,slrkak'

iy kHdi fol i,lkak'

g" AB .=Ks;h w: oelafjk njm%ldY lrkak'

iy k

f,i .Kh

jQ AB kHdih w: olajkak'

idOdrK jYfhka" nj m%ldYlrkak'

ksoiqkau.ska meye,s lr .eg iùgisiqka fhduq lrkak'

A, B, C .Kh jQ" iup;=ri%kHdi iòydmy; m%;sM, bm;a lrkak'

(i)

(ii) (kHdfoaYh)

04

ksmqK;dugu


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12.4

3' kHdihl m%;sf,dauh

fidhhs'

kHdi Nd;fhka iu.dilrK i`ohs'

(iii) (>gkh)

(iv) (>gkh)(v)

(Ohkq Y=kH kHdihhs)

(vi) AIn= A = I

nA

(vii)

(viii) AB = O u i`oydA =Ofyda B=Ou wjYH fkdf'

hehs.ksuq' A hkq ;ru njQ

iup;=ri% kHdihla k"

u.ska fokq ,nk nj fmkajd fokak'

fuys

f,i we; s g

kHdihl ksYapdhlh fidhkak'A ksYaphlh =det A

A =

nj meye,s lrkak'

AkHdih we;sg AB =I2= BA jk m

B kHdihla w: olajkak'

we;s g iu.dilrK AX =C wdldrhg ,sh yels njm%ldY lrkak'

fuys iy

mj;sk g

nj fmkajd fokak'

06

ksmqK;dugu


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081' ksYapdhlhl w.h w:olajhs'

2' ksY apdhlhl

wjhjhl lKsIaGh w:olajhs'

iu.d ilrKj, my; iòyka iìdlPd lrkak'

(i) wkkH iù(ii) wm; i` ;su

(iii) i` fkdue;s g

ksoiqkau.ska meye,s lr .eg iùg

isiqka fhduq lrkak'

ksYapdhl

(i) iy wdldrfha ksYapdhl

y`kajkak'

(ii) ksYapdhlhl w.h

k

(iii) ksYapdhlhl w.h

k

m

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3' ksYapdhlhlwjhjhl iyidOlh w:

olajhs'

4' ksYapdhlhl ,laIKm%ldY lrhs'

k

aijwjhjfhaiyidOlh A

iju.ska wxlkh

lr Aij

ysw.h u.ska,nd

fok nj meye,s lrkak'fuys i,j=1, 2, 3

ksYapdhlhkays iyidOl fiug

isiqka fhduq lrkak'

my; i`oyka ,laIK i;Hdmkh lridlPd lrkak'

(i) A hkq;ru 3 jQiup;=ri%ksYapdhlhlak" det A =det AT f'

(ii) tla fma

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ksmqK;dugu


5' p,H follaiys; iu.dilrK iù iòyd

ksY apdhl Nd;lrhs'

k tg"

tk f'

p,H folla iys; iu.d ilrKj,i` idlPd lrkak'

l%euf.akS;sh (Cramer's Rule) u.ska

ilrKj, iù

iy ,

f,i m%ldY l< yels nj fmkajd fokak'

ilrK iù iòyd l%euf.akS;sh Nd;lsug isiqka fhduq lrkak'

p,H ;=kla iys; iu.d ilrKj,

i` idlPd lrkak'

hk ilrKj, iù l%euf.akS;sh wkqj

,

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ksmqK;dugu


fuys

nj m%ldY lr p,H 3la iys; iu.d

ilrK l%euf.akS;sh Nd;fhkai`ug

isiqka fhduq lrkak'

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ixhqla; .Ks;hixhqla; .Ks;hixhqla; .Ks;hixhqla; .Ks;hixhqla; .Ks;h IIIIIIIIII ( ( ( ( (;=kajeks jdrh;=kajeks jdrh;=kajeks jdrh;=kajeks jdrh;=kajeks jdrh)))))

1' ir, wkqj;S p,s;h w:

olajhs'

2' ir, wkqj;S p,s;fh a

wjl,k ilrKh iy tys

idOdrK iù ,nd .kshs'

3' ia:dmkfhaY%s;hlaf,i

m%f.h ,nd .kshs'

4' ia;drh yd wdj; ld,h

w: olajhs'

3.16ir, wkqj;S p,s;hir, wkqj;Sp,s;h hkq" jHla;sl foda,k

p,s; m%fNaohla nj m%ldY lrkak'

ir, fLdjlau; p,kh jk wxY=jlfh ;ajrKh" fLdj u; jQ wp,

,laIHhl isg wxY=f ia:dmkhg

Yd,;ajfhkaiudkqmd;sl o" tysYdj

wp, ,laIHh fj; fhduq mj;So

k" tu wxY=f p,s;h ir, wkqj;S

hehs lshkq,ef'

by; w: oelau bm;a lrkak'

by; lSwp, ,laIHh foda,k flakahf,i y`kajkq ,nk nj o m%ldY

lrkak'

by; oelafjkafka ir, wkqj;S p,s;fha

wjl,k ilrKhhs' fuys hkqksh;hls'

by; wjl,k ilrKfhaidOdrK iù

nj i;Hdmkhlrkak' fuys A, B yd ksh; jk w;r"t hkq ld,hhs'

u.ska

, fuys

,efnk nj fmkajd fokak'

t ld,fha ia:dmkh iòyd

hk iQ;%h o Nd; l

ksmqK;dugu


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5' taldldr jD;a; p,s;hweiqfrka ir, wkqj;S

p,s;h w:l:kh lrhs'

6' p,s; ld, m%dka;r fidhhs'

1' isria fLdjla Tiafiair,

wkqj;Sp,s;fhaiajNdjh

ia;r lrhs'

my; i`oyka oE idlPd lrkak'

P ,laIHh" wrh a jQ jD;a;hl ksh;fldaKsl m%f.fhka p,kh jk g"

jD;a;fha wp, IalNhla u; P ysm%lafIamKh jk Q,laIHfha p,s;h ir,wkqj;S jk nj by; olajd we;s whqka

fmkajd fokak'

.

ir, wkqj;S p,s;fha fhfok wxY=jl

msys folla w;r ld, m%dka;rh

nj"

by; rEmfham jD;a; p,s;h weiqfrka

fmkajd fokak'

by; ld, m%dka;rh ir, wkqj;S p,s;h

ms

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3'18

5'1

5'2

iajdNdl .

wkql,kh Nd;fhkam%;Hdia: Nj Yla;sh

nj idOkh lrkak'

m%;Hdia: n,j, l%shdj hgf;a" wxY=jl isria

fh ir, wkqj;Sp,s;h'

m%;Hdia: n, tfrys l%shdj hgf;a isria

fLdjla Tiafia wxY=jl ir, wkqj;S

p,s;h iy ir, wkqj;S p,s;hlska yd

.=re;ajh hgf;a ksoe,af,a p,s;hlska

iuka; ixhqla; p,s; idlPd lrkak'

ixLHdkh

ixLHdkh hkqm%udKd;aul o;a; ,nd f.k

Yaf,aIKh lsfuka ;SrKj,g t

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5.3

5.4

5.5

2' mlaIKhla hkql=ulaoehs

ia;r lrhs'

3' o;a; m%fNao ia;r lrhs'

o;a; yd f;dr;=re j.SlrKh

lrhs'

o;a; yd f;dr;=re j.=.; lrhs'

o;a; yd f;dr;=re m%ia;dlj

olajhs'

o;a; hkq ieliSu i`oyd m%odkh jk w;r"

f;dr;=re hkq ieliSf m%;sodkh f'

mlaIKhla hkq o;a; ,nd .ekSf

l%shdldrlula nj fmkajd fokak'

mlaIK m%fNao ms

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5.6 flakasl m%jK;d kq f,iuOHkHh" uOHia:h yd ud;h

ia;r lrhs'

iòyd w`kq,nk ia:N m%ia;drhls'

(iv) fLd m%ia;dr

fh m%ia;drhla isria ir, fLdLKavj,skaiuka; f' tlatlafLd

LKavfha.ska" wkqrEm la; o;a;fha

ixLHd;h ksrEmKh f'

fLd m%ia;dr we`h yelafla la;

o;a; iòyd muKs'

(v) fldgq flòsigyk

p;=:l w;r w.hkafldgqjlskao b;s

w.hhkafLd LKv follskao olajkq,nk w;r" tu fLd LKav fofla"

fldgqfjkamsg; wka; ,laIH foflka

je;u w.h;a" wvq;u w.h;a olajkq

,ef'

uOHkHh" uOHia:h yd ud;h hkq o;a;l=,lh flakasl m%jK;d kq nj m%ldY

lrkak'

my; oelafjk w: oela yd iQ;%bm;a

lrkak'

hkq o;a; l=,lhla hehs o

tajdfhaixLHd; ms

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5.7 idfmalaI msysgq Nd;fhka

ixLHd; jHdma;shla jrKh

lrhs'

N; uOHkHh

fuys hkq ys Ndrhhs'

jHdma;shl p,Hfha je;u ixLHd;h

iys; w.hg ud;h hehs w: olajkq ,nk

nj m%ldY lrkak'

iuqys; ixLHd; jHdma;shlai`oyd

ud;h= u.ska fokq

,ef'

fuys

=ud; mka;sfha hg;a udhsu

c =mx;s ;ru

iy

=ud; mka;sfhaixLHd;h

wdfrdayK fydawjfrdayK& mmdhg ilia

l< o;a; jHdma;shl ueo w.h uOHia:h

f,i w: olajkq ,ef'

1. hkq wdfrdayK ms

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2. iuqys; ixLHd; jHdma;shla i`oyd

uOHia:h f,i w:

olajkq ,ef'

fuys

b = uOHia:h wvx.= mka;sfhamygk kshuh (iv) o fuda.ka kshuh

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(4) my; i`oyka m%;sM,j,ska i;H m%;sM, hka brla w`kak'

(i) (ii) (iii)

(iv) (v)

(5) (i) iiNd mlaIKh w:l:kh lrkak'

(ii) my; i`oyka mlaIKj,ska iiNd mlaIK f;darkak'

(a) fyg br mdhhs'

(b) ldishlaWvoud u;=msg jefgk me;a; mlaId lsu'

(c) me;sj, 1-6 olajd wxl fh odleghla Wvoud u;=msgg jefgkme;a; mlaId lsu'

(d) mdi,ald,h ;=, wikSm f.or hjk isiqka .Kk mlaId lsu'

(e) ,snqnq,l wdhq ld,h uekSu'

(f) r;=mdg fnda, ;=klayd ks,amdg fnda,hlawe;su,a,lskawyUqf,i fnda;,hlabj;g .ekSu

(iii) Tn by; f;dard.;a iiNd mrSlaIKj, kshe wjldY ,shkak'

(6) ldisfollatljr Wvoud u;=msgg jefgk me;a; kslaIKh lsu hk iiNd mlaIKfha

(i) kshe wjldYh ,shkak'

(ii) tys ir, isoa folla ,shkak'

(iii) ixhqla; isoa folla,shkak'

(7) wfkHdkH jYfhka nysIaldr isoa hkql=ula o@ WodyrKhla u.skamye,slrkak'

(8) ldishla 50 jrla Wvoud jfgk me;a; kslaIKh lr my; j.=j imQK lrkak'

jdrh jegqk me;a; isri fydaw.h&

1

2

3

.

.

.

25

(i) ldishla 25 jrla Wv oef ysi ,ef id:l Nd.h fidhkak'

(ii) by; mlaIKfha 50 jrla" 100 jrlaislf

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(9) iNjH isoahla hkq l=ula o@ my; iòykaiiNd mrSlaIKj,skaiNjH iso ,efnkmlaIK f;darkak'

(i) ldishla Wvoud u;=msg jefgk me;a; kslaIKh lsu'

(ii) 1-6 olajd wxl fh idOdrK od leghla Wvoud u;=msgg jefgk me;a; kslaIKhlsu'

(iii) ks,a fnda, folla yd r;= fnda, 3la we;s u,a,lskawyUqf,i fnda,hla f.k mdgkslaIKh lsu'

(iv) 1-9 olajd wxl ,shd we;s ldm;a w;ka1la wyUq f,i f;dard wxlh igyka lsu'

(10) (i) by; .egf (ii) yd iiNd mlaIKh iòyd kshe wjldYh ,shkak'

A = { brf ixLHdjla ,eu}

B = { m%:ul ixLHdjla ,eu}

C = {y;/ia ixLHdjla ,eu }

D = { T;af;a ixLHdjla ,eu} f,i f.k

(ii) (a) P (A) (b) P (B) (c) P(C) (d) P(D) (e) P(A B)(f) P(A C) (g) P(C A) (h) P(A B) (i) P(A B C) (j) P(A B C)

fidhkak'

(iii) (a) P(A B) = P(A) + P(B) - P(A B)

(b) P(A B C) = P(A) + P(B) + P(C) - P(A B) - P(B C)

- P(C A) + P(A B C)

nj o idOkh lrkak'

(iv) (a) wfkHdkH jYfhkanysIaldr isoa follaf;darkak'

(b) P(A D) fidhkak'

we.hS ksKdhl

1. wjYH okqu ,nd .ekSu iòyd fmd;am;a mYS,kh'

2. l=,l h ms

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,s; mlaIK i`oyd .=rejreka yg my; i`oyka wdldrfha.eg fhdod.; yels h'

wkql,kh

1. (a) Nskak Nd.j,g fjkalrkak'

tkhska nj fmkajkak'

(b) x-1 = u2wdfoaYfhkafydawka l%uhlskafyda fidhkak'

(c) fldgia jYfhka wkql,kh Nd;fhka w.hkak'

(d) nj fmkajkak' w.hkak'

2. (a) Nskak Nd.j,g fjkalrkak'

t= tanxwdfoaYh Nd;fhka

nj fmkajkak'

tkhska nj fmkajkak'

(b) fldgia jYfhka wkql,kh Nd;fhka

w.hkak'

(c) iy hk jl%j,ska udhs jk j.M,h fidhkak'

3. (a) , wdfoaYh Nd;fhka fyda wka l%uhlska fyda w.hkak'

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(b) k"

jk A, B, C ksh; fidhkak'

nj fmkajkak'

(c) fldgia jYfhka wkql,kh Nd;fhka w.hkak'

(d) nj fmkajkak'

nj fmkajkak'

ys w.h fidhkak'

jD;a; p,s;h

1. . 14a jQ ieye,a w;kH ;ka;=jl fofl

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(iii) k" OP Wvqisri iu`.cos-1 fldaKhla idok g mn`:j;alh;a w;r

m%;sls%hdj Y=kHh nj fmkajd mn`:j m%:u jrg ksYap,;djhg m;a jk gOP isri iu`.idok fldaKh fidhkak'

3. wrh ajQ wp, iqug f.da,hl by< u ,laIHfha ksYap,;djfhawe;swxY=jlg l=vd ia:dmkhla

fokq,ef'

(i) wxY=j yryd hk wrh;aisri;a w;r fldaKhcos-1 jk g wxY=j" f.da,h yer hk nj

fmkajkak'

(ii) f.da,h msys ;,hg my

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ksmqK;d ug wxlj,g wod< ksmqK;d ugksmqK;d ug wxlj,g wod< ksmqK;d ugksmqK;d ug wxlj,g wod< ksmqK;d ugksmqK;d ug wxlj,g wod< ksmqK;d ugksmqK;d ug wxlj,g wod< ksmqK;d ug

13 fY%aKshg wod< tlatlaksmqK;d ug wxlj,g wod< ksmqK;d ug my; oelaf'

m

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fojk jdrhfojk jdrhfojk jdrhfojk jdrhfojk jdrh

ixhqla; .Ks;hixhqla; .Ks;hixhqla; .Ks;hixhqla; .Ks;hixhqla; .Ks;h I

25'1 Y%s;hl jHq;amkakh ms

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;=kajk jdrh;=kajk jdrh;=kajk jdrh;=kajk jdrh;=kajk jdrh

ixhqla; .Ks;hixhqla; .Ks;hixhqla; .Ks;hixhqla; .Ks;hixhqla; .Ks;h I

10'1 oamo m%idrKfha uQ,sl ,laIK .fIKh lrhs'

10'2 oamo m%idrKfha mo yd ix.=Kl w;r inkaOh uYkh lrhs'

14'1 ixLHd moaO;sh ia;SrKh lrhs'

14'2 ixlSK ixLHd ms

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wdY%s; .%ka:

Bstock, L. and Chandler, J. Pure Mathematics I

Stanley Thrones (Publishers) Ltd.- 1993

Bstock, L. and Chandler, J. Pure Mathematics II


Bostock, L. and Chandler, J. Applied Mathematics I


Bostock, L. and Chandler, J. Applied Mathematics II


cd;sl wOHdmk wdh;kh u.skam%ldYs; im;a .%ka:

wkql,kh

ir, fh p,s;h

ixlrK y ixfhdack

wxY=jl iu;=,s;;j

j.c Y%s; yd j.c ilrK

nyqmo Y%s; yd mfh Y%s;

.Ks;uh wNHqykh yd oamo m%fhh

;d;a;al ixLHd yd Y%s;

;%sfldaK;sh

wiudk;d

ffoYsl rdYsms

Com.maths 13

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