maths ijso stage-1

7/23/2019 Maths IJSO Stage-1

1/15

>>

>

>/ La 0 5 n 5 j 5 i 5 m xdbzb $n% j% i% m, nzb pkyl}lqb lo}bhbzy% xdlid nckoh }db akeekxloh dny }db ebny} qnerb ;

$N,mi

jn

$J,ij

mn

$I,jn

mi

$M,in

mj

:/ ]dzbb jk|y P% % Z nhzbb }k mlqlmb n jnh ka cnzjeby ny akeekxy 7

P }nfby kob ckzb }dno dnea ka }db cnzjeby6

^ }nfby n }dlzm ka }db zbcnloloh cnzjeby6

Z }nfby }db cnzjeby eba} kr} okx lo }db jnh/

]db kzlhlone orcjbz ka cnzjeby akrom n} }db jbhlooloh lo }db jnh cry} jb

$N, n cre}lpeb ka 1 $J, kob ckzb }dno n cre}lpeb ka 1

$I, ]xk ckzb }dno n cre}lpeb ka 1 $M, }dzbb ckzb }dno n cre}lpeb ka 1/

9/ La n > 3 j & : 3 i 9 3 m & = }dbo }db enzhby} nckoh n% j% i% m ly 7$N, n $J, j $I, i $M, m

=/ =nj2 ly n akrz mlhl} orcjbz mlqlyljeb j| 22 xdbzb n%j nzb rofokxo mlhl}y/ ]dbo j n ly 7$N, > $J, = $I, 2 $M, 0

2/ $n >,: & $j :,: & $i 9,: & $m =,: 3 0/]dbo n j i m & > ly 7$N, 0: $J, >0: $I, 2: $M, >: & :: & 9: & =: & >

1/ Hlqbo }dn} n%j%i nom m nzb on}rzne orcjbzy nom }dn} n 3 jim% j 3 imn% m 3 nji }dbo $n & j & i & m ,: ly 7$N, >1 $J, 4 $I, : $M, >

8/ ]db orcjbz ka 9 mlhl} orcjbzy xdlid bom lo 8 nom nzb mlqlyljeb j| >> ly$N, : $J, = $I, 1 $M, 4

4/ ]db pzkmri} ka }xk orcjbzy ly :8/ 99/ 22/ 89/ ]dbo }db yrc ka }dbyb }xk orcjbzy cn| jb mlqlyljeb j| 7$N, >1 $J, < $I, :2 $M, =0/ L} ly hlqbo }dn} 2 n

9

j :

>

3 >< $xdbzb }db }xk azni}lkoy nzb cltbm azni}lkoy,6 }dbo n & j 3

$N, >0 $J, >: $I, < $M, >2

>>/ n nom j nzb }xk pzlcby ka }db akzc p nom p &> nom C 3 nn & jj 6 O 3 nj & jn }dbo 7

$N, C nom O nzb ikcpkyl}b

$J, C ly n pzlcb jr} O ly ikcpkyl}b

$I, C nom O nzb pzlcby

$M, C ly ikcpkyl}b% O ly pzlcb

>:/ Xdn} ly }db qnerb ka t la=

:2tekhtekhtekhtekh 4>:8 $M, Okob ka }dbyb

Yrjgbi} 7 Cn}dbcn}liy ]kpli 7 Orcjbz Y|y}bc MPP Ok/ 0>

MNLE\ PZNI]LIB PZKJEBCY

YBYYLKO#:0>:#>9


2/15

::

:

>9/ ]db pnhby ka n jkkf nzb orcjbzbm > }dzkrhd o/ Xdbo }db pnhb orcjbzy ka }db jkkf xbzb nmmbm% kob ka}db pnhb orcjbzy xny cly}nfboe| nmmbm }xlib zbyre}loh lo }db loikzzbi} yrc >=/ La t nom | nzb on}rzne orcjbzy% alom }db orcjbz pnlzy $t% |, akz xdlid t: |: 3 9>/

$N, = $J, 9 $I, > $M, 0

>2/ Alom }db eny} mlhl} lo }db alol}b mbilcne zbpzbybo}n}lko ka }db orcjbz >+2:009 ;

$N, : $J, = $I, 4 $M, 1

>1/ La n 3 9:9 nom J 3 9:9 % alom }db qnerb ka $n & >,> & $j & >,>$N, = $J, 9 $I, > $M, 0

>8/ Alom }db ycneeby} pkyl}lqb orcjbz azkc }db orcjbzy jbekx >0 9 >> % 9 >> >0% >4 2 >9 %

2> >0 :1 % >0 :1 2>/

$N, 2> >0 :1 $J, >0 :1 2> $I, >0 9 >> $M, >0 & 9 >>

>4/ Alom }db orcjbz ka }xk mlhl} orcjbzy mlqlyljeb j| }db pzkmri} ka }db mlhl}y/

$N, 8 $J, >> $I, = $M, 2

>:9=21840>>>:>9///// Alom }db zbcnlombz xdbo }dly orcjbz ly mlqlmbm j| 4/ 7

$N, 1 $J, 8 $I, : $M, 0


3/15

>>

>

>/ Lo NJI % JB nom IA nzb cbmlnoy/ JB3 : ic/ La JB ly pbzpbomlirenz }k IA% alom }db nzbn ka

NJI lo y~/ icy/

$N, 8: $J, := $I, >== $M, Inook} jb mb}bzclobm

:/ Lo NJI% JI 3 :0 % cbmlnoy JB 3 >4 nom cbmlno IA 3 := $B% A nzb clmpklo}y ka NI% NJ zbypbi}lqbe|,/

Alom }db nzbn ka NJI/

$N, :== y~/ rol}y $J, :44 y~/ rol}y $I, >== y~/ rol}y $M, Okob ka }dbyb

9/ Lo NJI % }db cbmlno azkc N ly pbzpbomlirenz }k }db cbmlno azkc J/ La JI 3 8 nom NI 3 1 alom NJ/

$N,>2

rol}y $J, >8 rol} $I, >9 rol} $M, Okob ka }dbyb

=/ Eb} NJI jb no nir}b nohebm }zlnoheb nom IM jb }db ne}l}rmb }dzkrhd I/ La NJ 3 4 nom IM 3 1% alom }db

mly}noib jb}xbbo }db clm#pklo}y ka NM nom JI/

$N, > rol} $J, : rol} $I, 2 rol} $M, >0 rol}

2/ Lo n }zlnoheb NJI% cbmlnoy NM nom JB nzb mznxo/ La NM 3 =% MNJ 31

nom NJB 3

9

% }dbo }db nzbn

ka }db NJI ly 7

$N,94 $J,

9>1 $I,

99

9: $M,9

1= /

1/ Lo n }zlnoheb NJI% la n 7 j 7 i 3 9 7 8 7 4% }dbo Z 7 z ly b~rne }k

$N, : 7 8 $J, 8 7 : $I, 9 7 8 $M, 8 7 9

8/ Eb} NJI jb no b~rlen}bzne }zlnoheb nom NM jb }db ne}l}rmb }dzkrhd N/ ]dbo

$N, NM: 3 9JM: $J, NM: 3 2JM: $I, NJ: & NI: 3 JI: $M, NM: 3 :JM:

4/ Lo }zlnoheb NJI xl}d noheb N 3 0/ Lo n NJI% NI ? NJ/ ]db jlybi}kz ka N cbb}y JI n} B% }dbo 7

$N, IB ? JB $J, IB 3 JB $I, IB 5 JB $M, Okob ka }dbyb

>>/ NJI ly no lykyibeby }zlnoheb xl}d cN 3 :0 nom NJ 3 NI/ M nom B nzb pklo}y ko NJ nom NI yrid }dn}

NM 3 NB/ L ly }db clmpklo} ka }db ybhcbo} MB/ La JM 3 LM% }dbo }db noheb ka LJI nzb 7

$N, >>0% 92% 92 $J, >00% =0%=0 $I, 40%20%20 $M, MPP Ok/ 0:


YBYYLKO#:0>:#>9


4/15

::

:

>:/ N% J% I nom M nzb pklo}y ko n elob/ B ly n pklo} kr}ylmb }dly elob/ Hlqbo }dn} NB 3 JB 3 NJ 3 JI nom

IB 3 IM% xb alom }dn} }db cbnyrzb ka MBN ly 7

$N, 02 $I, >:0 $M, >20

>9/ Lo no lykyibeby nir}b nohebm }zlnoheb kob noheb ly 20/

L/ ]db k}dbzb }xk noheby nzb 12 nom 12

LL/ ]db k}dbz }xk noheby nzb 20 nom 40

]dbo xdlid kob ka }db njkqb y}y}bcbo}y ino jb }zrb ;

$N, L koe| $J, LL koe| $I, L nom LL jk}d $M, bl}dbz L kz LL jr} ok} jk}d

>=/ Lo }db nmgkloloh alhrzb alom }db ylwb ka NIB% hlqbo NM 3 MJ nom MB 3 MI/

$N, =2 $J, >2 $I, :0 $M, 20

>2/ Lo }zlnoheb NJI% JM jlybi}y noheb J/ La cN 39

:cJ nom cJ 3 9cI% }dbo cJMI ly 7

$N, 82 $J, >02 $I, :0

>1/ Lo }db nmgnibo} alhrzb% MB jlybi}y JMN nom NM jlybi}y JNI/ ]db cbnyrzb ka JBM ly 7

$N, 42 $J, 02

>8/ NJI ly no b~rlen}bzne }zlnoheb $ydkxo lo alhrzb,/ M ly ykcb pklo} ko JI/ LA MB 3 9 nom MA 3 8 alom }db

eboh}d ka ne}l}rmb akzc N }k JI/

$N, 2 $J, 8 $I, >0 $M, >:


5/15

99

9

>4/ Hlqbo }zlnoheb P^Z xl}d ZY jlybi}loh Z% P^ bt}bombm }k M nom o n zlhd} noheb% }dbo 7

Z

P^

Mp

co

~

Y

m

$N, c 3:

>$p~, $J, c 3

:

>$p &~,

$I, m 3:

>$~ &p, $M, m 3

:

>c

>/ Alom }db orcjbz ka lykyibeby }znloheby dnqloh lo}bhzne ylmby nom pbzlcb}bz ebyy }dno kz b~rne }k >00 ly 7

$N, := $J, :0 $I, :8 $M, Okob ka }dbyb


6/15

>>

>

>/ P^ZY ly n }znpbwlrc% lo xdlid P^ ly pnzneebe }k ZY% nom P^ 3 9 ZY/ ]db mlnhkone ka }db }znpbwlrc

lo}bzybi} bnid k}dbz n} T% }dbo }db zn}lk ka PT^ nom ZTY ly 7

$N, 1 7 > $J, 9 7> $I, < 7> $M, 8 7 >

:/ ]xk ilzieby NP^I nom PJM^ lo}bzybi} bnid k}dbz n} }db pklo}y P nom ^ nom NPJ nom I^M nzb }xk

pnzneebe y}znlhd} eloby/ ]dbo koe| kob ka }db akeekxloh y}n}bcbo}y ly nexn|y }zrb/ Xdlid kob ly l} ;

$N, NJMI ly n i|ieli ~rnmzlen}bzne $J, NI ly pnzneebe }k JM

$I, NJMI ly n zbi}noheb $M, NI^ ly n zlhd} noheb

9/ N }zlnoheb NJI xl}d no kj}ryb noheb J ly loyizljbm lo n ilzieb/ ]db ne}l}rmb NM ka }db }zlnoheb ly }nohbo} }k

}db ilzieb/ ]db ne}l}rmb NM ka }db }zlnoheb ly }nohbo} }k }db ilzieb/ ]db ylmb JI dny eboh}d = ic/ Alom }dbnzbn ka }db }zlnoheb NJI $lo ic:,/

$N, =4 $J, 10 $I, 8: $M, 91

=/ ]db eboh}d ka }db ikccko idkzm ka }xk ilzieby ka znmll >2 ic nom :0 ic% xdkyb ibo}zby nzb :2 ic npnz}

ly 7

$N, := ic $J, :2 ic $I, >2 ic $M, :0 ic

2/ Idkzmy NJ nom P^ cbb} n} F nom nzb pbzpbomlirenz }k kob nok}dbz/ La NF 3 =% FJ 3 1 nom PF 3 :% }dbo

}db nzbn ka }db ilzieb ly 7

$N, :2y~/ rol}y $J, :0y~/ rol}y $I, >00y~/ rol}y $M, 20y~/ rol}y

1/ Lo ~rnmzlen}bzne NJIM % mlnhkoney NI nom JM cbb} n} K/ La NKJ% MKI nomJKI dnqb nzbny 9% >0 nom

: zbypbi}lqbe|% alom }db nzbn ka NKM/

$N, >0 y~/ rol}y $J, :0 y~/ rol}y $I, >2 y~/ rol}y $M, >: y~/ rol}y

8/ La P ly n pklo} loylmb n zbi}noheb NJIM yrid }dn} PN 3 9% PJ 3 = nom PI 3 3 2 alom PM/

$N, 9 : rol}y $J, : 9 rol}y $I, 2 rol}y $M, Okob ka }dbyb

4/ Lo n }znpbwlrc NJIM % NJ LL IM 6 }db cbnyrzb ka noheb M ly }xlib }dn} ka J/ La NM 3 n nom IM 3 j% alom }db

eboh}d ka NJ/

$N, n & j $J, :nj $I, n

j $M, Okob ka }dbyb

0/ Lo n zlhd} }zlnoheb NJI }db loilzieb }kridby }db d|pk}boryb NI n} M % La NM 3 >0 nom MI 3 9 }dbo }db

loznmlry ly 7

$N, > $J, : $I, = $M, 1

>>/ Eb} P jb no| pklo} lo }db lo}bzlkz ka }db zbi}noheb NJIM xdlid ka }db akeekxloh yb}y ka orcjbzy ino akzc}db nzbny ka }db akrz }zlnoheby PNJ% PJI% PIM% PMN/

$N, >0% :% 2 $J, :>% >2% 1% >: $I, >0% :% 4% 8% 2

Yrjgbi} 7 Cn}dbcn}liy ]kpli 7 Hbkcb}z| # : MPP Ok/ 09


YBYYLKO#:0>:#>9


7/15

::

:

>:/ Lo n }zlnoheb NJI % NJ 3 NI 3 :0 ic% M nom B nzb pklo}y ko NJ nom NI zypbi}lqbe| yrid }dn}

NM 3 NB 3 >: ic % La A ly }db lo}bzybi}lko pklo} ka JB nom IM nom nzbn ka NMAB ly := ic: / Alom }db nzbn

ka }db }zlnoheb JAI lo y~/ ic

$N, := $J, :0 $I,9

=0$M, Okob ka }dbyb

>9/ ZY] ly no noheb lo }db clokz ybhcbo} ka n ilzieby ka ibo}zb K% }dbo }db noheb $lo mbhzbby, ZY] ebyy }db

noheb KZ] ly 7

$N, =/ ]zlnoheb NJI ly mlqlmbm lo}k akrz zbhlkoy xl}d nzbny ny ydkxo lo }db mlnhznc/ Alom t/

$N,18

>>

2=$I,

18

>

2==

>2/ N ilzieb ly loyizljbm lo n zdkcjry% kob ka xdkyb noheby ly 10/ Alom }db zn}lk ka nzbn ka }db zdkcjry }k }db

nzbn ka }db loyizljbm ilzieb/

$N, 8 7 9 $J, 4 7 9 $I, = 7 9 $M, Okob ka }dbyb

>1/ Lo }db alhrzb% IM ly }db mlncb}bz ka n ybclilzieb IJBM xl}d ibo}zb K% nom NJ 3 KM/ La BKM 3 10% }dbo

JNI ly 7

I K M

B

J

N

$N, >2 $J, :0 $I, 90 $M, =2

>8/ Ybcl#ilzieb I>

ly mznxo xl}d n elob ybhcbo} P^ ny l}y mlncb}bz xl}d ibo}zb n} Z/ Ybclilzieby I:

nom I9

nzb mznxo xl}d PZ nom Z ny l}y mlncb}bz zbypbi}lqbe|% jk}d I:

nom I9

e|loh loylmb I>/ N aree ilzieb I

=ly

mznxo lo yrid n xn| }dn} l} ly }nohbo} }k nee }db }dzbb ybclilzieby I>% I

:nom I

9/ I

=elby loylmb I

>nom

kr}ylmb jk}d I:nom I

9/ ]db znmlry I

=ly 7

$N, P^9

>$J, P^

1

>$I, P^

:

>$M, P^

=

>

>4/ NJIM ly n pnzneebekhznc nom P ly no| pklo} xl}dlo l}/ La }db nzbn ka }db pnzneebekhznc NJIM ly :0 y~/ rol}y%

}dbo xdn} ly }db yrc ka }db nzbny ka }db MPNJ nom MPIM ;

$N, 2 y~/ rol}y $J, >0 y~/ rol}y $I, >: y~/ rol}y $M, Inook} jb mb}bzclobm

> 7 > $J, 9 7 : $I, 9 7 > $M, : 7 >

:0/ Lo no| ~rnmzlen}bzne NJIM% }db mlnhkone NI nom JM lo}bzybi} n} n pklo} T/ La B% A% H nom D nzb }db clmpklo}y

ka NT% JT% IT nom MT zbypbi}lqbe|% }dbo xdn} ly }db zn}lk ka $BA & AH & HD & HB, 7 $NM & MI & IJ & JN,;

$N,:

>$J,

:

9$I,

=

9$M, Mn}n loyraalilbo}


8/15

>>

>

>/ Alom }db nzbn ka }db enzhby} y~rnzb xdlid ino jb loyizljbm lo n zlhd} nohebm }zlnoheb xl}d ebhy = nom 4/

$N,9

4$J,

9

8$I, = $M, Okob ka }dbyb

:/ Lo n zlhd} nohebm }zlnoheb% la }db y~rnzb ka }db d|pk}boryb ly }xlib }db pzkmri} ka }db k}dbz }xk ylmby% }dbo

xdlid ka }db akeekxloh ly }zrb /

$N, }zlnoheb ly lykyibey $J, ]zlnoheb ly b~rlen}bzne$I, ]zlnoheb ly yinebob $M, Okob ka }dbyb

9/ Alom }db zn}lk ka }db nzbn ka }db b~rlen}bzne }zlnoheb loyizljbm lo n ilzieb }k }dn} ka n zbhrenz dbtnhko

loyizljbm lo }db yncb ilzieb/

$N, > 7 : $J, > 7 = $I, : 7 9 $M, Okob ka }dbyb

=/ La }db ne}l}rmby ka n }zlnoheb nzb lo }db zn}lk : 7 9 7 =% }dbo }db eboh}dy ka }db ikzzbypkomloh ylmby nzb lo }db

zn}lk 7

$N, : 7 9 7 = $J, 1 7 = 7 9 $I, 9 7 : 7 = $M, 9 7 : 7 >

2/ Lo inyb ka n zlhd} ilzirenz i|elombz }db znmlry ka jnyb nom dblhd} nzb lo }db zn}lk : 7 9/ ]dbzbakzb% }db zn}lk

ka en}bzne yrzanib nzbn }k }db }k}ne yrzanib nzbn ly 7

$N, 2 7 9 $J, 9 7 2 $I, : 7 2 $M, : 7 9

1/ NJI ly no lykyibeby zlhd} }zlnoheb xl}d nzbn P/ ]db znmlry ka }db ilzieb }dn} pnyyby }dzkrhd }db pklo}

N% J nom I ly 7

$N, P $J, :P $I,

:P $M, P:

8/ ]db mlnhkoney ka n zdkcjry nzb >: nom :=/ ]db znmlry ka }db ilzieb loyizljbm lo }db zdkcjry% ly 7

$N,2

>:$J,

2

1

$I, 21

$M, ok} pkyyljeb ny n ilzieb lo n zdkcjry ino ok} jb loyizljbm

4/ N zkrom pboile dny eboh}d 4 rol}y xdbo roy}zbidbm nom mlncb}bz >+=/ L} ly ydnzpbobm pbzabi}e| yk }dn} l}

zbcnloy 4 rol}y ekoh xl}d 8 rol}y ybi}lko y}lee i|elomzline nom zbcnloloh > rol} hlqloh n ikoline }lp/ Qkercb

ka }db pboile okx ly 7

$N,>$J,

>c:>

$I, c $M, :c4>

Yrjgbi} 7 Cn}dbcn}liy ]kpli 7 Cboyrzn}lko MPP Ok/ 0=


YBYYLKO#:0>:#>9


9/15

::

:

>0/ Lo }dly alhrzb% NKJ ly n ~rnz}bz ilzieb ka znmlry >0 nom P^ZK ly n zbi}noheb ka pbzlcb}bz :1/ ]db pbzlcb}bz

ka }db ydnmbm zbhlko ly 7J

^Z

K NP

$N, >9 & 2 $J, >8 & 2 $I, 8 & >0 $M, 8 & 2

>>/ ]dzbb pnzneebe eloby >%

:nom

9nzb mznxo }dzkrhd }db qbz}liby N% J nom I ka n y~rnzb NJIM/ La }db

mly}noib jb}xbbo >

nom :

ly 8 nom jb}xbbo :

nom 9

ly >:% }dbo }db nzbn ka }db y~rnzb NJIM ly 7

$N, >1< $I, >:/ Bnid ka }db ikohzrbo} ilzieby ydkxo ly bt}bzonee| }nohbo} }k k}dbz ilzieby nom+kz }k }db ylmb$y, ka }db

zbi}noheb ny ydkxo/ La bnid ilzieb dny ilzircabzboib >1% }dbo }db eboh}d ka n mlnhkone ka }db zbi}noheb%

ly 7

$N, 40 $J, =0 $I, :0 $M, >2

>9/ NJIM ly n zbi}noheb nom eloby MT% M\ nom T\ nzb mznxo ny ydkxo/ Nzbn ka NTM ly 2% Nzbn ka JT\ ly

= nom nzbn ka I\M ly 9/ La }db nzbn ka MT\ ino jb btpzbyybm ny t xdbzb t O }dbo t ly b~rne }k

NT

J

\

IM

$N, 8: $J, 82 $I, 4= $M, =/ N ypdbzb ly loyizljbm lo n ikob ka znmlry / 99 nom yeno} dblhd} 91 / ]db znmlry ka }db ypdbzb% ly 7

$N, 0 $J, 99 $I, 91 $M,:

99

>2/ NJIM ly n zbi}noheb xl}d NJ 3 >: ic nom JI 3 8 ic/ Pklo} B ly ko NM xl}d MB 3 : ic/ Pklo} P ly ko

NJ/ Dkx anz }k }db zlhd} ka pklo}/ N ydkrem pklo} P jb penibm yk }dn} }db ydnmbm nzbn ikcpzlyby btni}e|

=0" ka }db nzbn ka }db zbi}noheb ;

M I

JNP

B

$N, 4 $J, 4/= $I, 4/: $M, 4/1


10/15

99

9

>1/ N ebnm jnee ka znmlry := ic ly cbe}bm mkxo nom zbiny} lo}k ycneebz jneey ka znmlry 1 ic/

Nyyrcloh }dn} ok cb}ne ly eky} lo }dly pzkibyy% orcjbz ka ikcpeb}b ycneebz jneey }dn} ino jb cnmb% ly 7

$N, = $J, >1 $I, 91 $M, 1=

>8/ ]db ylmby ka n }zlnoheb nzb lo }db zn}lk = 7 1 7 >>/ Xdlid ka }db akeekxloh xkzmy jby} mbyizljbm }db }zlnoheb;

$N, kj}ryb $J, lykyibeby $I, nir}b $M, lcpkyyljeb

>4/ ]db qkercb ka n irjb $lo irjli ic, pery }dzbb }lcby }db }k}ne eboh}d ka l}y bmhby $lo icy, ly b~rne }k }xlib

l}y yrzanib nzbn $lo y~/ ic,/ ]db eboh}d ka l}y mlnhkone ly 7$N, 1 $J, 91 $I, 19 $M, 11

> ly loyizljbm lo n ybclilzieb yrid }dn} kob ylmb ka }db y~rnzb ly ko }db mlncb}bz

ka }db ybclilzieb/ ]db pbzlcb}bz ka }db ybclilzieb ly 7

$N, 2 $J,:

2$I,

>

:2 $M, >

:

2

:0/ N ybclilzieb ly mznxo xl}d NJ ny l}y mlncb}bz/ Azkc I% n pklo} ko NJ% n elob pbzpbomlirenz }k NJ ly mznxo

cbb}loh }db ilzircabzboib ka }db ybclilzieb n} M/ Hlqbo }dn} NI 3 : ic nom IM 3 1 ic% }db nzbn ka }db

ybclilzieb ly 7

$N, 9: $J, 20 $I, =0 $M, Okob ka }dbyb


11/15

>/ n% j% i nzb zbne orcjbzy yrid }dn} n &

j

>3

9

86 j &

i

>3 = 6 i &

n

>3>% alom nji/

$N, 0 $J, > $I, : $M, 9

:/ La n & j & i 3 0% alominj

nij:

::: /

$N, 0 $J, > $I, : $M, 9

9/ La t & | 3 2t|% | & w 3 1|w% w & t 3 8wt alom }db qnerb ka t & | & w/$N, 0 $J, > $I, : $M, Okob ka }dbyb

=/ La>t>t

>t>t

3 9 alom t/

$N,9

2$J,

9

=$I, : $M, 9

2/ La>9

983 : &

w>|

>t

>

xdbzb t% |% w nzb pkyl}lqb lo}bhbzy alom t% |% w/

$N, $>% 2% :, $J, $>% 2% =, $I, $>% 9% :, $M, $>% 9% =,

1/ Akz t: & :t & 2 }k jb n ani}kz ka t= & pt: & ~% alom }db qnerby ka p nom ~/$N, p 3 1 % ~ 3 := $J, p 3 1 % ~ 3 :2 $I, p 3 := % ~ 3 1 $M, Okob ka }dbyb

8/ La :t 3 =| 3 4w nom t|w 3 :44% }dbo w4

>

|=

>

t:

>

$N,$I,

9$M,

2

4/ La n & j & i 3 9% n: & j: & i: 3 >9 nom n9 & j9 & i9 3 :8% }dbo i

>

j

>

n

>

$N, 9 $J,9 $I,9

>$M,

9

>

, $:| >,/

$N, = $J, 9 $I, 2 $M, Inook} jb mb}bzclobm

>0/ ]db hznpd ka }db b~rn}lko | 3 :t: & =t & 9 dny l}y ekxby} pklo} n} 7

$N, $ >% % % >, $M, $0% 9,

Yrjgbi} 7 Cn}dbcn}liy ]kpli 7 Nehbjzn #> MPP Ok/ 02


YBYYLKO#:0>:#>9


12/15

>>/ La }db ikccko pklo}y ka }db hznpdy ka | 3 t: 1t & : nom t & :| 3 = nzb N nom J alom }db ikbaalilbo}y ka

}db clmpklo} ka NJ

$N, N 3=

>>% J 3

4

2$J, N 3

4

2% J 3

9

>$I, N 3

=

>>% J 3

4

2$M, N 3

4

2% J 3

9

>

>:/ N ~rlw dny :0 ~rby}lkoy xl}d ybqbo pklo}y nxnzmbm akz bnid ikzzbi} noyxbz6 }xk pklo}y mbmri}bm akz bnidxzkoh noyxbz nom wbzk cnzf hlqbo akz bnid ~rby}lko kcl}}bm/ Znc yikzby 48 pklo}y/ Dkx cno| ~rby#}lkoy mlm db kcl} ;$N, : $J, 2 $I, 8 $M, 9/ ]xk inomeby ka yncb eboh}d nzb elhd}bm n} >: okko/ ]db alzy} ly ikoyrcbm lo 1 dkrzy nom }zdb ybikom lo= dkrzy/ Nyyrcroh }dn} bnid inomeb jrzoy n} n ikoy}no} zn}b% lo dkx cno| dkrzy na}bz jbloh elhd}bm% xny}db alzy} inomeb }xlib }db eboh}d ka }db ybikom ;$N, 9 p/c/ $J, : p/c/ $I, >/90 p/c/ $M, :/90 p/c/

>=/ Lajn

i

ni

j

ij

n

% }dbo bnid azni}lko ly b~rne }k 7

$N,:

>$J, > $I, : $M, :

>2/ La n: 3 j| & iw% j: 3 iw & nt% i: 3 nt & j|% }dbowi

w

|j

j

tn

t

3 ;

$N, nji $J, > $I,t|w

nji$M,

nji

t|w

>1/ La :t 9| & =w 3 0 ! t & :| 2w 3 0% }dbo t 7 | 7 w ly 7

$N, : 7 9 7= $J, > 7 > 7 > $I, > 7 : 7 > $M, 9 7 =7 :

>8/ Hlqbo n orcjbz ka }db akzc n & j : % xdbzb n% j nzb zn}lkone orcjbzy xl}d n kz j 0% }dbzb btly}y n

orcjbz p & ~ : % xl}d p% ~ zn}lkone orcjbz% yrid }dn} $n & j : ,$p & ~ : , 3 >/ ]db qnerb ka $p: :~: ,% ly

$N, :::

::

,j=n$

j:n

$J, ::

::

j:n

j:n

$I, :: j:n

>

$M, :: j=n

>

>4/ ]db orcjbz ka }zlpeb}y $n% j% i, ka }db pkyl}lqb lo}bhbz% xdlid yn}lya| ylcre}nobkry b~rn}lko

nj & ji 3 == ! ni & ji 3 :9

$N, > $J, : $I, = $M, Loalol}b yker}lkoy

>04

>$M, >04

:0/oo 99 |t ly mlqlyljeb j| t & | la 7

$N, o ly no| lo}bhbz o $J, o ly no kmm pkyl}lqb lo}bhbz$I, o ly no bqbo pkyl}lqb lo}bhbz $M, o ly n zn}lkone orcjbz


13/15

>/ nom nzb }xk orcjbzy yrid }dn} & 3 1% 3 4/ ]dbo }znib }db b~rn}lko xdkyb zkk}y nzb nom

/

$N, t: 1t 8 $J, t: 8t 1 $I, t: & 1t & 8 $M, Okob ka }dbyb

:/ La nom nzb }db zkk}y ka }db b~rn}lko t: 0t: >:: t 1> 3 0 $J, t: >::t 1> 3 0

$I, :0t: >::t 1> 3 0 $M, Okob ka }dbyb

9/ Akz }db on}rzne orcjbz o% Yo3 > : & 9 = & ///// & $>,o#>o6 }db qnerb ka Y

>8& Y

99& Y

20ly 7

$N, 0 $J, > $I,> $M, :

=/ La % nzb }db zkk}y ka t : & t & > 3 0 nom % nzb }db zkk} ka t : & 9t & > 3 0% }dbo

3

$N, : $J, = $I, 1 $M, 4

2/ La T & \ & W 3 90% $T%\% W ? 0,% }dbo }db qnerb ka $T :, $\ 9, $W =, xlee jb 7

$N, >000 $J, 400 $I, 200 $M, 9=9

1/ Akz xdn} qnerby ka (n( % }db b~rn}lkoy > 3 0 $I, n 3 0 $M, n & j & > 3 0

9, 7 $2o & :>,/ Alom }db zn}lk ka }dblz :=}d }bzcy/

$N, > 7 : $J, > 7 9 $I, : 7 9 $M, : 7 2

>0/ N H/P/ ikoyly}y ka no bqbo orcjbz ka }bzcy/ La }db yrc ka nee }db }bzcy ly 2 }lcby }db yrc ka }db }bzcy

kiirp|loh kmm peniby% }dbo }db ikccko zn}lk xlee jb

$N, : $J, 9 $I, = $M, 2

Yrjgbi} 7 Cn}dbcn}liy ]kpli 7 Nehbjzn # : MPP Ok/ 01


YBYYLKO#:0>:#>9


14/15

>>/ La n% j% i nzb lo N/P/% }dbojn

>

%

in

>

%

ij

>

nzb lo 7

$N, N/P/ $J, H/P/ $I, D/P/ $M, Okob ka }dbyb

>:/ Yrppkyb n% j% i nzb lo N/P/ nom n:% j:% i: nzb lo H/P/ la n 5 j 5 i nom n & j & i 3:

9% }dbo }db qnerb

ka n ly 7

$N,::

> $J,9:

> $I,:>

9> $M,

:>

:>

>9/ Lo }db ~rnmzn}li b~rn}lko nt: & jt & i 3 0% 3 j: =ni nom & % : & :% 9 & 9% nzb lo H/P/ xdbzb

nzb }db zkk} ka nt: & jt & i 3 0% }dbo

$N, 0 $J, j 0 $I, i 0 $M, 0

>=/ ]db orcjbz ka }bzcy lo no NP ly bqbo/ ]db yrcy ka }db kmm nom bqbo orcjbzbm }bzcy nzb := nom 90

zbypbi}lqbe|% la }db eny} }bzc btibbmy }db alzy} }bzc j| >0/2% }dbo }db orcjbz ka }bzcy lo }db NP ly 7

$N, 1 $J, 4 $I, >0 $M, >:

>2/ Eb} n% j% i jb }db ylmby ka n }zlnoheb $Ok }xk ka }dbc nzb b~rne, nom Z/ La }db zkk}y ka }db b~rn}lkot: & :$n & j & i,t & 9 $nj & ji & in, 3 0 nzb zbne% }dbo 7

$N, 59

=$J, ?

9

2$I,

9

2%

9

>$M,

9

2%

9

=

>1/ La zkk}y ka }db b~rn}lko t: >0nt >>j 3 0 nzb i nom m nom }dkyb ka t: >0it >>m 3 0 nzb n nom j% }dbo

alom }db qnerb ka n & j & i & m/ $xdbzb n% j% i% m nzb nee mly}loi} orcjbzy,

$N, >000 $J, >:00 $I, >:>0 $M, >:20

>8/ N ilzieb xl}d nzbn N>ly iko}nlobm lo }db lo}bzlkz ka n enzhb ilzieb xl}d nzbn N

>& N

:/ La }db znmlry ka }db enzhbz

ilzieb ly 9 nom N>

% N:

% N>

& N:

nzb lo NP% }dbo }db znmlry ka }db ycneebz ilzieb ly 7

$N,:

9$J, > $I,

9

:$M, 9

>4/ La j>% j

:% j

9///////jbekohy }k N/P/ yrid }dn} j

>& j

=& j

8& ///// & j

:43 ::0% }dbo }db qnerb ka j

>& j

:& j

9

///////&/////////& j:4

b~rney 7

$N, 1>1 $J, 904 $I, ::00 $M, >:9:

>9$ t & 9 : 9 3 0% }dbo }db ybikom zkk} ly 7

$N, 9 : $J, 9 $I, : & 9 $M, 9

:0/ La n ly n zkk}% zbpbn}bm }xlib% ka }db ~rnmzn}li b~rn}lko $n m, t: & nt & $n & m, 3 0 }dbo :

:

n

mdny }db qnerb

b~rne }k 7

$N, ylo:


15/15

CN]DBCN]LIY [LGYK Y]NHB#L 7 MPP#:

CN]DBCN]LIY [LGYK Y]NHB#L 7 MPP#2

^rby/ > : 9 = 2 1 8 4 < >0

Noy/ N I I N I N M N I N

^rby/ >> >: >9 >= >2 >1 >8 >4 >< :0

Noy/ I M N I I I N M

^rby/ > : 9 = 2 1 8 4 < >0

Noy/ N J J I I J N I I I

^rby/ >> >: >9 >= >2 >1 >8 >4 >< :0

Noy/ J J I I J N I I J J

Orcjbz y|y}bc 7

Hbkcb}z| 7 L

^rby/ > : 9 = 2 1 8 4 < >0

Noy/ N N N J I N N N N J

^rby/ >> >: >9 >= >2 >1 >8 >4 >< :0

Noy/ N N I J M M J I M

Cboyrzn}lko 7

^rby/ > : 9 = 2 1 8 4 < >0

Noy/ J I N N N J J I N I

^rby/ >> >: >9 >= >2 >1 >8 >4 >< :0

Noy/ I J N N J I I J M N

Nehbjzn 7 L

^rby/ > : 9 = 2 1 8 4 < >0Noy/ I J N N M I N N N J

^rby/ >> >: >9 >= >2 >1 >8 >4 >< :0

Noy/ J I N I J J J J I N

Hbkcb}z| 7 LL

^rby/ > : 9 = 2 1 8 4 < >0

Noy/ N I J M N J M N I

^rby/ >> >: >9 >= >2 >1 >8 >4 >< :0

Noy/ N M I I N I M N M M

Nehbjzn 7 LL

maths ijso stage-1

Documents