class 9 imo 5 years ebook

8/19/2019 Class 9 Imo 5 Years EBook

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Nlpyrhift © :2;= ̂ nhm`nm Lcyephkd Glu`dkthl`. Rrh`tmd whtf tfm pmrehsshl` lg ̂ nhm`nm Lcyephkd Glu`dkthl`. @l pkrt

lg tfhs pujchnkthl` eky jm rmprldunmd, trk`sehttmd, h` k`y glre lr jy k`y emk`s, mcmntrl`hn, emnfk`hnkc, pfltlnlpyhì,rmnlrdhì lr ltfmrwhsm, whtflut tfm prhlr pmrehsshl` lg tfm nlpyrhift flcdmr. Lw`mrsfhp lg k` mjlla dlms `lt ihvm tfm

plssmsslr tfm mjlla nlpyrhift.

Kcc dhsputms sujomnt tl Dmcfh ourhsdhnthl` l`cy.

Dhsnckhemr ? Tfm h`glrekthl` h` tfhs jlla hs tl ihvm ylu tfm pktf tl sunnmss jut ht dlms ̀ lt iukrk`tmm ;22% sunnmss ks

tfm strktmiy hs nlepcmtmcy dmpm`dm`t l` hts mxmnuthl`. K`d ht hs jksmd l` ckst ymkrs pkpmrs lg HEL mxke.

Rujchsfmd jy ? ETI Cmkr`hì Emdhk (R) Ctd.

Nlrplrktm Lgnm ? Rclt 88, :`d Gcllr, ^mntlr 44 H`sthtuthl`kc Krmk, Iurikl`, Fkryk`k.

Rfl`m ? 2;:4 - 48=;:22

Ymj? eti.h` Mekhc? h`glBeti.h`

Zmid. Lgnm ? 427, Tko Kpt., Zhì Zlkd, @mkr ^kgdkrouì Flsphtkc, @mw Dmcfh-;;22:8

Whsht www.eti.h ̀glr juyhì jllas l`ch`m.


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4ª tf HEL :2;2

=ª tf HEL :2;;

7ª tf HEL :2;: - ^MT K

7ª tf HEL :2;: - ^MT J

9ª tf HEL :2;> - ^MT K

9ª tf HEL :2;> - ^MT J

6ª tf HEL :2;4 - ^MT K

6ª tf HEL :2;4 - ^MT J

Nl`tm`ts

NCK^^ ;:


4/69

H`tmr`kthl`kcEktfmekthns

Lcyephkd

H`tmr`kthl`kc

Ektfmekthns

Lcyephkd

H`tmr`kthl`kc

Ektfmekthns

Lcyephkd

@kthl`kc^nhm`nm

Lcyephkd

@kthl`kc

^nhm`nm

Lcyephkd

@kthl`kc

^nhm`nm

Lcyephkd

@kthl`kc

Nyjmr

Lcyephkd

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H`tmr`kthl`kcMìchsf

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H`tmr`kthl`kc

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H`tmr`kthl`kc

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ETIN^^

^mrhms

ETI

N^^

^mrhms

ETI

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^mrhms

ETI YLZAJLLA^ / LCXERHKD JLLA^

NCK^^ ;

NCK^^ :

NCK^^ >


5/69

H`tmr`kthl`kc

Ektfmekthns

Lcyephkd

H`tmr`kthl`kc

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H`tmr`kthl`kc

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Lcyephkd

@kthl`kc

Nyjmr

Lcyephkd

H`tmr`kthl`kc

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H`tmr`kthl`kc

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H`tmr`kthl`kc

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ETI

N^^

^mrhms

ETI

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^mrhms

ETI

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^mrhms

NCK^^ 4

NCK^^ =

NCK^^ 7



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H`tmr`kthl`kc

Ektfmekthns

Lcyephkd

Ektf H[

Nfkccmìm

Ektf H[

Nfkccmìm

H`tmr`kthl`kc

Ektfmekthns

Lcyephkd

@kthl`kc

^nhm`nm

Lcyephkd

^nhm`nm H[

Nfkccmìm

^nhm`nm H[

Nfkccmìm

@kthl`kc

^nhm`nm

Lcyephkd

@kthl`kc

Nyjmr

Lcyephkd

Rsynflcliy lg

ûnnmss

@kthl`kc

Nyjmr

Lcyephkd

H`tmr`kthl`kc

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Lcyephkd

Tfm ^mnrmts lg

^]NNM^^

H`tmr`kthl`kc

Mìchsf

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ETI

N^^

^mrhms

Ekstmr Em`tkc

Kjhchty h` >2 Dkys

Ekstmr Em`tkc

Kjhchty h` >2 Dkys

ETI

N^^

^mrhms


NCK^^ 9

NCK^^ 6


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H`tmr`kthl`kc

Ektfmekthns

Lcyephkd

@kthl`kc

^nhm`nm

Lcyephkd

@kthl`kc

Nyjmr

Lcyephkd

H`tmr`kthl`kc

Mìchsf

Lcyephkd


NCK^^ ;2


Lcyephkd

@kthl`kc^nhm`nm

Lcyephkd

@kthl`kcNyjmr

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H`tmr`kthl`kcMìchsf

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Ektf H[

Nfkccmìm

^nhm`nm H[

Nfkccmìm

Rsynflcliy lg

ûnnmss

Tfm ^mnrmts lg

^]NNM^^

Ekstmr Em`tkc

Kjhchty h` >2 Dkys

Ektf H[

Nfkccmìm

^nhm`nm H[

Nfkccmìm

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ûnnmss

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^]NNM^^

Ekstmr Em`tkc

Kjhchty h` >2 Dkys


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@kthl`kc

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9/69

Nckss

; tl ;2


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GL]@DKTHL@ NL]Z^MGlr Nckssms 9, 6, 8 & ;2

OMM (Ekh` & Kdvk`nmd) | KHRET | JLKZD^ | LCXERHKD | @T^M

Nckss 9

Nckss 8

Nckss ;2

Nckss 6


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4tf

Xmkr :2;2

Nckss 8

Nlpyrhift©:2;=. ̂ nhm`nm Lcyephkd Glu`dkthl` (^LG)


12/69

:4tf HEL | Cmvmc-H | Nckss 8

^MNTHL@ H ? CLIHNKC ZMK^L@H@I

;. K rkt ru`s :2 e tlwkrds Mkst k`d tur`s tl rhift, ru`s ;2 e k`d tur`s tl rhift, ru`s 8 e k`d kikh`

tur`s tl cmgt, ru`s = e k`d tur`s tl cmgt, ru`s ;: e k`d gh`kccy tur`s tl cmgt k`d ru`s 7 e. @lw wfhnf

dhrmnthl` hs tfm rkt gknhì<

(K) Mkst (J) Ymst (N) @lrtf (D) ^lutf

:. Nfllsm tfm ldd ùemrkc pkhr/irlup h` tfm ihvm` qumsthl` ?

(K) : „ 6 (J) > „ :9 (N) 4 „ >: (D) = „ ;:=

>. Tfm ihvm` qumsthl` nl`tkh`s glur prljcme ghiurms ekramd ;, :, > k`d 4. ^mcmnt k ghiurm grle kelìst

tfm lpthl`s wfhnf whcc nl`thùm tfm skem smrhms ks ihvm` h` tfm Rrljcme ghiurms.

; : > 4

<

Rrljcme Ghiurms

(K) (J) (N) (D)

4. Yfkt nlems `mxt h` tfm ihvm` pkttmr` <

;2, ;8, 42, 99, ;=6, \\\;; (J) >29 (N) >2; (D) :88

=. Nlu`t tfm ùejmr lg nujms h` tfm ihvm` ghiurm.

(K) :>

(J) :4

(N) :=

(D) @l`m lg tfmsm

7. Twl plshthl`s lg k dhnm krm ihvm`. Yfm` : hs kt tfm tlp, wfhnf lg tfm glcclwhì

ùejmrs nlucd jm kt tfm jlttle<

(K) ; (J) :

(h) (hh)(N) > (D) 4

9. Hg 9 ; 5 74Ͱ > 8 5 ;44. Yfkt hs tfm vkcum lg = 7 <

(K) :: (J) == (N) 77 (D) ;:;

6. :2 grhm`ds emmt kt k ekrrhkim rmnmpthl` lg tfmhr nleel` grhm`d. Mvmryl`m lg :2 grhm`ds sflla fk`ds

whtf mknf ltfmr l`cy l`nm. Gh`d tfm ùejmr lg fk`dsfkams.

(K) 422 (J) >62 (N) 42 (D) ;82

8. Yfhnf lg tfm ihvm` lpthl`s whcc nlem `mxt h` tfm ihvm` smrhms <

_]K, VLN, WHM, TNI, \\\\


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> 4tf HEL | Cmvmc-H | Nckss 8

;2. Tfm ihvm` qumsthl` nl`shsts lg twl smts lg ghiurms. Ghiurms ;, :, > k`d 4 nl`sthtutm tfm Rrljcme

smt. Tfmrm hs k dmgh`htm rmckthl`sfhp jmtwmm` ghiurms ; k`d :. Mstkjchsf k shehckr rmckthl`sfhp jmtwmm`

ghiurms > k`d 4 jy nfllshì ghiurm 4 grle tfm kctmr`kthvms.

; : > 4

<

Rrljcme ^mt

(K) (J) (N) (D)

;;. L`m mvm`hì jmglrm su`smt twl grhm`ds ûeht k`d Elfht wmrm tkcahì tl mknf ltfmr gknm tl gknm. Hg

Elfht's sfkdlw wks mxkntcy tl fhs rhift shdm, wfhnf dhrmnthl` wks ûeht gknhì<

(K) @lrtf (J) ^lutf (N) Ymst (D) @l`m lg tfmsm

;:. ^krtfka rmemejmrs tfkt fhs jrltfmr' s jhrtfdky hs kgtmr ;=tf jut jmglrm ;6 tf lg Gmjrukry wfmrmks fhs

shstmr Aksfhsf rmemejmrs tfkt fmr jrltfmr's jhrtfdky hs kgtmr ;7 tf jut jmglrm ;8 tf lg Gmjrukry. L`

wfhnf dky h` Gmjrukry hs ^krtfka's jrltfmr's jhrtfdky<

(K) ;7tf (J) ;9tf (N) ;6tf (D) ;8tf

;>. Lut lg tfm glur ghiurms (K), (J), (N) k`d (D), tfrmm krm shehckr h` k nmrtkh` wky. Flwmvmr, l`m ghiurm

hs `lt cham tfm ltfmr tfrmm. Nfllsm tfm ghiurm wfhnf hs dhggmrm`t grle tfm rmst.

(K) (J) (N) (D)

;4. Gh`d tfm ehsshì nfkrkntmr h` tfm ihvm` qumsthl`. 9 8 :; :9

4 : >7 ;6

8 4 =4 <(K) ;6 (J) :4

(N) >7 (D) 46

;=. H` tfm ihvm` ùejmr smqum`nm, flw ek`y sunf mvm` ùejmrs krm tfmrm wfhnf krm mxkntcy dhvhshjcm

jy hts heemdhktm prmnmdhì ùejmr jut `lt mxkntcy dhvhshjcm jy hts heemdhktm glcclwhì ùejmr<

> 6 4 ; = 9 : 6 > 4 6 8 > 8 4 : ; = 6 :

(K) L`m (J) Twl (N) Tfrmm (D) Glur

;7. Hg 'k' emk`s 'pcus', 'j' emk`s 'ehùs', 'n' emk`s 'eucthpchmd jy' k`d 'd' emk`s 'dhvhdmd jy' tfm`;6 n ;4 k 7 j ;7 d 4 5 <

(K) 7> (J) :=4 (N) :66 (D) ;:26

;9. Tfm ùejmrs h` tfm ihvm` ghiurms krm krrkìmd knnlrdhì tl k pkrthnuckr rucm. ^mcmnt tfm nlrrmnt

k`swmr wfhnf hs tl jm wrhttm` kt tfm pcknm lg shi` lg h`tmrrlikthl` glr tfhrd ghiurm.

(K) >; 8

:= ;6

>7

;7

4

6; :7

48

74

:=

74 <

>7

;44(J) :>

(N) :4

(D) :=

4tf HEL - :2;2



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44tf HEL | Cmvmc-H | Nckss 8

;6. Flw ek`y squkrms dlms tfm glcclwhì ghiurm nl`tkh`<

(K) :9 (J) ;8 (N) >2 (D) @l`m lg tfmsm

;8. Flw ek`y pkhrs lg cmttmrs krm tfmrm h` tfm wlrd 'CK@I]H^F' wfhnf fkvm ks ek`y cmttmrs jmtwmm`

tfme h` tfm wlrd ks h` tfm kcpfkjmt<

(K) @hc (J) L`m (N) Tfrmm (D) Glur

:2. K jus stkrts grle nhty V. Tfm ùejmr lg wlem` h` tfm j us hs fkcg lg tfm ùejmr lg em`. H`

nhty X, ;2 em` cmkvm tfm jus k`d ghvm wlem` m`tmr. @lw, ùejmr lg em` k`d wlem` hs mqukc. Flw

ek`y pkssmìmrs m`tmrmd tfm jus h` tfm jmih``hì<

(K) ;= (J) >2 (N) >7 (D) 4=

^MNTHL@ HH ? EKTFMEKTHNKC ZMK^L@H@I

:;. Tfm ùejmr -(> >)(> + >) hs k/k` \\\\ .

(K) Zkthl`kc ùejmr (J) @kturkc ùejmr (N) Zmkc ùejmr (D) Kcc lg tfmsm

::. Yfhnf lg tfm glcclwhì plcy`lehkcs fks ( x + ;) ks k gkntlr<

H. x > + x : + x + ; HH. x 4 + x > + x : + x + ;

HHH. x 4 + > x > + > x „: + x + ; HW. x > + x : „ (: + : )x + :

(K) L`cy H (J) L`cy HHH (N) HH k`d HW (D) H k`d HH

:>. Twl dhsth` nt ch` ms \\\\\ .

(K) Kcwkys h`tmrsmnt (J) Kcwkys mhtfmr h`tmrsmnt lr krm pkrkccmc

(N) Kcwkys fkvm twl nleel` plh`ts (D) @l`m lg tfmsm

:4. H` tfm ihvm` ghiurm, vkcum lg x hs \\\\ .

K D

N

J

>4² 4=²

>2² x

(K) 4=² (J) >4² (N) 74² (D) ;28²

:=. Yfhnf lg tfm glcclwhì stktmem`ts hs nlrrmnt <

(K) K trhkìcm fks twl rhift k ìcms.

(J) Kcc tfm kìcms lg k trhkìcm krm elrm tfk` 72².

(N) K` mxtmrhlr kìcm lg k trhkìcm hs kcwkys irmktmr tfk` tfm lpplshtm h`tmrhlr kìcms.

(D) Kcc tfm kìcms lg k trhkìcm krm cmss tfk` 72².

:7. K plh`t hs dmgh`md ks \\\\\ .

(K) Tfkt wfhnf fks `l cmìtf `l jrmkdtf `l fmhift. (J) êkcc pkrt lg k ch`m whtf `l cmìtf.

(N) Dhem`shl`cmss, jut rmprmsm`tmd jy dlt l`cy. (D) ]`dmgh`md tmre k`d rmprmsm`tmd jy k dlt.

4tf HEL - :2;2



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= 4tf HEL | Cmvmc-H | Nckss 8

:9. L` pcltthì tfm plh`ts L (2, 2), K (>, 2), J(>, 4), N (2, 4) k`d olh`hì LK, KJ, JN k`d NL , wfhnf lg

tfm glcclwhì ghiurm hs ljtkh`md <

(K) ^qukrm (J) Zmntkìcm (N) Trkpmzhue (D) Zflejus

:6. K studm`t hs ihvm` tfrmm sthnas lg cmìt fs ;: ne, 7 ne k`d 4 ne rmspmnthvmcy. Fm hs ksamd tl ekam

k trhkìcm k`d tfm` gh`d tfm krmk lg tfm trhkìcm glremd jy tfm > sthnas <(K) >7 ne: (J) ;: ne:

(N) :4 ne: (D) Rrlvhdhì krmk `lt plsshjcm

:8. Hg ch`ms c || e k`d Òk ? Òj 5 > ? :, Ò[ 5 82² k`d Òj + Òn 5 ;22², tfm` gh`d ÒR grle ihvm` ghiurm.

c

e

K

R

[

J

k

jn

(K) :7² (J) >:² (N) ;:² (D) 7:²

>2. Yfhnf lg tfm glcclwhì hs k gkntlr lg ( x + y )> „ ( x > + y >) <

(K) x : + y : + : xy (J) x : + y : „ xy (N) xy : (D) > xy

>;. Tfrluif flw ek`y ekxheue ùejmr lg qukdrk`ts nk` k strkhift ch`m pkss <

(K) : (J) > (N) ; (D) 4

>:. Yfkt eust jm sujtrkntmd grle 4 x 4 „ : x > „ 7 x : + x „ =, sl tfkt tfm rmsuct hs mxkntcy dhvhshjcm jy

: x : + x „ ; <

(K) = (J) ;: (N) „ 4 (D) „ 7

>>. H` tfm ihvm` ghiurm, KJ || DM , tfm` emksurm lg Ò KND hs \\\\\ .

c K

N

D

J

M

42²

4>²

(K) 4>² (J) 42² (N) 6>² (D) 89²

>4. Hg -

-

-

9 ; 9 + ;5 + 9,

9 + ; 9 ; k j tfm` gh`d tfm vkcums lg k k`d j.

(K) k 5 2, j 5>

: (J)

>

: k

-

5 , j 5 ; (N) :

2,>

k j -

5 5 (D) k 5 4, j 5 :

>=. Hg k + j + n 5 8 k`d k : + j : + n : 5 >=, tfm` gh`d tfm vkcum lg k > + j > + n > „ >kjn.

(K) =: (J) ;26 (N) :;7 (D) ;6:

>7. Hg lrdh`ktm lg k plh`t hs zmrl, tfm` tfhs plh`t kcwkys chms \\\\ .

(K) L` tfm x-kxhs (J) L` tfm y-kxhs (N) H` tfm HHHrd qukdrk`t (D) H` tfm HWtf qukdrk`t

4tf HEL - :2;2



16/69

74tf HEL | Cmvmc-H | Nckss 8

>9. KJND hs k ihvm` ghmcd wflsm shdms krm h`dhnktmd. Hg ÒDKJ 5 82², tfm` krmk lg tfm ghmcd hs \\\.

D N

KJ

:6 e

;= e

42 e

8 e

(K) ;62 e: (J) ;:7 e: (N) >27 e: (D) >22 e:

>6. Rlh`ts h` wfhnf kjsnhssk k`d lrdh`ktm fkvm dhggmrm`t shi`s whcc chm h` \\\\ .

(K) Hst k`d HHHrd qukdrk`ts (J) HHHrd k`d HWtf qukdrk`ts (N) HH`d k`d HHHrd qukdrk`ts (D) HH`d k`d HWtf qukdrk`ts

>8. KJN hs k` hslsnmcms trhkìcm whtf KJ 5 KN . Kcthtudms krm drkw` tl tfm shdms KJ k`d KN grle vmrthnms

J k`d N . L`m kcthtudm NG hs glu`d tl jm 4 ne k`d JN 5 = ne. Gh`d MN , wfmrm JM hs kcthtudm tl

shdm KN .

(K) 4 ne (J) = ne (N) > ne (D) @l`m lg tfmsm

42. H` ihvm` ghiurm, hg KJ || ND || MG , R[ || Z^ , ÒZ[D 5 :=² k`d ÒN[R 5 72², tfm` Ò[Z^ hs mqukctl \\\\ .

K

N

M

J

D

G

^

Z

[

R

72²

:=²

(K) 6=² (J) ;>=² (N) ;4=² (D) ;;2²

^MNTHL@ HHH ? MWMZXDKX EKTFMEKTHN^

4;. Tfm E.R. lg k nkemrk hs>

:lg tfm N.R. k`d ^.R. hs

8

;2lg E.R. Gh`d tfm pmrnm`tkim lg prlght lr clss.

(K) :=% prlght (J) >=% prlght (N) >>.>>% clss (D) @l`m lg tfmsm

4:. R nk` dl k olj h` ;2 dkys, [ nk` dl tfm skem olj h` ;: dkys k`d Z nk` dl tfm skem olj h` ;= dkys.

H` flw ek`y dkys tfmy whcc gh`hsf tfm wlra tlimtfmr<

(K) : (J) 4 (N) 7 (D) ;:

4>. Krekk` ilms ;2 ae dhstk`nm whtf kvmrkim spmmd lg 7 ae/fr wfh cm tfm rmst :2 ae fm trkvmcs whtf

k` kvmrkim spmmd lg ;= ae/fr. Yfkt hs tfm kvmrkim spmmd lg Krekk` durhì tfm wflcm olur`my<

(K) ;2 ae/fr (J) ;: ae/fr (N) ;> ae/fr (D) ;4.= ae/fr

44. K gktfmr hs tfrmm thems ks lcd ks fhs sl`. Kgtmr twmcvm ymkrs, fhs kim whc c jm twhnm tfkt lg fhs sl`.

Gh`d tfmhr prmsm`t kims.

(K) ;2, >2 (J) ;:, >7 (N) 7, >7 (D) ;:4, :4

4=. :=2 em` tlla k dhp h` k wktmr tkà kt k them, wfhnf hs 62 e Ù =2 e. Yfkt hs tfm rhsm h` tfm wktmr

cmvmc hg tfm kvmrkim dhspcknmem`t lg ; ek` hs 4 e> <

(K) :: ne (J) := ne (N) ;6 ne (D) >2 ne

4tf HEL - :2;2



17/69

9 4tf HEL | Cmvmc-H | Nckss 8

47. Zkfuc wm`t tl purnfksm k @lahk eljhcm fk`dsmt. Tfm sflpammpmr tlcd fhe tl pky :2% tkx hg fm ksamd

glr tfm jhcc. Zkfuc ek`kims tl imt tfm dhsnlu`t lg =% l` tfm kntukc skcm prhnm lg tfm eljhcm k`d fm

pkhd tfm sflpammpmr >>:= whtflut tkx. Jmshdms fm ek`kims tl kvlhd tl pky :2% tkx l` tfm kcrmkdy

dhsnlu`tmd prhnm. Yfkt hs tfm kelu`t lg dhsnlu`t tfkt fm fks ilt <

(K) b 9=2 (J) b >9= (N) b 69= (D) b =:=

49. KJN hs k trhkìcm. D, M k`d G krm tfm ehd-plh`ts lg tfm shdms JN , NK k`d KJ rmspmnthvmcy. Tfm rkthl

lg tfm krmk lg D KJN k`d DDMG hs \\\\\

(K) 4 ? ; (J) = ? ; (N) > ? ; (D) Nk`'t jm dmtmreh`md

46. R k`d [ nk` dl k phmnm lg wlra h` ;: dkys, [ k`d Z h` ;= dkys, Z k`d R h` :2 dkys. H` flw ek`y

dkys nk` Z kcl`m dl ht<

(K) 72 (J) =2 (N) := (D) :4

48. K tm`t hs h` tfm glre lg rhift nhrnuckr nl`m ;2.= e fhif, tfm dhkemtmr lg tfm jksm jmhì ;> e. Hg

6 em` krm h` tfm tm`t, gh`d tfm kvmrkim ùejmr lg nujhn emtrms lg khr spknm pmr ek`.

(K) >

>::6

e> (J) =8.9= e> (N) 8

>7;>

e> (D) >

=6>:

e>

=2. Hg tfm k`ùkc h`nrmksm h` tfm plpuckthl` jm :2% k`d tfm prmsm`t plpuckthl` jm ;2,222. Yfkt whcc

jm tfm plpuckthl` kgtmr > ymkrs <

(K) ;7,222 (J) ;9,:62 (N) ;4,422 (D) ;,9:6

^RKNM GLZ ZL]IF YLZA

4tf HEL - :2;2



18/69

=tf

Xmkr :2;;

Nckss 8



19/69

: =tf HEL - :2;;


;. ^tudy tfm glcclwhì h`glrekthl` k`d k`swmr tfm qumsthl` ihvm` jmclw ht.

K jknasehtf fks m hrl` krthnms K, J, N, D k`d M, mknf fkhì k dhggmrm`t wmhift.

(h) K wmhifs twhnm ks eunf ks J. (hh) J wmhifs glur k`d k fkg thems ks eunf ks N.

(hhh) N wmhifs fkg ks eunf ks D. (h) D wmhifs fkg ks eunf ks M.

(v) M wmhifs cmss tfk` K jut elrm tfk` N.

Yfhnf lg tfm glcclwhì hs tfm chiftmst<

(K) K (J) J (N) N (D) D

:. Nfllsm tfm ldd ùemrkc pkhr/irlup.

(K) 8 „ > (J) ;

:

;

6√ (N)

;

>

;

;:√ (D) :4 „ 7

>. ^mmnt k iurm grle kelìst tfm lpthl`s wfhnf wh nl`thùm tfm skem smrhms ks mstkjhsfmd jy

tfm m Rrljme Ghiurms.

(K) (J) (N) (D)

4. Lut lg glur iurms ekramd (K), (J), (N) k`d (D) tfrmm krm shehkr h` k nmrtkh` ek``mr. Flwmmr l`m

iurm hs `lt ham tfm ltfmr tfrmm. Nfllsm tfm iurm wfhnf hs dhggmrm`t grle tfm rmst.

(K) (J) (N) (D)

=. H` tfm ektrhx tfmrm krm mhift dmshi`s k`d l`m spknm hs cmgt jckà ks sflw` jy k qumsthl` ekra.Yfhnf k`swmr iurms wh rmpknm tfm qumsthl` ekra<

<

(K) (J) (N) (D)

7. Tfm jkà jkk`nm lg Rurk` hs elrm tfk` tfkt lg ûsfek jut mss tfk` tfm jkà jkk`nm lg ^hìf.

Hg tfm jkà jkk`nm lg Rurk`, ûsfek k`d ^hìf jm x, y k`d z rmspmnthvmcy tfm` wfhnf lg tfm

glcclwhì hs nlrrmnt<

(K) x 3 y 3 z (J) y 3 x 3 z (N) z 3 x 3 y (D) x 3 z 3 y

9. Gh`d tfm ùejmr lg trhkìms h` tfm ihm` iurm.

(K) ;6

(J) :2

(N) :4

(D) @l`m lg tfmsm



20/69

>=tf HEL - :2;;

6. Yfhnf ùejmr whcc rmpcknm tfm qumsthl` ekra<

6 6 4

7 7 7;4 ;4 <

4 6 =

;2 ;4 ;;;6 :: ;=

(K) 6 (J) 4 (N) ;2 (D) 7

8. Tfmrm krm tfrmm phc ckrs V, X k`d _ lg dhggmrm`t fmhifts. Tfrmm sphdmrs K, J k`d N stkrt tl nchej l`

tfmsm phcckrs sheuctk`mluscy. H` l`m nfk`nm K nchejs l` V = ne jut schps dlw` ; ne. J nchejs

l` X 7 ne jut schps dlw` > ne. N nchejs l` _ 9 ne jut schps dlw` : ne. Hg mknf rmquhrms =2

nfk`nms tl rmknf tfm tlp lg tfm phkr, wfkt hs tfm fmhift lg tfm sflrtmst phkr<

(K) ;44 ne (J) ;=: ne (N) ;=> ne (D) ;4; ne

;2. Irlup tfm ihm` iurms h`tl tfrmm nkssms ushì mknf iurm l ̀y l`nm.

(K) >, 4, 81 =, 9, 61 ;, :, 7 ; : >

4 = 7

9 6 8

(J) ;, =, 71 :, 4, 61 >, 9, 8

(N) 4, 7, 61 >, =, 91 ;, :, 8

(D) ;, :, 91 >, =, 81 4, 7, 6

;;. Hg >:4 Ù ;=2 5 =4, :=; Ù 42: 5 46 k`d =:> Ù >4= 5 ;:2, tfm` 7=; Ù >4= 5 <

(K) ;:2 (J) 6= (N) ;44 (D) 72

;:. Gh`d tfm iurm wfhnf nl`tkh`s tfm Ghi. (V) ks hts mejmddmd pkrt.

Ghi. (V)

(K) (J) (N) (D)

;>. H` tfm ùejmr =8247:96;> rst k`d shxtf dhihts krm h`tmrnfkìmd1 k`d shehkry tfm plshthl`s lg

smnl`d k`d smvm`tf dhihts k`d sl l` krm h`tmrnfkìmd. Yfhnf lg tfm glcclwhì whcc jm tfm 4 tf dhiht

grle tfm rhift kgtmr tfm `mw krrkìmem`t<

(K) ; (J) 8 (N) 4 (D) 2

;4. H` tfm ihvm` ektrhx tfm vkcums lg K, J k`d N rmspmnthvmcy krm \\\\. (K) K 5 ;>, J 5 ;;, N 5 8 (J) K 5 ;>, J 5 8, N 5 ;;

8

J

N

K

;2

6

;:

9

;;

(N) K 5 8, J 5 ;;, N 5 ;> (D) K 5 8, J 5 ;>, N 5 ;;

;=. Twl nkrs stkrt grle lpplshtm pknms l` k ekh` rlkd, ;=2 ae kpkrt. Ghrst nkr ru`s glr := ae k`d

tkams k rhift tur` k`d tfm` ru`s ;= ae. Ht tfm` tur`s cmgt k`d ru`s glr k`ltfmr := ae k`d tfm`

tkams tfm dhrmnthl` tl rmknf tfm ekh` rlkd. H` tfm emk` them, dum tl k eh`lr jrmka dlw` tfm ltfmr

nkr fks ru` l`cy >= ae kclì tfm ekh` rlkd. Yfkt wlucd jm tfm dhstk`nm jmtwmm` tfm twl nkrs kt

tfhs plh`t<

(K) 7= ae (J) 9= ae (N) 62 ae (D) 6= ae



21/69

4 =tf HEL - :2;;

;7. @mmke, wfl hs Zlfht's dkuiftmr, skys tl H`du, "Xlur eltfmr Zmmtk hs tfm yluìmr shstmr lg ey

gktfmr, wfl hs tfm tfhrd nfhd lg ^lfkòh." Flw hs ^lfkòh rmktmd tl H`du<

(K) Ektmr`kc u`ncm (J) Gktfmr (N) Irk`dgktfmr (D) Gktfmr-h`-ckw

;9. Hg Ell` hs nkmd ^tkr, ^tkr hs û`, û` hs Mkrtf, Mkrtf hs Ouphtmr, Ouphtmr hs Ekrs k`d Ekrs hs

Emrnury, wfmrm dlms ek` hm<

(K) Ekrs (J) Ouphtmr (N) Mkrtf (D) û`

;6. H` tfm ihm` iurm, squkrm rmprmsm`ts dlntlrs, trhkìm rmprmsm`ts kdhms k`d nhrnm rmprmsm`ts

suriml`s. Yfhnf cmttmr rmprmsm`ts tfm ckdhms wfl krm jltf dlntlrs k`d suriml`s<

R

^ T

Z

]

[

(K) ] (J) T (N) ^ (D) R

;8. H` tfm ihm` qumsthl`, wfhnf ùejmr wh rmpknm tfm qumsthl` ekra<

2 ; <

4 6 2

= 9 ;;7 7 :

9 4 :

(K) 2 (J) : (N) ;; (D) ;:

:2. Hg tfm plshthl`s lg tfm tfhrd k`d tm`tf mttmrs lg tfm wlrd DLN]EM@TKTHL@ krm h`tmrnfkìmd, k`d

hamwhsm tfm plshthl`s lg tfm glurtf k`d smm`tf mttmrs, tfm smnl`d k`d shxtf mttmrs, krm ksl

h`tmrnfkìmd, tfm` wfhnf lg tfm gllwhì wh jm mmm`tf mttmr grle tfm rhift m`d<

(K) N (J) H (N) T (D) ]

^MNTHL@ HH ? EKTFMEKTHNKc ZMK^L@H@I

:;. Hg x 3 „;, tfm` wfhnf lg tfm gllwhì mxprmsshl`s flds<

(K) x 3 x: 3 x> (J) x 3 x> 3 x: (N) x: 3 x> 3 x (D) x> 3 x 3 x:

::. Hg tfm pmrhemtmr lg k rmntkìukr ikrdm` plt hs 62 emtrms, wfhnf lg tfm gllwhì nlud jm tfm

cmìtf lg l`m lg hts shdms<

H. >2 emtrms HH. 42 emtrms HHH. =2 emtrms

(K) H l`cy (J) HH l`cy (N) HHH l`cy (D) H k`d HH

:>. H` tfm kdolh`hì iurm, nhrnms whtf nm`trms kt C, E k`d @ mknf fkvm k rkdhus lg : u`hts k`d krmpcknmd ks sflw` fmrm. Hg R[Z^ hs tfm sekmst rmntkìm tfkt wh m`nlsm tfm > nhrnms, wfkt hs

tfm krmk lg R[Z^<

C E @

R [

Z ^

(K) 6 sq.u`hts (J) ;: sq.u`hts (N) ;7 sq.u`hts (D) >: sq.u`hts

:4. Hg >x + :y 5 ;9 k`d x k`d y krm plshthm h`tmimrs, tfm` y nlucd jm wfhnf lg tfm glcclwhì<

(K) : (J) > (N) 4 (D) =



22/69

==tf HEL - :2;;

:=. H` tfm ihm` iurm c;

|| c:. Yfhnf lg tfm glcclwhì eust jm trum<

(K) g 5 j

(J) j 5 n

(N) n 5 m

(D) d 5 g

:7. H` tfm kdolh`hì iurm, plh`t R tfm h`tmrsmnthl` lg ch`ms c; k`d c

: fks nllrdh`ktms (k, j) ks sflw`

fmrm. Yfhnf lg tfm glcclwhì nlucd jm tfm lrdmrmd pkhr (k, j)<

X

c :

c ;

( )k,j

V

R

L

(K) = =

:,

√

(J) √

; =

6, (N) (2, 4) (D)

:

>

;

>,

:9. H` tfm ihm` iurm, tfrmm mquhktmrk trhkìms fkm k nleel` mrtmx tfm` x + y + z 5

(K) 82² (J) ;:2² (N) ;=2² (D) ;62²

:6. Hg k rhift t rhkìcm fks shdms lg cmìtf ; k`d :, wfhnf lg tfm glcclwhì nlucd jm tfm cmìtf lg tfm

rmekh`hì shdm<

H. ; HH. : HHH. >

(K) H l`cy (J) HH l`cy (N) HHH l`cy (D) H k`d HHH l`cy

:8. Tfm mxprmsshl` (k + j + n): + (k + j „ n): + (k „ j + n): + (j + n „ k): mqukcs \\\\.

(K) 4(kj + kn + jn) (J) :(k: + j: + n: + kj + jn + kn)

(N) 4(k: + j: + n:) (D) (k: + j: + n:)

>2. K dhm hs rlmd ;2,=22 thems. Tfm grmqum`ny lg mknf lutnlem hs sflw` h` tfm tkjm. Yfkt hs tfm

mephrhnkc prljkjhchty lg tfm lutnlems lg eucthpcms lg ><

Lutnlem

Grmqum`ny ;79= ;9:= ;74: ;976 ;69> ;6;9

(K) ;;=>

>=22 (J)

;;=>

>4=8 (N)

;;=>

;2=22 (D)

>4=8

;2=222

>;. H` D's KJN k`d R[Z, KJ 5 R[, JN 5 [Z krm mxtm`dmd tl V k`d X rmspmnthvmcy k`d ∢ KJV 5 ∢R[X.

]`dmr wfhnf nlìrum`ny nrhtmrhl`, tfm trhkìms krm nlìrum`t<

(K) ^^^ (J) ^KK (N) ^^K (D) ^K^

>:. Gh`d tfm kum lg ;;9748

;99;=7;

; 7ç

æééé

÷

öùùù

/

.

(K) >/;; (J) ;>/9 (N) 9/;; (D) 9/;>



23/69

7 =tf HEL - :2;;

>>. KJND hs k trkpmzhue, h` wfhnf KJ || DN, KD P KJ k`d M & G krm plh`ts l` KD & JN rmspmnthvmcy.

JD hs olh`md. Hg ∢MGN 5 ;;2², ∢ KJD 5 72², ∢JDN 5 x ² k`d ∢DNG 5 y ², tfm` kums lg x k`d y krm

\\\\.

(K) 72², 92² (J) =2², 62² (N) 82², 42² (D) >2², ;22²

>4. Gh h` tfm jkà ?

Hg k strkhift ch`m emmts twl ltfmr strkhift ch`ms sl ks tl ekam tfm sue lg tfm twl h`tmrhlr kìcms

l` l`m shdm lg tfm trk`smrsk mss tfk` twl rhift kìms, tfm` tfm ltfmr strkhift h`ms mxtm`dmd

h``htmy, wh emmt \\\\ tfm trk`smrsk.

(K) L` tfkt shdm lg (J) L` k`ltfmr shdm lg (N) L` (D) Nk`'t jm dmtmreh`md

>=. Yfhnf lg tfm glcclwhì lpth l`s h` Nlcue` H whtf rmksl`s h` Nlcue` HH hs nlrrmnt whtf rmspmnt tl

tfm glcclwhì qumsthl` ?

Flw ek`y h`mkr mqukthl`s h` x k`d y nk` jm skthsmd jy x 5 ; k`d y 5 ><

Nlcue` H Nlcue` HH

(K) L`cy l`m (h) ks l`cy x 5 ;, y 5 > hs ihvm`.

(J) Mxkntcy twl (hh) l`m glr x 5 ;, smnl`d glr y 5 >.(N) H``htmcy ek`y (hhh) l`m glr x 5 ;, smnl`d glr y 5 > k`d tfhrd glr x + y 5 >.

(D) Mxkntcy tfrmm (hv) ks plh`t (;, >) chms l` irkpf k`d tfrluif l`m plh`t h``htm ch`ms nk` pkss, sl

wm imt h``htm irkpfs lr h``htm mqukthl`s.

>7. Hg tfm prldunt lg twl surds hs k rkthl`k ùejmr, tfm` mknf l`m lg tfme hs nkmd tfm \\\\\ lg tfm

ltfmr \\\\\.

(K) @mikthvm (J) Zkthl`kchshì gkntlr (N) Nlòuiktm surd (D) Jh`lehkc surd

>9. Hg l`m cmi lg k` hslsnmcms rhift-kìcmd trhkìcm hs h`n rmksmd jy 7 ne k`d tfm ltfmr cmi hs h`n rmksmd

jy 4 ne, tfm` nfkìm h` krmk lg tfm trhkìms hs :4 sq ne. Gh`d tfm mìtf lg tfm mi lg tfm lrhih`k

trhkìcm.

(K) =

;:ne (J)

;:

=ne (N)

;

=ne (D)

;

;:ne

>6. Zmekh`dmr wfm` k: + j: + :(kj + jn + nk) hs dhvhdmd jy (k + j + :n) hs \\\\\\\.

(K) k + j (J) kj (N) k „ j (D) 2

>8. Tfm vkcum lg x

x

x

x

x

x

c

e

c e

e

`

e `

`

c

` c

:

:

:

:

:

:

+ + +⋍ ⋍ 5 \\\\\\.

(K) x (J) „; (N) ; (D) 2

42. Kcc tfm tfrmm qukdrhcktmrkcs KDMN, KJHF k`d JNIG krm squkrms k`d ∢ KJ N 5 82². Hg tfm krmk lg

KDMN 5 x: k`d krmk lg KFHJ 5 y:(x: 0 y:), tfm` `d tfm krmk lg JNIG<

K

J N

D

M

G I

F

H

(K) x: + y: (J) :y: (N) :x: (D) x: „ y:



24/69

9=tf HEL - :2;;

^MNTHL@ HHH ? MvMZXDKX EKTFMEKTHN^

4;. K nkss stkrts kt ;2 k.e. k`d ksts th ;.:9 p.e. Glur pmrhlds krm fmd durhì tfhs h`tmrk. Kgtmr mmry

pmrhld, = ehùtms krm ihm` grmm tl tfm studm`ts. Tfm mxknt durkthl` lg mknf pmrhld hs \\\\.

(K) 4: ehùtms (J) 46 ehùtms (N) =; ehùtms (D) => ehùtms

4:. H` Kru`'s lph`hl`, fhs wmhift hs irmktmr tfk` 7= ai jut mss tfk` 9: ai. Fhs jrltfmr dlms `lt kirmmwhtf Kru` k`d fm tfhàs tfkt Kru`'s wmhift hs irmktmr tfk` 72 ai jut mss tfk` 92 ai. Fhs eltfmr's

hmw hs tfkt fhs wmhift nk``lt jm irmktmr tfk` 76 ai. Hg k lg tfme krm nlrrmnt h` tfmhr msthekthl`s,

wfkt hs tfm kvmrkim lg dhggmrm`t prljkjcm wmhifts lg Kru`<

(K) 79 ai (J) 76 ai (N) 78 ai (D) @l`m lg tfmsm

4>. K ek` wkamd dhkil`ky knrlss k squkrm plt. Kpprlxhektmy, wfkt wks tfm pmrnm`t skmd jy `lt

wkcahì kclì tfm mdims<

(K) :2 (J) :4 (N) >2 (D) >>

44. K ek` purnfksms twl nclnas K k`d J kt k tltkc nlst lgb 7=2. Fm sms K kt :2% prlt k`d J kt k

clss lg :=% k`d imts tfm skem smcchì prhnm glr jltf tfm nclnas. Yfkt krm tfm purnfkshì prhnms

lg K k`d J rmspmnthvmcy<

(K) b ::=, b 4:= (J) b :=2, b 422 (N) b :9=, b >9= (D) b >22, b >=2

4=. Mhift pmlpcm krm pck``hì tl sfkrm mqukccy tfm nlst lg k rm`tkc nkr. Hg l`m pmrsl` whtfdrkws grle

tfm krrkìmem`t k`d tfm ltfmrs sfkrm mquky tfm m`thrm rm`tk lg tfm nkr, tfm` tfm sfkrm lg mknf

lg tfm rmekh`hì pmrsl`s hs h`nrmksmd jy \\\\ lg tfm lrhih`kc sfkrm.

(K) ;/8 (J) ;/6 (N) ;/9 (D) 9/6

47. K studm`t wks ksamd tl dhhdm k ùejmr jy 7 k`d kdd ;: tl tfm qulthm`t. Fm, flwmmr, rst kddmd

;: tl tfm ùejmr k`d tfm` dhhdmd ht jy 7, imtthì ;;: ks tfm k`swmr. Tfm nlrrmnt k`swmr sflud

fkvm jmm` \\\\.

(K) ;:: (J) ;;6 (N) ;;4 (D) ;:4

49. Zmmek jluift x pm`s kt b :.72 mknf k`d y irmmthì nkrds kt 62 pkhsm mknf. Hg tfm pm`s nlst

b ;: elrm tfk` tfm nkrds, tfm mqukthl` h`lhì x k`d y hs \\\\\.

(K) ;>x „ 4y 5 7 (J) ;>x „ 4y 5 72 (N) :72x „ 6y 5 ;22 (D) :72x „ 6y 5 ;:

46. Tl ekam k ekrrhkim tm`t, plms krm pk`tmd klì tfm pmrhemtmr lg k squkrm md kt k dhstk`nm lg

= emtrms grle mknf ltfmr k`d tfm tltkc ùejmr lg plcms usmd hs :2. Yfkt hs tfm krmk (h` sq. emtrms)

lg tfm squkrm md<

(K) =22 (J) 422 (N) 822 (D) @l`m lg tfmsm

48. Fusskh`'s wmhift hs ; ;

4thems tfm wmhift lg Zkfhe. Tfmhr tltk wmhift hs 82 ai. Yfkt hs Fusskh`'s

wmhift<

(K) 82 ai (J) =2 ai (N) 42 ai (D) :2 ai

=2. H` k nkss, tfm ùejmr lg jlys hs elrm tfk` tfm ùejmr lg ihrs jy ;:% lg tfm tltk strmìtf. Tfm

rkthl lg jlys tl ihrcs hs \\\\\.

(K) ;= ? ;; (J) ;; ? ;4 (N) ;4 ? ;; (J) 6 ? ;;



25/69

7tf

Xmkr :2;:

^MT K

Nckss 8



26/69

: 7tf HEL - ^MT K


;. H` tfm glcc lwhì qumsthl`, tfm syejl cs B, © , $ k`d % krm usmd whtf tfm glcclwhì emk`hìs ks

hccustrktmd jmclw ?

'K $ J' emk`s 'K hs `lt sekccmr tfk` J'1

'K B J' emk`s 'K hs `mhtfmr sekccmr tfk` `lr mqukc tl J'1

'K J' emk`s 'K hs `mhtfmr sekccmr tfk` `lr irmktmr tfk` J'1

'K % J' emk`s 'K hs `mhtfmr irmktmr tfk` `lr mqukc tl J'.

@lw h` tfm glcclwhì qumsthl`, kssuehì tfm ihvm` stktmem`ts tl jm trum, `d wfhnf lg tfm

tfrmm nl`ncushl`s, H, HH k`d HHH ihvm` jmclw tfme hs/krm dm`htmcy trum k`d ihvm ylur k`swmr

knnlrdhìcy.

^tktmem`ts ? A © R, R B [, [ $ Z

Nl`ncushl`s ? H A B Z HH. Z % R HHH. [ % A

(K) L`cy H k`d HH krm trum (J) L`cy HH k`d HHH krm trum

(N) L`cy HHH hs trum (D) Kcc H, HH k`d HHH krm trum

:. ^mcmnt k iurm grle kelìst tfm lpthl`s wfhnf whcc nl`thùm tfm skem smrhms ks mstkjchsfmd jy

tfm vm Rrljcme Ghiurms R, [, Z, ^ k`d T.

(K) +

N ^ (J)

+

N

^

(N)

^

N+

(D)

+

N^ +

>. ^tudy tfm glcclwhì h`glrekthl` nkrmguccy k`d k`swmr tfm qumsthl` ihvm` jmclw.

R, [, Z, ^, T, W k`d Y krm smvm` pkssmìmrs k`d H, HH, HHH krm tfrmm dhggmrm`t vmfhncms. Tfmrm krm

ktcmkst twl pkssmìmrs h` mknf vmfhncm H, HH k`d HHH k`d l`m lg tfme hs k ckdy. Tfmrm krm twl

mìh`mmrs, twl dlntlrs k`d tfrmm tmknfmrs kelì tfme. Z hs ckdy dlntlr k`d sfm dlms `lt trkvmcwhtf tfm pkhr lg shstmrs R k`d W. [, k ekcm mìh`mmr trkvmcs whtf l`cy Y, k tmknfmr h` vmfhncm H. ^

hs k ekcm dlntlr. Twl pmrsl`s jmclì tl skem prlgmsshl` dl `lt trkvmc h` tfm skem vmfhncm. R hs

`lt k` mìh`mmr k`d trkvmcs h` vmfhncm HH.

Flw ek`y ckdy emejmrs krm tfmrm kelìst tfme<

(K) Tfrmm (J) Glur (N) Tfrmm lr Glur (D) Dktk h`kdmquktm

4. H`spmntlr Okth` trkvmccmd grle fhs plchnm stkthl` glr 422 emtrms. Fm tfm` tur`md cmgt k`d trkvmccmd

=22 emtrms strkhift kgtmr wfhnf fm tur`md cmgt kikh` k`d trkvmccmd glr 422 emtrms strkhift. Fm tfm`

tur`md rhift k`d wkcamd glr k`ltfmr 722 emtrms strkhift. Flw gkr hs fm grle tfm Rlchnm stkthl`<

(K) ;.2 ae (J) ;.; ae (N) ;.4 ae (D) ;.6 ae

=. Zmkd tfm glcclwhì h`glrekthl` nkrmguccy k`d k`swmr tfm qumsthl` ihvm` jmclw ht.

(h) Tfmrm hs k irlup lg shx pmrsl`s K, J, N, D, M k`d G h` k gkehcy. Tfmy krm Rsynflclihst, Ek`kimr,

Ckwymr, Omwmccmr, Dlntlr k`d Mìh`mmr.

(hh) Tfm dlntlr hs tfm irk`dgktfmr lg G wfl hs k Rsynflclihst.

(hhh) Tfm Ek`kimr D hs ekrrhmd tl K.

(hv) N, tfm Omwmccmr, hs ekrrhmd tl tfm Ckwymr.

(v) J hs tfm eltfmr lg G k`d M.

(vh) Tfmrm krm twl ekrrhmd nlupcms h` tfm gkehcy.

Flw hs K rmcktmd tl M<

(K) Jrltfmr (J) ]`ncm (N) Gktfmr (D) Irk`dgktfmr



27/69

>7tf HEL - ^MT K

7. Whoky hs gtmm`tf grle tfm grl`t h` k nlcue` lg jlys. Tfmrm wmrm tfrhnm ks ek`y jmfh`d fhe ks

tfmrm wmrm h` grl`t. Flw ek`y jlys krm tfmrm jmtwmm` Whoky k`d tfm smvm`tf jly grle tfm m`d lg

tfm nlcue`<

(K) >> (J) >4 (N) >= (D) Dktk h`kdmquktm

9. Yfhnf lg tfm lpthl`s whcc nlem `mxt h` tfm smrhms<

OK_, CMV, @HW, RLT, \\ , flw whcc ylu nldm ‖JMKT‘<

(K) :=-:>-:4-9 (J) :=-:;-:7-9 (N) :=-::-:=-9 (D) :=-::-:7-9

;2. Hg ;:% pmlpcm h` k vhcckim krm suggmrhì grle nk`nmr k`d ;>% grle jclld prmssurm, wfhnf lg tfm

glcclwhì dhkirke jmst rmprmsm`ts tfm shna plpuckthl` lg tfm vhcckim<

(K) (J) (N)

(D)

;;. Clla kt tfm syejlc-cmttmr-ùejmr smqum`nm ihvm` jmclw.

: R O B 6 $ C J ; W # [ 7 d I Y 8 A N D > • £ = G Z 9 K X 4

Tfrm m lg tfm glcclwhì glur krm shehckr h` rmckthl` tl tfmhr plshthl`s h` tfm kjlvm smqum`nm k`d

fm`nm glre k irlup. Yfhnf l`m dlms `lt jmclì tl tfkt irlup<

(K) [ A = (J) C 7 D (N) R C d (D) ; I

;:. K nfhcd wm`t 82 e h` tfm Mkst tl clla glr fhs gktfmr, tfm` fm tur`md rhift k`d wm`t :2 e. Kgtmr tfhs

fm tur`md rhift k`d kgtmr ilhì >2 e, fm rmknfmd tl fhs u`ncm's flusm. Fhs gktfmr wks `lt tfmrm.Grle tfmrm fm wm`t ;22 e tl fhs @lrtf k`d emt fhs gktfmr h` tfm sflp. Flw gkr dhd fm emmt fhs

gktfmr grle tfm stkrthì plh`t<

(K) 62 e (J) ;22 e (N) ;42 e (D) :72 e

;>. Ektnf tfm ihvm` `mt whtf tfm nlrrmnt phnturm.

(K)

(J)

(N)

(D)

;4. Gh`d lut wfhnf lg tfm lpthl`s nlepcmtms tfm iurm ektrhx<

(K) (J)

(N)

(D)



28/69

4 7tf HEL - ^MT K

;=. K ilcdsehtf fks vm ilcd rhìs, mknf fkvhì k dhggmrm`t wmhift ?

^tktmem`t ; ? Zhì D hs wmhifhì twhnm ks eunf ks rhì M.

^tktmem`t : ? Zhì M hs wmhifhì glur thems ks eunf ks rhì G.

^tktmem`t > ? Zhì G hs wmhifhì fkcg ks eunf ks rhì I.

^tktmem`t 4 ? Zhì I hs wmhifhì fkcg ks eunf ks rhì F.

^tktmem`t = ? Zhì F hs wmhifhì cmss tfk` rhì D jut elrm tfk` rhì G.

Yfhnf lg tfm glcclwhì rmprmsm`ts tfm dmsnm`dhì lrdmr lg wmhifts lg tfm rhìs <

(K) D, M, I, F, G (J) M, I, F, D, G

(N) D, M, G, I, F (D) Dktk h`kdmquktm

;7. H` tfm glcclwhì qumsthl` grle kelìst tfm lpthl`s, smcmnt tfm l`m wfhnf skthsms tfm skem

nl`dhthl`s lg pcknmem`t lg tfm dlt ks h` Ghi. (V).

(K)

(J) (N)

(D)

;9. H` tfm ihvm` qumsthl`, wfhnf ùejmr whcc rmpcknm tfm qumsthl` ekra<

48:

7

6

8

49

=

=9:

=

4

8

67

9

>

=

=

:9

4

<

(K) ;;= (J) ;>2 (N) ;>= (D) ;42

;6. ^mcmnt k iurm grle kelìst tfm lpthl`s, wfhnf wfm` pcknmd h` tfm jckà spknm lg i. (V) wlucd

nlepcmtm tfm pkttmr`.

(K)

(J)

(N) (D)

;8. Gh`d tfm ùejmr lg qukdrhcktmrkcs h` tfm ihvm` iurm.

(K) ;2

(J) 7

(N) 8

(D) @l`m lg tfmsm

:2. Zhtk drhvms tl tfm `lrtf lg fmr pcknm lg stky kt K k`d kgtmr trkvmcchì := ae, `ds tfkt sfm fks

drhvm` h` tfm wrlì dhrmnthl`. ^fm tfm` tur`s tl fmr rhift k`d trkvmcs : ae, k`d tfm` sfm kikh`

tur`s tl tfm rhift k`d drhvms strkhift k`ltfmr := ae. Flw eunf dhstk`nm fks sfm `lw tl nlvmr tl

il jkna tl tfm stkrthì plh`t <

(K) := ae (J) : ae (N) 4 ae (D) 42 ae



29/69

=7tf HEL - ^MT K


:;. Tfm mxprmsshl` :x> + kx : + jx + >, wfmrm k k`d j krm nl`stk`ts, fks k gkntlr lg x „ ; k`d cmkvms

k rmekh`dmr lg ;= wfm` dhvhdmd jy x + :. Gh`d tfm vkcum lg k k`d j rmspmnthvmcy.

(K) „>, 6 (J) >, „6 (N) „>, „6 (D) >, 6

::. Hg 'c', '

j' k`d '

f' lg k nujlhd krm h`nrmksmd, dmnrmksmd k`d h`nrmksmd jy ;%, >% k`d :% rmspmnthvmcy,

tfm` tfm vlcuem lg tfm nujlhd \\\\\\.

(K) H`nrmksms

(J) Dmnrmksms

(N) H`nrmksms lr dmnrmksms dmpm`dh`i l` lrhih`kc dhem`shl`s

(D) Nk`'t jm nkcnucktmd whtf ihvm` dktk

:>. K jlx lg nflnlcktms nl`tkh` = nflnlcktms whtf fkrd nm`trms k`d 4 whtf slgt nm`trms.

Keht tkams k nflnlcktm, smcmntmd kt rk`dle, grle tfm jlx k`d mkts ht.

Koky tfm` tkams k nflnlcktm, smcmntmd kt rk`dle, grle tfm jlx.

Gh`d tfm prljkjhchty tfkt Keht k`d Koky jltf nfllsm k nflnlcktm whtf k fkrd nm`trm.

(K)

=8

(J)

48

(N)

>

;6 (D)

=

;6

:4. H` ihvm` iurm, KJND k`d KJMG krm twl nynchn qukdrhcktmrkcs. Hg ∢JND 5 ;;2², tfm` ∢JMG 5 <

(K) ==²

G

D

N J

K

M ; ; 2 ²

(J) 92²

(N) 82²

(D) ;;2²

:=. Tfm vkcum lg >

: : > : : > : : >

> > >

( ) ( ) ( )

( ) ( ) ( ) <

k j j n n k

k j j n n k

√ + √ + √

√ + √ + √

5

(K) >(k + j)(j + n)(n + k) (J) >(k „ j)(j „ n)(n „ k)

(N) (k „ j)(j „ n)(n „ k) (D) ;

:7. Flw ek`y pck`ms nk` jm ekdm tl pkss tfrluif tfrmm dhsth`nt plh`ts<

(K) L`m hg tfmy krm nlcch`mkr (J) H``htm hg tfmy krm nlcch`mkr

(N) L`cy l`m hg tfmy krm `l` nlcch`mkr (D) Jltf (J) k`d (N)

:9. Tfm ch`m JM hs k dhkemtmr lg tfm ihvm` nhrncm. Hg ∢JKN 5 >>² k`d

∢MJN 5 =9². Tfm` ∢NKM 5

(K) =9²

(J) >>²

(N) 46²

(D) 82²

:6. Tfm tmre nl`tkh`h`i tfm fhifmst plwmr lg x h` tfm plcy`lehkc g (x) hs :x4. Twl lg tfm rllts lg

tfm mqukthl` g (x ) 5 2 krm „ ; k`d :. Ihvm` tfkt x: „ >x + ; hs k qukdrkthn gkntlr lg g (x ), `d tfm

rmekh`dmr wfm` g (x) hs dhvhdmd jy :x „ ;.

(K) ;;

6 (J) : (N) 2 (D) „;/>



30/69

7 7tf HEL - ^MT K

:8. Tfm sue lg k ùejmr k`d hts rmnhprlnkc hs tfrhnm tfm dhggmrm`nm lg tfm ùejmr k`d hts rmnhprlnkc.

Tfm ùejmr hs \\\\\\\\\.

(K) » : (J)

» ;

: (N) » > (D) Jltf (K) k`d (J)

>2. ^lcvm glr x ?:

6

>:

4

>

; :

x

x x

√

√ 5

( / ).

(K) :;

= (J)

;

;

= (N) >

;

= (D) ;

>

=

>;. : 7 2 6:. . \\\\\\\\\ .√ 5

(K)

;6:

88 (J)

;62

888 (N)

;9=

88 (D)

;64

888

>:. Tfm jksm lg k` hslsnmcms trhkìcm hs 4 ne k`d hts krmk hs ;7 ne:. Hg l`m lg tfm twl mqukc shdms lg

tfm trhkìcm hs a ne, tfm kpprlxhektm vkcum lg a „ ;.:4 hs \\\\\\\\\\\.

(K) 8 ne (J) 9 ne (N) ;2 ne (D) 6 ne

>>. KJND hs k rmntkìcm. Hg KJR k`d JN[ krm mquhcktmrkc trhkìcms, ∢RJ[ 5 \\\\.

(K) 7=² K

D

J

N

R

[(J) 9=²

(N) 72²

(D) 82²

>4. K nmrtkh̀ dhstk`nm hs nlvmrmd kt k nmrtkh̀ spmmd (s;). Hg fkcg lg tfhs dhstk`nm hs nlvmrmd h` dlujcm

tfm them kt spmmd (s:). Gh`d tfm rkthl lg tfm twl spmmds.

Kcsl, hg s; hs 72 ae/fr, `d s

:.

(K) ; ? ;7, >.9= ae/fr (J) 4 ? ;, ;= ae/fr (N) : ? ;, >2 ae/fr (D) : ? 6, :42 ae/fr

>=. Hg prldunt lg kjsnhssk k`d lrdh`ktm lg k plh`t hs plshthvm, tfm` tfm plh`t chms h`

(K) H qukdrk`t (J) HHH qukdrk`t (N) HW qukdrk`t (D) Jltf (K) k`d (J)

>7. Tfm twl nhrncms fkvm rkdhh x k`d >x. K plh`t hs nflsm`, kt rk`dle, h`shdm

tfm ckrimr nhrncm. Gh`d, h` hts shepcmst grknthl`kc glre, tfm prljkjhchty

tfkt tfhs plh`t hs h` tfm sfkdmd krmk.

(K) 9/6 (J) 6/8>x

x

(N) ;/8 (D) ;/6

>9. Gh`d tfm ehsshì vkcum. ( )( ) <

;> 9;> 9

:2

> >

: :++ √5

(K) 7 (J) :2 (N) 8; (D) ;8

>6. Tfm studm`ts h` k nlccmim wmrm ksamd tl vltm glr tfmhr gkvlurhtm

sujomnt. Tfm phm nfkrt rmprmsm`ts tfm ùejmr lg vltms glr mknf sujomnt.

Ektfmekthns ljtkh`md := elrm vltms tfk` Nfmehstry. Nkcnucktm tfm

ùejmr lg studm`ts wfl tlla pkrt h` tfm survmy.

(K) :=2 (J) =22

E k t f m e

k t h n

s

Rfyshns

I m l i r k p f y

Nfmehstry

;:2²

;2=²

4=²

(N) 4=2 (D) 722



31/69

97tf HEL - ^MT K

>8. K nujlhdkc emtkc jclna lg dhem`shl`s :2 ne Ù ;7 ne Ù ;: ne wmhifs 7 ai. Gh`d tfm wmhift lg

jclna lg tfm skem emtkc lg shzm ;2 ne Ù 6 ne Ù 6 ne.

(K) > ai (J) 6 ai (N) 9 ai (D) ; ai

42. Yfkt pmrnm`tkim lg k dky hs shx flurs k`d 4= ehùtms<

(K) 9.:;6% (J) 6.>% (N) :6.;:=% (D) @l`m lg tfmsm


4;. Tfm plpuckthl` lg k tlw` wks ;72222 tfrmm ymkrs kil. Hg ht fkd h`nrmksmd jy >%, :.=% k`d =%

h` tfm ckst tfrmm ymkrs, `d hts prmsm`t plpuckthl`.

(K) ;79>77 (J) ;99477 (N) ;99>77 (D) ;99>7=

4:. Tfm tkxh nfkrims h` k nhty nleprhsm lg k xmd nfkrim, tlimtfmr whtf tfm nfkrim lg tfm dhstk`nm

nlvmrmd. Glr k olur`my lg ;7 ae, tfm nfkrims pkhd krm Zs. ;=7 k`d glr k olur`my lg :4 ae, tfm

nfkrim pkhd krm Zs. :24. Yfkt whcc k pmrsl` fkvm tl pky glr trkvmcchì k dhstk`nm lg >2 ae<

(K) Zs. :>7 (J) Zs. :42 (N) Zs. :46 (D) Zs. :=:

4>. ^kvhtk fks Zs. :9 h` tfm glre lg gty pkhsm k`d twm`ty-vm pkhsm nlh`s. ^fm fks twhnm ks ek`y

twm`ty-vm pkhsm nlh`s ks sfm fks =2 pkhsm nlh`s. Flw ek`y nlh`s lg mknf ah`d dlms sfm

fkvm<

(K) :9, =4 (J) >2, 72 (N) :=, =2 (D) 42, 62

44. K trkdmr purnfksms 92 ai lg tmk kt Zs. ;= pmr ai k`d >2 ai lg tmk kt Zs. ;6.=2 pmr ai. Hg tfm

pknahì nfkrims krm : pmrnm`t, tfm` kt wfkt prhnm fm eust smcc tfm ehxturm lg twl tl ikh`

;=%<

(K) Zs ;6.6: pmr ai (J) Zs. ;6 pmr ai (N) Zs. ;6.=2 pmr ai (D) Zs.;9.62 pmr ai

4=. Tfm kvmrkim kim lg k gkehcy lg 7 emejmrs 4 ymkrs kil wks := ymkrs. Emk`wfhcm k nfhcd wksjlr` h` tfhs gkehcy k`d sthcc tfm kvmrkim kim lg tfm wflcm gkehcy hs skem tldky. Tfm prmsm`t kim

lg nfhcd hs \\\\\\\.

(K) : ymkrs (J) ; ymkrs;

: (N) ; ymkr (D) Dktk h`sugnhm`t

47. : em` k`d > wlem` `hsf :=% lg tfm wlra h` ; dky, wfhcm 7 em` k`d ;4 wlem` nk` `hsf

tfm wflcm wlra h` = dkys. H` flw ek`y dkys whcc :2 wlem` `hsf ht<

(K) :2 (J) := (N) :4 (D) @l`m lg tfmsm

49. Twl phpms V k`d X nk` cc k nhstmr` h` :4 eh`. k`d >: eh`. rmspmnthvmcy. Hg jltf tfm phpms krm

lpm`md tlimtfmr, tfm` kgtmr flw eunf them X sflucd jm nclsmd sl tfkt tfm tkà hs gucc h` ;6

ehùtms<

(K) 7 eh`s (J) 6 eh`s (N) ;2 eh`s (D) @l`m lg tfmsm

46. ûrmsf trkvmccmd ;:22 ae jy khr wfhnf glremd (:/=) lg fhs trhp. L`m tfhrd lg tfm wflcm trhp, fm

trkvmccmd jy nkr k`d tfm rmst lg tfm olur`my fm pmrglremd jy trkh`. Gh`d tfm dhstk`nm trkvmccmd jy

trkh`. Kcsl, `d tfm spmmd lg tfm trkh` hg tfm them tkam` glr tfm trkh` tl trkvmc tfm wflcm dhstk`nm hs

6 frs.

(K) ;722 ae, >=2 ae/fr (J) 622 ae, >9= ae/fr

(N) ;622 ae, >22 ae/fr (D) 462 ae, >62 ae/fr



32/69

6 7tf HEL - ^MT K

48. Tfrmm chiftsfhps ksf sheuctk`mluscy kt 7?22 k.e. Tfm rst chiftsfhp ksfms mvmry ;: smnl`ds,

tfm smnl`d chiftsfhp mvmry >2 smnl`ds k`d tfm tfhrd chiftsfhp mvmry 77 smnl`ds. Kt wfkt them

whcc tfm tfrmm chiftsfhps `mxt ksf tlimtfmr<

(K) 7?28 k.e. (J) 7?;2 k.e. (N) 7?;; k.e. (D) 7?;: k.e.

=2. K gruht smccmr fks :4 ai lg kppcms. Fm smccs k pkrt lg tfmsm kt k ikh` lg :2% k`d tfm jkck`nm kt k

clss lg =%. Hg l` tfm wflcm fm mkr`s k prlt lg ;2%, tfm kelu`t lg kppcms slcd kt k clss hs \\\. (K) 4.7 ai (J) 7 ai (N) 8.7 ai (D) ;;.4 ai




33/69

7tf

Xmkr :2;:

^MT J

Nckss 8



34/69

: 7tf HEL - ^MT J


;. Ljsmrvm tfm ihvm` dhkirkes glremd jy u`ht squkrms. @lt h`ncudhì tfm ehddcm squkrm flcm, tfm ùejmr

lg u`ht squkrms `mmdmd tl juhcd tfm tm`tf pkttmr` hs \\\\\.

(K) 82

(J) 8;

(N) 8:

(D) 8>

:. Ilhì =2 e tl tfm slutf lg ey flusm, H tur` cmgt k`d il k`ltfmr :2 e. Tfm` tur`hì tl tfm `lrtf ,

H il >2 e k`d tfm` stkrt wkcahì tlwkrds ey flusm. H` wfhnf dhrmnthl` ke H wkcahì `lw <

(K) @lrtf (J) Mkst (N) @lrtf-Ymst (D) ^lutf-Mkst

>. Hg LCXERHN^ hs nldmd ks RE_@LFJZ, k`d O]ER hs nldmd ks AWCL, tfm` NLER]TMZ wh cc jm nldmd

ks \\\\\\\.

(K) DR@[W]G^ (J) DR@[T^G[ (N) DR@[T^D[ (D) J@CLT^D[

4. Gh`d lut tfm nlrrmnt lpth l` sunf tfkt Ghi. (V ) hs mejmddmd h` l`m lg tfme.

Ghi. (V)

(K)

(J)

(N)

(D)

=. Tfm ihvm` qumsthl` nl`shsts lg twl smts lg iurms. Ghiurms ;, :, >

k`d 4 nl`sthtutm tfm prljcme smt wfhcm lpthl` iurms K, J, N k`d D nl`sthtutmtfm k`swmr smt. Tfmrm hs k dm`htm rmckthl`sfhp jmtwmm` iurms ; k`d :.

Mstkjchsf k shehckr rmckthl`sfhp jmtwmm` iurms > k`d 4 jy smcmnthì k

suhtkjcm iurm grle tfm k`swmr smt tfkt wlucd rmpcknm tfm qumsthl` ekra (,7,8

; : >

4 = 7

9 6 8

(J) ;,4,61 :,=,81 >,7,9

(N) ;,>,41 :,=,61 7,9,8

(D) ;,:,>1 4,=,71 9,6,8

9. Lut lg tfm ihvm` vm iurms, glur krm shehckr h` k nmrtkh` wky. Gh`d tfm ldd l`m lut.

(K)

(J)

(N)

(D)



35/69

>7tf HEL - ^MT J

6. H` tfm kdolh`hì Wm`` dhkirke, tfm squkrm rmprmsm`ts wlem`, tfm

trhkìcm rmprmsm`ts pmrsl`s wfl krm h` ilvmrèm`t smrvhnms, tfm

nhrncm rmprmsm`ts mdunktmd pmrsl`s k`d tfm rmntkìcm rmprmsm`ts

pmrsl`s wlrahì h` prhvktm smntlr. Mknf smnthl` lg tfm dhkirke hs

ùejmrmd tfm` wfhnf ùejmr rmprmsm`ts tfm u`mdunktmd wlem`,

wfl fkvm ilvmrèm`t smrvhnm ks wmcc ks oljs h` prhvktm smntlrs <

(K) 7 (J) 4 (N) ;: (D) 8

8. Yfhnf lg tfm glcc lwhì cmttmrs/ùejmrs h` tfm ihvm` cmttmr-ùejmr smqum`nm jmclw hs mxkntcy h`

tfm ehddcm lg tfm 8tf cmttmr/ùejmr grle tfm cmgt m`d k`d 9 tf cmttmr/ùejmr grle tfm rhift m`d <

J > A I = R D 9 8 M Z O H E T 7 _ F [ > Y : K

(K) H (J) Z (N) O (D) E

;2. Tfm ihvm` smt lg iurms nkrry nmrtkh` nfkrkntmrs. Kssuehì tfkt tfm nfkrkntmrs h` smt glcclw k

shehckr pkttmr`, `d tfm ehsshì nfkrkntmr.

(K) : (J) 8 (N) ;9 (D) ;6

;;. Tfrmm plshthl`s lg tfm skem dhnm fks jmm` sflw` h` tfm iurm. Yfkt dhiht whcc jm l` tfm tlp hg

dhiht : hs l` tfm jlttle<

(K) ; (J) 4 (N) = (D) 7

;:. Hg ht hs plsshjcm tl ekam l`cy l`m emk`hìguc wlrd whtf tfm rst, tfm smnl`d, tfm shxtf k`d tfm

tm`tf cmttmrs lg tfm wlrd DH^NCKHEMZ wfhnf lg tfm glcclwhì whcc jm tfm tfhrd cmttmr grle tfm cmgtm`d< Hg `l sunf wlrd nk` jm ekdm, ihvm V ks ylur k`swmr k`d hg elrm tfk` l`m sunf wlrd nk`

jm ekdm, ihvm X ks tfm k`swmr.

(K) H (J) Z (N) X (D) V

;>. Zlfht, Au`kc, Ksfhsf k`d Olf` krm studm`ts lg k snfllc . Tfrmm lg tfme stky gkr grle tfm snfllc

k`d l`m `mkr ht. Twl study h` nckss HW, l`m h` nckss W k`d l`m h` nckss WH. Tfmy study Fh`dh,

Ektfmekthns, ^lnhkc ^nhm`nm k`d ^nhm`nm. L`m hs illd kt kcc tfm glur sujomnts wfhcm k`ltfmr

hs wmka h` kcc lg tfmsm. Zlfht stkys gkr grle tfm snfllc k`d hs illd kt Ektfmekthns l`cy wfhcm

Au`kc hs wmka h` Ektfmekthns l`cy k`d stkys nclsm tl tfm snfllc. @mhtfmr Au`kc, Zlfht `lr Ksfhsf

studhms h` nckss WH. L`m wfl hs illd kt kcc tfm sujomnts studhms h` nckss W. @kem tfm jly wfl

hs illd kt kcc tfm sujomnts.

(K) Zlfht (J) Au`kc (N) Ksfhsf (D) Olf`

;4. Krrkìm tfm ihvm` wlrds h` tfm smqum`nm h` wfhnf tfmy lnnu r h` tfm dhnt hl`kry k`d tfm` nfllsm

tfm nlrrmnt smqum`nm.

;. Yrhà cm :. Yrhii cm >. Yrhtfm 4. Yrmtnf =. Yrktf

(K) 4, =, ;, :, > (J) =, 4, :, ;, > (N) 4, :, =, ;, > (D) =, :, ;, >, 4

;=. Hg K * J emk`s ' K euct hp c hmd jy J ' 1 K B J emk`s ' K ehùs J ' 1 K $ J emk`s ' K pcus J ' 1

K # J emk`s ' K dhvhdmd jy J ' , tfm` wfkt whc c jm tfm tltkc krmk lg :; nhrncms, mknf whtf tfm

skem rkdhus lg r ne<

(K) :: * r * 9 * r # :; (J) :: # :; * r * r (N) 77 * r : # 9 (D) 77 * r * r



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4 7tf HEL - ^MT J

;7. Tfm ihvm` qumsthl` nl`shsts lg vm iurms ekramd R, [, Z, ^ k`d T nkccmd tfm Rrljcme Ghiurms

glcclwmd jy glur lpthl`s. ^mcmnt k iurm grle kelìst lpthl`s wfhnf whcc nl`thùm tfm skem smrhms

ks mstkjchsfmd jy tfm vm Rrljcme Ghiurms.

(K)

(J)

(N)

(D)

;9. Gh`d tfm ehrrlr hekim lg tfm ihvm` wlrd, hg tfm ehrrl r hs pcknmd vmrthnkccy tl tfm cmgt.

KDEH@H^TZKTHL@

(K) K E H @ H ^ T Z K T H L @ D

(J) K E H @ H ^ T Z K T H L @ D (N) K E H @ H ^ T Z K TH L @ D (D) K E H @ H ^T Z K T H L @ D

;6. Gh`d tfm ùejmr lg trhkìcms h` tfm ihvm` iurm.

(K) :7

(J) :9

(N) :6

(D) @l`m lg tfmsm

;8. Rlh`thì tlwkrds k pfltlirkpf, Elfht skhd, 'Fhs shstmr hs tfm eltfmr lg Wh`ky, tfm sl` lg ey jrlt fmr'.

Flw Elfht hs rmcktmd tl Wh`ky<

(K) Jrltfmr (J) ]`ncm (N) @mpfmw (D) Jrltfmr-h`-ckw

:2. Hg ; hs sujt rkntmd grle tfm ckst dhiht lg mknf lg tfm ihvm` jmclw tfrmm dhiht ùejmrs, tfm sue lg

tfm dhihts lg flw ek`y lg tfme krm prhem ùejmrs<

89: =:7 469 >=8 :=;

(K) @l`m (J) Twl (N) L`m (D) Tfrmm


:;. H` tfm kdoknm`t iurm KM 5 KG, tfm` wfhnf lg tfm glcclwhì hs trum<

(K) k + j + n 5 ;62²

kx

n

y

K

J N

M

Gx

jD

(J) k + n 5 j

(N) :n + k 5 j

(D) :k + n 5 j

::. Tfm vkcum lg ;+:226 ;+:228 ;+:2;2 ;+:2;; :2;> hs⋍ \\\\\.

(K) :228 (J) :2;2 (N) :2;; (D) :2;>

:>. ^hepch gy ?7

: > 7+

7

> + :

4 >

7 :√ √

√

(K) 2 (J) ; (N) : (D) >

:4. Hg (x „ :y )7 5 K2x7 „ K

;x= . y; + K

:x4 . y: „ K

>x> . y> + K

4x: . y4 „ K

=x . y= + K

7y7, `d tfm vkcum lg

K2 „ K

; + K

: „ K

> + K

4 „ K

= + K

7.

(K) 2 (J) : (N) ; (D) „>



37/69

=7tf HEL - ^MT J

:=. Kjsn hssk lg kcc tfm plh`ts l` x-kxhs hs \\\\\.

(K) 2 (J) ; (N) : (D) K`y ùejmr

:7. ;=22 gkehchms wht f : nfhc drm` wmrm smcmntmd rk`dlecy, k`d tfm glcclwhì dktk wks rmnlrdmd?

@uejmr lg ihrcs h` k gkehcy : ; 2

@uejmr lg gkehchms 49= 6;4 :;;

Tfm prljkjhc hty lg k gkehcy, nflsm` kt rk`dle, fkvhì ; ihrc hs \\\\.

(K)6;4

767 (J)

6;4

49= (N)6;4

:;; (D)

6;4

;=22

:9. H` tfm ihvm` iurm (`lt drkw` tl snkcm), T] || ^Z k`d TZ || ^W, tfm` `d ∢k k`d ∢j.

(K) k 5 ;;=², j 5 42²

R [

Z

^ T

]

W

k

j=2²

82²

:=²

(J) k 5 ;:2², j 5 7=²

(N) k 5 ;4=², j 5 ==²

(D) k 5 ;2=², j 5 >=²

DHZMNTHL@ (:6 & :8) ? Tfm ch`m irkpf sflws tfm smntlrwhsm jrmka-up lg vm`turm nkphtkc gu`dhì h` H`dhk

glr tfm ymkr :2VV.

:6. Gu`dhì h` tfm nl`suemr-rmcktmd smntlr mxnmmds tfkt h` tfm m`mriy-rmcktmd smntlr kpprlx

jy \\\\\.

(K) 422% (J) 722% (N) =22% (D) 4=2%

:8. Tfm rkthl lg gu`dh ì h` tfm nleputmr slg twkrm smrvhn m k`d tfm jhl-tmnf`lcliy smntlrs (tkam`

tlimtfmr) tl tfkt h` tfm h`dustrhkc prldunts k`d eknfh`mry smntlr hs \\\\\\\.

(K) ;2 ? ; (J) ; ? ; (N) : ? > (D) > ? :



38/69

7 7tf HEL - ^MT J

>2. H` tfm ihvm` iurm, ekra tfm rmckthl` jmtwmm` KJ k`d KD.

(K) KJ 5 KD

K

JN D

; :

(J) KJ 3 KD

(N) KJ 0 KD

(D) Dktk h`kdmquktm

>;. Ihvm` k ch`m c k`d k plh`t R l` ht. Flw ek`y ch`ms nk` jm drkw` pksshì tfrluif tfm plh`t R < (K) H`g`htm (J) L`m (N) Twl (D) Tfrmm

>:. Tfm plsht hvm slcuthl`s lg tfm mqukthl` kx + jy + n 5 2 kcwkys chm h` tfm \\\\\\.

(K) ;st qukdrk`t (J) :`d qukdrk`t (N) >rd qukdrk`t (D) 4tf qukdrk`t

>>. Gh`d tfm vkcum lg> 7 86

= ; / := (;=) >

> :

: > 4/> ;/>

√

√

.

(K) ;2 (J) :6 : (N) >

: (D)

;:=

:9

>4. K fk`d gk` hs ekdm jy sth tnfh ì ;2 mqukc shzm trhkìuc kr strhps l g twl dhg gmrm`t typms lg pkpmr ks

sflw` h` iurm. Tfm dhem`shl`s lg mqukc strhps krm := ne, := ne k`d ;4 ne. Gh`d tfm krmk lg

mknf typm lg pkpmr `mmdmd tl ekam tfm fk`d gk`.

(K) :62 ne:

(J) 4:2 ne:

(N) 642 ne:

(D) >64 ne:

>=. Yfhnf lg tfm glcc lwhì stktmem`ts hs trum <

(K) K ch`m smiem`t fks `l m`d plh`t.

(J) K rky fks dmg`htm cmìtf.(N) K rky R[

hs tfm skem ks rky [R

.

(D) Tfrmm lr elrm ch`ms krm nl`nurrm`t hg tfmy fkvm k nleel` plh`t.

>7. H` tfm ihvm` iurm, ∢x k`d ∢y krm \\\\\.

(K) x 5 92², y 5 >9²

(J) x 5 >9², y 5 92²

(N) x 5 =2², y 5 =9²

(D) x 5 =9², y 5 =2²

>9. Mxprmss ;= 9;:. h` tfm glre lgp

q, q ≢ 2.

(K) =;6=

>22 (J)

=;6=

;22 (N)

=;66

> (D)

=;6=

>>2

>6. Yfkt eust jm kddmd tl x4 + :x> „ :x: + x „ ; sl tfkt rmsuct hs mxkntcy dhvhshjcm jy x: + :x „ ><

(K) „ x + : (J) > (N) x „ : (D) 4x „ >

>8. Tfm rkdhus lg tfm nych`dmr hs fkcg hts fmhift k`d krmk lg tfm h``mr pkrt hs 7;7 sq. nes. Flw ek`y

chtrms lg ehca kpprlxhektmcy, nk` ht nl`tkh`<

(K) ;.4 C (J) ;.= C (N) ;.9 C (D) ;.8 C



39/69

97tf HEL - ^MT J

42. H` tfm ihvm` iurm, T hs k plh`t l` shdm [Z lg R[Z k`d ^ hs tfm plh`t sunf tfkt ZT 5 ^T. Tfm`

R[ + RZ 0 \\\\\.

(K) [Z

(J) [T

(N) [^

(D) ^T


4;. Tfm prljkjhc hthms lg k studm`t imtthì K, J, N k`d D irkdm krm 2.>=, 2.:=, 2.>= k`d 2.2=, tfm` tfm

prljkjhchty tfkt k studm`t imts kt elst irkdm N hs \\\\\\.

(K) 2.>= (J) 2.42 (N) 2.8= (D) 2.7=

4:. K pmrsl` cm`t lut k nmrtkh` sue l` shep cm h`tmrmst k`d tfm skem sue l` nlepl u`d h`tmrmst kt

nmrtkh` rktm lg h`tmrmst pmr k`ùe. Fm `lthnmd tfkt tfm rkthl jmtwmm` tfm dhggmrm`nm lg nleplu`d

h`tmrmst k`d shepcm h`tmrmst lg > ymkrs k`d tfkt lg : ymkrs hs := ? 6. Tfm rktm lg h`tmrmst pmrk`ùe hs \\\\\\.

(K) ;2% (J) ;;% (N) ;:% (D) ;: ;

:%

4>. K nclsmd emtkcchn nyc h`dr hnkc jlx hs ;.:= e fhif k`d hts jksm rkdhus hs >= ne. Hg tfm emtkc sfmmt

nlsts b 62 pmr e:, tfm nlst lg tfm ektmrhkc usmd h` tfm jlx hs \\\\\\.

(K) b :6;.72 (J) b :82 (N) b >42.=2 (D) b =22

44. Ckthak jluift k rkdhl smt k`d spm`t b ;;2 l` hts rmpkhrs. ^fm tfm` slcd ht tl Ikrhek kt :2% prlt,

Ikrhek slcd ht tl Emifk kt k clss lg ;2% k`d Emifk slcd ht glr b ;;66 kt k prlt lg ;2%. Yfkt hs

tfm kelu`t glr wfhnf Ckthak jluift tfm rkdhl smt < (K) b 6=2 (J) b 682 (N) b 8>2 (D) b 8=2

4=. H` tfm el`tf lg Okùkry, tfm Zkhcwky Rlch nm nkuift 4222 thnamtcmss trkvmccmrs. H` Gmjrukry, tfm

ùejmr rlsm jy =%. Flwmvmr, dum tl nl`stk`t vhihc jy tfm Rlchnm k`d tfm Zkhcwky stkgg, tfm ùejmr

rmdunmd jy =% k`d h` Kprhc ht gurtfmr rmdunmd jy ;2%. Tfm tltkc ùejmr lg thnamtcmss trkvmccmrs

nkuift h` tfm el`tf lg Kprhc wks \\\\\\.

(K) >;:= (J) >:== (N) >=9= (D) >=8;

47. Rrmsm`t kims lg ^kemmr k`d K`k`d krm h` tfm rkt hl lg = ? 4 rmspmnthvmcy. Tfrmm ymkrs

fm`nm, tfm rkthl lg tfmhr kims whcc jmnlem ;; ? 8 rmspmnthvmcy. Yfkt hs K`k`d's prmsm`t kim h`ymkrs <

(K) :4 ymkrs (J) :9 ymkrs (N) 42 ymkrs (D) >2 ymkrs

49. Glur mqukc shzmd ekxheue nhrnuckr pcktms krm nut lgg grle k squkrm pkpmr sfmmt lg krmk 964 ne:.

Tfm nhrnuegmrm`nm lg mknf pcktm hs \\\\\\.

(K) :: ne (J) 44 ne (N) 77 ne (D) 66 ne

46. Rrhyk pck`ts >>;:4 ekìl tr mms h` fmr ikrdm` k`d krrkìms tfme sl tfkt tfmrm krm ks ek`y rlws

ks tfmrm krm ekìl trmms h` mknf rlw. Tfm ùejmr lg rlws krm \\\\\\.

(K) ;:6 (J) ;6: (N) :6; (D) :;6



40/69

6 7tf HEL - ^MT J

48. H` k` mxkeh`kthl` , k studm`t snlrms 4 ekras glr mvmry nlr rmnt k`swmr k`d clsms ; ekra glr mvmry

wrlì k`swmr. Hg sfm kttmepts h` kcc =2 qumsthl`s k`d snlrms ;:2 ekras, tfm ùejmr lg qumsthl`s

sfm kttmepts nlrrmnt hs \\\\\.

(K) 7: (J) 44 (N) 4: (D) >4

=2. K nrhnamtmr wflsm jlwchì kvmrkim hs ;:.4 ru`s pmr whnamt tkams = whnamts glr :7 ru`s k`d tfmrmjy

dmnrmksms fhs kvmrkim jy 2.4. Tfm ùejmr lg whnamts tkam` jy fhe thcc tfm ckst ektnf wks \\\\\.(K) 74 (J) 9: (N) 62 (D) 6=




41/69

9tf

Xmkr :2;>

^MT K

Nckss 8



42/69

: 9tf HEL - ^mt K

;. Nfllsm tfm nlrrmnt lpthl` sl tfkt k smrhms nk` jm

mstkjchsfmd.

;9, ;8, :>, :8, (.....), >9

K. >;

J. >> N. >=

D. >7

:. H` tfm ihvm` qumsthl`, twl rlws lg ùejmrs krm ihvm`.

Tfm rmsuctk`t ùejmr h` mknf rlw hs tl jm wlramdlut smpkrktmcy jksmd l` tfm glcclwhì rucms k`d tfm

qumsthl` jmclw tfm rlws hs tl jm k`swmrmd. Tfm

lpmrkthl`s lg ùejmrs prlirmss grle cmgt tl rhift.

Zucms ?

(h) Hg k` mvm` ùejmr hs glcclwmd jy k`ltfmr mvm`ùejmr tfmy krm tl jm kddmd.

(hh) Hg k` mvm` ùejmr hs glcclwmd jy k prhem ùejmr

tfmy krm tl jm eucthpchmd.

(hhh) Hg k` ldd ùejmr hs glcclwmd jy k` mvm` ùejmr,tfm mvm` ùejmr hs tl jm sujtrkntmd grle tfm ldd

ùejmr.

(hv) Hg k` ldd ùejmr hs glcclwmd jy k`ltfmr ldd

ùejmr, tfm rst ùejmr hs tl jm kddmd tl tfm

squkrm lg tfm smnl`d ùejmr.

(v) Hg k` mvm` ̀ uejmr hs glcclwmd jy k nleplshtm lddùejmr, tfm mvm` ùejmr hs tl jm dhvhdmd jy tfm

ldd ùejmr.

7= ;; ;:

;= > ;; Yfkt hs tfm sue lg tfm rmsuctk`ts lg tfm rlws<

K. >77

J. 77 N. :74

D. 47:

>. ^mcmnt tfm nlrrmnt ehrrlr hekim lg tfm ihvm` Ghi.(V),

hg tfm ehrrlr hs pcknmd kclì E@.

K.

J.

N. D.

4. Zhtk stk`ds tfhrd h` k rlw lg twm`ty studm`ts, krrkìmd

h` ksnm`dhì lrdmr lg fmhift. Ghvm `mw studm`ts olh`

tfm irlup, kcc tkccmr tfk` Zhtk. Yfkt whcc jm Zhtk's

plshthl` hg tfm studm`ts krm `lw krrkìmd h` dmsnm`dhìlrdmr lg tfmhr fmhifts<

K. ::`d

J. :>rd

N. ;6tf

D. Dktk h`kdmquktm

=. Hg 'Jlla' hs nkccmd 'Rm`', 'Rm`' hs nkccmd 'Rkpmr', 'Rkpmr'hs nkccmd 'Mrksmr', 'Mrksmr' hs nkccmd '^nkcm' k`d '^nkcm'

hs nkccmd 'Nkcnucktlr', tfm` whtf wfhnf dlms k studm`t

wrhtm<

K. Jlla

J. Rkpmr N. Rm`

D. Nkcnucktlr

7. ^mcmnt k ùejmr wfhnf whcc rmpcknm tfm qumsthl` ekra

h` tfm ùejmr pkttmr` ihvm` jmclw.

K. ;7

J. ;= N. :6

D. :;

9. ^mcmnt k iurm grle tfm lpthl`s wfhnf skthsms tfm

nl`dhthl` lg pcknmem`t lg dlts ks h` Ghi. (V).

K.

J.

N.

D.

CLIHNKC ZMK^L@H@I



43/69

>9tf HEL - ^mt K

6. ^mcmnt k iurm grle tfm lpthl`s wfhnf whcc nlepcmtm

tfm pkttmr` h` Ghi. (V).

K.

J.

N.

D.

8. Flw ek`y trhk`icms krm tfmrm h`

tfm ihvm` iurm< K. 6

J. ;2 N. ;:

D. ;4

;2. Rkhr lg rst twl iurms l` cmgt shdm lg '? ?' fkvm k

nmrtkh` rmckthl`sfhp jmtwmm` tfme. Mstkjchsf tfm skem

rmckthl`sfhp jmtwmm` tfm pkhr lg iurms l` rhift shdm

lg '? ?', wfhnf whcc rmpcknm tfm "


44/69

4 9tf HEL - ^mt K

;9. ^mcmnt grle tfm lpthl`s wfhnf glres tfm nlrrmnt wktmrhekim lg tfm ihvm` wlrd.

NKZH@I

K.J.

N.

D.

;6. ^mcmnt k Wm`` dhkirke grle tfm lpthl`s wfhnf jmst

rmprmsm`ts tfm rmckthl`sfhp kelìst"Dli, Rkrrlt, Rmt k`hekcs"<

K.

J.

N.

D.

;8. ^mcmnt k iurm grle tfm lpthl`s h` wfhnf Ghi. (V) hs

mejmddmd ks l`m lg hts pkrt.

K.

J.

N.

D.

:2. Zmkd tfm glcclwhì h`glrekthl` k`d k`swmr tfm qumsthl`

tfkt glcclw.

(h) Glur pmrsl`s K, J, N k`d D mkt ekìl, jk`k`k,

lrkìm lr pmknf grle El`dky tl Tfursdky. @ltwl pmrsl`s mkt tfm skem gruht l` skem dky. Mknf

lg tfme mkts l`cy l`m gruht l` k dky k`d dlms `lt

rmpmkt ht l` k`y ltfmr dky.

(hh) @mhtf mr N `lr D mkts lrkì m lr pmknf l`Tumsdky.

(hhh) J mkts jk`k`k l` Ymd`msdky.

(hv) K mkts pmknf l` El`dky.

(v) N dlms `lt mkt ekìl l` Tfursdky.

(vh) D mkts jk`k`k l` El`dky.

Yfl mkts lrkìm l` Tumsdky<

K. K

J. J

N. N

D. Mhtfmr K lr J

EKTFMEKTHNKC ZMK^L@H@I

:;. H` tfm ihvm` ghiurm, KLJ hs k strkhift ch`m k`d

∢ KLV > 5 =9², ∢ V ;LV 4 5 89², ∢ V >LJ 5 ;:>² k`d∢ V 4LJ 5 76². Gh`d ∢ KLV ;.

K. 42²

J. >2²

N. :=² D. ;=²

::. Tfm krmk lg tfm trhkìcm glremd jy : x + > y 5 7 k`d

tfm nllrdh`ktm kxms hs \\\\.

K. > sq. u`hts

J. : sq. u`hts

N. 7 sq. u`hts D. = sq. u`hts

:>. Gh`d tfm rmekh`dmr wfm` : x> „ 8 x: + x + ;: hs dhvhdmd

jy : + > x.

K. 2

J. ;;7/8 N. „:

D. ;6:/:9

:4. R[Z^ hs k rflejus k`d ^ZT hs k` mquhcktmrkc trhkìcm.Hg ∢[Z^ 5 62², tfm` ∢[TZ 5

R

T

Z

^

62²[

K. 42²

J. :2² N. >2²

D. =2²



45/69

=9tf HEL - ^mt K

:=. H` wfhnf qukdrk`t dlms tfm plh`t R( x, y) chm hg

xy 3 2<

K. H lr HH

J. HH lr HW

N. H lr HHH

D. HHH lr HW

:7. Tfm dmirmm lg tfm plcy`lehkc

> ;: > ;: ;: 4: : x x x + √ +( ) + + hsK. ;

J. :

N. 4

D. 2

:9. H` tfm ihvm` ghiurm, ∢ J 3 ∢ K k`d ∢N 3 ∢ D.

Tfm` wfhnf lg tfm glcclwhì stktmem`ts hs trum

rmikrdhì tfm rmckthl`sfhp jmtwmm` KD k`d JN <

K. KD 5 JN

J. KD 3 JN

N. KD 0 JN

D. @ltfhì nk` jm skhd

:6. KJND hs k ghmcd h` tfm glre lg k qukdrhcktmrkc wflsm

shdms krm KJ 5 42 e, JN 5 ;= e, ND 5 :6 e k`d

KD 5 8 e. Hg ∢ DKJ 5 82², tfm krmk lg tfm ghmcd hs

K. >27 e:

J. >;: e:

N. ;:7 e:

D. :;6 e:

:8. R[Z^ hs k pkrkccmclirke. Hg V k`d X krm ehd-plh`ts

lg R[ k`d ^Z rmspmnthvmcy k`d dhkil`kc ^[ hs olh`md.

Tfm rkthl kr (||ie V[ZX ) ? kr (D[^Z) 5

R

Z

V

X ^

[

K. ; ? 4

J. : ? ;

N. ; ? :

D. ; ? ;

>2. Tfm prljkjhchty lg smcmnthì k jly h` k nckss hs 2.7

k`d tfmrm krm 4= studm`ts h` k nckss. Gh`d tfm ùejmr

lg ihrcs h` tfm nckss.

K. ;6

J. ;8

N. :2 D. ;=

>;. ^hepchgy ?;

9 7

=

; 79

+ √

√ √

K. 2

J.;

:

N. ;4

D. ;

>:. Yfkt hs tfm krmk lg tfm sfkdmd pkrt h` tfm ihvm` ghiurm

ς 5

::

9<

;6 ne

K. 9: ne:

J. ;26 ne:

N. >:4 ne:

D. 746 ne:

>>. Tfm ihvm` iurm hs ̀ lt drkw` tl snkcm. Gh`d tfm vkcums

lg ∢[R^ k`d ∢TZ[ rmspmnthvmcy.

R T

Z ^

]

:>²

7=²

;>=²

[

K. 96², ;42²

J. 66², ;;2²

N. 7:², ;=2²

D. 6:², ;;2²

>4. Tfm phm nfkrt sflws tfm irkdms kttkh`md jy k irlup

lg studm`ts glr k nleel` tmst.

;2%D

:2%K

J

:=%N

=%M

Hg :42 studm`ts skt glr tfm nleel` tmst k`d tflsm

wfl ljtkh`md Irkdm D k`d M gkhcmd tfm tmst, flw

ek`y studm`ts pkssmd tfm tmst<

K. 4:

J. ;6:

N. :;= D. :24



46/69

7 9tf HEL - ^mt K

>=. Tfrmm nujms lg emtkc wflsm mdims krm h` tfm rkthl

> ? 4 ? = krm emctmd tl glre k nujm wflsm dhkil`kc hs

;: > ne. Gh`d tfm mdims (h` ne) lg tfm tfrmm nujms.

K. 7, 6, ;2J. 8, ;:, ;=

N. 6, 8, ;;

D. >, 4, =

MWMZXDKX EKTFMEKTHN^

>7. Tfm shdms lg k qukdrkìuckr ghmcd, tkam` h` lrdmr krm:7 e, :9 e, 9 e k`d :4 e rmspmnthvmcy. Tfm kìcm

nl`tkh`md jy tfm ckst twl shdms hs k rhift kìcm. Gh`d

hts krmk.

K. >:4 e:

J. :>6.=8 e:

N. >9=.64 e:

D. >64.78 e:

>9. Tfm tkxh gkrm h` k nhty hs b := glr ghrst ahclemtrm k`d

b ;2.= glr `mxt mknf sujsmqum`t ahclemtrm. K trkvmccmr

hs nfkrimd b ;28 ks tfm gkrm. Flw ek`y ahclemtrms

dhd fm trkvmc<

K. 6 ae

J. 8 ae

N. ;2 ae

D. @l`m lg tfmsm

>6. Glur ru``mrs stkrtmd ru``hì tfm rknm h` tfm skem

dhrmnthl` krlu`d k nhrnuckr pktf lg 9 ae. Tfmhr spmmds krm

4 ae/fr, > ae/fr, 8 ae/fr k`d >.= ae/fr h`dhvhdukccy.

Hg tfmy fkvm stkrtmd tfmhr rknm kt 7 l' nclna h` tfm

elr`hì, tfm` kt wfkt them tfmy whcc jm kt tfm stkrthì

plh`t flurs

N. ;2 flurs

D. ;= flurs

>8. K jllasmccmr prlnurms 42 jllas glr b >:22 k`d smccs

tfme kt k prlght mqukc tl tfm smcchì prhnm lg 6 jllas.

Yfkt hs tfm smcchì prhnm lg l`m dlzm` jllas, hg tfm

prhnm lg mknf jlla hs skem<

K. b 9:2

J. b 872

N. b ;:22

D. b ;442

42. Tfm plpuckthl` lg k nhty fkd h`nrmksmd sunnmsshvmcy

kt tfm rktm lg 7%, 4% k`d :% pmr k`ùe durhì ckst

tfrmm ymkrs. Hg hts prmsm`t plpuckthl` hs ;;:4446, tfm`

wfkt wks hts plpuckthl` tfrmm ymkrs kil<

K. ;222222

J. ;2=2222

N. ;262222

D. ;;22222

4;. Tfm cmìtf lg clìmst plcm tfkt nk` jm pcknmd l` tfmgcllr lg k rlle hs ;: e k`d tfm cmìtf lg clìmst plcm

tfkt nk` jm pcknmd h` tfm rlle hs ;= e. Tfm fmhift

lg tfm rlle hs

K. > e

J. 7 e

N. 8 e

D. 4 e

4:. K k`d J nk` dl k phmnm lg wlra h` ;2 dkys1 J k`d

N h` ;: dkys1 K, J k`d N h` 6 dkys. H` flw ek`y

dkys K k`d N tlimtfmr nk` dl tfm skem wlra<

K. 6

J. ;=

N. :2

D. Nk`'t jm dmtmreh`md

4>. Tfmrm krm glur jmccs. Tfmy rhì kgtmr mvmry l`m

ehùtm, twl k`d fkcg ehùtms, =2 smnl`ds k`d =

smnl`ds rmspmnthvmcy. Hg kcc tfm glur jmccs rkì ckst

them tlimtfmr kt 6 ? :2 p.e., tfm` kt wfkt them whcc

tfmy kcc `mxt rhì sheuctk`mluscy<

K. 6 ? :> p.e.

J. 6 ? :4 p.e. N. 6 ? := p.e.

D. 6 ? :7 p.e.

44. Tfm dhem`shl`s lg k pfltlirkpf krm 4 ne k`d

;.6 nes. Hg tfm jrmkdtf lg tfm m`ckrimd pfltl hs

4.= ne k`d ht wks m`ckrimd prlplrthl`kccy tfm` wfkt

hs tfm `mw cmìtf lg `mw pfltlirkpf<

K. 7 ne

J. =.4 ne

N. ;2 ne

D. 8 ne

4=. Tfm prhnm lg k nkr dmprmnhktms h` tfm ghrst ymkr jy

:=%, h` tfm smnl`d ymkr jy :2%, h` tfm tfhrd ymkr

jy ;=% k`d sl l`. Tfm gh`kc prhnm lg tfm nkr kgtmr

> ymkrs, hg tfm prmsm`t nlst lg tfm nkr hs b ;2,22,222

hs

K. b 9,62,222

J. b =,;2,222

N. b 7,82,222

D. b ;,92,222



47/69

99tf HEL - ^mt K

47. Nl`shdmr tfm iurm jmclw.

H

HH

HHH

Tfm rkthl lg tfm krmk lg H tl HH hs 6 ? ;. Tfm krmk lgHHH hs ;

:

>ks eunf ks tfm krmk lg HH. Hg tfm dhggmrm`nm

jmtwmm` tfm krmk lg H k`d HH hs :=: ne:, tfm`

(R) Krmk lg H

([) Krmk lg HH + HHH R [

K. 87 ne: :66 ne:

J. :66 ne: 87 ne:

N. ;66 ne: 67 ne:

D. 67 ne: ;66 ne:

49. ^mcmnt tfm nlrrmnt lpthl`. ^tktmem`t ; ? ( x + y)> 5 x> + y> + > xy ( x + y) k`d

( x: + y:) 5 ( x + y): + : xy

^tktmem`t : ? Hg tfm` tfm vkcum lg x x

::

;9+ 5 ,

x

x

>>

;;8+ 5

K. ^tktmem`t ; hs trum jut stktmem`t : hs gkcsm.

J. ^tktmem`t ; hs gkcsm jut stktmem`t : hs trum.

N. Jltf tfm stktmem`ts krm trum.

D. Jltf tfm stktmem`ts krm gkcsm.

46. Yfhnf lg tfm glcclwhì stktmem`ts hs nlrrmnt<

K. Kcc tfm kìcms lg k trhkìcm nk` jm cmss tfk` 72².

J. K trhkìcm nk` fkvm elrm tfk` l`m ljtusm kìcm.

N. K` mxtmrhlr kìcm lg k trhkìcm hs cmss tfk` mhtfmr

lg hts h`tmrhlr lpplshtm kìcms.

D. K` mxtmrhlr kìcm lg k trhkìcm hs mqukc tl tfm suelg tfm twl h`tmrhlr lpplshtm kìcms.

48. ^mcmnt tfm nlrrmnt lpthl`.

^tktmem`t ; ? Hg tfm kcthtudm grle l`m vmrtmx lg k

trhkìcm jhsmnts tfm lpplshtm shdm, tfm` tfm trhkìcm hs

`lt hslsnmcms. ^tktmem`t : ? Hg tfm jhsmntlr lg tfm vmrthnkc kìcm lg

k trhkìcm jhsmnts tfm jksm, tfm` tfm trhkìcm hs `lt

hslsnmcms.

K. ^tktmem`t ; hs trum jut stktmem`t : hs gkcsm. J. ^tktmem`t ; hs gkcsm jut stktmem`t : hs trum.

N. Jltf tfm stktmem`ts krm trum. D. Jltf tfm stktmem`ts krm gkcsm.

=2. k, j, n krm tfrmm smts lg vkcums lg x ?

k ? :, >, 9, ;, >, :, >

j ? 9, =, 8, ;:, =, >, 6

n ? 4, 4, ;;, 9, :, >, 4 Yfhnf l`m lg tfm glcclwhì stktmem`ts hs nlrrmnt<

K. Emk` lg k 5 Eldm lg n

J. Emk` lg n 5 Emdhk` lg n N. Emdhk` lg j 5 Eldm lg k

D. Emk`, Emdhk` k`d Eldm lg k krm mqukc

KNFHMWMZ^ ^MNTHL@




48/69

9tf

Xmkr :2;>

^MT J

Nckss 8



49/69

: 9tf HEL - ^mt J

;. Gh`d lut flw whcc tfm amy Ghi. (V) clla cham kgtmr

rltkthl`<

K.

J.

N.

D.

:. Tfmrm hs k smt lg iurms nkrryhì nmrtkh` ùejmrs.

Kssuehì tfkt tfm ̀ uejmrs h` mknf smt glcclw k shehckr pkttmr`, `d tfm ehsshì ùejmr.

K. :

J. 7

N. 6

D. 74

>. Yfm` tfm ihvm` iurm hs glcdmd

tl glre k nujm, flw ek`ydlts wlucd chm lpplshtm tfm

gknm jmkrhì vm dlts<

K. ;

J. :

N. >

D. 4

4. ^mcmnt tfm pkhr grle lpthl`s tfkt fks k rmckthl`sfhp

shehckr tl tfm iurm (V).

K.

Ghiurm (V)

J.

N.

D.

=. Hg mknf lg tfm ldd dhihts h` tfm ùejmr =47>6 hs

dmnrmksmd jy ; k`d mknf lg tfm mvm` dhihts hs h`nrmksmd

jy ;, tfm` wfhnf lg tfm glcclwhì whcc jm tfm sue lg

tfm dhihts lg tfm `mw ùejmr<

K. := J. :7

N. :6

D. :9

7. Tfm ihvm` qumsthl` hs jksmd l` tfm dhkirke ihvm`

jmclw sflwhì glur pmrsl`s kt tfm glur nlr`mrs lg k

squkrm rmihl` ks sflw`.

Grle tfm plshthl`s h` ihvm` iurm, N k`d K elvm

dhkil`kccy tl lpplshtm nlr`mrs k`d tfm` l`m shdm mknf

nclnawhsm k`d k`th-nclnawhsm rmspmnthvmcy. J k`d D

elvm twl shdms mknf nclnawhsm k`d k`th-nclnawhsm

rmspmnthvmcy. Yfmrm hs K `lw<

K. Kt tfm `lrtf-wmst nlr`mr

J. Kt tfm `lrtf-mkst nlr`mr

N. Kt tfm slutf-mkst nlr`mr

D. Kt tfm slutf-wmst nlr`mr

9. ^lem lg tfm nrhnamt pckymrs krm tm``hs pckymrs, slem

tm``hs pckymrs krm flnamy pckymrs, `l nrhnamt pckymr

hs k flnamy pckymr. Yfhnf lg tfm glcclwhì dhkirkes

nlrrmntcy rmprmsm`ts tfm kjlvm stktmem`ts<

K.

J.

N.

D.

CLIHNKC ZMK^L@H@I



50/69

>9tf HEL - ^mt J

6. Tfm glcclwhì qumsthl` nl`shsts lg ghvm ghiurms ekramd

;, :, >, 4 k`d = nkccmd tfm prljcme ghiurms. ^mcmnt k

ghiurm grle kelìst tfm lpthl`s wfhnf whcc nl`thùm

tfm skem smrhms ks mstkjchsfmd jy tfm ghvm prljcme

ghiurms.

Rrljcme Ghiurms

K. J.

N. D.

8. H` k nldhì ckìukim, tfm cmttmrs lg tfm Mìchsf kcpfkjmt

krm krrkìmd h` sunf k ek``mr tfkt kcc tfm vlwmcs krm

put h` tfm m`d k`d tfm rmekh`hì cmttmrs krm krrkìmd

grle tfm rst cmttmr l`wkrds. Tfm rmkrrkìmd kcpfkjmts

krm usmd tl dm`ltm tfm plshthl` lnnuphmd jy cmttmrs h`

tfm lrhih`kc kcpfkjmts. Yfkt hs tfm nldm lg EMTK<

K. TMKE

J. RYCW

N. CYRW

D. [IXJ

;2. Tfmrm krm dmmr k`d pmknlnas h` k zll. Jy nlu`thì

fmkds tfmy krm 62. Tfm ùejmr lg tfmhr cmis hs :22.

Flw ek`y pmknlnas krm tfmrm<

K. :2

J. >2

N. =2

D. 72

;;. Tfmrm hs k nmrtkh` rmckthl`sfhp jmtwmm` pkhr lg ùejmrs

ihvm` l` mhtfmr shdm lg ? ?. Hdm`thgy tfm rmckthl`sfhp

jmtwmm` tfm pkhr lg ùejmrs k`d smcmnt tfm lpthl`

wfhnf whcc rmpcknm tfm qumsthl` ekra<

2.;7 ? 2.22;7 ? ? ;.2: ? <

K. 2.2;2:

J. 2.;2:

N. ;.2:2

D. ;2.:2

;:. H` tfm glcclwhì qumsthl`, Ghiurm (V) hs glcclwmd jy

glur kctmr`kthvm ghiurms (K), (J), (N) k`d (D) sunf

tfkt Ghiurm (V) hs mejmddmd h` l`m lg tfme. Trknm

lut tfm kctmr`kthvm ghiurm wfhnf nl`tkh`s Ghiurm (V)ks hts pkrt.

Ghiurm (V)

K.

J.

N.

D.

;>. ^tudy tfm glcclwhì h`glrekthl` nkrmguccy k`d k`swmr

tfm qumsthl` ihvm` jmclw ht?

Tfmrm krm shx pmrsl`s K, J, N, D, M k`d G. N hs tfm

shstmr lg G. J hs tfm jrltfmr lg M‘s fusjk`d. D hs tfm

gktfmr lg K k`d irk`dgktfmr lg G. Tfmrm krm twl gktfmrs,

tfrmm jrltfmrs k`d k eltfmr h` tfm irlup.

Yfl hs tfm eltfmr< K. K

J. J

N. D

D. M

;4. Nlepcmtm tfm pkttmr` ihvm` h` ghiurm (V).

K.

J.

N.

D.



51/69

4 9tf HEL - ^mt J

;=. H` tfm ihvm` qumsthl ,̀ tfmrm hs smt lg ghvm ghiurms

nkccmd tfm prljcme smt. ^mcmnt k suhtkjcm iurm wfhnf

whcc rmpcknm tfm qumsthl` ekra h` iurm (>) sl tfkt k

smrhms hs glremd jy tfm iurms ;, :, >, 4 k`d = tkam`

h` lrdmr.

Rrljcme ^mt

K.

J.

N.

D.

;7. ^mcmnt tfm nlrrmnt ehrrlr hekim lg Ghiurm (V).

Ghiurm (V)

K.

J.

N.

D.

;9. Flw ek`y pkrkccmclirkes krm

tfmrm h` tfm glcclwhì iurm<

K. ;7

J. ;4

N. ;2

D. @l`m lg tfmsm

;6. Hg ù emk`s + , „ emk`s ù, Ù emk`s „ k`d + emk`s Ù,

tfm`( )>7 4 6 4

4 6 : ;7 ;

´ - ´

+ ´ + ¶ 5 <

K. 2

J. 6

N. ;:

D. ;7

;8. H` tfm ihvm` qumsthl`, tfrmm iurms V, X k`d _ krmsflwhì k smqum`nm lg glcdhì k nhrnuckr sfmmt lg

pkpmr. Tfm tfhrd iurm _ dmphnts tfm nuts ekdm h` tfm

glcdmd pkpmr. ̂ mcmnt k iurm wfhnf wlucd elst nclsmcy

rmsmejcm tfm pkpmr h` i. (_) wfm` u`glcdmd.

K.

J.

N.

D.

:2. Tfm ihvm` qumsthl` nl`shst lg twl smts lg iurms.

Ghiurms ;, :, > k`d 4 nl`sthtutm tfm prljcme smt.

Tfmrm hs k dmgh`htm rmckthl`sfhp jmtwmm` ghiurms

; k`d :. Mstkjchsf k shehckr rmckthl`sfhp jmtwmm`

iurms > k`d 4 jy smcmnthì k suhtkjcm iurm grle tfm

lpthl`s tfkt wlucd rmpcknm tfm qumsthl` ekra (


52/69


53/69

7 9tf HEL - ^mt J

>:. Flw ek`y jrhnas (ùejmr `mkr tl `mxt fu`drmd)

whcc jm rmquhrmd tl juhcd k wkcc >2 e clì, >2 ne

tfhna k`d = e fhif whtf k prlvhshl` lg : dllrs, mknf

4 e Ù :.= e k`d mknf jrhna jmhì :2 ne Ù ;7 ne Ù 6 ne

wfm` l`m-`h`tf lg tfm wkcc hs ccmd whtf chem<

K. ;>=22

J. ;>722

N. :22=2

D. ;6=22

>>. H` ihvm` iurm, R k`d [ krm nm`trms lg twl nhrncms

h`tmrsmnthì kt J k`d N . KND hs k strkhift ch`m. Tfm`,

rkthl lg ∢ J[D k`d ∢ KNJ hs

K. ; ? ;

J. : ? ;

N. ; ? :

D. ; :?

>4. H` ihvm` ghiurm, KJND hs k rmntkìcm h` wfhnf

ND 5 7 ne, KD 5 6 ne. Gh`d tfm krmk lg pkrkccmclirke

NDMG .

K. >7 ne:

J. :4 ne:

N. 46 ne:

D. 72 ne:

>=. 42% lg < + 87: 5 >=% lg 862 + ;=2% lg 6=2

K. >9:

J. 64:

N. ;742

D. ;2=:

MWMZXDKX EKTFMEKTHN^

>7. Mhift pmlpcm krm pck``hì tl sfkrm mqukccy tfm nlst

lg k rm`tkc nkr. Hg l`m pmrsl` whtfdrkws grle tfm

krrkìmem`t k`d tfm ltfmrs sfkrm mqukccy tfm m`thrm

nlst lg tfm nkr, tfm` tfm sfkrm lg tfm rmekh`hì pmrsl`s

h`nrmksmd jy

K.;

9

J.;

6

N.;

8

D.9

6

>9. K nmrtkh` gkntlry mepclymd 722 em` k`d 422 wlem`

k`d tfm kvmrkim wkim wks b :=.=2 pmr dky. Hg k wlek`

ilt b = cmss tfk` k ek`, tfm` wfkt krm tfmhr dkhcy

wkims<

K. Ek` ? b :=1 Ylek` ? b :2

J. Ek` ? b :9.=21 Ylek` ? b ::.=2

N. Ek` ? b >21 Ylek` ? b :=

D. Ek` ? b >:.=21 Ylek` ? b :9.=2

>6. K nych`dmr whtf fmhift k`d rkdhus : ? ; hs ccmd whtf

slgt drhà k`d tfm` ht hs thctmd sl ks tl kcclw slem

slgt drhà tl lw lgg tl k` mxtm`t wfmrm tfm cmvmc lg

slgt drhà oust tlunfms tfm clwmst plh`t lg tfm uppmr

elutf. Hg :.; C lg slgt drhà hs rmtkh`md h` tfm nych`dmr,

wfkt hs tfm nkpknhty lg tfm nych`dmr<

K. >.7 C

J. 4 C

N. 4.: C

D. @l`m lg tfmsm

>8. H` k clttmry lg ;22 thnamts ùejmrmd ; tl ;22, twl

thnamts krm drkw` sheuctk`mluscy. Gh`d tfm prljkjhchty

tfkt jltf tfm thnamts drkw` fkvm prhem ùejmrs.

K.:

>>

J.9

=2

N.9

:2

D.=

77

42. Tfm prhnm lg k Ekruth nkr rhsms jy >2%, wfhcm tfm skcms

lg tfm nkr ilms dlw` jy :2%. Yfkt hs tfm pmrnm`tkimnfkìm h` tfm tltkc rmvmùm<

K. = %

J. 4 %

N. 7 %

D. 6 %

4;. Zkemsf jluift x kppcms kt b 2.=2 mknf k`d y ahwh

gruht kt b 2.62 mknf. Fm slcd tfm kppcms kt b 2.6=

mknf k`d tfm ahwh gruht kt b ;.22 mknf. Yfhnf lg tfm

glcclwhì kcimjrkhn mxprmsshl`s nlrrmntcy sflws tfm

prlt mkr`md jy Zkemsf<



54/69

99tf HEL - ^mt J

K. >= x + :2 y

J. >= xy

N. :2 xy

D. >2 x + ;= y

4:. K rmntk`iuckr nlurtykrd >.96 emtrms cl`i k`d =.:= emtrms

whdm hs tl jm pkvmd mxkntcy whtf squkrm thcms, kcc lg tfm

skem shzm. Tfm` tfm ckrimst shzm lg tfm thcm wfhnf nlucd

jm usmd glr tfm purplsm hs (` Ù >)ne. Gh`d `.

K. ;4

J. :;

N. 4:

class 9 imo 5 years ebook

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