Class 11 CM Batches Phase Test 1
August 18, 2022 | Author: Anonymous | Category: N/A
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NIIWJMM ‖ Uabsm Wmst (JMM-Bgvbkfmg)
UAYVIFV, FAMCIVW_Y & CBWAMCBWIFV Ubttmrk - FUW-2 FUW-2
RU F`gm:
Wicm Bll`ttmg: 6 A`urs
UBUM_ - 2 Cbxicuc Cbrhs: 216
Ulmbsm rmbg tam ik ikstrufti`ks strufti`ks fbrmnully. Y`u brm bll`tt bll`ttmg mg = cikutms spmfinifblly n`r tais purp`sm. Y`u brm k`t bll`wmg tt` ` lmbvm tam Mx Mxbcikbti`k bcikbti`k Abll omn` omn`rm rm tam mkg `n tam tms tmst. t.
IKVW_]FWI@KV Fbuti`k: Rumsti`k Ubpmr F@GM bs divmk bo`vm C]VW om f`rrmftly cbrhmg ik tam bkswmr @C_ sammt omn`rm bttmcptikd tam pbpmr. Tr`kd F@GM `r k` F@GM will divm wr`kd rmsults.
B. Dmkmrbl Ikstrufti`ks 2. ?. 6. 7.
‖ A F W B O
Bttmcpt BLL tam qumsti`ks. Bkswmrs abvm t` om cbrhmg ` `k k tam @C_ sammts. Wais qumsti`k pbpmr f`ktbiks Warmm Vmfti`ks. Vmfti`ks. Vmfti`k-I is Vmfti`k-I is Uaysifs, Vmfti`k-II Vmfti`k-II is is Famcistry bkg Vmfti`k-III is Cbtamcbtifs. Mbfa Vmfti`k Vmfti`k is is nurtamr givigmg ikt` Ww` Ubrts: Ubrts: Ubrt-B & O ik O ik tam @C_.
=. _`uda spbfms brm pr`vigmg n`r r`uda w`rh iksigm tam qumsti`k pbpmr. K` bggiti`kbl sammts will om pr`vigmg n`r r`uda w`rh. >. Olbkh Ubpmrs, flip o`brgs, l`d tbolms, sligm rulm, fblfulbt`r, fmllulbr pa`kms, pbd pbdmrs mrs bkg mlmftr`kif gmvifms, ik bky n`rc, brm k`t bll`wmg.
O. Nillikd `n @C_ Vammt 2. Mksurm cbtfaikd `n @C_ sammt wita tam Rumsti`k pbpmr omn` omn`rm rm y`u stbrt cbrhikd y`ur bkswmrs `k @C_ sammt. ?. @k tam @C_ sammt, gbrhmk tam bppr bppr`pribtm `pribtm ouoolm wita AO pmkfil n`r mbfa fabrbftmr `n y`ur Mkr`lcmkt K`. bkg writm ik ikh y`ur Kbcm, Wmst Fmktrm bkg `tamr gmtbils bt tam gmsidkbtmg plbfms. 6. @C_ sammt f`ktbiks b blpabomts, lpabomts, kucmrbls & spmfibl fabrbftmrs fabrbftmrs n`r cbrhikd bkswmrs.
F. Cbrhikd Vfamcm N`r Bll Ww` Ubrts. (i) Ubrt-B (52-54) ‖ F`ktbiks smvmk (54) cultiplm fa`ifm qumsti`ks waifa abvm @km `r C`rm f`rrmft C`rm f`rrmft bkswmr. Null Cbrhs: Cbrhs: +7 +7 In In `kly tam ouoolm(s) f`rrmsp`kgikd t` bll tam f`rrmft `pti`ks(s) is (brm) gbrhmkmg. Ubrtibl Cbrhs: Cbrhs: +2 +2 N`r gbrhmkikd b ouoolm f`rrmsp`kgikd t` mbfa f`rrmft `pti`k, `pti`k, pr`vigmg K@ ikf`rrmft `pti`k is gbrhmkmg. Zmr` Cbrhs: Cbrhs: 5 In k`km `n tam ouoolms is gbrhmkmg. Kmdbtivm Cbrhs: 2 Ik bll `tamr fbsms. N`r mxbcplm, in (B), (F) bkg (G) brm (G) brm bll tam f`rrmft `pti`ks n`r b qumsti`k, gbrhmkikd bll tamsm tarmm will rmsult ik +7 +7 cbrhs cbrhs88 gbrhmkikd `kly (B) bkg (G) will (G) will rmsult ik +? +? cbrhs cbrhs88 bkg gbrhmkikd (B) bkg (O) (O) will rmsult ik 2 cbrhs, bs b wr`kd `pti`k is bls` gbrhmkmg. (i) (i) Ubrt-B (51-26) ‖ F`ktbiks six (5>) cultiplm fa`ifm qumsti`ks waifa abvm @KLY @KM F@__MFW bkswmr Mbfa qumsti`k fbrrims +6 cbrhs n`r cbrhs n`r f`rrmft bkswmr bkg -2 cbrhs n`r cbrhs n`r wr`kd bkswmr. (ii) (ii)
Ubrt-O (52-5=) f`ktbiks nivm (5=) Kucmrifbl obsmg qumsti`ks, tam bkswmr `n waifa cbyom p`sitivm `r kmdbtivm kucomrs `r gmficbls (m.d. >.?=, 4.55, -5.66, -.65, 65.?4, -2?4.65) bkg mbfa qumsti`k fbrrims +6 cbrhs n`r f`rrmft bkswmr bkg tamrm will om k` kmdbtivm cbrhikd.
Kbcm `n tam Fbkgigbtm :PPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP Obtfa :PPPPPPPPPPPPPPPPPPPP Gbtm `n Mxbcikbti`k :PPPPPPPPPPPPPPPPPPP Mkr`lcmkt Kucomr :PPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Fmktrm, 62-6?-66, Fmktrbl Cbrhmt, Tmst Bvmkum _`bg, Uukjboi Obda (Tmst), Kmw Gmlai - 2255?>, Ua: 522-7=>67555 NIIWJMM Ltg. Uukjboi Obda Fmktrm,
?
IW ?5?2 KTFC9?2N2T (U-2) (UW-2)-(UFC) JMMB
VMFWI@K ‖ II: U UA YVIFV UB_W ‖ B : (@km (@ km `r c`rm tabk `km @pti`ks F`rrmft Wypm) Wais smfti`k f`ktbiks 4 cultiplm fa`ifm qumsti`ks. qumsti`ks. Mbfa qumsti`k abs 7 fa`ifms (B), (O), (F) bkg (G), `ut `n waifa @KM `r C@_M WABK @KM @KM is f`rrmft. f`rrmft. 2.
B o`y ik bk mlmvbt`r wita `pmk r``n sa``ts b oullmt ik vmrtifblly upwbrg girmfti`k nr`c b amidat `n 2.= c bo`vm tam nl``r `n tam mlmvbt`r. Wam ikitibl spmmg `n tam oullmt wita rmspmft t` mlmvbt`r is 2= c/s. Wam oullmt strihms tam nl``r bntmr ? smf`kgs. Wamk ?
(Bssucikd d 325 wita c/s f`kstbkt ) (B) Lint is c`vikd spmmg (O) Lint is c`vikd wita upwbrg upwbrg bffmlmrbti`k `n =.4= c/s? (F) Lint is c`vikd wita g`wkwbrg bffmlmrbti`k `n =.4= c/s? (G) Gistbkfm trbvmllmg oy oullmt gurikd its nlidat fbk k`t om fblfulbtmg nr`c tam divmk gbtb.
2.
O, G
?.
Wrbjmft`ry `n tw` pbrtiflms pr`jmftmg nr`c `ridik wita spmmg v2 bkg v ? bkg bkdlms 2 bkg ? wita p`sitivm x-bxis rmspmftivlmy bs
?
sa`wk ik tam nidurm. Divmk tabt d 25 c/s jˎ . Fa``sm tam f`rrmft `pti`k rmlbtmg t`
?.
V`l.
gibdrbc. (B) v2 v?
(O) ?
(F)
(G)
?v2 6 v2 v? v2
2 ? 2 6 ? 2 2
G
25
v2? sik ? 2 ? d
... i
v ? sik ? ? 2 75 2 d
... ii
nr`c i bkg ii
2 7
25
sik 7 f`s 2
tbk 2 7
, 2
7=
v2? 2 / ?
? 25 v2 ?5 c/s Vicilbr n`r smf`kg pbrtiflm ? >5 bkg v? ?5 c/s
NIIWJMM Ltg. Uukjboi Obda Fmktrm, Fmktrm, 62-6?-66, Fmktrbl Cbrhmt, Tmst Bvmkum _`bg, Uukjboi Obda (Tmst), Kmw Gmlai - 2255?>, Ua: 522-7=>67555
6
IW ?5?2 KTFC9?2N2T (U-2) (UW-2)-(UFC) JMMB
6.
c2 bkg c? brm f`kkmftmg tar`uda b cbsslmss ikmxtmksiolm strikd. Ol`fh `n cbss c2 is plbfmg bt tam nixmg ridig ikflikmg surnbfm wailm tam ol`fh `n cbss c? abkdikd bt tam `tamr mkg `n tam strikd, str ikd, waifa pbssms tar`uda b nixmg cbsslmss nrifti`klmss pullmy sa`wk ik nidurm. Wam f`mnnifimkt `n stbtif nrifti`k omtwmmk tam ol`fh bkg tam ikflikmg plbkm ik 5.1. Wam systmc `n cbssms c2 bkg
Ww` ol`fhs `n cbssms
c? is rmlmbsmg nr`c rmst. (B) tam tmksi`k ik tam strikd is ?5 K bntmr rmlmbsikd tam systmc (O) tam f`ktbft n`rfm oy tam ikflikmg surnbfm `k tam ol`fh is bl`kd k`rcbl t` tam ikflikmg surnbfm (F) tam cbdkitugm `n f`ktbft n`rfm oy tam ikflikmg surnbfm `k tam ol`fh c2 is ?5 6 K (G) K`km `n tamsm
6.
B, O, F
7.
Wam nidurm sa`ws b ol`fh `n cbss c plbfmg `k b sc``ta wmgdm `n cbss C. Fblfulbtm tam vblum `n C bkg tmksi`k ik tam strikd, s` tabt tam ol`fh `n cbss c will c`vm vmrtifblly g`wkwbrg wita bffmlmrbti`k 25 c/s?. (Wbhm d 3 25 c/s?) (B) tam vblum `n C is (O) tam vblum `n C is
C f`t 2 f`t C tbk 2 tbk
(F) tam vblum `n tmksi`k ik tam strikd is (G) tam vblum `n tmksi`k is
d tbk
d f`t
7.
B, F
=.
Ik tam divmk gibdrbc, pullmy is nrifti`klmss bkg cbsslmss. O`ta tam sprikds brm abvikd sbcm n`rfm f`kstbkt 25 K/c. Ikitiblly wita tam strikds bttbfamg t` tam dr`ukgs, tam t`tbl systmc is bt rmst. K`w in tam strikd is fut, tamk iccmgibtmly bntmr futtikd tam strikd. (B) Bffmlmrbti`k `n 4 hd ol`fh is zmr` (O) Bffmlmrbti`k `n = hd ol`fh is zmr` (F) Bffmlmrbti`k `n > hd ol`fh is 255/> c/s ? (G) Bffmlmrbti`k `n 7 hd ol`fh is = c/s?
e
=.
B, O, G NIIWJMM Ltg. Uukjboi Obda Fmktrm, Fmktrm, 62-6?-66, Fmktrbl Cbrhmt, Tmst Bvmkum _`bg, Uukjboi Obda (Tmst), Kmw Gmlai - 2255?>, Ua: 522-7=>67555
7
IW ?5?2 KTFC9?2N2T (U-2) (UW-2)-(UFC) JMMB
>.
B Ol`fh ‑B’ is plbfmg `k b sc``ta a`riz`ktbl a`riz`ktbl surnbfm bkg b pbrtiflm F is suspmkgmg wita tam amlp `n lidat r`g nr`c p`ikt O `n tam ol`fh bs sa`wk. K`w o`ta tam ol`fh B bkg tam pbrtiflm F brm divmk vml`fity v 5 t`wbrgs lmnt. Wam ol`fh B strihms b nixmg wbll bkg suggmkly st`ps tamk. (Wam r`g OF is nrmm t` r`tbtm r `tbtm bo`ut O) (B) tam scbllmst vml`fity v 5 5 n`r waifa tam pbrtiflm F will
7 l (O) Wam scbllmst vml`fity v 5 5 n`r waifa tam pbrtiflm F will swikd ik b null firflm bo`ut tam p`ikt O is
swikd ik b null firflm bo`ut tam p`ikt O is l (F) ^ml`fity `n p`ikt F bt tam aidamst p`ikt `n tam firflm (n`r tam scbllmst vblum `n v5) is zmr`. zmr`. (G) ^ml`fity `n p`ikt F bt tam aidamst p`ikt `n tam firflm (n`r tam scbllmst vblum `n v5) is
l .
>.
B, F
4.
B o`gy is lintmg qubsi stbtifblly t` tam t`p `n b c`uktbik tar`uda pbta 2 bkg pbta ? oy bpplyikd b tbkdmktibl n`rfm nr`c o`tt`c ik tam nidurm. F`mnnifimkt `n nrifti`k omtwmmk tam o`gy bkg surnbfm is tamk (B) T`rh g`km oy drbvity bkg nrifti`k is lmss tar`uda pbta 2 tabk ? (O) w`rh g`km oy drbvity bkg nrifti`k is c`rm tar`uda pbta 2 tabk ? (F) T`rh g`km oy drbvity is sbcm ik o`ta pbta. (G) T`rh g`km oy nrifti`k is sbcm ik o`ta pbta.
4.
FG Vikdlm F`rrmft Bkswmr Wypm
Wais smfti`k f`ktbiks > cultiplm fa`ifm qumsti`ks. qumsti`ks. Mbfa qumsti`k abs 7 fa`ifms (B), (O), (F) bkg (G), `ut `n waifa @KLY @KM @KM is f`rrmft. f`rrmft. 1.
Wam nidurm sa`wk b amxbd`kbl swiccikd p``l. B pmrs`k stbkgikd bt p`ikt B `k dr`ukg wbkts t` rmbfa (smm wita nidurm) ik lmbst^p`ssilm ticm. bkg Wam pmrs`kp`ikt fbk Oc`vm b spmmg `k dr`ukg wita b spmmg
^
ik p``l. Nikg tam lmbst p`ssiolm ? ticm ik waifa tam pmrs`k fbk d` nr`c B t` O. Divmk @B @O = l. (B) (F)
1.
? =l ^ 7 ?l ^
(O)
(G)
6 ?l ^
?.= ? l ^
O
NIIWJMM Ltg. Uukjboi Obda Fmktrm, Fmktrm, 62-6?-66, Fmktrbl Cbrhmt, Tmst Bvmkum _`bg, Uukjboi Obda (Tmst), Kmw Gmlai - 2255?>, Ua: 522-7=>67555
=
IW ?5?2 KTFC9?2N2T (U-2) (UW-2)-(UFC) JMMB
9.
B pbrtiflm is plbfmg ik b fbrt. Ikitiblly l`fbti`k `n tam pbrtiflm is tbhmk bs `ridik ik dr`ukg nrbcm. Bt t 5, tam fbrt stbrts c`vikd bl`kd x-bxis wita ukin`rc vml`fity ? c/s bkg bt tam sbcm ikstbkt tam pbrtiflm stbrts c`vikd wita ? xjˎ rmlbtivm t` fbrt wamrm x is xf``rgikbtm `n tam fbr. Taifa `n tam n`ll`wikd is tam rbgius `n furvbturm `n tam trbjmft`ry `n tam pbrtiflm ik dr`ukg nrbcm wamk it’s tbkdmktibl bffmlmrbti`k is mqubl t` k`rcbl bffmlmrbti`k ik cbdkitugm0
?
2
?c 7 c (G) ?
?c 6
(B)
(O)
(F) ? ? c
9.
G
V`l.
^UF ^FD ? xˎj ?iˎ
^ UD
Amkfm, n`r tam pbrtiflm,
^ x
?c / s bkg ^ y ? x 7t
b x
5, b y 7c / s ?
?t , y ?t ? bt`tbl 7c / s ?
b bl`kd y bxis ?
bkg trbjmft`ry
y ?.
wamk b2 | b K |, | , b f`s
V`, ^ x
_F
b
7? 7f`s7=
K
?
b sik 7=
^y ? ^ ? ^ ?
7
x ?
?
?
?c
7
c
?
. 25.
Ikitiblly sprikd is rmlbxmg bkg c2 is rmlmbsmg nr`c rmst. Tamk T amk
c2 f`cm t` rmst n`r n `r b c`cmkt strikd BO is fut bt tam sbcm bc`ukt. Nikg tam bffmlmrbti`k `n c? just bntmr futtikd tarmbg.
c2
25.
2 d c? c b 2 2 d ?c?
?c2
2 d c? 6c b 2 2 d c?
(B) b
(O) b
(F)
(G)
B
NIIWJMM Ltg. Uukjboi Obda Fmktrm, Fmktrm, 62-6?-66, Fmktrbl Cbrhmt, Tmst Bvmkum _`bg, Uukjboi Obda (Tmst), Kmw Gmlai - 2255?>, Ua: 522-7=>67555
>
IW ?5?2 KTFC9?2N2T (U-2) (UW-2)-(UFC) JMMB
22.
Ik tam divmk nidurm systmc is ik mquilioriuc. K`w tam ol`fh `n cbss c is pr`jmftmg a`riz`ktbl wita ikitibl vml`fity v. Nikg tam cikicuc vblum `n v sufa tabt `km `n ol`fhs, mitamr B `r O just l`sms f`ktbft wita tam dr`ukg (B)
(F)
?c l d
?c
c l d
?c
(O)
(G)
?c l d ?c
C c l d ?c
22.
O
2?
Wam p`tmkitbl mkmrdy ] ik j`ulm `n b pbrtiflm `n cbss ? hd c`vikd ik Q-Y plbkm n`ll`ws tam lbw ] 3 ?x + 7y, wamrm (x, y) brm tam f`-`rgikbtms (ik cmtmr) `n tam pbrtiflm. In tam pbrtiflm is bt rmst bt (7, 7) bt ticm t 3 5 tamk, XFa``sm tam ikf`rrmft stbtmcmktS (B) bt t ? ? smf, tam pbrtiflm fr`ssms tam y-bxis (O) bt t ?smf, tam pbrtiflm fr`ssms tam x-bxis (F) Wam pbrtiflm abs hikmtif mkmrdy `n 75 j`ulm wamk it fr`ssms y-bxis (G) Wam hikmtif mkmdy `n tam pbrtiflm wamk it fr`ssms x-bxis is 75 j`ulm.
2?.
G
26. 26.
Wam uppmr abln `n b nixmg ikflikmg plbkm `n ikflikbti`k is pmrnmftly sc``ta tam l`wmr abln is r`uda. B ol`fh stbrtikd nr`c rmst bt tam t`p `n tam plbkm will f`cm t` rmst bt tam o`tt`c in tam f`mnnifimkt `n nrifti`k omtwmmk tam ol`fh bkg tam l`wmr abln `n tam plbkm is (B)
?tbk
(F) 26.
? tbk
(O)
tbk
(G)
2 tbk
B
UB_W-F Iktmdmr Bkswmr Wypm Wais smfti`k f`ktbiks = qumsti`ks qumsti`ks.. Wam bkswmr `n waifa cby om p`sitivm `r kmdbtivm kucomr `r gmficbls 2. 2.
Wam p`wmr supplimg oy b n`rfm bftikd `k b pbrtiflm c`vikd ik b strbidat likm is f`kstbkt. 2 H
Wam vml`fity `n b pbrtiflm vbrims wita gisplbfmcmkt bs x . Nikg tam vblum `n H . 2.
6
V`l.
U N .v U cb. v U cv
gv gx
(f`kstbkt)
.v
gx v gv ?
NIIWJMM Ltg. Uukjboi Obda Fmktrm, Fmktrm, 62-6?-66, Fmktrbl Cbrhmt, Tmst Bvmkum _`bg, Uukjboi Obda (Tmst), Kmw Gmlai - 2255?>, Ua: 522-7=>67555
4
IW ?5?2 KTFC9?2N2T (U-2) (UW-2)-(UFC) JMMB
?.
Va`ts brm nirmg sicultbkm`usly sicultbkm`usly nr`c tam t`p bkg o`tt`c `n b vmrtifbl flinn wita mlmvbti`k 65 bkg >5 rmspmftivmly bkg strihms tam `ojmft sicultbkm`usly bt tam sbcm p`ikt. In b 65 6 c is tam a`riz`ktbl gistbkfm `n tam `ojmft nr`c tam flinn, tamk tam amidat `n tam flinn is H 255 c. Nikg tam vblum `n H .
?.
5.>
V`l.
v2 f`s t v? f`s t 6 5 v2 sik t
2 ?
...2
6
dt dt ? a v? sik t
2 ?
dt dt ?
... ?
Nr`c (2) bkg (?)
a >5 c 6.
6.
B pbrtiflm `n cbss c 3 ? hd is plbfmg `k tam t`p `n b sc``ta amcisapmrm `n cbss C 3 7 hd. Wam amcispamrm is plbfmg `k sc``ta dr`ukg. Wam pbrtiflm is gisplbfmg dmktly. Wamk rbti` `n cbdkitugm `n k`rcbl rmbfti`k bkg psmug` n`rfm (smmk nr`c tam amcispamrm-nrbcm) bftikd `k tam pbrtiflm bkdlm 3 65 (smm nidurm). (Bssucm tabt tam pbrtiflm rmcbiks ik f`ktbft wita tam amcispamrm)
7
7.
BO is b plbtn`rc `n lmkdta 25 c hmpt `k nrifti`klmss a`riz`ktbl surnbfm. B cbk `n sbcm cbss is stbkgikd `k mkg B. Nrifti`k f`mnnifimkt omtwmmk sa`m `n tam cbk bkg plbtn`rc is 5.=. Cbk stbrts rukkikd nr`c B bkg st`ps bt O. Nikg tam cikicuc ticm (ik smf`kgs) rmquirmg oy tam pmrs`k t` brrivm bt O.
7.
?
=.
Wam bkdulbr gisplbfmcmkt (ik rbgius) `n bk bffmlmrbtmg nlywamml is divmk oy
9t 6
. Wam likmbr vml`fity `n b p`ikt bt gistbkfm 5.4= c nr`c tam bxis `n 6? r`tbti`k bt tam ikstbkt, wamk cbdkitugm `n its tbkdmktibl bffmlmrbti`k bkg k`rcbl bffmlmrbti`k brm mqubl, is mqubl t` x c/s. Nikg vblum `n x.
=ss.
2.2?=
NIIWJMM Ltg. Uukjboi Obda Fmktrm, Fmktrm, 62-6?-66, Fmktrbl Cbrhmt, Tmst Bvmkum _`bg, Uukjboi Obda (Tmst), Kmw Gmlai - 2255?>, Ua: 522-7=>67555
IW ?5?2 KTFC9?2N2T (U-2) (UW-2)-(UFC) JMMB
1
VMFWI@K ‖ III: F Famcistr y UB_W ‖ B : (@km (@ km `r c`rm tabk `km @pti`ks F`rrmft Wypm) Wais smfti`k f`ktbiks 4 cultiplm fa`ifm qumsti`ks. qumsti`ks. Mbfa qumsti`k abs 7 fa`ifms (B), (O), (F) bkg (G), `ut `n waifa @KM `r C@_M WABK @KM @KM is f`rrmft. f`rrmft. 2.
Taifa `n tam n`ll`wikd stbtmcmkt(s) brm f`rrmft0 (B) IFl 7 abs =, Fl I Fl o`kg bkdlms 3 95 bkg it abs `ftbamgrbl brrbkdmcmkt `n k`k-o`kgikd mlmftr`ks wita l`km pbirs `n fmktrbl bt`c fis t` mbfa `tamr. o`kgikd bkg k`k-likmbr bkg is`-strufturbl. (O) VFl ? bkg I 6 brm k`k-likmbr
(F) Cbxicuc kucomr `n -o`kgs prmsmkt ik sbcm plbkm ik F6V? c`lmfulm is tw`. (G) O?A>, Bl?(FA6)>, p`lycmrif OmA? f`ktbik 6 fmktrm-?mlmftr`k o`kg. 2.
O, F, G
?.
Taifa `n tam n`ll`wikd stbtmcmkt(s) brm f`rrmft0 (B) _bgibl pr`oboility gistriouti`k nukfti`k ikgifbtms ikgifbtms tabt tamrm is b aidamr pr`oboility `n nikgikd 6s mlmftr`k fl`sm t` tam kuflmus tabk ik fbsm `n 6p bkg 6g mlmftr`ks. (O) _bgibl pr`oboility gistriouti`k nukfti`k cby abvm ZM_@ vblum out fbk kmvmr abvm KMDBWI^M vblum. (F) Rubktuc kucomrs l bkg c gmtmrcikm tam vblum `n bkdulbr wbvm-nukfti`k. wbvm-nukfti`k. (G) A-bt`c abs abln nillmg n illmg samll, abln-nillmg suosamll bkg abln-nillmg `roitbl.
?.
B, O, F, G
6.
Taifa `n tam n`ll`wikd stbtmcmkts bo`ut aygr`dmk is/brm f`rrmft0 (B) Ur`tiuc is tam c`st f`cc`k is`t`pm `n aygr`dmk. (O) Aygr`dmk kmvmr bfts bs fbti`k ik i`kif sblts. (F) Aygr`dmk i`k A+, mxists nrmmly ik s`luti`k. (G) Giaygr`dmk g`msk’t bft bs b rmgufikd bdmkt.
6.
B, O
V`l.
Nbft obsmg M/F
7.
B 75 cl `n b cixturm `n A?(d) bkg @?(d) wbs plbfmg ik b dbs ourmttm bt 21F bkg 2 btc. Urmssurm. B spbrh wbs bpplimg s` tabt tam n`rcbti`k `n wbtmr wbs f`cplmtm. Wam rmcbikikd purm dbs abg b v`lucm `n 25 cL bt 21 F bkg 2 btc. prmssurm. In tam rmcbikikd dbs wbs A?, tamk a`w cbky `n tam n`ll`wikd stbtmcmkt(s) brm IKF@__MFW0 (B) Kucomr `n c`lms A?(d) 3 ? kucomr `n c`lm `n @?(d) ik `ridikbl cixturm (O) C`lm-pmrfmkt `n A?(d) ik `ridikbl cixturm wbs 4=%
2?5
cl ik `ridikbl cixturm 6 (G) Wam v`lucm `n A?(d) ik `ridikbl cixturm is ?5 cl. (F) X^`lucm `n @?(d) + v`lucm `n A?(d)S 3
7.
B, G
NIIWJMM Ltg. Uukjboi Obda Fmktrm, Fmktrm, 62-6?-66, Fmktrbl Cbrhmt, Tmst Bvmkum _`bg, Uukjboi Obda (Tmst), Kmw Gmlai - 2255?>, Ua: 522-7=>67555
9
IW ?5?2 KTFC9?2N2T (U-2) (UW-2)-(UFC) JMMB
A ?
V`l.
^`lucm (`ridikbl) ^`lucm bntmr Vpbrhikd (bntmr rmbfti`k)
2 @ ? ? A ?@ l
b b ‖ ?o
o 5
K`w, rmbfti`k wbs fbrrimg `ut bt f`kstbkt U bkg f`kstbkt W bkg A ? wbs lmnt ukrmbftmg, (25 cL) (divmk) V`, b `k + os`lvikd 3 75 b (i) bkgcL b ‖bkg ?o o 33 2525 cL. 3 65 s`, c`l % `n A? 3 v`l % `n A?
65
65 25
255
4=% =.
Vmlmft f`rrmft stbtmcmkt(s) (B) Bk blhbli cmtbl f`cp`ukg turks rmg litcus waitm wamk rmg litcus is gippmg ik bqum`us s`luti`k `n tais blhbli cmtbl f`cp`ukg. Wais blhbli cmtbl f`cp`ukg f`ulg om Kb?@? (O) Litaiuc oifbro`kbtm bkg fblfiuc oifbro`kbtm g`msk’t g`msk’t mxist ik s`lig stbtm. (F) Fr`wk Mtamrs n`rc f`cplmxms wita blhbli cmtbls. (G) F`rrmft `rgmr `n cmltikd p`ikt is LiFl ; KbFl ; HFl ; _oFl ; FsFl
=.
B, O, F
V`l.
(B) Kb?@? (bq.) is b olmbfaikd bdmkt. It olmbfams rmg litcus t` waitm. (O) Nbft (F) @
@ Li
@
@
Fr`wk mtamr n`rc f`cplmxms wita blhbli cmtbls oy oikgikd tamc ik its fbvity. Wais oikgikd gmpmkgs up`k sizm `n cmtbl-i`k bkg sizm `n fbvity. (G) LiFl (f`vblmkt) abs lmss cmltikd p`ikt tamk t amk bky `tamr blhbli cmtbl fal`rigm. >.
Vmlmft F@__MFW stbtmcmkt(s) (B) Tamk bk mquic`lbr cixturm `n Fu?V bkg FuV is titrbtmg wita Ob(Ck@7)? ik bfigif cmgiuc, tam nikbl pr`guft f`ktbiks Fu?+, V@?. Ck?+. Waus mquivblmkt cbss `n Fu?V 3
2
wamrm C2 is c`lmfulbr cbss `n Fu ?V. 1 (O) N`r 24 dL2 `n A?@? s`luti`k, v`lucm strmkdta is =.> bkg 2 cL `n tais s`luti`k will divm ?.1 cL @ ?(d) bt ?46 H bkg ? btc, prmssurm (F) HCk@7 abs cbxicuc mquivblmkt cbss ik bfigif cmgiuc. (G) _A? (i`k mxfabkdm rmsik) fbk rmplbfm Fb ?+ i`ks ik abrg wbtmr bs _A? + Fb?+ _Fb + ?A+. In 2 litrm `n abrg wbtmr bntmr pbssikd tar`uda _A ? abs pA 3 6, tamk abrgkmss `n Fb?+ ik pbrts pmr cilli`k is ?5.
NIIWJMM Ltg. Uukjboi Obda Fmktrm, Fmktrm, 62-6?-66, Fmktrbl Cbrhmt, Tmst Bvmkum _`bg, Uukjboi Obda (Tmst), Kmw Gmlai - 2255?>, Ua: 522-7=>67555
25
IW ?5?2 KTFC9?2N2T (U-2) (UW-2)-(UFC) JMMB
>.
B, O, G
V`l. +? +7 ?+ Fu + V@?
+2 ? Fu? V (B)
k nbft`r 3? + > 3 1 V`, M Fu ? s
(O)
C 2 1
24 d L2 A?@? 3
24
, i.m. 2 mq `n A?@? ik 2 L 24 V`, K 3 2 bkg amkfm ^`l. Vtrmkdta 3 K =.> 2 = .> =.> bkg ? A ?@? ?A?@ ? c`lm 2 c`lm 24 2 24 , i.m. c`lm 67 ? Out tais is ik 2555 cL
I
+ @? (d) ??755 cL bt VWU 22?55 cL bt VWU =>55 cL bt VWU
=>55
=.> cL 2555 bt ?46 H bkg 2 btc . V`, bt ?46 H bkg ? btc (W f`kstbkt out U g`uolms), v`lucm dmts ablvmg. V`, ^ @? 3 ?.1 cL (F)
2 cL
Ik bfigif cmgiuc8 Ck@ 7 1 A =m
Ck? 7 A ?@ ,
Mq. cbss `n HCk@7 4
Ik blhblikm cmgiuc, C k@7
=
Ck7 8 M HCk@ 7
4
>
62.>
2=1
6 =?.>
4
C k@7? , M HCk@
Ik str`kd blhblikm cmgiuc C k@7 (G)
2=1
7
A+ 3 256 c`lm ik 2 L wbtmr Fb?+ ik wbtmr wbs 3 5.= 256 c`lm 3 5.= 256 75 3 ?5 256 d
ppc
?5 256 6
25
2=1 2
2=1
25> ?5
NIIWJMM Ltg. Uukjboi Obda Fmktrm, Fmktrm, 62-6?-66, Fmktrbl Cbrhmt, Tmst Bvmkum _`bg, Uukjboi Obda (Tmst), Kmw Gmlai - 2255?>, Ua: 522-7=>67555
22
IW ?5?2 KTFC9?2N2T (U-2) (UW-2)-(UFC) JMMB
4.
U bkg R brm igmbl dbsms tabt g` k`t rmbft t`dmtamr. Wam cbss `n 2 c`lm `n U is n`ur ticms tabk tabt `n R. Bt stbkgbrg tmcpmrbturm bkg prmssurm, prmssurm, it n`ll`ws tabt. XVmlmft f`rrmft stbtmcmktsS (B) Bvmrbdm hikmtif mkmrdy `n b c`lmfulm `n U is n`ur ticms tabt `n b c`lmfulm `n R (O) Wam cbss `n 2 gc 6 `n U is n`ur ticms tam cbss `n 2 gc 6 `n R (F) @k cixikd 2 gc 6 `n U wita 2 gc6 `n R, tam pbrtibl prmssurm `n mbfa dbs ik tam cixturm will om 5.= btc (G) Wam ginnusi`k rbtm `n U is n`ur n `ur ticms tabt `n R
4.
O, F
V`l.
(B) Bv. H.M. W (O) Bt f`kstbkt W bkg U, g C g p
e
7g R .
(F) Bt f`kstbkt U bkg W, mqubl v`lucms `n dbsms f`ktbik mqubl k`. `n c`lms. V`, x U xR 5.= ik cixturm V`, p `n mbfa dbs 3 x dbs Ut`tbl
5.= 2 5.= btc.
.
(G) Bt f`kstbkt tmcp. bkg prmssurm
r p rR
CR CU
C R 7 C R
2 7
2 ?
r p 2? r R Vikdlm F`rrmft Bkswmr Wypm Wais smfti`k f`ktbiks > cultiplm fa`ifm qumsti`ks. qumsti`ks. Mbfa qumsti`k abs 7 fa`ifms (B), (O), (F) bkg (G), `ut `n waifa @KLY @KM @KM is f`rrmft. f`rrmft. 1.
Wam dr`ukg stbtm mkmrdims `n A-bt`c bkg A? c`lmfulm brm rmspmftivmly.. Wam giss`fibti`k mkmrdy `n A? is rmspmftivmly (B) 21.2 m^ (O) 9 m^ (F) 7.= m^ (G) ?.= m^
1.
F
V`l.
A
?A
26.> m^ bkg 62.4 m^
d
3 (Mkmrdy p`ssmssmg oy tw` Giss`fibti`k mkmrdy t w` A-bt`cs) (Mkmrdy p`ssmssmg oy A? c`lmfulm). 26.> 62.4 ? 26 ?
62.4 62.4 ?4.? ?4.? 7.= 7.= m^ m^ 9.
B f`l`rlmss wbtmr s`luolm sblt ‑Q’ wamk trmbtmg wita ObFl?(bq.) s`luti`k, b waitm prmfipitbtm is `otbikmg waifa is s`luolm ik gilutm AFl. Vblt ‑Q’ divms d`lgmk ymll`w f`l`rbti`k ik nlbcm-tmst. Wamk ‑Q’ cby om (B) Kb?F@5 (O Kb?V@7 (F) CdF@6 (G) VrF@6
9.
B
NIIWJMM Ltg. Uukjboi Obda Fmktrm, Fmktrm, 62-6?-66, Fmktrbl Cbrhmt, Tmst Bvmkum _`bg, Uukjboi Obda (Tmst), Kmw Gmlai - 2255?>, Ua: 522-7=>67555
IW ?5?2 KTFC9?2N2T (U-2) (UW-2)-(UFC) JMMB
V`l.
2?
b?F@6 ObFl? ObF@6 ? KbFl Gum t` Kb, Taitm divms d`lgmk ymll`w (sblt `n V.O. & .T.B) F`l`rbti`k ik nlbcm tmst giss`lvmg ik bfig AFl
25.
Taifa `n tam n`ll`wikd liomrbtms @? up`k aygr`lysis0 (B) Uo6@7 (O) H@? (F) Kb?@? (G) Li?@?
25.
O
V`l.
(B) Uo6@7 + A?@ K` rmbfti`k (O) ?H@? + ?A?@ ?H@A + A?@? +@? (F) Kb?@? + ?A?@ ?Kb@A + A?@? (G) Li?@? + ?A?@ ?Li@A + A?@?
22.
Vmlmft tam f`rrmft stbtmcmkt (B) L]C@ lmvml n`r F? c`lmfulm is ?pz `roitbl (O) Ik F? c`lmfulm, o`ta tam o`kgs brm -o`kgs ? (F) Ik F ? i`k, tamrm is @KM bkg WT@ -o`kgs (G) Bll (B), (O) bkg (F) brm F@__MFW.
22.
G
V`l.
X]sm C@ mkmrdy gibdrbcS
2?.
F`ksigmr n`ll`wikd rmbfti`ks: B O `xigm F@ ?
O A ? @ F F F@?
B(cilhy ) F KA 7Fl G ( dbs ) G A ? @ F@? M M KbFl ?F@ 6N F@? A ?@ N Kb K`w smlmft tam f`rrmft stbtmcmkt `k tam obsis `n bo`vm rmbfti`ks:(B) ‑N’ fbk’t om usmg ik V`gb-bfig nirm mxitikduisamr. (O) Blhbli cmtbls wamk giss`lvmg ik G tbhmk bs liquig s`lvmkt n`rcs b s`luti`k waifa is pbrbcbdkmtif bkg olum bt f`kfmktrbti`k lmss tamk 6 C. (F) F is K@W usmg ik prmpbrikd olmbfaikd p`wgmr. (G) O is b cik`r cik`r f`kstitumkt `n `n FMCMKW. 2?.
O
NIIWJMM Ltg. Uukjboi Obda Fmktrm, Fmktrm, 62-6?-66, Fmktrbl Cbrhmt, Tmst Bvmkum _`bg, Uukjboi Obda (Tmst), Kmw Gmlai - 2255?>, Ua: 522-7=>67555
26
IW ?5?2 KTFC9?2N2T (U-2) (UW-2)-(UFC) JMMB
V`l.
(B) FbF@6 B Fb@ O F@? XFaimn f`kstitumkt `n fmcmktS (O) Fb @
(G)
Fb @A ? f f ? Fb@Fl? Olmbfaikd U`wgmr A ?@ Fl
Fb (@A ) ? f F@? FbF@6 cilhy B Fb F @6 ? KA 7 Fl ? K A 6 d FbFl? F@? A ?@ O
(F)
f
( G )
Blhbli cmtbls giss`lvm ik liquig KA6 t` n`rc b s`luti`k f`ktbikikd bcc`kibtmg blhbli
cmtbls fbti`k, i.m. C KA 6 bkg bcc`kibtmg mlmftr`ks gum t` tais ukpbirmg
m KA 6
M
m, s`luti`k is UC bkg iktmksmly olum bt f`kfmk. < 6C.
KA 6 G
A ?@
F@?
KA 7 AF@6 XObhikd s`gb, usmg bs bfig-s`gb-nirm M
mxtikduisamrS (N)
A 7 AF@6 KbFl
Kb A F@6 KA 7Fl N
(d) ? bAF@6 Kb?F@6 F@? A ?@
26.
?= cL `n b s`luti`k `n Kb?F@6 abvikd spmfinif drbvity `n 2.?= d cL 2 rmquirmg 6?.9 cL `n b s`luti`k `n AFl f`ktbikikd 259.= d `n tam bfig pmr litrm n`r f`cplmtm kmutrblisbti`k. Waus tam v`lucm `n 5.17 K A?V@7 tabt will om f`cplmtmly kmutrblismg oy 2?= d `n Kb ?F@6 s`luti`k is: (B) 975 cL (O) ?6= cL (F) 745 cL (G) 2=5 cL
26.
F
V`l.
K AFl
259.=
6 6> 6>.= .=2 Bs Kb?F@6 is f`cplmtmly kmutrblismg oy AFl C-mq `n Kb?F@6 3 c-mq `n AFl K ?= 6?.9 6 K Kb F@ 6.971 ?
6
K`w, Kb?F@6 nrmsa s`luti`k rmbfts wita A?V@7. ^`lucm `n Kb?F@6 s`luti`k 3
2?= 2.?=
3 255 cL
K`w, c-q `n A?V@7 3 c-mq `n Kb?F@6 5.17 ^ 255 6.971
^
5 6.97 25 255 6.971 1
5.17 745 cL.
X^ 3 v`lucm `r A?V@7S
NIIWJMM Ltg. Uukjboi Obda Fmktrm, Fmktrm, 62-6?-66, Fmktrbl Cbrhmt, Tmst Bvmkum _`bg, Uukjboi Obda (Tmst), Kmw Gmlai - 2255?>, Ua: 522-7=>67555
27
IW ?5?2 KTFC9?2N2T (U-2) (UW-2)-(UFC) JMMB
UB_W-F Iktmdmr Bkswmr Wypm Wais smfti`k f`ktbiks = qumsti`ks qumsti`ks.. Wam bkswmr `n waifa cby om p`sitivm `r kmdbtivm kucomr `r gmficbls 2.
Wam nidurm oml`w is tam pl`t `n p`tmktibl mkmrdy vmrsus iktmr-kuflmbr gistbkfm (g) `n A? c`lmfulm ik tam mlmftr`kif dr`ukg stbtm. Tabt is tam vblum `n kmt p`tmktibl mkmrdy M 5 (bs ikgifbtmg ik nidurm) ik HJ c`l 2 n`r
g g 5 bt waifa tam mlmftr`k-mlmftr`k rmpulsi`k bkg tam kuflmus-kuflmus rmpulsi`k mkmrdims brm bosmkt0 Bs rmnmrmkfm, p`tmktibl mkmrdy `n A-bt`c is tbhmk bs ZM_@ wamk its mlmftr`k bkg kuflmus brm iknikitmly nbr bpbrt. XK B 3 >.5?6 25?6 c`lS
2.
X =?7>.=5S U.M.
hq2q? r
U.M. `n A-bt`c ik dr`ukg stbtm
h
m m
9 25 259 2.> 25 2529
r
?
5.=? 5.=?9 9 2525 76. 76.==6 ==61 1 2529 J bt` bt`c c 2 V`, U.M. `n tw` A-bt`cs (i.m `n `km A? c`lmfulm) 6.==6 61 2529 ? 76.== 14.254> 2529 J (c`lmfulm) 2
14.254> 25 2529 >.5?6 25?6 =?7 =?7.>7 .>795 95 257 J =?7>.795 HJ =?7>.=5 =?7>.=5 HJ HJ
V`, U.M `n 2 c`lm A? c`lmfulm 3
NIIWJMM Ltg. Uukjboi Obda Fmktrm, Fmktrm, 62-6?-66, Fmktrbl Cbrhmt, Tmst Bvmkum _`bg, Uukjboi Obda (Tmst), Kmw Gmlai - 2255?>, Ua: 522-7=>67555
2=
IW ?5?2 KTFC9?2N2T (U-2) (UW-2)-(UFC) JMMB
?.
Bk igmbl dbs is hmpt ik b f`ktbikmr bttbfamg wita cbk`cmtmr bs sa`wk ik nidurm oml`w. Tabt sa`ulg om tam v`lucm `n tam f`ktbikmr0
2 divmkS ^
X_mp`rt y`ur bkswmr ik Litrm.S Xl`d U vs. l`d
U 3 4>5 cc
Dbs 4> fc
X Liquig ik cbk`cmtmr abs gmksity 3 >.1 d cL 2S
?.
?.55
V`l.
Ik tmrcs `n liquig Ad,
a Ad 26.> dcL2 4> fc >.1 d cL2
a Ad
4> ?
61 fc 5.= btc.
V`, p dbs 2 5.= 2.= btc K`w, U^ H (f`kstbkt)
U
H ^
l`d U l`d H l`d
2
XBs sl`pm 3 tbk 7= 3 2S ^ Tm abvm l`d H 5.744 l` l `d 6 H 6 6 6 ^ ? L U 2.= 6.
Bc`kd tam tribt`cif c`lmfulms OmFl?, K 6 , K?@, K@ ? , @6, VFl?, IFl ? , I 6 bkg QmN?, tam t`tbl kucomr `n likmbr c`lmfulm(s)/ i`k(s) wamrm tam ayorigisbti`k `n fmktrbl bt`c g`msk’t abvm f`ktriouti`k nr`c g-`roitbl(s) is:XZ `n V 3 2>, Fl 3 24, I 3 =6, Qm 3 =7S
6.
7.55 NIIWJMM Ltg. Uukjboi Obda Fmktrm, Fmktrm, 62-6?-66, Fmktrbl Cbrhmt, Tmst Bvmkum _`bg, Uukjboi Obda (Tmst), Kmw Gmlai - 2255?>, Ua: 522-7=>67555
2>
IW ?5?2 KTFC9?2N2T (U-2) (UW-2)-(UFC) JMMB
V`l.
XOmFl?, K 6 , K ?@, K@? (oy bpplyikd ayorigisbti`k tam`ry)
7.
A`w cbky `n tam n`ll`wikd mlmcmkts brm s-ol`fh mlmcmkts0 _o, Bl, O, H, V, Fg, Zk, Wa, Vr
7.
6.55
V`l.
_o, H, Vr
=. O`kg-bkdlm O`kg-bkdl m ik K@? 3 W wamrm
O`kg bkdlm `n W
K@6 O`kg bkdlm `n K@? ?
6=
K @ bkdlmS V`, W 30 XAmrm o`kg-bkdlm cmbks @ bkg o`kg-bkdlm is ik gmdrmm
=.
22=.55
V`l.
2?5 215 W ? 6= 2=5 6= 22=
NIIWJMM Ltg. Uukjboi Obda Fmktrm, Fmktrm, 62-6?-66, Fmktrbl Cbrhmt, Tmst Bvmkum _`bg, Uukjboi Obda (Tmst), Kmw Gmlai - 2255?>, Ua: 522-7=>67555
24
IW ?5?2 KTFC9?2N2T (U-2) (UW-2)-(UFC) JMMB
VMFWI@K ‖ II: C Cbtamcbtifs UB_W ‖ B : (@km (@ km `r c`rm tabk `km @pti`ks F`rrmft Wypm) Wais smfti`k f`ktbiks 4 cultiplm fa`ifm qumsti`ks. qumsti`ks. Mbfa qumsti`k abs 7 fa`ifms (B), (O), (F) bkg (G), `ut `n waifa @KM `r C@_M WABK @KM @KM is f`rrmft. f`rrmft. 2.
Divmk
5, ? bkg in
r 6
r 2
r sm f r 2 7 tamk > >
smf
waifa `n tam
n`ll`wikd bltmrkbtivm is/brm f`rrmft
2.
(B) 6 7 4 (F) 7 B, F
?.
In tam mqubti`k bx
(O) 1 6 (G) ?
?
> xy y ? ox fy g 5 _mprmsmkts
b pbir `n likms wamrm sl`pms
?
brm c bkg c , tamk vblum(s) `n b is/brm (B) b 1 (F) b ?4 ?.
O, G
6.
Ik
BOF,
(O) b 1 (G) b ?4
B , , O 2, ? , F ?, 6 bkg p`ikt B lims `k tam likm y ? x 6
wamrm , iktmdmr bkg brmb `n tam tribkdlm is V sufa tabt
V ? wmrm
X.S gmk`tms
tam drmbtmst iktmdmr nukfti`k. Wamk bll p`ssiolm f``rgik f``rgikbtms btms `n B is/brm (B) ( 4, 22) (O) (>, 9) (F) (?, 4) (G) (6, 9) 6.
B, O, F, G
7.
Wam fmktrm(s) `n tam firflm(s) pbssikd tar`uda tam p`ikts (5, 5), (2, 5) bkg t`ufaikd tam firflm x ? y ? 9 is/brm (B) (F)
7. =.
6, ?
2
?
(O)
2? , ?
(G)
Wam smt `n rmbl x sufa tabt
x
, 2 ?, 6 (F) ?,6 >.
?
2? , ?
?
6x ? x ? ? x ? 5 fbk om ? x 6 x 2 ? x (O) 2, ? (G) ?, 6
B&G l`d64
l`d242
?= l`d22
l`d46
?
l`d242
?4, o 79, f 22, tam vblum `n b In b o wamrm tam suc `n gidits `n H is (B) b pricm kucomr (O) bk `gg kucomr (F) bk mvmk kucomr
>.
6
F, G
(B)
=.
2, ?
?
?
f
l`d2?2=
is
(G) b pmrnmft squbrm
B&O NIIWJMM Ltg. Uukjboi Obda Fmktrm, Fmktrm, 62-6?-66, Fmktrbl Cbrhmt, Tmst Bvmkum _`bg, Uukjboi Obda (Tmst), Kmw Gmlai - 2255?>, Ua: 522-7=>67555
H
21
IW ?5?2 KTFC9?2N2T (U-2) (UW-2)-(UFC) JMMB
4.
4.
Wam vblum `n
f`s22 s22 sik2 k22 2
f`s22 s22 sik2 k22 2 (B) tbk657 (F) f` f`tt ?2 ?27 7 B, O, F, G
is (O) tbk=> (G) f`t67
Vikdlm F`rrmft Bkswmr Wypm Wais smfti`k f`ktbiks > cultiplm fa`ifm qumsti`ks. qumsti`ks. Mbfa qumsti`k abs 7 fa`ifms (B), (O), (F) bkg (G), `ut `n waifa @KLY @KM @KM is f`rrmft. f`rrmft. 1.
Wbkdmkts brm grbwk t` tam firflm x
?
y ? 2
bt tam p`ikts p`ikts wamk wamk it is cmt cmt oy tam firflms
x ? y ? > x 1 ? y 6 5, omikd tam vbribolm. Wam l`fus `n tam p`ikt `n
1.
iktmrsmfti`k `n tamsm tbkdmkts is (B) ? x y 25 5 (F) x ? y 25 5 B
9.
In tam likm y x ? 5 is saintmg pbrbllml t` itsmln t`wbrgs tam p`sitivm girmfti`k `n tam x-
bxis oy b pmrpmkgifulbr pmrpmkgifulbr gistbkfm `n 6 ? ukits, tamk tam mqubti`k `n tam kmw likm is (O) y x 2 (B) y x 7
(O) x ? y 25 5 (G) ? x y 25 5
x 1
9.
(F) y x ? 6 ? G
25.
In B tbk> tbk7? bkg O f`t >> f`t 41 , tamk
(G) y
(O) B
(B) B ? O
O 6 (G) 6 ? O
(F) B O 25.
F
22.
Wam
p`ikt
2
nr`c
waifa
tam
tbkdmkts
t`
tam
firflm
x ? y ? 1 x 75 5 ,
= x ? = y ? ?= x 15 15 5, x ? y ? 1 x 2> y 2> 2>5 5 brm mqubl ik lmkdta is (B) 1, 2=
(O)
? 2= (F) 1, ? 22.
F
2?.
In
tbk tbk
(B) 2 (F) 2?.
7 6
tbk 6
(G) K`km `n tamsm
2 6
tamk tam vblum `n
f`t f` t
f`t 6 (O)
1, 2= ?
? 6
is
(G) ?
O
NIIWJMM Ltg. Uukjboi Obda Fmktrm, Fmktrm, 62-6?-66, Fmktrbl Cbrhmt, Tmst Bvmkum _`bg, Uukjboi Obda (Tmst), Kmw Gmlai - 2255?>, Ua: 522-7=>67555
IW ?5?2 KTFC9?2N2T (U-2) (UW-2)-(UFC) JMMB
26.
Wam f``rgikbtm `n b p`ikt U `k tam likm ? x y = 5 sufa tabt | UB UO | is cbxicuc wamk B is 7, (B) 22, ?4 (F)
26.
29
? bkg O is ?, 7 will om (O) 22, 24
22, 24
(G) 5, =
O
UB_W-F Iktmdmr Bkswmr Wypm Wais smfti`k f`ktbiks = qumsti`ks qumsti`ks.. Wam bkswmr `n waifa cby om p`sitivm `r kmdbtivm kucomr `r gmficbls 2.
Wam kucomr `n iktmdrbl vblums `n h n`r waifa tam mqubti`k 4 f`s s`luti`k is
2.
1
?.
Wam kucomr `n s`luti`ks `n tam mqubti`k | 6 |
?.
7
6.
Wam p`ikts
l`d ? x l`d x?
>, 2 , >, 25 , 9, > bkg 6, 6 brm
= sik x ?h 2 abs
b
| 6 x |6
tam vmrtifms `n b rmftbkdlm. In tam
b brmb `n tam p`rti`k `n tais rmftbkdlm tabt lims bo`vm tam x-bxis is
b o , divmk
6.
=66.
7.
In
b, 2 , b
o
, nikg tam vblum `n
b bkg o brm f`-pricm.
o, 2 , f, 2 & g , 2 brm o f g
n`ur gistikft p`ikts `k b firflm `n rbgius 7 ukits
tamk vblum `n bofg is PPPPPPP 7.
2
=.
Wam vblum `n 4 f` f`s
=.
1s
> si sik x is c `r k wamk ? f`s sik x 2 tamk
c k is
NIIWJMM Ltg. Uukjboi Obda Fmktrm, Fmktrm, 62-6?-66, Fmktrbl Cbrhmt, Tmst Bvmkum _`bg, Uukjboi Obda (Tmst), Kmw Gmlai - 2255?>, Ua: 522-7=>67555
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