1 direction sense

8/12/2019 1 Direction Sense

1/6

ghlksfaughrpfyskds.kl

^fmrm hrm ojur nkrmdtkjls sudf hs Ljrtf, Tjutf,

Mhst hln Pmst. ^fm wjrn LMPT dhgm orjg

Ljrtf, Mhst, Pmst hln Tjutf. ^fmrm hrm ojur

rm`kjls 5 Ljrtf-Mhst (k)1 Ljrtf-Pmst (kk)1 Tjutf-

Mhst (kkk)1 Tjutf-Pmst (kv).

^fm nkrmdtkjls JY, JT, JX hln JR hrm -

Ljrt f-Mhst nk rmdt kj l1 Ljrt f-Pm st nk rm dtkjl1

Tjutf-Pmst nkrmdtkjl1 hln Tjutf-Mhst nkrmdtkjlrmspmdtkvmcy.

Ljtm 5 ^fm dhlnknhtm gust nkstkl`uksf bmtwmml tfm

rm`kjls hln nkrmdtkjls, k.m., bmtwmml Ljrtf-Mhst

rm`kjl hln ljrtf-Mhst nkrmdtkjl. Ko yju gjvm wktf

yjur ohdm Mhst-whrns, yjur cmot fhln ks tjwhrns

Ljrtf hln yjur rk`ft fhln ks tjwhrns Tjutf.

Tkgkchrcy tfm pjsktkjls jo tfm nkrmdtkjls jo tfm

fhlns dhl bm okxmn wfml yju gjvm kl hly jo tfm

jtfmr tfrmm nkrmdtkjls.

MVHGYCMTMx.8 Thlehy wmlt 09 gmtrms kl tfm Mhst bmojrm turlkl`

tj fks rk`ft. Fm wmlt 89 gmtrms bmojrm turlkl` tj

fks rk`ft h`hkl hln wmlt 89 gmtrms orjg tfks

pjklt. Orjg fmrm fm wmlt ;9 gmtrms tj tfm Ljrtf.

Fjw ohr whs fm orjg tfm sthrtkl` pjklt :

(H) 69 gmtrms (B) 899 gmtrms

(D) 8>9 gmtrms (N) 2?9 gmtrms

Tjc.(B)

^fm gjvmgmlt jo Thlehy orjg H tj M hrm hs

sfjwl kl ok`urm.

Ljw, Ho 7 (HB OB)

7 (HB ND) 7 (09 89) g 7 ?9 g

MO 7 (NM NO) 7 (NM BD)

7 (;9 89) g 7 69 g.

Rmqukrmn nksthldm 7 HM 7 22 MOHO

7 22

)69()?9( 7 899 g

Mx.2 K sthrt orjg gy fjgm hln `j twj akcjgmtrms

strhk`ft. ^fml K turl tjwhrns gy rk`ft hln `j

jlm akcjgmtrm. K turl h`hkl tjwhrns gy rk`ft hln

`j jlm akcjgmtrm h`hkl. Ko K hg Ljrtf-wmst orjg

gy fjusm tfml kl wfkdf nkrmdtkjl nkn K `j kl tfm

bm`kllkl` :

(H) Ljrtf (B) Tjutf

(D) Mhst (N) Pmst

Tjc. (N)^fm ojccjwkl` nkh`rhgs dchrkokms gy gjvmgmlts.

P T M

L

J

8DFHY^MR

KRM ^KJL TMLTM


2/6


Mx.4 Rhe whcamn 29 gmtrms tjwhrns Tjutf. ^fml fm

turlmn tj fks cmot hln whcamn 2= gmtrms. Fm tfml

turlmn tj fks cmot hln whcamn 29 gmtrms. Fm h`hkl

turlmn tj fks rk`ft hln whcamn 89 gmtrms. Ht wfht

nksthldm ks fm orjg tfm sthrtkl` pjklt hln kl

wfkdf nkrmdtkjl :

(H) 4= gmtrms, Mhst (B) 4= gmtrms, Ljrtf

(D) >9 gmtrms, Mhst (N) ?9 gmtrms, Mhst

Tjc.(H)

^fm gjvmgmlts jo Rhe hrm hs sfjwl kl okùrm

Rhe's nksthldm orjg sthrtkl pjklt H7 HM 7 (HN + NM)

7 (BD + NM) 7 (2= + 89) g 7 4= g

Tj, M ks tj tfm MHst jo H

Mx.> Gjfhl sthrtmn orjg fks fjusm, whcamn 2 ag Ljrtf,

tfml 4 ag Pmst, tfml ? ag Tjutf. Fjw ohrhwhy

orjg fks fjusm whs fm tfml :

Tjc. Tmm tfm okùrm.

T

P L

HFjusm

D

B

4 ag

4 ag

? ag

> ag

2 ag2 ag

(HD)2 7 (HB)2 + (BD)2

7 ; + 8?

7 = ag. Hls.

Mx.= Hlkc cmot fjgm hln dydcmn 89 ag Tjutfwhrns,

turlmn rk`ft hln dydcmn = ag & turlmn rk`ft hln

dydcmn 89 ag hln turlmn cmot hln dydcmn 89 ag.

Fjw ghly akcjgmtrms wkcc fm fhvm tj dydcm tj

rmhdf fks fjgm strhk`ft :

(H) 89 ag (B) 8= ag

(D) 29 ag (N) 2= ag

Tjc.(B)

Dcmhrcy, Hlkc sthrts orjg fjgm ht H, gjvms 89 ag

Tjutfwhrns uptj B, turls rk`ft hln gjvms = ag

uptj D, turls rk`ft h`hkl hln gjvms 89 ag uptj

N hln oklhccy turls cmot hln gjvms 89 ag uptj M.

^fus, fks nksthldm orjg klktkhc pjsktkjl H

7 HM 7 HN + NM

7 BD + NM 7 (= + 89) ag 7 8= ag.

Fmldm, tfm hlswmr ks (B).

Mx.? Hgkt ohdms tjwhrns Ljrtf. ûrlkl` tj fks rk`ft

fm whcas 2= gmtrms. Fm tfml turls tj fks cmot hln

whcas 49 gmtrms. Lmxt, fm gjvms 2= gmtrms tj fks

rk`ft. Fm tfml turls tj fks rk`ft h`hkl hln whcas

== gmtrms. Oklhccy, fm turls tj tfm rk`ft hln gjvms

>9 gmtrms. Kl wfkdf nkrmdtkjl ks fm ljw orjg fks

sthrtkl` pjklt :

(H) Tjutf-Pmst (B) Tjutf

(D) Ljrtf-Pmst (N) Tjutf-Mhst

Tjc.(N)

Hgkt turls tjwhrns rk`ft orjg Ljrtf nkrmdtkjl.

Tj, fm whcas 2= g tjwhrns Mhst uptj B, turls cmot

hln gjvms 49 g uptj D, turls rk`ft hln gjvms

2= g uptj N. Ht N fm turls tj rk`ft tjwhrns tfm

Tjutf hln whcas == g uptj M. Lmxt, fm h`hkl

turls tj rk`ft hln whcas >9 g uptj O. Pfkdf ks

fks oklhc pjsktkjl. O ks tj tfm Tjutf-Mhst jo H. H

Tj, fm ks tj tfm Tjutf-Mhst orjg fks sthrtkl`

pjklt. Fmldm, tfm hlswmr ks (N).

Mx.0 Orjg fks fjusm, Rhehl wmlt 2= ags tj tfm Ljrtf.

^fml fm turlmn Pmst hln djvmrmn 29 ags. ^fml

fm turlmn Tjutf hln djvmrmn 8= Ags/ Oklhccy,

turlkl` tj Mhst, fm djvmrmn 29 ags. Kl wfkdf

nkrmdtkjl whs fm orjg fks fjusm :

(H) Mhst (B) Pmst (D) Ljrtf (N) Tjutf


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Tjc.(D) ^fm gjvmgmlts jo Rhehl hrm hs sfjwl kl okùrm.

(H tj B, B tj D, D tj N hln N tj M)

Dcmhrcy, fks oklhc pjsktkjl ks M wfkdf ks tj tfm

Ljrtf jo fks fjusm ht H.

Mx.6 H ghl ks ohdkl` Ljrtf-Pmst. Fm turls ;9 kl tfm

dcjdawksm nkrmdtkjl, tfml 869 kl tfm hltkdcjdawksm

nkrmdtkjl hln tfml hljtfmr ;9 kl tfm shgmnkrmdtkjl. Pfkdf nkrmdtkjl ks fm ohdkl` ljw :

(H) Tjutf (B) Tjutf-Pmst

(D) Pmst (N) Tjutf-Pmst

Tjc.

Hs sfjwl kl okùrm tfm ghl klktkhccy ohdms kl tfm

nkrmdtkjl JH. Jl gjvkl` ;9 dcjdawksm, fm ohdms

kl tfm nkrmdtkjl JB. Jl ourtfmr gjvkl` 869

hltkdcjdawksm, fm ohdms kl tfm nkrmdtkjl JD. Oklhccy

jl gjvkl` ;9 hltk-dcjdawksm, fm ohdms kl tfm

nkrmdtkjl JN, wfkdf ks Tjutf-Mhst.

Mx.; Aksfml whcas 89 ag tjwhrns Ljrtf. Orjg tfmrm,

fm whcas ? ag tjwhrns Tjutf. ^fml, fm whcas 4

ag tjwhrns Mhst. Fjw ohr hln kl wfkdf nkrmdtkjl

ks fm wktf rmomrmldm tj fks sthrtkl` pjklt :

(H) = ag, Ljrtf (B) = ag, Ljrtf-Mhst

(D) 0 ag, Mhst (N) 0 ag, Pmst

Tjc.

^fm gjvmgmlts jo aksfml hrm hs sfjwl kl okùrm

(H tj B, B tj D hln D tj N). HD 7 (HB BD) 7

(89 ?) ag 7 > ag. Dcmhrcy, N ks tj tfm Ljrtf-Mhst

jo H.

Aksfml's nksthldm orjg sthrtkl` pjklt H

7 HN 7 22 DNHD 7

22 4> 7 2= 7 = ag

Tj, aksfml ks =ag tj tfm Ljrtf-Mhst jo fks sthrtkl`

pjklt .

Mx.89 H rhbbkt rul 49 tjwhrns Mhst hln turls tj rk ft,

ruls 29' hln turls tj rk`ft1 ruls 8;' hln h`hkl

turls tj cmot, ruls 8=' hln tfml turls tj cmot, ruls

22' hln oklhcy turls tj cmot hln ruls 8?'. Ljw,

wfkdf nkrmdtkjl ks tfm rhbbkt ohdkl` :

(H) Mhst (B) Pmst (D) Ljrtf (N) Tjutf

Tjc.(D)

^fm gjvmgmlt jo tfm rhbbkt orjg H tj @ hrm hs

sfjw kl okùrm. Tj, tfm rhbbkt's ohdm ks kl Ljrtf

nkrmdtkjl ht tfm mln jo ruls.

Mx.88 K hg ohdkl` Tjutf. K turl rk`ft hln whca 29 g.

^fml K turl rk`ft h`hkl hln whca 89 g. ^fml K

turl cmot hln whca 89 g hln tfml turlkl` rk`ft

whca 29 g. ^fml K turl rk`ft h`hkl hln whca

?9 g. Kl wfkdf nkrmdtkjl hg K orjg tfm sthrtkl`

pjklt :

(H) Ljrtf (B) Ljrtf-wmst

(D) Mhst (N) Ljrtf-Mhst

Tjc.(N) ^fm gjvmgmlt jo tfm pmrsjl hrm orjg H tj O, hs

sfjwl kl okùrm. Dcmhrcy, tfm oklhc pjsktkjl ks O

wfkdf ks tj tfm Ljtf-Mhst jo tfm sthrtkl` pjklt H.


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X.8 H ghl ks ohdkl` sjutf. Fm turls 84= kl tfmhltkdcjdawksm nkrmdtkjl hln tfml 869 kl tfm

dcjdawksm nkrmdtkjl. Pfkdf nkrmdtkjl ks fm ohdkl`

ljw :

(H) Ljrtf-mhst (B) Ljrtf-wmst

(D) Tjutf-mhst (N) Tjutf-wmst

X.2 H ghl ks ohdkl` ljrtf-wmst. Fm turls ;9 kl tfm

d c jd aw ksm n k rm d tk j l h l n t f ml 8 4 = k l t f m

hltkdcjdawksm nkrmdtkjl. Pfkdf nkrmdtkjl ks fm

ohdkl` ljw :

(H) Mhst (B) Pmst

(D) Ljrtf (N) Tjutf

X.4 H ghl ks ohdkl` ljrtf-wmst. Fm turls ;9 kl tfm

dcjdawksm nkrmdtkjl, tfml 869 kl tfm hltkdcjdawksm

nkrmdtkjl hln tfml hljtfmr ;9 kl tfm shgm

nkrmdtkjl. Pfkdf nkrmdtkjl ks fm ohdkl` ljw :

(H) Tjutf (B) Tjutf wmst

(D) Pmst (N) Tjutf-mhst

X.> K hg ohdkl` mhst. K turl 899 kl tfm dcjdawksm

nkrmdtkjl hln tfml 8>= kl tfm hltkdcjdawksm

nkrmdtkjl. Pfkdf nkrmdtkjl hg K ohdkl` ljw :

(H) Mhst (B) Ljrtf-mhst

(D) Ljrtf (N) Tjutf-wmst

X.= Nmmpha sthrts whcakl` strhk`ft tjwhrns mhst. Hotmr

whcakl` 0= gmtrms, fm turls tj tfm cmot hln whcas

2= gmtrms strhk`ft. H`hkl fm turls tj tfm cmot,

whcas h nksthldm jo >9 gmtrms strhk`ft, h`hkl fm

turls tj tfm cmot hln whcas h nksthldm jo 2= gmtrms.

Fjw ohr ks fm orjg tfm sthrtkl` pjklt :(H) 2= gmtrms (B) =9 gmtrms

(D) 8>9 gmtrms (N) Ljlm jo tfmsm

X.? Aksfmlahlt whcas 89 akcjgmtrms tjwhrns Ljrtf.

Orjg tfmrm, fm whcas ? akcjgmtrms tjwhrns Tjutf.

tfml, fm whcas 4 akcjgmtrms tjwhrns Mhst. Fjw

ohr hln kl wfkdf nkrmdtkjl ks fm wktf rmomrmldm tj

fks sthrtkl` pjklt :

(H) = akcjgmtrms Pmst(B) = akcjgmtrms Ljrtf-mhst

(D) 0 akcjgmtrms Mhst

(N) 0 akcjgmtrms Pmst

X.0 H ghl cmhvms ojr fks jookdm orjg fks fjusm. Fm

whcas tjwhrns Mhst. Hotmr gjvkl` h nksthldm jo

29 g, fm turls tjwhrns Tjutf hln whcas 89 g.

^fml fm whcas 4= g tjwhrns tfm Pmst hln ourtfmr

= g tjwhrns tfm Ljrtf. Fm tfml turls tjwhrns

Mhst hln whcas 8= g. Pfht ks tfm strhk`ft

nksthldm kl gmtrms bmtwmml fks klktkhc hln oklhc

pjsktkjls :

(H) 9 (B) =

(D) 89 (N) dhlljt bm nmtmrgklmn

(M) Ljlm jo tfmsm

X.6 @hurhv whcas 29 gmtrms tjwhrns Ljrtf. Fm tfml

turls cmot hln whcas >9 gmtrms. Fm h`hkl turls

cmot hln whcas 29 gmtrms. Ourtfmr, fm gjvms 29

gmtrms hotmr turlkl` tj tfm rk`ft. Fjw ohr ks fm

orjg fks jrk`klhc pjsktkjl :


(D) ?9 gmtrms (N) Ljlm jo tfmsm

X.; Rhnfh gjvms tjwhrns Tjutf-Mhst h nksthldm jo

0 ag, tfml sfm gjvms twjhrns Pmst hln trhvmcs

h nksthldm jo 8> g. Orjg fmrm, sfm gjvms tjwhrns

Ljrtf-wmst h nksthldm jo 0 g hln oklhccy sfm

gjvms h nksthldm jo > g tjwhrns Mhst hln stjjn

ht tfht pjklt. Fjw ohr ks tfm sthrtkl` pjklt orjg

wfmrm sfm stjjn :

(H) 4 g (B) > g (D) 89 g (N) 88 g

X.89 @jphc sthrts orjg fks fjusm tjwhrns Pmst. Hotmr

whcakl` nksthldm jo 49 gmtrms, fm turlmn tjwhrns

rk`ft hln whcamn 29 gmtrms. Fm tfml turlmn cmot

hln gjvkl` h nksthldm jo 89 gmtrms, turlmn tj

fks cmot h`hkl hln whcamn >9 gmtrms. Fm ljw

turls tj tfm cmot hln whcas = gmtrms. Oklhccy fm

turls tj fks cmot. Kl wfkdf nkrmdtkjl ks fm whcakl`

ljw :

(H) Ljrtf (B) Tjutf

(D) Mhst (N) Pmst

MVMRDKTM


5/6


X.8? Rhghahlt whcas ljrtfwhrns. Hotmr h wfkcm, fm

turls tj fks rk`ft hln h ckttcm ourtfmr tj fks cmot.

Oklhccy, hotmr whcakl` h nksthldm jo jlm akcjgmtrm,

fm turls tj fks cmot h`hkl. Kl wfkdf nkrmdtkjl ks

fm gjvkl` ljw :

(H) Ljrtf (B) Tjutf

(D) Mhst (N) Pmst

X.80 H ghl whcas 8 ag tjwhrns Mhst hln tfml fm

turls tj Tjutf hln whcas = ag. H`hkl fm turls

tj Mhst hln whcas 2 ag, hotmr tfks fm turls tj

Ljrtf hln whcas ; ag. Ljw, fjw ohr fks sthrtkl`

pjklt :

(H) 4 ag (B) > ag (D) = ag (N) 0 ag

X.86 Rhe trhvmccmn orjg h pjklt V strhk`ft tj [ ht h

nksthldm jo 69 gmtrms. Fm turlmn rk`ft hln whcamn

=9 gmtrms, tfml h`hkl turlmn rk`ft hln whcamn 09

gmtrms. Oklhccy, fm turlmn rk`ft hln whcamn =9

gmtrms. Fjw ohr ks fm orjg tfm sthrtkl` pjklt :


(D) =9 gmtrms (N) 09 gmtrms

(M) Ljlm jo tfmsm

X.8; Chxghl wmlt 8= ags tj tfm wmst orjg gy fjusm,

tfml turlmn cmot hln whcamn 29 ags. Fm tfml

turlmn Mhst hln whcamn 2= ags oklhccy turlkl`

cmot djvmrmn 29 ags. Fjw ohr whs fm orjg fks

fjusm :

(H) = ags (B) 89 ags

(D) >9 ags (N) 69 ags

X.29 Orjg fks fjusm, Cjamsf wmlt 8= ags tj tfm

Ljrtf. ^fml fm turlmn Pmst hln djvmrmn 89 ags.

^fml, fm turlmn Tjutf hln djvmrmn = ags. Oklhccy,

turlkl` tj Mhst, fm djvmrmn 89 ags. Kl wfkdf

nkrmdtkjl ks fm orjg fks fjusm :

(H) Mhst (B) Pmst(D) Ljrtf (N) Tjutf

X.28 @jkl` =9 g tj tfm Tjutf jo fmr fjusm, Rhnfkah

turls cmot hln `jms hljtfmr 29 g. ^fml, turlkl`

tj tfm Ljrtf, sfm `jms 49 g hln tfml sthrts

whcakl` tj fmr fjusm. Kl wfkdf nkrmdtkjl ks sfm

whcakl` ljw :

(H) Ljrtf-wmst (B) Ljrtf

(D) Tjutf-wmst (N) Mhst

X.88 H `krc cmhvms orjg fmr fjgm. Tfm okrst whcas 49

gmtrms kl Ljrtf-wmst nkrmdtkjl hln tfml 49 gmtrms

kl Tjutf-wmst nkrmdtkjl. Lmxt, sfm whcas 49 gmtrms

kl Tjutf-mhst nkrmdtkjl. Oklhccy, sfm turls tjwhrns

fmr fjusm. Kl wfkdf nkrmdtkjl ks sfm gjvkl` :

(H) Ljrtf-mhst (B) Ljrtf-wmst

(D) Tjutf-wmst (N) Ljlm jo tfmsm

X.82 Thlemmv whcas 89 gmtrms tjwhrns tfm Tjutf.

^urlkl` tj tfm cmot, fm whcas 29 gmtrms hln tfml

gjvms tj fks rk`ft. Hotmr gjvkl` h nksthldm jo 29

gmtrms, fm turls tj tfm rk`ft hln whcas 29 gmtrms.

Oklhccy, fm turls tj tfm rk`ft hln gjvms h nksthldm

jo 89 gmtrms. Fjw ohr hln kl wfkdf nkrmdtkjl ks

fm orjg tfm sthrtkl` pjklt :

(H) 89 gmtrms Ljrtf (B) 29 gmtrms Tjutf

(D) 29 gmtrms Ljrtf (N) 89 gmtrms Tjutf

(M) Ljlm jo tfmsm

X.84 Ahsfksf `jms 49 gmtrms Ljrtf, tfml turls rk`ft

hln whcas >9 gmtrms, tfml h`hkl turls rk`ft hln

whcas 29 gmtrms, tfml h`hkl turls rk`ft hln whcas

>9 gmtrms. Fjw ghly gmtrms ks fm orjg fks

jrk`klhc pjsktkjl :

(H) 9 (B) 89

(D) 29 (N) >9

(M) Ljlm jo tfmsm

X.8> K hg ohdkl Tjutf, K turl rk`ft h`hkl hln whca

89 g. ^fml K turl cmot hln whca 89 g hln tfml

turlkl` rk`ft whca 29 g. tfml K turl rk`ft h`hkl

hln whca ?9 g,. Kl wfkdf nkrmdtkjl hg K orjg tfm

sthrtkl` pjklt :

(H) Ljrtf (B) Ljrtf-wmst

(D) Mhst (N) Ljrtf-mhst

X.8= H ghl whcas 49 gmtrms tjwhrns Tjutf. ^fml,turlkl` tj fks rk`ft, fm whcas 49 gmtrms. ^fml,

tulkl` tj fks cmot, fm whcas 29 gmtrms. H`hkl, fm

turls tj fks cmot hln whcas 49 gmtrms. Fjw ohr ks

fm orjg fks klktkhc pjsktkjl :


(D) ?9 gmtrms (N) 69 gmtrms

(N) Ljlm jo tfmsm


6/6


X.22 H whcas 89 gmtrms kl orjlt hln 89 gmtrms tj tfm

rk`ft. ^fml mvmry tkgm turlkl` tj fks cmot, fm

whcas =, 8= hln 8= gmtrms rmspmdtkvmcy. Fjw ohr

ks fm ljw orjg fks sthrtkl` pjklt :

(H) = gmtrms (B) 89 gmtrms

(D) 8= gmtrms (N) 29 gmtrms

(M) 24 gmtrms

X.24 Rhska whcas 29 g Ljrtf. ^fml tfm turls rk`ft hln

whcas 49 g. ^fml fm turls rk`ft hln whcas 4= g.

^fml fm turls cmot hln whcas 8= g. ^fml fm h`hkl

turls cmot hln whcas 8= g. Kl wfkdf nkrmdtkjl hln

fjw ghly gmtrms hwhy ks fm orjg fks jrk`klhc

pjsktkjl :

HLTPMR AM[

Xums. 8 2 4 > = ? 0 6 ; 89 8 8 82 8 4 8> 8 =

Hls. N B N B M B B N D H H B B N M

Xums. 8? 80 86 8; 29 28 22 24 2>

Hls. N D H B D H H N B

(H) 8= gmtrms Pmst (B) 49 gmtrms Mhst

(D) 49 gmtrms Pmst (N) >= gmtrms Mhst

X.2> H dfkcn ks cjjakl` ojr fks ohtfmr. Fm wmlt ;9

gmtrms kl tfm Mhst bmojrm turlkl` tj fks rk`ft. Fm

wmlt 29 gmtrms bmojrm turlkl` tj fks rk`ft h`hkltj cjja ojr fks ohtfmr ht fks uldcm's pchdm 49

gmtrms orjg tfks pjklt. Fks ohtfmr whs ljt tfmrm.

Orjg fmrm fm wmlt 899 gmtrms tj tfm Ljrtf bmojrm

gmmtkl` fks ohtfmr kl h strmmt. Fjw ohr nkn tfm

sjl gmmt fks ohtfmr orjg tfm sthrtkl` pjklt :


(D) 8>9 gmtrms (N) 2?9 gmtrms

1 direction sense

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