jee 2014 booklet5 hwt permutations and combinations
TRANSCRIPT
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7/22/2019 Jee 2014 Booklet5 Hwt Permutations and Combinations
1/10
Qomyjbjgmor @djssks
QB@/Ykrbutjtong & @nblogjtong ;? HV]/Bjthkbjto`s
MJ]K 3 ]OBK 3 09 Bogutks BJ\EP 3 U ^^ /:9R ]KP] @NMK 3 Y&@ U:R
P]J\] ]OBK 3 KGM ]OBK 3 ]OBK ]JEKG3 YJ\KG]P POFGJ][\K 3
]hos tkst `ngtjogs j tntjd na :9 Nlck`tovk ]ypk Zukstongs. Kj`h qukstong `jrroks : bjre. ]hkrk os GN GKFJ]OQK bjreogf.
@hnnsk thk `nrrk`t jdtkrgjtovk. Ngdy ngk `hno`k os `nrrk`t.
:. ]hk dkjst pnsotovk ogtkfkrganr who`h : :; 1 6g g g
@ @ @ os 3
(J) := (L) :; (@) :1 (M)
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7/22/2019 Jee 2014 Booklet5 Hwt Permutations and Combinations
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Qomyjbjgmor @djssks
QB@/Ykrbutjtong & @nblogjtong 19 HV]/Bjthkbjto`s
MJ]K 3 ]OBK 3 09 Bogutks BJ\EP 3 U ^^ /:9R ]KP] @NMK 3 Y&@ U
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7/22/2019 Jee 2014 Booklet5 Hwt Permutations and Combinations
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Qomyjbjgmor @djssks
QB@/Ykrbutjtong & @nblogjtong 1: HV]/Bjthkbjto`s
MJ]K 3 ]OBK 3 09 Bogutks BJ\EP 3 U ^^ /:9R ]KP] @NMK 3 Y&@ U0R
P]J\] ]OBK 3 KGM ]OBK 3 ]OBK ]JEKG3 YJ\KG]P POFGJ][\K 3
]hos tkst `ngtjogs j tntjd na :9 Nlck tovk ]ypk Zukstongs. Kj`h qukstong `jrroks : bjre. ]hkrk os GN GKFJ]OQK bjreogf.
@hnnsk thk `nrrk`t jdtkrgjtovk. Ngdy ngk `hno`k os `nrrk`t.
:. Og hnw bjgy wjys ; lnys jgm 0 fords `jg lk skjtkm og j rnw sn thjt gn twn fords jrk tnfkthkr >
(J) 6(J) :;0 (L) 00 (@) 60 (M) :86
=. ]hk gublkr na wjys og who`h thk mojfrjb og aofurk `jg lk `ndnurkm sn
thjt kj h na thk sbjddkr trojgfdks os pjogtkm woth ngk na thk thrkk ndnurs
ykddnw, poge nr frkkg jgm gn twn jmcj`kgt rkfongs jrk pjogtkm woth thk
sjbk ndnur, os 3
(J)
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7/22/2019 Jee 2014 Booklet5 Hwt Permutations and Combinations
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Qomyjbjgmor @djssks
QB@/Ykrbutjtong & @nblogjtong 1< HV]/Bjthkbjto`s
MJ]K 3 ]OBK 3 09 Bogutks BJ\EP 3 U ^^ /:9R ]KP] @NMK 3 Y&@ U=R
P]J\] ]OBK 3 KGM ]OBK 3 ]OBK ]JEKG3 YJ\KG]P POFGJ][\K 3
]hos tkst `ngtjogs j tntjd na :9 Nlck`tovk ]ypk Zukstongs. Kj`h qukstong `jrroks : bjre. ]hkrk os GN GKFJ]OQK bjreogf.
@hnnsk thk `nrrk`t jdtkrgjtovk. Ngdy ngk `hno`k os `nrrk`t.
:. ]hk dkttkrs na thk wnrm @N@HOG jrk pkrbutkm jgm jdd thk pkrbutjtongs jrk jrrjgfkm og jg jdphjlkto`jd nrmkr js og jg Kgfdosh
mo`tongjry. ]hk gublkr na wnrms thjt jppkjr lkanrk @N@HOG os 3
(J) 019 (L) :?< (@) ?1 (M) =8
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7/22/2019 Jee 2014 Booklet5 Hwt Permutations and Combinations
5/10
Qomyjbjgmor @djssks
QB@/Ykrbutjtong & @nblogjtong 10 HV]/Bjthkbjto`s
MJ]K 3 ]OBK 3 09 Bogutks BJ\EP 3 U ^^ /:9R ]KP] @NMK 3 Y&@ U;R
P]J\] ]OBK 3 KGM ]OBK 3 ]OBK ]JEKG3 YJ\KG]P POFGJ][\K 3
]hos tkst `ngtjogs j tntjd na :9 Nlck`tovk ]ypk Zukstongs. Kj`h qukstong `jrroks : bjre. ]hkrk os GN GKFJ]OQK bjreogf.
@hnnsk thk `nrrk`t jdtkrgjtovk. Ngdy ngk `hno`k os `nrrk`t.
:. ]hk rksudts na
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7/22/2019 Jee 2014 Booklet5 Hwt Permutations and Combinations
6/10
Qomyjbjgmor @djssks
QB@/Ykrbutjtong & @nblogjtong 1= HV]/Bjthkbjto`s
MJ]K 3 ]OBK 3 09 Bogutks BJ\EP 3 U ^^ /:9R ]KP] @NMK 3 Y&@ U1R
P]J\] ]OBK 3 KGM ]OBK 3 ]OBK ]JEKG3 YJ\KG]P POFGJ][\K 3
]hos tkst `ngtjogs j tntjd na :9 Nlck`tovk ]ypk Zukstongs. Kj`h qukstong `jrroks : bjre. ]hkrk os GN GKFJ]OQK bjreogf.
@hnnsk thk `nrrk`t jdtkrgjtovk. Ngdy ngk `hno`k os `nrrk`t.
:. Dkttkrs na thk wnrm OGMOJDNOD jrk jrrjgfkm og jdd pnssoldk wjys. ]hk gublkr na pkrbutjtongs og who h J, O, N n` ur ngdy jt nmm
pdj`ks, os 3
(J) 6(J) 09 (L) 19 (@) ?9 (M) Gngk na thksk
?. ]hk gublkr na wjys na mostrolutogf 8 omkgto`jd ljdds og 0 mostog`t lnxks sn thjt gngk na thk lnxks os kbpty os 3
(J) 08 (L)
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7/22/2019 Jee 2014 Booklet5 Hwt Permutations and Combinations
7/10
Qomyjbjgmor @djssks
QB@/Ykrbutjtong & @nblogjtong 1; HV]/Bjthkbjto`s
MJ]K 3 ]OBK 3 09 Bogutks BJ\EP 3 U ^^ /:9R ]KP] @NMK 3 Y&@ U6R
P]J\] ]OBK 3 KGM ]OBK 3 ]OBK ]JEKG3 YJ\KG]P POFGJ][\K 3
]hos tkst `ngtjogs j tntjd na :9 Nlck`tovk ]ypk Zukstongs. Kj`h qukstong `jrroks : bjre. ]hkrk os GN GKFJ]OQK bjreogf.
@hnnsk thk `nrrk`t jdtkrgjtovk. Ngdy ngk `hno`k os `nrrk`t.
:. Hnw bjgy wjys jrk thkrk tn jrrjgfk thk dkttkrs og thk wnrm FJ\MKG woth thk vnwkds og jdphjlkto jd nrmkr >
(J) 019 (L)
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7/22/2019 Jee 2014 Booklet5 Hwt Permutations and Combinations
8/10
Qomyjbjgmor @djssks
QB@/Ykrbutjtong & @nblogjtong 11 HV]/Bjthkbjto`s
MJ]K 3 ]OBK 3 09 Bogutks BJ\EP 3 U ^^ /:9R ]KP] @NMK 3 Y&@ U8R
P]J\] ]OBK 3 KGM ]OBK 3 ]OBK ]JEKG3 YJ\KG]P POFGJ][\K 3
]hos tkst `ngtjogs j tntjd na :9 Nlck`tovk ]ypk Zukstongs. Kj`h qukstong `jrroks : bjre. ]hkrk os GN GKFJ]OQK bjreogf.
@hnnsk thk `nrrk`t jdtkrgjtovk. Ngdy ngk `hno`k os `nrrk`t.
:. ]hk vjduk na
1;9 ;1
= 0
:
r
r
@ @
os 3
(J);1
0@ (L);1
=@ (@);;
=@ (M);;
0@
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7/22/2019 Jee 2014 Booklet5 Hwt Permutations and Combinations
9/10
Qomyjbjgmor @djssks
QB@/Ykrbutjtong & @nblogjtong 16 HV]/Bjthkbjto`s
MJ]K 3 ]OBK 3 09 Bogutks BJ\EP 3 U ^^ /:9R ]KP] @NMK 3 Y&@ U?R
P]J\] ]OBK 3 KGM ]OBK 3 ]OBK ]JEKG3 YJ\KG]P POFGJ][\K 3
]hos tkst `ngtjogs j tntjd na :9 Nlck`tovk ]ypk Zukstongs. Kj`h qukstong `jrroks : bjre. ]hkrk os GN GKFJ]OQK bjreogf.
@hnnsk thk `nrrk`t jdtkrgjtovk. Ngdy ngk `hno`k os `nrrk`t.
:. Og j `ro`ekt `hjbpongshop thkrk jrk 01 bjt hks. ]hk gublkr na tkrbs, oa kj`h pdjys : bjt`h woth nthkr jrk 3
(J) ? (L) :9 (@) 8 (M) :