Jee 2014 Booklet5 Hwt Permutations and Combinations

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  • 7/22/2019 Jee 2014 Booklet5 Hwt Permutations and Combinations

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    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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    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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    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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    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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    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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    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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    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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    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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    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) :