ntse stage 2 - mat paper-2009

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  • 8/7/2019 NTSE STAGE 2 - MAT Paper-2009

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  • 8/7/2019 NTSE STAGE 2 - MAT Paper-2009

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    Zigl & 11

    Ekqlfukmov 2 .9 um 9:+ Ko lifn mh unl hm``mwkog y|lvukmov,unlql kv i ql`iukmovnkz aluwllo unl uwm ulqcv.`luulq f`|vulq-hkg|ql-o|calq+ mo unl `lhu mh unlvkgo .2 2+/ Unl vicl ql`iukmovnkz l~kvuv aluwllounl uwm ulqc mo unl qkgnu mh unl vkgo .2 2+ mh wnkfnmol kv ckvvkog/ Hkoe unl ckvvkog mol hqmc unlgkxlo i`ulqoiukxlv/

    9/ FLND 2 ^XVY 2 2 LGB@ 2 =.I+ XUYM .A+ XUQZ.F+ WUQM .E+ XVYO

    1/ FHDO 2 IKGV 2 2 = 2 EM@^.I+ AQNF .A+ HCYU.F+ H@ZV .E+ H@NV

    6/ EHKC 2 WVZO 2 2 = 2 [WUZ.I+ FGB@ .A+ AHKD.F+ AENB .E+ AHB@

    5/ IRF^ 2 EWGU 2 2 A[LX 2 =.I+ F^LX .A+ ILRX.F+ H\BY .E+ GUBY

    / =

    .I+ .A+ .F+ .E+

    h|oR v'd 2 .9 `v 9:+ h|L| kr'| lv i `v krQ4ve lv iS odv kodvi 'dFo`lwgdviS xdhq4dviS iT4dxdvi ev l-4 hz\g.2 2+/ev fd4viqbY e Lf\-d gVI mgn Lf\-d hz\g.2 2+ev odhg|vxdvb md{vodvkodv i evl-4 gVhu`lv i `v e {yKq gVI ho4vgy hme[kdvilvi v c` {yKq ko edv Ddq enhu4vI

    9/ FLND 2 ^XVY 2 2 LGB@ 2 =.I+ XUYM .A+ XUQZ.F+ WUQM .E+ XVYO

    1/ FHDO 2 IKGV 2 2 = 2 EM@^.I+ AQNF .A+ HCYU.F+ H@ZV .E+ H@NV

    6/ EHKC 2 WVZO 2 2 = 2 [WUZ.I+ FGB@ .A+ AHKD.F+ AENB .E+ AHB@

    5/ IRF^ 2 EWGU 2 2 A[LX 2 =.I+ F^LX .A+ ILRX.F+ H\BY .E+ GUBY

    / =

    .I+ .A+ .F+ .E+

  • 8/7/2019 NTSE STAGE 2 - MAT Paper-2009

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    Zigl & 16

    ;/ 9> 2 >9 2 2 11 2 =.I+ ;> .A+ 919.F+ 191 .E+ 111

    9:/ 9 2 2 851 2 =.I+ ;9 .A+ 999.F+ 955 .E+ 9;8

    Ekqlfukmov 2 .99 um 9.F+ 5: .E+ 51

    91/ Nmw cio{ u|qov wk`` X uidl um fmcl m|u mh unlcirl =.I+ 9: .A+ >.F+ 7 .E+ 8

    96/ Nmw cio{ ukclv ^ niv um gm umwiqev Vm|un, kh nl wiouv um cllu R =.I+ < .A+ 8.F+ > .E+ 9:

    95/ Nmw cio{ ukclv W niv um gm umwiqev Livu, kh nl wiouv um cllu X =.I+ < .A+ 8.F+ 7 .E+ >

    9 2 >9 2 2 11 2 =.I+ ;> .A+ 919.F+ 191 .E+ 111

    9:/ 9 2 2 851 2 =.I+ ;9 .A+ 999.F+ 955 .E+ 9;8

    h|oR v'd 2 .99 `v 9

  • 8/7/2019 NTSE STAGE 2 - MAT Paper-2009

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    Zigl & 15

    Ekqlfukmov 2 .98 um 11+ Ko lifn mh unl hm``mwkog y|lvukmov,hm|q kulcv .`luulq f`|vulq-o|calq-hkg|ql+ iql gkxlo/Unqll mh unlc iql i`kdl ko i flquiko wi{/ Hkoeunl mol wnkfn kv ekhhlqlou hqmc munlq/

    98/ .I+ IHFB .A+ [email protected]+ DZCU .E+ NCBZ

    97/ .I+ UMBE .A+ EHNB.F+ ODNL .E+ @ZU^

    9>/ .I+ : .A+ 7.F+ 1> .E+ 86

    9;/ .I+ ;, 9:9 .A+ >, >1.F+ 6, 97 .E+ < 8 ; .A+ 7 > < 8

    .F+ 8 7 > < .E+ < 8 7 >

    19/

    .I+ .A+ .F+ .E+

    11/

    .I+ .A+ .F+ .E+

    16/ I ekfl kv unqmwo hm|q ukclv ioe kuv hm|q ekhhlqlouzmvkukmov iql gkxlo al`mw/

    5 88 / ky3d en mqRld| xd4y E4d gV PeHd| ,K/ kdz m!dR kwmRS hkqd en xd4y ky3d `v oy~y|n HKK/ xf hkqd en xd4y ky3d v9> m!dR xh-de gVIKKK/ hkqd xdVb lden i4yEq xd4yS ky 3d v 6: m!dRxh-de gVI.I+ evm{K xdVb KKKk4dRKq gViI.A+evm{ KKxdVb KKKk4dRKq gViI.F+ evm{ KxdVb KKk4dRKq gV iI.E+ K, KKxdVb KKK `Ndn xk4dRKq gViI

    1;/ odv vf xdVb qn| |dbih~4dvi ed lw[4 heq|d gV PeHd| ,K/ 6 `vf xdVb< |dbih~4dvi ed lw[4 < gVKK/ < `vf xdVb7 |dbih~4dvi ed lw[4 gVKKK/ 9 `vfS9 |dbi~n xdVb9 xl2o ed lw[4 > gV.I+ evm{ KxdVb KKk4dRKq gViI.A+evm{ K xdVb KKKk4dRKq gViI.F+ evm{ KKxdVbKKK k4dRKq gViI.E+ K, KK xdVb KKK Ndn xdm'4e gV iI

  • 8/7/2019 NTSE STAGE 2 - MAT Paper-2009

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    Zigl & 18

    6:/ Wniu kv unl ekvuiofl aluwllo I ioe E =Vuiulclouv 2K/ A kv > dc Livu mh I ioe < dc Omqun mh F/KK/ E kv `mfiule < dcv Vm|un mh L/KKK/ L kv mfiule 5 dc Livu mh A ioe < dc Omqunmh E.I+ Mo`{ K ioe KKiql v|hhkfklou

    .A+ Mo`{Kioe KKKiql v|hhkfklou

    .F+ Mo`{ KKioe KKKiql v|hhkfklou

    .E+ I`` mhK, KK ioe KKKiql qly|kqle

    Ekqlfukmov 2 .69 um 66+ Unl `luulq vlqklv gkxlo ko lifny|lvukmov hm``mwv i ziuulqo/ Hkoe m|u unl ckvvkog`luulqv um fmcz`lul unl ziuulqo/

    69/ A]O]RH]NOU]HAN]UR] .I+ N A U R O H .A+ N U A H O R.F+ U A R N O H .E+ N U A R O H

    61/ \]U]D]Z]FD\Z]FD.I+ U F Z U \ .A+ F U Z \ U.F+ Z F \ U U .E+ Z \ U F U

    66/ B]N@]D]KN]@DBK]@@D.I+ N K @ B @ .A+ K @ B @ N.F+ @ B @ N K .E+ B @ N K @

    Ekqlfukmov 2 .65 um 6;+ Ko lifn mh unl hm``mwkog y|lvukmov`luulq f`|vulqv-o|calqv iql wqkuulo iffmqekog umi ziuulqo um hmqc i vlqklv/ Vmcl ulqcv iql

    ckvvkog/ Hkoe unl ckvvkog ulqc mq ulqcv hqmcunl gkxlo i`ulqoiukxlv/

    65/ IANQ, LHKM, KBB@, CODK, =, \XCF.I+ YQ@C .A+ YQVU.F+ Y\@C .E+ YQ@H

    6

  • 8/7/2019 NTSE STAGE 2 - MAT Paper-2009

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    Zigl & 17

    Ekqlfukmov 2 .5: um 56+ Unl hkg|qlv ko lifn mh unly|lvukmov hm``mw i vlqklv/ Vl`lfu unl hkg|ql hmqcunl gkxlo i`ulqoiukxlv wnkfn wm|`e fmouko|l unlvlqklv/

    5:/

    .I+ .A+ .F+ .E+

    59/

    .I+ .A+ .F+ .E+

    51/

    .I+ .A+ .F+ .E+

    56/

    .I+ .A+ .F+ .E+

    Ekqlfukmo 2 .55+Unl fizkui` luulqv ko lifn mh unl hm``mwkogwmqev iql fmele ioe wqkuulo ko vci`` `luulqv,a|u omu ko unl vicl mqelq iv unl `luulqv ko unlwmqe/ Hkoe unl fmelv hmq luulqv ioe iovwlq unly|lvukmo/

    O L F D 2 a k c d@ \ F D 2 c e o a@ K D L 2 c d b o

    55/ Wniu wm|`e al unl fmel ko fmqqlfu mqelq hmq unlwmqeOKFL =.I+ d b o a .A+ b k d a.F+ k b a c .E+ k b a d

    h|ov R'd2 .5: `v 56+ h|L| krQ4ve kr'| lvi xdhq4di Bv/dn lvi gV iIho4v gy hme[kdvi lvi v c` xdhq edv zyh|4v udv Bv/dnedvxd~v f0$dqn gVI

    5:/

    .I+ .A+ .F+ .E+

    59/

    .I+ .A+ .F+ .E+

    51/

    .I+ .A+ .F+ .E+

    56/

    .I+ .A+ .F+ .E+

    h|ov R'd2 .55+ |nzv ho4v ~4v 'dFodvi ev krQ4ve fC$ v xtdb edv`ievhqq ebevOdvXvxtdbdv i lv ih{Tdd ~4d gVS he\qymvc`nl lvi |gni gV uV`v ev 'dFo lviI xtdbdvi ev ievq Ddqenhu4v xdVb kr'| ed cdb onhu4vIO L F D 2 a k c d@ \ F D 2 c e o a@ K D L 2 c d b o

    55/ OKFL 'dFo ev h{4v gn l lv i ievqdtdb E4d gdv~vP.I+ d b o a .A+ b k d a

    .F+ k b a c .E+ k b a d

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    Zigl & 1>

    5 um /

    9

    6

    11 5

    1 3 :.F+ 5 > 8 3 1 .E+ 5 > 1 3 um 8;+ Ko unl hm``mwkog y|lvukmo,ly|iukmov nixl alfmcl wqmog e|l um wqmogmqelq mh vkgov/ Fnmmvl unl fmqqlfu mqelq mh vkgovko unl i`ulqoiukxlv gkxlo al`mw hmq lifny|lvukmov/

    8:/ 'df|l en @ey{ f` c`v xk|v =db `v {vqn gV xdVb@ey{ kgy z|v evh{4vodvfdb fd4v i lyC$qn gVxdVb e fdbodhg|vlyC$qn gVI 4ho f` @ey{ kgyzqv l4 kwmR ho'ddev`dl|v gV qdv =db kb mg he` ho'dd ev LlyTd Hdn=.I+ cdb .A+ohtd/d.F+ kw mR .E+ khbzl

    h|ov'd , .89 `v 8 gdv, qdvh|L| lv i `vedV|`n lneb/d gn gV P.I+ 8 > 5 3 9 .A+ 5 > 1 3 :.F+ 5 > 8 3 1 .E+ 5 > 1 3 9 um >6+ h|L| xiedv i en {da| ed x-44| enhu4vxdVb x|y~dln kr'|dvi ev cdb hohu4v I1 < ; 9 7 1 < 9 ; 7 6 ; < 1 5 8 > 9 ; 7 < 1 7 6 9; 7 > < 1 8 < 5 9 ; 7 > 1 : 9 : ; 7 > < 9 ; 7 6 9/ xie 6 `v heq|n fdb xie 7 kg{v xd4d gV xdVb `l `iT4d c`ev fdo |gni gV P.I+ 8 .A+ 1/ xie < ev fdo heq|n fdb xie9 4d1 xd4d gV he\qyc`ev kg{v xie > |gni gV P.I+ 5 .A+ 6/ Nmw cio{ ukclv kv o|calq ; zqlflele a{ 9ioe v|ffllele a{ 7 wnkfn kv omu hm``mwle a{ < =.I+ 6 .A+ 5.F+ < .E+ 8

    Ekqlfukmov 2 .>5 um >7+.Ko lifn mh unl hm``mwkog y|lvukmovi elvkgo-zluulqo kv gkxlo/ Mol vci`` vlgclou

    kv ckvvkoghqmc unl elvkgo/ Vl`lfu unl i`ulqoiukxl wnkfn wk``fmcz`lul unl elvkgo wnlo z`ifle mo unl ckvvkogiqli/

    >5/

    =

    .I+ .A+ .F+ .E+

    >6/ xie ; ev kg{v xie9 heq|n fdb xd4d gV xdvb xie 7c`ev knOv xd4d gV hu`ev knOv xie< |gni gVI.I+ 6 .A+ 5.F+ < .E+ 8

    h|ov R'd2 .>5 `v>7+ h|L| kr'|dv i lv i vkrQ4ve lv i e xhNde[k|dJ|lw |dho4d ~4d gVI a`ed e OdvXd xi'd {yKq gVI c` hme[kedvzyh|4vudv{yKq @Hdd| kb bTd|vkb xhNde[k|dJ|lw |vedvkw bd eb ov~dI

    >5/

    =

    .I+ .A+ .F+ .E+

    >

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    Zigl & 65

    >8/

    =

    .I+ .A+ .F+ .E+

    >7/

    =

    .I+ .A+ .F+ .E+

    >>/ Vk~ hqkloev @, C, O, M, Z ioe Y iql vliule ko ifkqf`l hifkog unl flouql/ Y kv aluwllo @ ioe M/O kv aluwllo Z ioe C/ Z kv omu aluwllo M ioeO/ M kv vlfmoe um unl `lhu mh O/

    Wnm kv aluwllo @ ioe O =.I+ C .A+ Z.F+ M .E+ O

    >;/ Nmw cio{ uqkiog`lv iql unlql ko unl hm``mwkoghkg|ql =

    .I+ 9: .A+ 99

    .F+ 91 .E+ 96

    >8/

    =

    .I+ .A+ .F+ .E+

    >7/

    =

    .I+ .A+ .F+ .E+

    >>/ e mjd ev ev\or en qbY lyTddhqf O, hl3d@, C, O,M, Z xdVbY mjd lvi fVAv gViI @xdVbM ev fnz lviY gVIZ xdVbC ev fnz lviO gVIM xdVbO ev fnz lviZ |gnigVIO ev fd4vi qbY M ow`bv @Hdd| kb gVI@xdVbO ev fnz lvi edV| gV P.I+ C .A+ Z.F+ M .E+ O

    >;/ h|L| xdhq lvi heq|v h3dNdyu gVi P

    .I+ 9: .A+ 99

    .F+ 91 .E+ 96

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    15/16

    Zigl & 6 .A+ 9