Part-II A
Part-II A
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Rl;nlz; : ........................................
Kf;fpak; : guPlr
; fupd; cgNahfj;jpw;F
,t;tpdhj;jhs; 12 gf;fq;fisf; nfhz;Ls;sJ. khj;jpuk;
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,uz;lhk; tpdhj;jhSf;F
,t;tpdhj;jhs; A, B
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vd;Dk; ,U
gFjp tpdh ,y. Gs;spfs;
gFjpfisf; nfhz;Ls;sJ. ,U
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gFjpfSf;Fk; xJf;fg;gl;l Neuk; ,uz;L
kzpj;jpahyq;;fs; gj;J epkplq;fs; MFk;. 2
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fzpg;ghidg; gad;gLj;jf;$lhJ
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gFjp A – mikg;Gf; fl;Liu
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vy;yh tpdhf;fSf;Fk; ,j;jhspNyNa tpil
vOJf. xt;nthU tpdhTf;Fk; tplg;gl;Ls;s 6
.b
,lj;jpy; ckJ tpilfis vOJf. B 7
nfhLf;fg;gl;Ls;s ,lk; ckJ tpilfSf;Fg;
,yf;fj;jpy;
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NghJkhdJ vd;gijAk; tpupthd tpilfs;
nkhj;jk;
mtrpakpy;iy vd;gijAk; ftdpf;f. vOj;jpy;
gFjp B – fl;Liu
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,g;gFjp %d;W tpdhf;fisf; nfhz;Ls;sJ.
mtw;wpy; ,uz;L tpdhf;fSf;F khj;jpuk; tpil
FwpaPl;nlz;fs;
vOJf. ckf;F toq;fg;gLk; jhs;fis ,jw;Fg;
gad;gLj;Jf. tpilj;jhs;fisg; guprPypj;jtu; 1
tpilj;jhs;fisg; guprPypj;jtu; 2
,t;tpdhj;jhSf;nfd toq;fg;gl;l Neu Kbtpy;
Gs;spfisg; guprPypj;jtu;
gFjp A NkNy ,Uf;Fk;gbahf A, B Mfpa
,uz;L gFjpfisAk; xd;whfr; Nru;j;Jf; fl;ba Nkw;ghu;it nra;jtu;
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gFjp - IIA
mikg;Gf; fl;Liu
01) (a) (i) Nfhskhdp gad;gLj;jg;gLk; re;ju;g;gq;fs; 2 jUf.
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(ii) Nfhskhdp tl;l mstpil xd;W ,U G+uz Rw;Wf;fis epfo;j;Jk; NghJ mJ
gpujhd mstpilapd; 1𝑚𝑚 J}uk; efu;fpwJ. mj;Jld; tl;l mstpilahdJ
50 gpupTfshf gpupf;fg;gl;Ls;sJ. ,f; Nfhskhdpapd; ,opT vz;zpf;if?
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(b)
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b
(i) Nkw;gb NfhskhdpahdJ fz;zhbj;jl;L xd;wpd; kPJ itf;fg;gl;L mjd;
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ehd;F fhy;fSk; fz;zhbj;jl;il njhLkhW itf;fg;gl;l NghJ mjd;
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thrpg;G Nkw;gb fhzg;gl;lJ. mjd; thrpg;ig jUf.
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(ii)
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NfhskhdpahdJ kPzL
; k; Ftpthd xU tisNkw;gug;gpy; itf;fg;gl;L mjd;
ehd;F fhy;fSk; tise;j Nkw;gug;ig njhLkhW nra;ag;gl;l NghJ
Nfhskhdpapd; thrpg;G epiy gpd;tUkhW mike;jJ.
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juk; - 12 (2025) 2k; jtiz (FWC) 2 ngsjpftpay; - II (A)
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xd;iwf; $Wf.
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(ii) ,f;Fiwghl;il mstPl;bd; NghJ vt;thW Fiwj;Jf; nfhs;syhk;.
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(iii) Nfhskhdpnahd;wpd; ,opntz;zpf;ifia Fiwg;gjw;F khw;wq;fis rpghupR
nra;f.
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02)
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Ma;T$lj;jpy; fz;zhbapd; mlu;j;jpia Jzptjw;F xU gf;f ePsk; Vwj;jho 3𝑐𝑚
MdJk; Vwj;jho 60𝑔 jpzpTs;sJkhd fz;zhbr; rJuKfp ckf;F toq;fg;gl;Ls;sJ.
(a) (i) rJuKfpapd; xU gf;fj;jpd; ePsj;ij (ℓ)1% ,Yk; $ba nrk;ikAld;
msg;gjw;F Ma;T$lj;jpy; ePu; gad;gLj;Jk; cgfuzk; ahJ?
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(ii) fz;zhbr; rJuKfpapd; fdtstpw;fhd xU Nfhitia ℓ ,d; rhu;gpy;
vOJf.
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(iv) fz;zhbr; rJuKfpapd; jpzpT> njupe;njLj;j epiwapd; jpzpT Mfpad
KiwNa 𝑚, 𝑀 vdf; nfhs;Nthk;. ,q;F ngwg;gLk; J}u mstPLfis (ℓ1 , ℓ2 ).
NkNy (𝑏)(𝑖𝑖𝑖)
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Mfpatw;iwj; njhlu;GgLj;Jk; Nfhitia vOJf.
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(v) NkNy (𝑎)(𝑖𝑖) ,Yk; (𝑏)(𝑖𝑣) ,Yk; vOjpa Nfhitfisg; gad;gLj;jpf;
fz;zhbapd; mlu;j;jp (𝑑𝑔) ,w;Fupa xU Nfhitia vOJf.
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(c) (i) xU ePu; Kfit toq;fg;gl;bUg;gpd; rJuKfpapd; fdtsitf; fzpf;fhky;
fz;zhbapd; mlu;j;jpia (𝑑𝑔) Jzpayhk;. fj;jpNahuj;jpypUe;J fz;zhbr;
rJuKfpf;F cs;s J}uj;ij khwhky; itj;Jf;nfhz;L 𝑑𝑔 iaj; Jzptjw;Fg;
ngw Ntz;ba Nkyjpf mstPL (ℓ3 ) ahJ?
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(ii) 𝑑𝑔 apw;;Fupa xU Nfhitia ℓ1 , ℓ2 , ℓ3 ePupd; mlu;j;jp (𝑑𝜔) Mfpatw;wpd;
rhu;gpy; ngWf.
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𝒉𝒘 𝒉𝓵
(ii) ,t; cgfuzj;jpy; gad;gLj;jg;gLk; Fohapd; 𝒙
𝒚
mz;zsthd tpl;lj;ij 𝑐𝑚 ,y; jUf.
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Fwpg;gpLf.
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(iv)
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,q;F ,izf;fg;gl;l nfstp 𝐺 ,d; gad;ghL ahJ?
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(b) (i) ePu;> jput epuy;fis FohapDs; vt;thW epiyepWj;JtPu; vd;gijj; njspthff;
Fwpg;gpLf.
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. b
(ii) 𝜔 - Kfit ePu; kl;lj;jpy; ,Ue;jhd ePu; epuypd; cauk;
𝑒 - Kfitapd; jput kl;lj;jpy; ,Ue;jhd jput epuypd; cauk;
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𝜌𝜔 - ePupd; mlu;j;jp
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𝜌ℓ - jputj;jpd; mlu;j;jp
𝑃𝑜 - tspkz;ly mKf;fk;
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Nkw;gb juTfisf; nfhz;L 𝑃𝑜 ,w;fhd ,U njhlu;Gfisg; ngWf.
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(v) vjpu;ghu;fF
; k; tiuig mz;zsthf tiue;J fhl;Lf.
(c) (i) jput epuy;fis FohapDs; epiy epWj;Jk; NghJ mjpf ftdk; nrYj;j
Ntz;ba jput epuy; ahJ? mjw;fhd fhuzk; ahJ?
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(ii) xt;nthU jlitAk; jput epuy;fis epiyepWj;jpa gpd; mstPl;il
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Nkw;nfhs;s Kd; rupnra;a Ntz;ba gFjpfs; vit? vt;thW rup nra;tuP ?;
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04) tspapy; xypapd; fjpiaj; Jzptjw;F ghlrhiy
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,irf;fit
Ma;T$lj;jpy; gad;gLj;jg;gLk; gupNrhjid cgfuz
. b
xOq;fikg;G glj;jpy; fhl;lg;gl;Ls;sJ.
(a) (i) Nkw;gb gupNrhjidapy; gad;gLj;jg;gLk; 𝑳
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gupTf; Fohapd; tpl;lj;jpidj; njupT nra;f.
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(I) 4𝑚𝑚 (II) 25𝑐𝑚 (III) 2.5𝑐𝑚
gupTf;Foha;
(ii) gad;gLj;jg;gLk; gupTf;Fohapd; mz;zsthd
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cauk; ahJ?
..................................................................................................... ePu;
cgfuzk; : .......................................................................
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juk; - 12 (2025) 2k; jtiz (FWC) 6 ngsjpftpay; - II (A)
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(c) (i) Kjyhk; mjpu;T tiff;F xj;j
. b
Nfhitia miyePsk; 𝜆 > Fohapd; Kidj;jpUj;jk; 𝑒 Mfpatw;wpy; vOJf.
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(ii) ,uz;lhk; mjpu;T tiff;F xj;j gupT ePsk; ℓ2 vdpd; ℓ2 ,w;Fupa xU
Nfhitia miyePsk; 𝜆> Fohapd; Kidj;jpUj;jk; 𝑒> Mfpatw;wpy; vOJf.
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(iii) ,jpypUe;J (ℓ2 − ℓ1 ) ,w;fhd xU Nfhitia 𝜆 ,y; vOJf.
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(iv) (ℓ2 − ℓ1 ) Ig; ngWtjd; mD$yk;.
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(v) Nkw;gb Nfhitapy; ,Ue;J ,irf;fUtpapd; kPbwd; 𝑓 tspapy; xypapd;
Ntfk; 𝑣 Mfpatw;iw njhlu;GgLj;jp xypapd; Ntfj;jpw;fhd Nfhitiag;
ngWf.
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