higher secondary level statistics book
TRANSCRIPT
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gTjvq
kZo Bz nvg kvev
†nvev¤§d Lvfy o fvbvg
B¨vnwfªqvj `vfwo‡Bbj ø̀ V √:, ¸obvj kv‡B© o √:, XvBv
B_© ― B `Ó Bvwb_
M‛T nvl¨wnB `wgksA¨vj `ÓYn `Å
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`wgksA¨vj Ó̀Yn `Å
NBvdb- Øvdb †bª wW
gTjvq
kZo Bz nvg kvev
wfcvKxq `Ólvj
`wgksA¨vj wfcvK B¨vnwfª qvj B‡ oZ, XvBv|
wbù vK_ †hvK¨_v? wfNkwk (Ljvk© ), NnNk (`wgksA¨vj), XvBv wfb¦ wfd¨voq| LwcÌ_v? `Ó v°j `ÓcvaB, †nvev¤§d`y g w`ª̀ v‡gwVgx B‡oZ, XvBv|
E]Z@L kjd`Ó vÙ|`gxù B? nvl¨wnB G M‛Tnvl¨wnB wb ù v‡fv^©, XvBv|
|||
†nvev¤§d Lvfy o fvbvg wkwjqg `Ó cvaB`wgksA¨vj wfcvK
B¨vnwfª qvj B‡oZ, XvBv| wbù vK_ †hvK¨_v? wfNkwk (k¤§vj),
NnNkwk (`wgksA¨vj) LwcÌ_v? `Ó v°j `Ó cvaB, KvZx`y g Kvo© k B‡oZ|
E]Z@L kjd`Ó vÙ|
B¨vnwfªqvj `vfwo‡Bbj `- V √:, ¸obvj kv‡B© o √:, XvBv
B_© ― B Ó̀ Bvwb_ †nvfvJo? 7884/84/74
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Ll¨vq wffgW `― ýv js
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_¡xq gTjvn~ oB Ls‡b `Ó w_wV `Ó ‡bŐ NBvwlB Lsb YvB‡_ `v‡g|
`wgksA¨vj `ÓYn `‡Å f¨fñ_ wfwcjŐ `Ó _x‡Bg `wgwTw_ `Ó _xB `wgwTw_
∜ (Pgnkl @lpgtla) ir (Pukkltgie) †hvKBgW wTû τ `vJ (@lpgtla) ¸WBgW wTû
x ( fvg ) jny jvg KvwWw_B Ki¶ ( wnM ) _Y¨ wf‡b¦ g KvwWw_B Ki
(Lrgthkftg` Kfle) KvwWw_B KiNK (Nfikftrg` Kfle) Z¨vwnw_B KiHK (Hlrkieg` Kfle) Mâj Ki
f (Kfmgle) nl¨nv
i (Kimf) `Ó Tz gB
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NBwV w^wZVvo B¨vnwfªqvj `Ó Bvbjv
`ÓYn Ll¨vq
`wgksA¨vj, ToB G wfwcjŐ `Ó _x‡Bg lvgWv P]L]GP]G@P, SLZGLJAF & @IE@FT]P IC MGCCFZFE] PWKJIAP
`wgksA¨vj bàwVg Js‡gZx `Ó w_bà Ptltgstg`s| Ng kvlvgW LY© e‡‛\ †Bvj EVjv fv wfa‡qg
kvswA¨B fW© jv| LY© vr, †Bvj ksA¨v wfaqB _Y¨ ksKÓ e, M`¯‗v`j, wf‡b ø aW Nfs f¨vA¨vg nvl¨‡n Hwfaq k¤ÿwB© _ wkÞvŬ Ë KÓ eWJ e‡ov `wgksA¨vj|
cvg‡_g wfA¨v_ `wgksA¨vjwfd w`.wk. neovjwfb ( T.@. Kihlaleijgs) kf© ̀ ÓYn Ptltgstg`s Ng
f»vjy fvd B‡gj `wgksA¨vj| fvsov‡d‡bg `wgksA¨vjwfd BvZx †nv_vevg †ev‡kj ‘Ptltgstg`s‗ bàwVg`wgcvav B‡gj Ý_Y¨ KwW_Ö| L‡j‡B N‡B ÝksA¨v_Â¡Ö f‡oG Lwcwe_ B‡gj| Lf‡b‡a Ý`wgksA¨vjÖ
Ptltgstg`s Ng kwSB `wgcvav we‡k‡f kf© Zj ¯U xB… _ eq|XvBv wfb¦ wfd¨vo‡qg Ll¨v`B ^. BvZx †nv_vevg †ev‡kj e‡oj fvsov‡d‡bg `wgksA¨vj wfa‡qg
LKÓ d~ _| _‡f `wgksA¨v‡jg wfBvb, MjŐ w_ G MrBa© kvl‡j Lvg.N. wmbvg ( Z.L. Cgshfr ) Ng Ngn~ o¨fvj Lfdv‡jg Zj¨ L‡j‡B _u v‡B Lvly wjB `wgksA¨v‡jg ZjB we‡k‡f wf‡fTjv B‡gj|
N Ll¨vq `vS †b‡a wb ùvYx©gv
• `wgksA¨v‡jg Mr`w f¨vA¨v Bg‡_
`vg‡f
|
• `wgksA¨vj Bx fo‡_ `vg‡f|
• Bw_`q `wgksA¨vj wf‡dg jvn fo‡_ `vg‡f|
• `wg ksA¨v‡jg •fwbð¨ f¨vA¨v Bg‡_ `vg‡f |
• `wgksA¨v‡jg ¸g ã_¡ G f¨fevg wf‡b ø aW Bg‡_ `vg‡f |
• `wgksA¨v‡jg Bvh©vfox fW©jv Bg‡_ `vg‡f |• ToB, lª ãfB, knKÓ B G jny jvg lvgWv f¨vA¨v Bg‡_ `vg‡f|
• To‡Bg `Ó Bvg‡cd f¨vA¨v Bg‡_ `vg‡f |
• ¸WfvTB G ksA¨vfvTB ToB k¤ÿ ‡B© fo‡_ `vg‡f|
• wfw‛\jŐ G Lwfw‛\jŐ ToB k¤ÿ‡B© fo‡_ `vg‡f9
• `wgnv`j wB _v fo‡_ `vg‡f| • `wgnv`j †¯‥‡og `Ó Bvg‡cd f¨vA¨v Bg‡_ `vg‡f|
• wfwcjŐ `Ó _x‡Bg lvgWv , f¨fevg G Bw_`q M``v‡d¨ g `Ó nvW k¤ÿ‡B© fo‡_ `vg‡f|
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M‛T nvl¨wnB `wgksA¨vj-`ÓYn ̀ Å
NBwV B¨vnwfªqvj w^wZVvo `Ó Bvbjv
:
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`wgksA¨vj, ToB G wfwcjŐ `Ó _x‡Bg lvgWv
M‛Tnvl¨wnB `wgksA¨vj
0
fòfT‡j `wgksA¨vj?
fòfTj L‡Y© `wgksA¨v‡jg LY© eo †Bvj EVjv fv wfa‡qg ksA¨v_¥B `Ó Bvb †hnj? B_B¸‡ov `wgfv‡g†\‡o wbbyg ksA¨v, B¨vnwfª qvj B‡o‡Z NBvdb †bªWxg \vÅ- \vÅx‡dg GZ‡jg gvwbnvov, wj_¨ `Ó ‡qvZjxq
dª ‡f¨g wfwcjŐ kn‡q Mr`vdj fv n~ o¨ fv Lvndvwj - gÙvwjg wekvf, `Ó w_ f\‡g fvsov‡d‡b Zj¥ - n― _z ¨gksA¨v, fvsov‡d‡b bª wnB‡dg nvYvw`\y Lvq ks¶vŬ Ë M`v J_¨vwd `wgksA¨vj|
_v\viv wfwcjŐ `wgksA¨vjwfd `wgksA¨vj‡B wfwcjŐcv‡f ksÌvwq_ B‡g‡\j| N‡dg nv‡P Z.L.
Cgshfr2 ^.G.Bgen, Jiwafy, @rixtie & `iwmfe, H. Pf`rgst Ng ksÌv M‡o øA‡hvK¨|
Z.L. Cgshfr Ng n‡_ , Ú`wgksA v̈j wjwô_gƚ‡`J mwo_ KwW‡_g NBwV bvAv hv `h© ‡f ùW Øvgv
`Ó vÙ KvwWw_B M v̀‡Âg M`g Ó̀ ‡qvK Bgv eq|Ð (L``irmgen ti Z.L.Cgshfr. ã]hf s`gfe`fic stltgstg`s gs fssfetglaay l jrle`h ic lppagfm klthfkltg`s lem kly jf
rfnlrmfm ls klthfkltg`s lppagfm ti ijsfrvltgiela mltl)
^.G.Bgen Ng n‡_ , Ú`wgksA¨vj e‡ov Lwjôq_vg wfaq k¤ÿ‡B© wkÞvŬ Ë †jGqvg wfÌvj|(^.G.Bgen slys, ãPtltgstg`s gs thf s`gfe`f mf`gsgie klbgen ge thf cgfam
ue`frtlgegty‛)
Jiwafy Ng n‡_ -†Bvj Ljy kÑv‡jg † ù ‡Å `g¯ÿg k¤ÿB© hy °cv‡f M`¯‗ vw`_ EVjvg ksA¨v_¥B fW© jvJ e‡‛\ `wgksA¨vj| (ãPtltgstg`s lrf eukfrg`la stltfkfet ic cl`ts
ge ley mfplrtkfet ic fequgry pal`fm ge rfaltgie ti fl`h ithfr.‛)
@rixtie & `iwmfe Ng n‡_ , `wgksA¨vj e‡‛\ ksA¨v_¥B, _Y¨ ksKÓ e, M`¯‗ v`j,
wf‡b ø aW G f¨vA¨v `Ó dvj Bgvg wfÌvj (ãPtltgstg`s kly jf mfcgefm ls thf s`gfe`f ic
`iaaf`tgie, Trfsfetltgie, lelaysgs lem getfrprftltgie ic eukfrg`la mltl‛)
H. Pf`rgst Ng n‡_ , Ú`w gksA¨vj wfÌvj Øvgv Lvngv †Bvj `~ f© wjl© vwg_ M‡É‡b¨`ÓWvoxfÞcv‡f ksK― ex_ Nfs `vg¯ÿwgB k¤ÿ‡B© ks¯‗ vw`_, wjc~ © o_vg hy w°ksK_ nvj Ljykv‡g
ksA¨vq `ÓBvwb_, KWjvB… _ fv wjgƚw`_ Nfs fòwfl BvgW Øvgv oùWxq nvÅvq `Ócvwf_
_Y¨vfwog knwð‡B fy PvJ |Ð (ãJy stltgstg`s wf kfle lnnrfnltf ic cl`ts lccftfm ti l
klrbfm fxtfet jy kuatgpag`gty ic `lusfs, eukfrg`laay fxprfssfm, feuklrltfm ir
fstgkltfm l``irmgen ti rflsieljaf stlemlrm ic l``url`y, `iaaf`tfm ge l systfkltg`kleefr ic l prfmftfrkgefm purpisf lem pal`fm ge rfaltgie ti fl`h ithfr‛)
`wg‡b‡a fov hvq, `wgksA¨vj e‡ov - wjqn_vwŬ¹ B M`v‡q ksA¨v_¥B _Y¨ ksKÓe, ksEfÞBgW,
M`¯‗ v`j, wf‡b øaW G f¨A¨v `Ódvj Bgvg wfÌvj|
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M‛T nvl¨wnB `wgksA¨vj-`ÓYn ̀ Å
NBwV B¨vnwfªqvj w^wZVvo `Ó Bvbjv
=
4‰ ............. J_¨vwd`wgksA¨vj jq| h_ù
W `h© Ŭ Ë
jv `Ó d ksA¨v¸‡ov B_¸‡ov †ov‡Bg M‛T_v wj‡d©b B‡g|(gv) `wgksA¨vj _Y¨ fòwfl BvgW Øvgv `Ó cvwf_ eq? `wgksA¨vwjB _Y¨ NBvwlB BvgW Øvgv`Ó cvwf_ e‡f| lv‡jg Mr`vdj Zwng Mf© g_v, kvg, `vwj kgfgve, k~ h©wBgW J_¨vwd M`vdvj¸‡ov Øvgv `Ó cvwf_ eq|
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`wgksA¨vj, ToB G wfwcjŐ `Ó _x‡Bg lvgWv
M‛Tnvl¨wnB `wgksA¨vj
6
(v) `wgksA¨vj _Y¨‡B kyb― Aocv‡f ksKÓ e Bg‡_ eq? `wgksA¨vwjB _Y¨vfox ky b Aocv‡f ksKÓe
Bg‡_ e‡f| M‡Éb¨exjcv‡f ksK― ex_ _Y¨ kwSB wkÞvŬ Ë wd‡_ f¨Y© e‡_ `v‡g Nfs N lg‡Wg
_Y¨ †Bvj EVjvg `wg`~W© fW© jv wd‡_ f¨Y© eq|
(vg) _‡Y¨g knZv_xq_v? `wgksA¨vjxq M`v‡B Lfb¨J knZv_xq e‡_ e‡f| knZv_xq eGqvg Zj¨ _Y¨¸‡ ov Lfb¨J NBJ wfa‡qg M`g e‡_ e‡f| †hnj -B_ B¸‡ ov f¯‘ g GZj G
B_B ̧‡ ov f¨w° GZj wj‡q KwS_ M`v `wgksA¨vj jq| BvgW, _Y¨¸‡ ov NBJ wfa‡qg
M`g jv eGqvq _v knZv_xq jq|
(vgg) _‡Y¨g _z ojv‡hvK¨_v ?`wgksA¨vjxq M`v‡B Lfb¨J _z ojv‡hvK¨ e‡_ e‡f| _y ojv‡hvK¨ eGqvg Zj¨ _Y¨ ̧‡ ov NBJ NB‡B `Ó Bvwb_ e‡_ e‡f| †hnj - VvBvq `wgwn_ wB\y †ov‡Bg Lvq Nfs
^ov‡g `wgwn_ wB\y †ov‡Bg Lvq wj‡q KwS_ M`v `wgksA¨vj jq BvgW, _Y¨¸‡ ov NBJ wfa‡qg M`g e‡oG NBJ NB‡B `Ó Bvwb_ jv eGqvq _v _z ojv‡hvK¨ jq|
(vggg) `wgksA¨vj wjgƚ`‡j hy w°ksK_ `wgnv‡W kwSB_v fZvq gvAvg `Ó ‡qvZj g‡q‡\? `wgksA¨vjK‡faWvq `Ó vÙ movm‡og wcw‡_ j_z j `wgBëjv KÓ eW Bgv eq| ky _gvs, movmo wjgƚ`‡W
NBwV hy w°k»_ `wgnv‡W kwSB_vg nvÅv fZvq gvAv dgBvg|
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M‛T nvl¨wnB `wgksA¨vj-`ÓYn ̀ Å
NBwV B¨vnwfªqvj w^wZVvo `Ó Bvbjv
3
(ggg) `wgksA¨vj Lj¨vj¨ wfÌvj‡B kvevh¨ B‡g? Lj¨vj¨ kvnvwZB G `Ó vB… w_B wfÌvj †hnj? `dvY© , gkvqj, Zxfwfd¨v, n‡jvwfÌvj, knvZ wfÌvj J_¨vwd wfa‡qg K‡faWvq G movm‡og kwSB_v
wjgƚ`‡W `wgksA¨vwjB `Þw_ f¨fevg Bgv eq|
(gv) `wgksA¨vj LY© ‣jw_B wf‡b ø a‡W kevq_v B‡g ? LY© jxw_‡_ Tvwedvg wf‡b ø aW, Bvoxj kvwgg wf‡b ø aW, k~ TB ksA¨v G nydª v ks¶vŬ Ë wekvf wjBv‡bg Bv‡Z `wgksA¨vwjB `Þw_ `Ó ‡qvK e‡qYv‡B| wfwcjŐ dª ‡f¨g Mr`vdj, Tvwedv, †hvKvj, wfwj‡qvK, Lvndvjx -gÙvjx, Lvq-f¨q, ¶q- wf¶q J_¨vwd Lf¯‗ vg wf‡b ø a‡Wg Bv‡Z `wgksA¨vj f¨fevg Bgv e‡q Yv‡B| Zjk¤ÿd, Bn© ks¯‗ vj, Bg, gvZ¯U J_¨vwd wekvf wjBv‡bg Bv‡Z `wgksA¨vj f¨fevg Bgv eq|
(v) f¨fkv-fvwW ‡ Z¨ `wgksA¨vj? nvjy ‡ag Zxf‡j g ã wT Nfs `Ó ‡qvZj `Ó w_wjq_J `wgf_© jbxo| †kJ
`wgf_©j L‡jB † ù ‡ÅJ eq kn‡qg †`Ó w ù ‡_| †hnj? fav© Bv‡o \v_vg Tvwedv f― wÞ `vq, b x_Bv‡o Kgn †`vbv‡Bg `Ó‡qvZj fv‡i| `wgksA¨v‡jg nvl¨‡n f¨fkvqxgv kn‡qg `wgf_© ‡j ¶q- wf¶‡qg `wgnv`, ovc -ù w_g wekvf `Óc― w_ Bg‡_ `v‡gj| hvg mobÓ ã w_‡_ †Bvj knq Bx
`wgnvW nvo þB Bg‡_ e‡f, fvZv‡gg Lf¯‗ v B_Vv cvo fv n‿d _v _vgv Zvj‡_ `v‡g Nfs kwSB kn‡q kwSB `d‡ ù` wj ‡_ `v‡g|
(vg) wTwBrkv bv‡ ¹̄ `wgksA¨vj ? f_© nv‡j wTwBrkv bv‡¯¹ `wgksA¨v‡jg ¸g ã _¡ L`wgkxn| wfwcjŐ
Oay ‡lg Bvh© Bvwg_v, †gv‡Kg kwSB o ù W Nfs `Ó Bvb `Óc― w_ `wgnv` Bg‡_ `wgksA¨vj Lvfb¨B evw_qvg (]iias) wekv‡f f¨fñ_ eq|
(vgg) LvfevGqvg `~f© vcvk `Ódv‡j `wgksA v̈j ? L vfevGqvg L_x_ G f_©nvj _‡Y¨g M`g wcw B‡g Lvngv LvKvnx wd‡jg LvfevGqvg `~fv©cvk †`‡_ `vwg| N‡ ù ‡Å `wgksA¨v‡jg ÚBvoxj kvwg Ð
f¨fñ_ e‡q Yv‡B| N\viv fj¨v, Agv, Z‡ov‛\¡ & vk fv Lj¨vj¨ `Ó vB… w_B dy‡hv© ‡Kg LvKnj k¤U ‡Ñ Lvngv Lv‡K †Y‡B Ljy nvj Bg‡_ `vwg| m‡o `ÓvB… w_B dy‡hv©K †nvBv‡fovq Lvngv Lv‡K †Y‡B
`Ó ¯‘ _ e‡_ ̀ vwg Nfs nvjy‡ag Zvjnv‡og wjgv`Âv L‡jBvs‡b wjwô_ Bg‡_ v̀wg|
(vggg) Zjwnw_g `wgksA¨vj? Zjwnw_ e‡ov †Bvj Zj‡Kvwýg fv k¤`Ó dv‡qg nvjy ‡ag Zxfj k¤ÿwB© _ EVjvfoxg fW©jv| NJ fW© jvq nvjy ‡ag Zj¥ - n― _z, •ffvweB Lf¯‗ v, †fBvg_¡ `Ó c― w_ k¤ÿ‡B© _Y¨ ksKÓ e Nfs ev‡gg `wgnv` Bgv eq| N\viv †Bvj Lʇog Lvdn énvwg‡_ `wgksA¨v‡jg
f¨fevg kf© Zjwfwd_|
(gx) Bw¤ÿMVvg wfÌv‡j `wgksA¨vj? k¤`Ów_ `v‡kv©jvo Bw¤ÿMVvg Nfs nvJ‡¶v - Bw¤ÿMVv‡gg f¨fevg f¨v`Bcv‡f f―wÞ †`‡q‡\| _Y¨ ksKÓe, M`¯‗v`j, wf‡b øaW J_¨vwd`wgksA¨vwjB `Þw_¸‡ov f¨fevg B‡g Bw¤ÿMVv‡gg nvl¨‡n L‡jB ZwVo knk¨v
knvlv‡jg `Y kyKn e‡q‡\|
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`wgksA¨vj, ToB G wfwcjŐ `Ó _x‡Bg lvgWv
M‛Tnvl¨wnB `wgksA¨vj
>
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M‛T nvl¨wnB `wgksA¨vj-`ÓYn ̀ Å
NBwV B¨vnwfªqvj w^wZVvo `Ó Bvbjv
8
lª ãfB? _‡Y¨g †h •fwbð¨ _Y¨wf‡b¦ g kBo NB‡B NBJ Yv‡B LY© vr L`wgfw_© _ Lf¯‗ vq Yv‡B _v‡Blª ã fB f‡o| Lj¨cv‡f knKÓ‡Bg †h kn¯ Ë oùW fv •fwbð¨ M`vdvj‡c‡d wfwcjŐ gƚ` eq jv| LY© vr M`vdvj fv †n․o‡c‡d _vg_n¨ `wgow ù _ eq jv, NBJ Yv‡B, †k kn¯ Ë •fwbð¨‡B lª ãfB
f‡o| †hnj -
nvjy ‡ag ev_, `v G ev_ -`v‡qg Lv»y ‡og ksA¨v J_¨vwd lª
ãfB| lªã fB‡B kvlvgW_ l, j, ` Øvgv `Ó Bvb Bgv eq|
knKÓ B (Tipualtgie)? †Bvj NBwV `gx ù ‡W fv `h© ‡f ù ‡W ky wjwd© ð wB\z •fwb‡ð¨g LwlBvgx k¤¢ vf¨ kBo M`vdv‡jg knwð‡B knKÓ B fv _Y¨wfb¦ f‡o| knKÓ ‡Bg LŬ ËK© _ M`vd vj¸‡ov‡B knKÓ ‡Bg NBB fov eq|†hnj? †Bvj †bªWxB‡ ùg \vŇd g Ki fqk Ljy kÑv‡j M° †bªWxB‡ ùg \vŇd g †kV e‡ov
NBwV knKÓ B| Lvg †bªWxB‡ ùg `Ó‡_¨B \vÅJ e‡ov knKÓ ‡Bg NB NBwV kdk¨ fv NBB|jny jv (Plkpaf)? †Bvj knKÓ ‡Bg NB fv NBvwlB •fwbð¨ wjW© ‡qg Zj¨ Jev e‡_ `Ó wjwl_¡ B vgx Lsb
wjf©vTj Bgv eq _Aj H wjf© vwT_ LsbwV‡BJ jny jv f‡o| LY© vr jny jv e‡ov knKÓ ‡Bg`Ó w_wjwl_¡ Bvgx Lsb hv knKÓ ‡Bg †Bvj •fwbð¨ `wgnv‡` f¨fñ_ eq| Lvg jny jvg LŬ ËK© _`Ó w_wV nvj‡B jny jvg NB NBwV NBB f‡o|
†hnj √ †Bvj †bª wWB‡ ùg
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`wgksA¨vj, ToB G wfwcjŐ `Ó _x‡Bg lvgWv
M‛Tnvl¨wnB `wgksA¨vj
7
`wgnvWfvTB / ksA¨vfvTB ToB (\uletgtltgvf vlrgljaf)?
†h To‡Bg nvj¸wo `wgnv` fv KWjv Bgv hvq LY© vr ksA¨vq `Ó Bvb Bgv hvq _v‡B `wgnvW fvTB ToB f‡o| `wgnvW fvTB ToB †hnj - fqk, GZj, M‛T_v J_¨vwd|
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M‛T nvl¨wnB `wgksA¨vj-`ÓYn `Å
NBwV B¨vnwfªqvj w^wZVvo `Ó Bvbjv
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`wgksA¨vj, ToB G wfwcjŐ `Ó_x‡Bg lvgWv
M‛Tnvl¨wnB `wgksA¨vj
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M‛T nvl¨wnB `wgksA¨vj- Ó̀Yn `Å
wV v w v w w Vv ` vb v
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`wgksA¨vj, ToB G wfwcjŐ `Ó _x‡Bg lvgWv
M‛Tnvl¨wnB `wgksA¨vj
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M‛T nvl¨wnB `wgksA¨vj- Ó̀Yn `Å
NBwV B¨vnwfªqvj w^wZVvo `Ó Bvbjv
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`wgksA¨vj, ToB G wfwcjŐ `Ó _x‡Bg lvgWv
M‛Tnvl¨wnB `wgksA¨vj
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M‛T nvl¨wnB `wgksA¨vj- Ó̀Yn `Å
NBwV B¨vnwfªqvj w^wZVvo `Ó Bvbjv
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`wgksA¨vj, ToB G wfwcjŐ `Ó _x‡Bg lvgWv
M‛Tnvl¨wnB `wgksA¨vj
; e` x x xj x x xl ee √+++√+++ )......()............( :<::
:
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g
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(gx) ∜;
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`Ó nvW? n‡j Bwg, †Bvj ToB x-Ng e ksA¨B nvjkn~ e e x x ..................., :< Nfs L`g ToB y-Ng
e ksA¨B nvjkn~ e e y y ..................., :<
∜;;+++∽
e
gge
x x x x<
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M‛T nvl¨wnB `wgksA¨vj- Ó̀Yn `Å
NBwV B¨vnwfªqvj w^wZVvo `Ó Bvbjv
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`wgksA¨vj, ToB G wfwcjŐ `Ó_x‡Bg lvgWv
M‛Tnvl¨wnB `wgksA¨vj
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M‛T nvl¨wnB `wgksA¨vj-`ÓYn `Å
NBwV B¨vnwfªqvj w^wZVvo `Ó Bvbjv
:4
; ∜;
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o
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`wgksA¨vj, ToB G wfwcjŐ `Ó _x‡Bg lvgWv
M‛Tnvl¨wnB ẁgksA¨vj
:<
(xgv) ∜;
√e
g
g ` x<
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`Ó nvW? n‡j Bwg, †Bvj ToB x-Ng e ksA¨B nvjkn~ e e x x ..................., :< Nfs ` NBwV lªãfB|
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ge x x x x<
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`Ó nvW? n‡j Bwg, †Bvj ToB x-Ng b ksA¨B nvjkn~ e b x x ..................., :< Nfs l G j dy wV lªãfB|
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M‛T nvl¨wnB `wgksA¨vj-`ÓYn ̀ Å::
∜ ∜∜; ≤
√
+;
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<
:
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NBwV w^wZVvo B¨vnwfªqvj `Ó Bvbjv
wØ_xq Ll¨vq
_Y¨ ksKÓ e, kswù ÙBgW G M`¯‗ v`j ML]L @IAAF@]GIE, PVKKLZGPL]GIE & TZFPFE]L]GIE
`wgksA¨vj `Þw_g `ÓYn ¸gã _¡̀ ~W© `d‡ ù ̀ e‡‛\ `wgksA¨vwjB _Y¨ fv M`v ksKÓ e Bgv| fv¯ Ë wfB
`‡ ù `wgksA¨vjxq wf‡b ø a‡Wg wcw e‡ov `wgksA¨vwjB _Y¨ fv M`vÂ| Ljy kÑvj † ù Å e‡_ ksK― ex_ _Y¨ L‡bvwl_ G Lwfj¨¯ Ë Yv‡B| NkBo _‡Y¨ g LvBvg fi eq Nfs_‡Y¨ wB\z Vv Å ã wV Yv‡B| m‡o L‡bvwl_ _‡Y¨g •fwbð¨ k¤ÿ‡B© lvgWv Bgv hvq jv Nfs NJ _Y¨KvwWw_B wf‡b ø a‡Wg M`‡hvKx jq| _vJ ksK― ex_ L‡bvwl_ _‡Y¨ g cy o Åã wV ks‡bvlj B‡g, _v‡Bkswù Ù LvBv‡ g `Ó Bvb Bgvg Zj ¨ `Ó w¶qvBgW Bgv eq| NwV eo _Y¨ M`¯‗ v`j|
N Ll¨vq `vS †b‡a wb ùvYx©gv
• _Y¨ G _‡Y¨g `Ó Bvg‡cd f¨vA¨v Bg‡_ `vg‡f|
• `Ó vYwnB _Y¨ ksKÓ ‡eg `Þw_ fW© jv Bg‡_ `vg‡f|
• `Ó vYwnB _Y¨ ksKÓ ‡eg `Þw_¸‡ov ky wflv G Lky wflv fW© jv Bg‡_ `vg‡f|
• nvl¨wnB _‡Y¨g Mr k ̧ ‡ov f¨vA¨v Bg‡_ `vg‡f|
• nvl¨wnB _‡Y¨g ¸g ã_¡ G kxnvfÞ_v fo ‡_ `vg‡f|
• `Ó vYwnB G nvl¨wnB _Y¨ NBJ _Y¨ fo ‡_ `vg‡f|
• _Y¨ ksKÓ ‡eg `Ó ‡qvZjxq_v G ¸g ã_¡ fW© jv Bg‡_ `vg‡f|
• nvl¨wnB _‡Y¨ ksKÓ ‡e k_B© _ v f¨vA¨v Bg‡_ `vg‡f|
• _Y¨ M`¯‗ v`j G _Y¨ M`¯‗ v`‡jg M`vq¸‡ov fW©jv Bg‡_ `vg‡f|
• †bª wWfÞBgW G †bª wWfÞBg‡Wg `Ó Bvg‡cd f¨vA¨v Bg‡_ `vg‡f|
• _vwoBvfÞBgW G wfwcjŐ Lsb f¨vA¨v Bg‡_ `vg‡f|
• KWksA¨v wj‡fbj G `Ó Bvg‡cd fo‡_ `vg‡f|
• KWksA¨v wj‡fb‡jg ¸g ã _¡ G `Ó‡qvZjx_v f¨vA¨v Bg‡_ `vg‡f|
• NBwV KWksA¨v wj‡fbj •_wgg lv` fW©jv Bg‡_ `vg‡f|
• _Y¨ M`¯‗ v`‡j †oA G wT‡Åg ¸g ã _¡ G `Ó ‡qvZjxq_v fo‡_ `vg‡f|
• wT‡Åg nvl¨‡n _Y¨ M`¯‗ v`j wfwcjŐ `Þw_g jvn G fW©jv Bg‡_ `vg‡f| • BvÒ G `Å fv bvAv G `ÅB knv‡fb f¨vA¨v Bg‡_ `vg‡f|
• bvAv G `ÅB knv‡f‡bg ¸gã_¡ fo‡_ `vg‡f|
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M‛T nvl¨wnB `wgksA¨vj -`ÓYn `Å
M‛Tnvl¨wnB `wgksA¨v j
:=
:.4< _Y¨ G _‡Y¨g `Ó Bvg ‡cd Mltl lem ]ypfs ic Mltl
_Y¨ (Mltl)?
_Y¨ e‡‛\ `wgkvswA¨B K‡faWvg Bvu Tvnvo| †h‡Bvj K‡faWvg Bv‡Z Ljy kÑvj † ù Å e‡_ †Bvj •fwbð¨KWjv B‡g fv `wgnv` B‡g †h ksA¨v_¥B `wgnv` fv Bvu Tvnvo ksKÓ e Bgv eq _v‡B _Y¨ f‡o| `Ó B… _`‡ ù _Y¨ e‡ov _Y¨ wf‡b¦ g `Ów_wV NB‡Bg `wgf_© jbxo •fwbð¨ k¤ÿwB© _ ksA¨vk~ TB lvgWv| N‡BM`vÂG fov eq|
MdvegW?
†Bvj †Zovg NBg `Ó w_ lvj Mr`vd‡jg evg wjW© ‡qg Zj¨ M° †Zovg B… a‡Bg Bv\ †Y‡B M° lvj
Mr`vd‡jg M`g †h ksA¨vfvTB wekvf fv `wgnv` ksKÓe Bgv eq _v‡B _Y¨ f‡o|_‡Y¨g `Ó Bvg‡ cd (@alssgcg`ltgie ic Mltl)? _Y¨‡B n~o_? dyJwV Mrk e‡_ ksKÓe Bgv hvq| _vJ Mr‡kg wcw‡_ _Y¨‡B dyJcv‡K cvK Bgv
hvq| hYv √
B. `Ó vYwnB _Y¨ (Trgklry Mltl)
A. nvl¨wnB _Y¨ (Pf`iemlry Mltl)
wj‡nŐ N‡dg fW©jv †dGqv e‡ov -
B. `ÓvYwnB _Y¨ (Trgklry Mltl)?
†h _Y¨ †n․woB Ljy kÑv‡jg nvl¨‡n fv kgvkwg `h©‡f ù ‡Wg nvl¨‡n n~ o Mrk e‡_ ksKÓ e Bgv eq _v‡B`Ó vYwnB _Y¨ f‡o| _Y¨ ksKÓe Bgvg `g hwd _v‡_ †Bvj `wgkvswA¨B `Þw_ `Ó ‡qvK Bgv jv eq _‡f_v‡B `Ó vYwnB _Y¨ f‡o|
MdvegW?
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_Y¨ ksKÓ e ksw³ÙBgW G M` ‗̄ v`j
NBwV B¨vnwfªqvj w^wZVvo `Ó Bvbjv
:6
MdvegW?
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M‛T nvl¨wnB `wgksA¨vj -`ÓYn `Å
M‛Tnvl¨wnB `wgksA¨v j
:3
(gv) ¯‗ vjx q Mrk? NJ `Þw_‡_ ¯‗ vjxq `Ó w_wjwl fv ksfvddv_vg nvl¨‡n _Y¨ ksKÓ e Bgv eq| wf‡ba B‡g LÊowcwÂB _Y¨ †hnj - b‡k¨g Mr`vdj, fj¨v `wgw¯‗w_, LwKŐ G E~ wW© P‡i ùqù w_g wffgW J_¨vwd † ù ‡Å ¯‗ vjxq Mr‡kg nvgm‡_ _Y¨ ksKÓ e Bgv hvq|
(v) ^vB nvgm_ `Ó bŐ̀ Å ksKÓ e `Þw_? NJ `Þw_‡_ K‡faWvg wfaqf¯‘g M`g NJ ky ‿dg G
keZ `Ó bŐ̀ Å •_wg B‡g ^vB‡hv‡K MÂgdv_vg wjBV `vSv‡jv eq| MÂgdv_v `Ó bŐ̀ ÅwV`~ gW B‡g †mg_ `vSvj| N‡_ knq G AgT Bn eq| kvlvgW_ n_vn_ hvTvJ Zv_xq Ljy kÑv‡j N `Þw_‡_ _Y¨ ksKÓ e Bgv eq|
(vg) †Vwo‡mvj kv ùvrBvg `Þw_? L‡jB knq Zg ã gx wcw‡_ ¯Uë `wgk‡g _Y¨ ksKÓ e Bgvg Zj¨ †Vwo‡mvj kv ù vrBvg `Þw_ `Ó ‡qvK Bgv eq| N‡_ knq G AgT Bn ov‡K| _‡f _Y¨ ksKÓ eBvgxg BYvfv_© v nvwZ© _ eGqv fvÀjxq|
:.40 `Ó vYwnB _Y¨ ksKÓ‡eg `Þw_¸‡ov ky wflv G Lky wflvKfrgts lem Mfkfrgts ic Trgklry Mltl @iaaf`tgie.
`Ó vYwnB _Y¨ n~ o Ljy kÑvj † ù Å LY© vr _‡Y¨g Mr`w ¯‗ o e‡_ ksKÓ e Bgv eq| `Ó vYwnB _Y¨ ksKÓ ‡eg
Zj¨ wB\y `Þw_ g‡q‡\| N¸‡ov e‡ov √
B. kgvkwg f¨w°K_ `h© ‡f ùW2
A. `‡gv ù Ljy kÑvj2K. KWjvBvgxg nvl¨‡n Ljy kÑvj2
E. ¯‗ vjxq Mrk2
I. ^vB nvgm_ `ÓbŐ Ő̀ Å ksKÓ e `Þw_2
T. †Vwo‡mv‡j k vùv_Bvg `Þw_|
B. kgvkwg f¨w°K_ `h© ‡f ùW?
ky wflv? (g) _Y¨ †fb kwSB G wjc©g‡hvK¨ eq2 (gg) f¨w°K_cv‡f †hvKv‡hv‡Kg dg ã W LwlB ksA¨B MÂg dv_vg wjBV e‡_ _Y¨ `vGqv hvq2
(ggg) `Ó ‡qvZ‡j Lw_wg° _Y¨ ksKÓe Bgv hvq2
(gv) _‡Y¨g †Kv`jxq_v g ùv Bgv hvq2
(v) †\vV Ljy kÑvj † ù ‡Å NwV †fwb M`‡hvKx|
Lky wflv? (g) NwV knq G f¨q kv‡` ù2(gg) f¨v`B Ljy kÑvj † ù ‡Å NJ `Þw_ `Ó ‡qvK Bgv hvq jv2
(ggg) _Y¨ f¨w°K_ `ù ̀ v_dy ð e‡_ `v‡g2
(gv) NwV Pz u wB`~W© e‡_ `v‡g|
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_Y¨ ksKÓe ksw³ÙBgW G M`¯‗ v`j
NBwV B¨vnwfªqvj w^wZVvo `Ó Bvbjv
:>
A. `‡gv ù Ljy kÑvj?
ky wflv? (g) NwV keZ G ky¯ÿð2(gg) NJ `Þw_‡_ knq, bª n G LY© wB\y Vv Bn ov‡K2 (ggg) NJ `Þw_wV Pu y wBexj2(gv) f― er _Y¨wf‡b¦ g † ù ‡Å NwV M`‡hvKx2 (v) ¸WfvTB _Y¨ ksKÓ ‡e N `Þw_wV LwlB KÓ eW‡hvK¨|
Lky wflv? (g) `Ó vÙ _Y¨ kfknq wjc© gbxo jvG e‡_ `v‡g2 (gg) f¨w° ¯U v‡Y© _Y¨ `Ó dvjBvgx L‡jB knq cy o _Y¨ `Ó dvj Bg‡_ `v‡g2 (ggg) Ljỳ h y ° Bn© x N Ljy kÑvj‡B wfm‡o wj‡_ `v‡g|
K. KWjvBvgxg nvl¨‡n Ljy kÑvj?
ky wflv? (g) NJ `Þw_‡_ kwSB _Y¨ ksKÓ e Bgv hvq2 (gg) f¨v`B Ljy kÑv‡jg † ù ‡Å NJ `Þw_ Ay f ky wflvZjB2 (ggg) N _Y¨ ksKÓ e Bg‡_ knq Bn ov‡K2 (gv) _Y¨ ksKÓ eBvgx `Ó ‡bŐ g ZwVo_v G Ljy kÑv‡jg M‡Éb¨ f¨v A¨v- wf‡b ø aW Bg‡_ `v‡gj Nfs
MÂgdv_v‡B fy Pv‡_ `v‡gj|Lky wflv? (g) NwV L_¨Ŭ Ë f¨qfòo `Þw_2
(gg) KWjvBvgx dù jv e‡o cyo _Y¨ ksK― ex_ e‡_ `v‡g2 (ggg) Zjbw° L‡` ù vB… _ †fwb ov‡K|
E. ‗̄ vjxq Mrk?ky wflv? (g) knq G LY© †fwb ov‡K jv2
(gg) kvf© ùwWB G _vrùwWB _Y¨ `vGqv hvq2(ggg) †_nj Zjbw°g `Ó ‡qvZj eq jv|
Lky wflv? (g) `wg‡fwb_ _Y¨ ` ù ̀ v_dy ð e‡_ `v‡g2
(gg) NJ `Þw_‡_ L‡jB knq Ljy nv‡jg M`g wjc©g B‡g _Y¨ ksKÓe Bgv eq f‡o EVjvg`y ‡gv`y wg wekvf `vGqv hvq jv| I. ^vB nvgm_ `ÓbŐ Ő̀ Å ksKÓ e `Þw_?ky wflv? (g) NJ `Þw_‡_ †Bvj KWjvBvgx wj‡qvK Bgv eq jv2
(gg) N‡_ LY© G knq Bn ov‡K2 (ggg) _Y¨ kwSB G wjc© y o eq2(gv) _‡Y¨g †Kv`jxq_v g ùv Bgv hvq|
Lky wflv? (g) Lwbwù _ Zj‡Kvýx‡_ N `Þw_ `Ó ‡qvK Bgv hvq jv2 (gg) L‡j‡B cy o _Y¨ `Ó dvj Bg‡_ `v‡g2 (ggg) L‡j‡B `ÓbŐ̀ Å Lk¤ÿ~W© cv‡f `vSvq2 (gv) `wg‡ fwb_ _Y¨ `ù ̀ v_dy ð e‡_ `v‡g|
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M‛T nvl¨wnB `wgksA¨vj -`ÓYn `Å
M‛Tnvl¨wnB `wgksA¨v j
:8
T. †Vwo‡mv‡j kv ùv_Bvg `Þw_?
ky wflv? (g) N‡_ knq G AgT Bn ov‡K2 (gg) Lë knq G ks‡ ù ‡` Lë _Y¨ ksKÓ e Bg‡_ NJ `Þw_ †fwb ky wflvZjB2
(ggg
) †\vV LvBv‡gg LjykÑvj‡ ù ‡Å NJ `Þw_ Ay fJ M`‡hvKx| Lky wflv? (g) MÂgdv_vg †Vwo‡mvj jv YvB‡o wBsfv †k M`w¯‗ _ jv YvB‡o N `Þw_‡_ _Y¨ ksKÓe Bgv hvq jv2
(gg) N `Þw_‡_ ksK― ex_ _Y¨ Ay f †\vV G ksw ùÙ eq|
:.4= nvl¨wnB _‡Y¨g Mrk Piur`f ic Pf`iemlry Mltl
nvl¨wnB _Y¨ `Ólvj_? d y wV Mrk e‡_ ksKÓ e Bgv eq| hYv √ B. `Ó Bvwb_ Mrk2A. L`Ó Bvwb_ Mrk|
B) `Ó Bvwb_ Mrk? `Ó w_ýv‡jg f¨f¯‗ v`jv G `wgTvojvg Zj¨ L‡jB knq †n․woB dwoo `Å fv`Ó w_‡fdj `gf_© x kn‡q nvl¨wnB _‡Y¨g Mrk we‡k‡f `wgKwW_ eq| nvl¨wnB _Y¨ wjãwowA_
w_j lg‡Wg `Ó Bvwb_ `Ó w_‡fdj e‡_ `vGqv hvq| * LvwY© B `Ó w_‡fdj2
* `wgTvojv ks¶vŬ Ë `Ów_‡fdj2 * wf‡ba `Ó w_‡fdj| wfwcj Ő `Ó w_‡fdj G nvl¨wnB _‡Y¨g Mrk wj‡T Lv‡ovTjv Bgv e‡ov
(g) LvŬ Ë Z© vw_B `Ów_ývj? wfwcjŐ LvŬ Ë Z© vw_B `ª w_ývj †hnj? Zvw_ksE, LvŬ Ë Z© vw_B LY© _ewfo (GKC), wfb¦ f¨vsB, LvŬ Ë Z© vw_B bª n ks¯‗ v (GAI), Avd¨ G B… wa ks¯‗ v(CLI), wfb¦ ¯Uv¯‗¨ ks¯‗v (^HI) J_¨vwd `Ó w_ýv‡jg fvwa©B wg‡`vV© G `Ó vw_ývwjB`Ó w_‡fdj †Y‡B nvl¨wnB _Y¨ ksKÓ e Bgv eq|
(gg) kgBvgx `Ó w_ývj? fvsov‡db †` -Bwnbj, `vfwoB kvwc© k Bwnbj, LY© dm_g,`wgksA¨vj fy ¨‡gv, wb ù v, fvwWZ¨, B… wa, bª n, LY© J_¨vwd nŬ¹Wvo‡qg fvwa© B wg‡`vV© †Y‡B nvl¨wnB _Y¨ ksKÓ e Bgv hvq|
(ggg) LvlvkgBvgx `Ów_ývj? LvlvkgBvgx Lwmk †hnj? †Zov `wgad, fvsov‡db wfnvj,
wnMwjwk`¨vo B‡`© v‡gbj, kvlvgW fxnv, f¨vsB, Tv †fv^© , nrk¨ MjŐ qj †fv^© , Zy V wno& k
B‡`© v‡gbj J_¨vwd `Ó w_ýv‡jg `Ó w_‡fdj †Y‡B nvl¨wnB _Y¨ ksKÓ e Bgv hvq|
(gv) K‡faWv `Ó w_ývj ? wfwcjŐ K‡faWv `Ó w_ývj †hnj? wf LvJ w^ Nk (JGMP), LvJ Nk
Lvg wV (GPZ]), wf N Lvg LvJ (JLZG), wfb¦ wfd¨voq nÍy gx Bwnbj J_¨vwd
`Ó w_ýv‡jg `Ó w_‡fdj †Y‡BG nvl¨wnB _Y¨ ksKÓ e Bgv hvq|
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_Y¨ ksKÓ e ksw³ÙBgW G M`¯‗v`j
NBwV B¨vnwfªqvj w^wZVvo `Ó Bvbjv
:7
(v) LY©owKŐ `Ó w_ývj? wfwcjŐ LY© owKŐ `Ó w_ývj †hnj f¨vsB, fxnv, ðB NB‡TÍ, †T¤U vg Lf
Bnvk© NÒ JÒvwðª Z, wfwcjŐ f¨fkvwqB kwnw_ `Ó c― w_ `Ó w_ýv‡jg Zvj© vo †Y‡B kswb ø ð
wfa‡qg _Y¨ ksKÓe Bgv hvq|
(vg) wfwcjŐ `Å `wÅBv? `Å `wÅBvg nvl¨‡n wfwcjŐ `Ó Bvg _Y¨ †hnj TvBwgg Tvwedv, •f‡dwbB ny dª v wfwjnq evg, †bqvg fvZvg _Y¨, †Aovly ov J_¨vwd `Ó Bvwb_ eq hv †Y‡B
nvl¨wnB _Y¨ ksKÓ e Bgv hvq|
(A) L Ó̀ Bvwb_ Mrk?
`Ó w_wV Lwmk fv `Ó w_ývj _v‡dg ‣djw‿dj Bv‡Z wfwcjŐ _Y¨ ksKÓe G ksg ù W B‡g Yv‡B| wBŬ‘
N‡dg kf _Y¨J `Ó w_‡fdj LvBv‡g `Ó Bvb B‡g jv| †k¸wo‡B L`Ó Bvwb_ _Y¨ we‡k‡f lgv eq| L‡jB f¨fkvqx `Ó w_ýv‡jgJ •djw‿dj Lvq - f¨‡qg wekvf gvAv eq LYT _v `Ó Bvb Bgv eq jv|
L‡j‡Bg f¨w°K_ K‡faWv, `w Ô _ f¨w°‡dg gTjv G ksKª e J_¨vwd L‡jB _Y¨ `ÓBvb Bgv eq jv|
Nkf _Y¨‡B L`Ó Bvwb_ _Y¨ fov eq Nfs `Ó ‡qvZj‡fv‡l Nkf Mrk †Y‡B _Y¨ ksKÓ e Bgv hvq|
:.46 nvl¨wnB _‡Y¨g ¸g ã_¡ G kxnvfÞ_v
]hf Gkpirtle`f lem Agkgtltgies ic Pf`iemlry Mltl.
nvl¨wnB _‡ Y¨g ¸gã_¡? wB\y wB\y kxnvfÞ_v YvBv k‡Â¡G `wgkvswA¨B K‡faWvg † ù ‡Å nvl¨wnB _‡Y¨g¸gã _¡ L`wgkxn| BvgW N _Y¨ L‡jB ky b―Ao G ky wfj¨¯ Ë LvBv‡g `vGqv hvq| `Ó vYwnB _Y¨‡BksEfÞBgW, †bªWxBgW G k¤ÿvdjvg nvl¨‡n wjcy © o LvBv‡g ksg ù W Bgv eq Nfs †kJ ksgw ù_ _Y¨†Y‡B nvl¨wnB _Y¨ ksKÓ e Bgv eq f‡o N _Y¨ †fb wjc© g‡hvK¨ eq| LwlBvsb nvl¨wnB _Y¨ Nnj †hN‡_ J‡_v`~ ‡f© †Bvj jv †Bvj `wgksA¨vwjB `Þw_ `Ó ‡qvK Bgv e‡q Yv‡B m‡o N _Y¨ †fb wjc©g‡hvK¨
G KÓ eW‡hvK¨ eq| nvl¨wnB _Y¨ k¤ÿvdjv G wf‡b ø a‡W L‡jB ky wflv|nvl¨wnB _‡Y¨g kxnvfÞ_v?
nvl¨w nB _Y¨ L‡jBVv ke‡Z ksKÓ e Bgv ‡K‡oG Ng wB\y wB\y kxnvfÞ_v Lv‡\| †hnj? (g) kvd―b¨_v ? L‡jB knq wcjŐ wcjŐ Mrk †Y‡B ª̀vÙ NBJ _‡Y¨g n‡l¨ †fb Kgwno `vGqv hvq|(gg) wjc© g‡hvK¨_vg Lcvf ? † ù Åwf‡b‡a L‡jB `Ó w_ývj dvqkvgv †Kv‡\g _Y¨ ksKÓ e B‡g
Yv‡B| Nkf _‡Y¨g wjc©g‡hvK¨_v L‡jB B n|(ggg) `h© vÙ_vg Lcvf ? L‡jB knq nvl¨wnB _Y¨ ksKÓ‡e J‛\yB f¨w° fv `Ów_ýv‡jg kwSB
Tvwedv Ljy hvqx `ÓvYwnB _Y¨ `vGqv hvq jv| BvgW Mcq `Ó Bvg _Y¨ ksKÓ eBvgx‡dg M‡É‡b¨g n‡l¨ wno YvB‡oG †Bvj †Bvj Ls‡b Lwno YvBvg k¤¢ vfjv Yv‡B|
(gv) `ù`v_dy ð ? N _Y¨ L‡jB knq ` ù ̀ v_dy ð e‡_ `v‡g |(v) `Þw_ ? L‡jB knq M`hy ° `Þw_‡_ _Y¨ ksKÓ e Bgv eq jv |
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M‛Tnvl¨wnB `wgksA¨v j
04
:.43 `ÓvYwnB G nvl¨wnB _Y¨ NBJ _Y¨Trgklry lem Pf`iemlry Mltl lrf Jlsg`laay Plkf
†Bvj K‡faWvg Zj¨ kgvkwg _‡Y¨g Mr`w¯‗ o †Y‡B †h _Y¨ ksKÓ e Bgv eq _v‡B `Ó vYwnB _Y¨ fov
eq| K‡faB fv K‡faWvBvgx `Ó w_ývj N _Y¨ wf‡b ø aW B‡g `Ó vÙ movm‡og M`g wkÞvŬ Ë KÓ eW B‡gj|L_?`g NJ wf‡b ø wa_ _Y¨ mvJof‿dx B‡g gv‡Aj fv `y¯ Ë B fv `Ó Bvbjv LvBv‡g `Ó Bvb B‡gj| LvfvgBAjG _Y¨ n~ o Lf¯‗ vq †g‡A †dqv eq| Lj¨ †Bvj f¨w° fv `Ó w_ývj wjZ¯U K‡faWvg Bv‡Z H _Y¨f¨fevg Bg‡o †k _Y¨‡B nvl¨wnB _Y¨ fov eq| _vJ `Ó vYwnB _Y¨ G nvl¨wnB _‡Y¨g n‡l¨•fwbð¨K_ †Bvj `vY©B¨ jvJ| †Bfo N‡dg f¨fevgK_ `vY© B¨ †dAv hvq|†hnj? lgv hvB c~ wn Bg LvdvqBvgx _ebxo Lwmk c~ wn gvZ¯U Lvdv‡qg Zj¨ Zwng `wgnvW G nvwoB
k¤ÿwB© _ _Y¨ †gB ©̂ B‡g‡\j| N _Y¨ `Ó vYwnB _Y¨| `u vT NB‡Bg LwlB Zwng nvwoB‡dg b_Bgvevg B_ _v c~ wn nŬ¹Wvoq Zvj‡_ Tvq| N o‡ ù ¨ hwd c~ wn nŬ¹Wvoq _ewbo Lwmk e‡_ _Y¨ ksKÓ eB‡gj, _‡f †k _Y¨ e‡f c~ wn nŬ¹Wvo‡qg Bv‡\ nvl¨wnB _Y¨| ky _gvs †dAv hv‡‛\ †h, nvl¨wnB _Y¨G `ÓvYwnB _Y¨ Bvh© _ NBJ _Y¨|
:.4> _Y¨ ksKÓ ‡eg `Ó‡qvZjxq_ v G ¸gã_¡ Ef`fssgty lem Gkpirtle`f ic @iaaf`tgen Mltl
_Y¨ ksKÓ ‡eg `Ó ‡qvZjxq_v G ¸g ã_¡?†h‡Bvj wfa‡q K‡faWvg `~ f©b_© e‡ov _Y¨| _vJ _Y¨ ksKÓ ‡eg `Ó ‡qvZjxq_v Lj¯U xBvh© | `wgkvswA¨BK‡faWvg Bv‡Z `wgBëjv fv¯ Ë fvq‡jg `ÓYn Nfs ¸g ã _¡`~W© `d‡ ù ̀ e‡‛\ _Y¨ ksKÓ e Bgv| _vJ †h†Bvj `wgksA¨vwjB Ljy kÑv‡j wkÞvŬ Ë KÓ eWBvgx‡B Ljy kÑvj wfa‡qg M`g _Y¨ ksKÓe Bg‡_ eq|ksK― ex_ _Y¨ wf‡b ø aW B‡g Ljy kÑv‡jg wfa‡qg M`g f¨vA¨v `Ó dvj G wkÞvŬ Ë KÓeW Bgv eq| ksK― ex__‡Y¨g wjc© y o_v G MrBa© _vg M`gJ wkÞv‡Ŭ Ë g kwSB_v wjc©g B‡g|
L_Nf `wgksA¨vj j xw_ Ljy kgW B‡gJ _Y¨ ksKÓ e Bgv MwT_| kwSB movmo G n~ o¨vq‡jg Zj¨knkvnwqB _Y¨ ksKÓ e Bgv MwT_|
:.48 nvl¨wnB _‡Y¨ ksKÓ ‡e k_B© _vTrf`lutgies ic Pf`iemlry Mltl
†Bvj ks¯‗v fv `Ó w_ýv‡jg ksK― ex_ _Y¨ e‡_ †h _Y¨ f¨fevg Bgv eq, _v‡B nvl¨wnB _Y¨ f‡o|
nvl¨wnB _ ‡Y¨g L‡jB ky wflv YvBv k‡Â¡G Ng wB\z kxnvfÞ_v g‡q‡\| NJ _Y¨ f¨fevg Bg‡_ wjnŐ gƚ`wfaq¸‡ovg M`g kZvK d― wð gvAv MwT_|
(g) LjykÑv‡jg M‡Éb¨ ? M‡É‡b¨ g kv‡Y ksKw_ †g‡A nvl¨wnB _Y¨ ksKÓe Bg‡_ eq| LjykÑvjBvgx‡B o ù ¨ gvA‡_ e‡f Ó̀ vYwnB _Y¨ ksKÓeBvgxg M‡Éb¨ G _vg M‡Éb¨ NBJ wBjv|
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NBwV B¨vnwfªqvj w^wZVvo `Ó Bvbjv
0<
(gg) Ljy kÑvj † ùÅ? nvl¨wnB _Y¨ f¨fevgBvgxg Ljy kÑvj † ùÅ Nfs `Ó vYwnB _Y¨ ksKÓ eBvgxg
Ljy kÑvj † ù Å NB e‡o ély nvÅ H _Y¨ f¨fevg Bgv hv‡f|
(ggg) _‡Y¨G Bvh© Bvwg_v? `Ó vYwnB _Y¨ G nvl¨wnB _‡Y¨ g n‡l¨ kn‡qg f¨flvj Ay f †fwb e‡o
_Y¨nv‡j f¨v`B `wgf_© j EV‡_ `v‡g| _vJ N lg‡Wg `Ó vYwnB _Y¨ e‡_ nvl¨wnB _Y¨ ksKÓ e Bgv MwT_ jq|
(gv) _‡Y¨g NBB? `Ó vYwnB _Y¨ †h NB‡B ksKÓ e Bgv e‡q‡\ nvl¨wnB _‡Y¨ g †kJ NBB f¨fevg
Bg‡_ e‡f| j_z fv _‡Y¨ g f¨fevg wSB e‡f jv|
(v) _‡Y¨ g wfb¦ Ë̄ _v? nvl¨wnB _Y¨ ksKÓe Bgvg `~ ‡f© _‡Y¨ g wfb¦ Ë̄ _v hv TvJ Bg‡_ e‡f †h, _Y¨
kwSB `Þw_‡_, M`hy °, d ù G `Ó wbù W`Ó vÙ Bn© x Øvgv ksKÓe Bgv e‡q‡\ wBjv| _v jv Zvj‡o nvl¨wnB _Y¨ f¨fev‡g wkÞvŬ Ë cy o e‡_ `v‡g|
M`‡gv° Lv‡ovTjv e‡_ ¯ÿð fy Pv hvq †h, nvl¨wnB _Y¨ wjwf© Tv‡ g f¨fevg Bgv MwT_ jq| nvl¨wnB_Y¨ f¨fev‡gg `~ ‡f© M‡o ø wA _ wfaq¸‡ovg M`g k_B© d― wð gvAv NBvŬ Ë `Ó ‡qvZj|
:.47 _Y¨ M`¯‗ v`j G _Y¨ M`¯‗ v`‡jg M`vq¸‡ov
Trfsfetltgie ic Mltl lem Mgccfrfet Kfthims ic Trfsfetltgie ic Mltl
_Y¨ M` ‗̄ v`j? †Bvj Ljy kÑv‡j ksK― ex_ L‡bvwl_ _Y¨ `Ów¶qvBg‡jg nvl¨‡n ksw ù Ù, LvBa© Wxq, keZ‡f vl¨ Gwf‡b ø a‡Wg M`‡hvKx B‡g `Ó Bvb Bgv‡B _Y¨ M`¯‗ v`j f‡o|
`Ólvj_? dy wV M`v‡q _Y¨‡B M`¯‗ v`j Bgv hvq †hnj? B. `wgksA¨vwjB kvgWx2
A. `wgksA¨vwjB †oA|
B) `wgksA¨vwjB kvgWx?
†Bvj wjwd© ð •fwb‡ð¨g †`Ó w ù ‡_ knZv_xq NBB¸wo‡B NBwV †bªWx‡_ wo‡A Nfs Ncv‡f `y ‡gv _Y¨‡B
B_B¸wo †bªWx‡_ kvwZ‡q wo‡A †h kvgWx `vGqv hvq _v‡B `wgksA¨vwjB kvgWx f‡o| w_j lg‡jg
kvgWxg kvev‡h¨ _Y¨‡B M`¯‗ v`j Bgv hvq| †hnj?
g. †bªWxfÞBgW2
gg. _vwoBvfÞBgW2
ggg. KWksA¨v wj‡fbj|
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M‛Tnvl¨wnB `wgksA¨v j
0:
A) `wgksA¨vwjB †oA? `wgksA¨vwjB M`v‡B ¯‗ vj, Bvo, `wgnvW J_¨vwd •fwb‡ð¨ Ljy kvv‡g wfwcjŐ lg‡Wg wT‡Åg kvev‡h¨M`¯‗ v`j Bgv hvq| NJ kf wTŸwo‡B `wgksA¨vwjB †oA f‡o| `wgksA¨vwjB _Y¨‡B M`¯‗ v`‡jgZj¨ wjnŐ wowA_ †oA¸wo f¨fevg Bgv e‡q Yv‡B|
g) Lvq_‡oA gg) KWksA¨v fòcy Z
ggg) KWksA¨v †gAv gv) LwZc † gAv|
:.644
Ay ojv 6>
wk‡oV >
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_Y¨ ksKÓe ksw³ÙBgW G M`¯‗ v`j
NBwV B¨vnwfªqvj w^wZVvo `Ó Bvbjv
00
(A) knqwcwÂB †bªWxfÞBgW? kn‡qg `wgf_©‡jg kv‡Y kv‡Y †Bvj EVjv fv wfa‡q B_Vz Bz `wgf_© j eq _vg wcw‡_ _Y¨nvov‡B †bªWxfÞBgW Bgvg `Þw_‡B knqwcwÂB †bªWxfÞBgW f‡o| kn‡qg wfwcjŐ `wgk‡g †hnj? †k‡BÒ,
wnwjV, E‿Vv, nvk J_¨vwd `wgk‡g To‡Bg `wgnv` `Ó db© j Bgvg Zj¨ †k‡BÒ, wnwjV, E‿Vv, nvk, wdj Gfrkg J_¨vwd knqBvo Ljy kv‡g †bªWxfÞBgW Bgv eq|
MdvegW? wj‡nŐ
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M‛T nvl¨wnB `wgksA¨vj -`ÓYn `Å
M‛Tnvl¨wnB `wgksA¨v j
0=
MdvegW? wj‡nŐ fvsov‡d‡bg fqkwcwÂB ZjksA¨vg b_Bgv evg †dAv‡jv e‡ov?
fqk KÓ ã` ZjksA¨v (b_Bgv evg)
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_Y¨ ksKÓ e ksw³ÙBgW G M` ‗̄ v`j
NBwV B¨vnwfªqvj w^wZVvo `Ó Bvbjv
06
0) kvwg wb‡gvjvn? _vwoBvq `Ów_wV kvwgg NBwV wjwd© ð wb‡gvjvn YvBv Lvfb¨B| Jev‡_ kvwgg LŬ Ë c© y ° wfaqf¯‘g ksw ù Ù wffgW wd‡q Yv‡B| kvwg wb‡gvjvn _vwoBvg fvn`v‡b¦ © g `ÓYn Bov‡n †oAv eq|
=)
kvwg fW© jv? _Y¨kvwgg wfwcjŐ Ls‡b wfgvZnvj _‡Y¨g ¸g ã ‡_¡ g wcw‡_ †h BqwV Ls‡b fv†bªWx‡_ wfc° Bgv eq _v‡dg‡B kvwg fW© jv f‡o| N LsbwV kvgWxg N‡Bfv‡g fvnwd‡B Nfs wb‡gvjv‡ng wj‡Tg wd‡B Yv‡B|
6) Bovn wb‡gvjvn? _vwoBvg wfwcjŐ Bov‡ng LŬ‘ cy ©° _Y¨vfoxg wfaqf¯‘g `wgwTw_ G fW©jv†dqvg Zj¨ `Ó w_wV Bov‡ng NBwV kwSB wb‡gvjvn YvBv Lvfb¨B| †Bvj Bov‡n †Bvj lg‡jg _Y¨ Lv‡\ _v †kJ Bov‡ng wb‡gvjvn †d‡AJ fy Pv hv‡f| _vwoBvq M` -Bovn f¨fevg Bgv
e‡o _vgG wb‡gvjvn wd‡_ e‡f|3) _vwoBvg wfaqf¯‘? ksK― ex_ _Y¨fox‡B _vwoBvg wfaqf¯‘ Ls‡b wow`fÞ Bgv eq| _Y¨‡B
kwSB hy w° keBv‡g ky ‿dg G ky¯ÿðcv‡f NJ Ls‡b M` ‗̄ v`j Bgv eq|
>) `vdVxBv? _vwoBvg wfaqf¯‘ fv _‡Y¨g †Bvj Ls‡bg ky ¯ÿð f¨vA¨v †dfvg `Ó ‡qvZj e‡o
_vwoBvg wj‡T ks‡ ù ‡` wf‡ba dª ðf¨ fv Ciiteitf LvBv‡g †oAv eq|
8) Mrk VxBv? N Ls‡b _‡Y¨g Mrk k¤U ‡Ñ Lfwe_ Bgv eq| Jev Ay f `Ó‡qvZjxh Lsb| Jev`vSB-`vwS Bv‡dg n~ o _Y¨ Ljy kÑv‡j kevq_v B‡g|
:.
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M‛T nvl¨wnB `wgksA¨vj -`ÓYn `Å
M‛Tnvl¨wnB `wgksA¨v j
03
wj‡T NBwV wfw‛\jŐ KWksA¨v wj‡fb‡jg MdvegW †dGqv eo? ksA¨v KWksA¨v
0 :6
gg. Lwfw‛\jŐ KWksA¨v wj‡fbj?†Bvj _Y¨kvwgg `wgkg‡B B_B¸wo wcjŐ wcjŐ †bªWx‡_ wfc° B‡g Nfs _vg KWksA¨v `vbv`vwb
kvwZ‡q wo‡A †h kvgWx `vGqv hvq _v‡B Lwfw‛\jŐ KWksA v̈ wj‡fbj f‡o| wfw‛\jŐ G Lwfw‛\jŐ Mcq lg‡jg ToB‡BJ Lwfw‛\jŐ KWksA¨v wj‡fb‡jg kvevh¨ M`¯‗ v`j Bgv e‡q Yv‡B|
wj‡T NBwV Lwfw‛\jŐ KWksA¨v wj‡fb‡jg MdvegW †dGqv eo? †bª wW kxnv KWksA¨v:4-04 6
04-=4
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_Y¨ ksKÓe ksw³ÙBgW G M`¯‗ v`j
NBwV B¨vnwfªqvj w^wZVvo `Ó Bvbjv
0>
:., =, 8, 6, =, 3, :, 8, >, 0,
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M‛T nvl¨wnB `wgksA¨vj -`ÓYn `Å
M‛Tnvl¨wnB `wgksA¨v j
08
Lwfw‛\jŐ KWksA¨v wj‡fbj •_wgg lv`?KWksA¨v wfj¨vk •_gxg ky wjwd©ð †Bvj wjqn †jJ| `wgksA¨vj K‡faBKW _v‡dg `Ó ‡qvZ‡j wfwcjŐ kn‡qwfwcjŐ cv‡f NJ KWksA¨v wfj¨vk •_wg B‡g Yv‡Bj| KWksA¨v wfj¨vk •_gxg kTgvTg f¨fñ_ lv`¸‡ovwj‡nŐ Lv‡ovTjv Bgv e‡ov?
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_Y¨ ksKÓe ksw³ÙBgW G M`¯‗ v`j
NBwV B¨vnwfªqvj w^wZVvo `Ó Bvbjv
07
wf wcjŐ †bªWxg kxnv wjW© q?
†bªWxkxnv Nnjcv‡f wjW© q Bg‡_ e‡f ‡hj †bªWx¸‡ov `vg¯ÿwgBcv‡f NBwV e‡_ Lj¨wV wcjŐ eq|
†bªWxkxnv wjW©q Bgvg knq †bªWx nl¨nvj Ng f¨v`vgwV n‡j gvAv fvÀjxq| KWksA¨v wfj¨vk `Ó¯‘ _
Bgvg knq †bªWxkxnv wjl© vg‡W kvlvgW_ dy wV `Þw_ f¨fevg Bgv e q| hYv? B) fwecy © ° `Þw_ 2
A) LŬ Ëcy © ° `Þw_|
B) fwec© y ° `Þw_? NJ `Øw_‡_ †Bvj †bªWxg Ml© Ÿkxnv `gf_© x †bªWxg wjnŐkxnv wekv‡f wjl© vgW Bgv eq|
N‡_ Ó̀Yn †bªWxg MlŸ© kxnv‡B H †bªWxg fwecy © ° l‡g `gf_© x †bªWxg LŬ Ëc© y ° Bgv eq|
†hnj? wjnŐ kxnv M‛Tkxnv
:4 04
04 =4
=4 64
64 34
NAv‡j 04 wØ_xq †bªWxg LŬ Ë c© y ° Nfs =4 _… _xq †bªWxg LŬ Ë c© y °|A) LŬ‘ c© y ° `Þw_? N `Øw_‡_ †Bvj †bªWxg M‛Tkxnv wj‡d© bB ksA¨vwV‡B H †bªWxcy ° Bgv eq
Nfs M° M‛T kxnvg `gf_© x ksA¨v †bªWxg wjnŐkxnv wj‡d© b B‡g| MdvegW?
wjnŐkxnv M‛Tkxnv :4 :7
04 07=4 =7
NAv‡j :4 Nfs :7 ksA¨v dy JwV `ÓYn †bªWxg 04 Nfs 07 ksA¨v dy JwV wØ_xq †bªWx‡_ `‡i‡\|
6) KWksA¨v G V¨voxnvB©?
_Y¨kvwgg `Ów_wV nvj †h †bªWxg LŬ‘© cy ° †k †bªWx fgvfg `gf_©x Bov‡n H nv‡jg Zj¨ NBwV V¨vwo (G) wTû †dGqv eq| †Bvj †bªWxg wf`gx‡_ T vgwV V¨vwo (G G G G) wT‡ûg `g `Ên V v̈wo wTûwV(G G G G) wd‡_ eq| _vg`g `Ów_wV †bªWxg kv‡Y kswb ø ð V¨vwo wTû KWjv B‡g †bªWx KWksA¨v wekv‡f`gf_x© Bov‡n wjZ wjZ †bªWxg wf`gx‡_ †oAv eq|
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M‛T nvl¨wnB `wgksA¨vj -`ÓYn `Å
M‛Tnvl¨wnB `wgksA¨v j
=4
:. 04-=4 >=4-=7
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_Y¨ ksKÓe ksw³ÙBgW G M`¯‗ v`j
NBwV B¨vnwfªqvj w^wZVvo `Ó Bvbjv
=<
KWksA¨v? †Bvj †bªWx‡_ †h BqwV ksA¨v Yv‡B _v‡B H †bªWxg KWksA¨v fv EVjksA¨v f‡o| †h nj M`‡gv° ÝBÖ wj‡fb‡j :4-:7 †bªWxg KWksA¨v 6|
†hvwZ_ KWksA¨v? †Bvj ksA¨v wj‡fb‡jg †bªWx KWksA¨v kn~ ‡eg `h© vq¶wnB †hvKmo‡B †hvwZ_KWksA¨v f‡o| KWksA¨v wj‡fb‡jg †Bvj wjwd© ð †bªWxg KWksA¨vg kv‡Y Mevg `~ f©f_©x
kBo †bªWxg KWksA¨v †hvKmo‡B H †bªWxg ¶n‡hvwZ_ KWksA¨v `vGqv hvq| wj‡nŐ kvgwWg nvl¨‡n M`¯‗ v`j Bgv e‡ov? †bªWx KWksA¨v MlŸ©nyAx ¶n‡hvwZ_
KWksA¨v wjnŐ nyAx ¶n‡hvwZ_ KWksA¨v
> ; :6
:4√ 04 8 > + 8 ;
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M‛T nvl¨wnB `wgksA¨vj -`ÓYn `Å
M‛Tnvl¨wnB `wgksA¨v j
=:
†Avov †bª wWkxnv? hwd †Bvj †bª wWg M‛Tkxnv fv wjnŐkxnvg †Bvj NBwV fv McqwV ky ¯ÿðcv‡f wj‡d© wb_jv Yv‡B _‡f `Ó vŬ Ë †Avov †bª wW f¨vwÙ f‡o | †bª wWB… _ KWksA¨vg † ù ‡Å `Ó vŬ Ë †Avov †bª wW YvB‡o _vkvlvgW_ kf© ̀ ÓYn fv kf© ‡ba jv Mcq †bª wW‡_ e‡q Yv‡B|MdvegW? †Bvj NovBvg 644 Zj †ov‡Bg •dwjB Lv‡qg KWksA¨v wj‡fbj †dqv eo?
•dwjB Lvq (VvBvq) †ovBksA¨v
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_Y¨ ksKÓe ksw³ÙBgW G M`¯‗ v`j
NBwV B¨vnwfªqvj w^wZVvo `Ó Bvbjv
=0
:.
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M‛T nvl¨wnB `wgksA¨vj -`ÓYn `Å
M‛Tnvl¨wnB `wgksA¨v j
==
f¨fevg? B. Lvq_‡o‡Ag kvev‡h¨ Lwfw‛\jŐ KWksA¨v wj‡fbj‡B M`¯‗ v`j Bgv eq |A. Lvq_‡oA e‡_ KWksA¨v fòcy Z, KWksA¨v †gAv J_¨vwd LsBj Bgv hvq| K. Lvq_‡o‡Ag nvl¨‡n `Ó TzgB wjW© q Bgv hvq|
MdvegW? wj‡nŐg KWksA¨v wj‡fbj‡B Lvq_‡o‡Ag kvev‡h¨ M` ‗̄ v`j Bg -†bªWx f¨vwÙ 64-34 34->4 >4-84 84-74 74-
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_Y¨ ksKÓe ksw³ÙBgW G M`¯‗ v`j
NBwV B¨vnwfªqvj w^wZVvo `Ó Bvbjv
=6
N KWksA¨v wj‡fbj e‡_ KWksA¨v fòcy Z LsBj Bg|
knvlvj? KWksA¨v fòcy Z LsBj Bgvg Zj¨ `Ó ‡qvZjxq _vwoBv?
†bªWx †bªWxg nl¨wf‿dy KWksA¨v
==√=3 =6 ==>√=7 =8 3
64√6: 6< :=
67√3< 34
wj‡nŐ `Ód KWksA¨v wj‡fbj‡B KWksA¨v fòcy ‡Zg nvl¨‡n M`¯‗ v`j Bgv e‡ov?
K) KWksA¨v †gAv (Crfqufe`y @urvf)? KWksA¨v †gAv eo KWksA¨v fòcy ‡Zg NBwV `wgfw_© _ gƚ`| †h nk― j f¶‡gAvg kvev‡h¨
KWksA¨v wj‡fbj‡B M`¯‗ v`j Bgv eq _v‡B KWksA¨v †gAv f‡o| KWksA¨v wj‡fb‡jg †bªWxg nl¨wf‿dy̧ wo‡B x Lù fgvfg Nfs _v‡dg KWksA¨v `Ó w_wV †bªWxg nl¨wf‿dyg M`g y Lù fgvfg ¯‗ v`j Bg‡_ e‡f| L_?`g NJ wf‿dy̧ ‡ov `h© vq¶‡n ny ° e‡¯ Ë †hvK B‡g †h †gAv`vGqv hvq _v‡B KWksA¨v †gAv f‡o|
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M‛T nvl¨wnB `wgksA¨vj -`ÓYn `Å
M‛Tnvl¨wnB `wgksA¨v j
=3
f¨fevg?
B) dy J fv _‡_vwlB KWksA¨v wj‡fbj‡B _z ojv Bg‡_ KWksA¨v †gAv ¸g ã_¡̀ ~W© cy wnBv`voj B‡g|
A)
Jevg kvev‡h¨ †Bvj KWksA¨v wj‡fb‡jg Ki, nl¨nv G `Ó Tz g‡Bg Lf¯‗ vj k¤ÿ‡B†nvVvny wV lvgWv `vGqv hvq|
K) Jevg kvev ‡h¨ KWksA¨v wfj¨vk‡B _vw¡ B k¤¢ vfjv wfj¨v‡kg kv‡Y wnoBgW Bgv eq|
MdvegW? wjnŐ wowA_ KWksA¨v kvgWx e‡_ NBwV KWksA¨v wj‡fbj •_wg Bg?
†bªWx 64√>4 >4√74 74√
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_Y¨ ksKÓe ksw³ÙBgW G M`¯‗ v`j
NBwV B¨vnwfªqvj w^wZVvo `Ó Bvbjv
=>
E) LwZc †gAv? ¶n‡hvwZ_ KWksA v̈ wj‡fbj †h f¶‡gAvg kvev‡h¨ M`¯‗v̀ j Bgv eq _v‡B LwZc †gAvf‡o| LwZc‡gAv LsBj Bg‡_ e‡o `ÓY‡n KWksA¨v wj‡fbj e‡_ ¶n‡hvwZ_ KWksA¨v wjW©q Bg‡_ e‡f|NJ kBo ¶n‡hvwZ_ Mev‡dg wjZ wjZ †bªWx f¨vwÙg M‛Tkxnvg wf`gx‡_ ‗̄v`j Bgv eq| Ngƚ‡` Ó̀vÙwf‿dy kn~ e ̀ h©vq¶‡n NBwV †gAv Øvgv ny °e‡¯ Ë †hvK Bgv eq| NJ LswB_ †gAv‡B LwZc †gAv f‡o|
f¨fevg? B) Jevg kvev‡h¨ nl¨nv, T_zY © B, dbnB G b_nB J_¨vwd wjW© q Bgv hvq|A) dy J fv _‡_vwlB KWksA¨v wj‡fbj _z ojv Bg‡_ LwZc †gAv ¸g ã _¡̀ ~W© cy wnBv `voj B‡g|K) Jevg kvev‡h¨ †Bvj KWksA¨v wj‡fb‡jg ¶n‡hvwZ_ KWksA¨v‡B M`¯‗ v`j Bgv hvq|
MdvegW? wj‡nŐ KWksA¨v wj‡fbj‡B LwZc †gAvg nvl¨‡n M` ‗̄ v`j Bg|†bªWx f¨vwÙ 64√34 34√>4 >4√84 84√74 74√
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M‛T nvl¨wnB `wgksA¨vj -`ÓYn `Å
M‛Tnvl¨wnB `wgksA¨v j
=8
:.<
6 >6
3 84
knvlvj? x L‡ ù kvo G y L‡ ù Mr`vdj fwk ‡q d ÔwTÅ LvuBv eo?
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_Y¨ ksKÓe ksw³ÙBgW G M`¯‗ v`j
NBwV B¨vnwfªqvj w^wZVvo `Ó Bvbjv
=7
A) f― ÂvBvg wTÅ (Tgf Mglnrlk)? †Bvj _Y¨kvwgg wfwcjŐ M`vdv‡jg Lvjỳ vw_B ev‡g NBwV f― ‡BB‡qBwV Ls‡b wfc° B‡g _Y¨‡B M`¯‗ v`j Bgvg Zj¨ †h wTÅ f¨fevg Bgv eq _v‡B f― ÂvBvg wTÅf‡o| N‡_ wfwcjŐ M`vdv‡jg _z ojv Bgv ky wflv eq| f― ‡Âg †B‡‿dª †nv‡Vg †Bv‡Wg `wgnvW 0344|_‡Y¨g wfwcjŐ M`vdv‡jg †nvV `wgnv‡`g kv‡Y †Bvj wjwd© ð M`vdv‡jg `wgnv‡Wg Ljỳ v‡_ f― ‡Â
B_B¸wo Ls‡b `vGqv hvq| NJ Ls‡b jx‡T `Ó d k~ ‡Åg kvev‡h¨ wjl© vgW Bgv eq|†Bvj wjwd© ð M`vdv‡jg `wgnvW ƚ Nfs †nvV M`vdv‡jg `wgnvW E e‡o M° M`vdv‡jg `wgnv‡Wg Zj¨
f― ‡Âg †B‡‿dªg wjl© vwg_ †Bv‡Wg `wgnvW e‡f √ 4034Þ; E
c θ
ky wflv? B) Lë ksA¨B M`vdvj‡B fv _Y¨‡B f― ÂvBvg wT‡Åg nvl¨‡n kwSBcv‡f †dAv‡jv hvq2 A) †Bvj _Y¨ knwðg wfwcjŐ Lsb‡B Lw_ ky ‿dg G wjAy u _cv‡f †dAv‡jv hvq|
Lky wflv? B) _Y¨ ksA¨v fv M`vdvj ksA¨v †fwb e‡o f― ÂvBvg wTÅ †dAv‡jv k¤¢ f jq|A) Jev LsBj `Þw_ †fb ZwVo|
MdvegW? wj‡Tg _Y¨‡B f― ÂvBvg wT‡Åg nvl¨‡n M`¯‗ v`j Bg? Ag‡Tg Av_ Ag‡Tg ` gnvW
Avd¨ =4 f ¹̄ f fl 3
knvlvj? f― ÂvBvg wTÅ LsB‡jg _vwoBv wj‡nŐ •_wg Bgv e‡ov| f― ‡Âg †B‡‿dª g †Bv‡Wg ̀ wgnvW )034Þ E
c (;θ
Ag‡Tg Av_ Ag‡Tg ` gnvW ƚ ӨAvd¨ =4 :44
f ¹̄ 06
f fl 3 04
E;>: 034
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M‛T nvl¨wnB `wgksA¨vj -`ÓYn `Å
M‛Tnvl¨wnB `wgksA¨v j
64
:. kv‡o|`ÅB (Aflc)? bvAv G `ÅB knv‡f‡b `ÅB (fv `v_v) e‡ov _Y¨k v wgg †h †Bvj ksA¨vnv‡jg †baLsB| †hnj -:> hwd _Y¨kvwgg NBwV nvj eq _‡f > e‡f `ÅB| bvAv (Ptfk)? bvAv G `ÅB knv‡f‡b bvAv e‡ov _Y¨kvwgg †h †Bvj ksA¨vnv‡jg `ÓYn NB fvNBvwlB LsB| †hnj -:> _Y¨kvwgg NBwV nvj e‡o : bvAv e‡f| bvAv G `ÅB knv‡f‡b bvAvg nvj¸‡ov Mo¤Ucv‡f (Sfrtg`laay) NBwV Lv‡gBwVg wj‡T f‡k| Lvg
`Ó ‡_¨B bvAvg kv‡Y kvnÍk¨`~W© `ÅB¸‡ov H bvAvg `v‡b N‡Bg `g NB Lvjy c~ wnBcv‡f NBwVkvwg‡_ fk‡f| N‡ ù ‡Å `ŇBg nvj¸‡ov †\vV †Y‡B fi ¶‡n kvZv‡jv eq|
:.:4 bvAv G `ÅB knv‡f‡bg ¸gã_¡ Gkpirtle`f ic Ptfk lem Aflc Mgspaly
(g) KWksA¨v wj‡fb‡jg KSj Zvj‡_ bvAv G `ÅB wfj¨vk Lvfb¨B|(gg) _Y¨kvwgg `wgkg wjW©q Bg‡_ NwV Bvh© Bg c~ wnBv gv‡A|
(ggg) _Y¨kvwgg nvj ‡̧ovg †B‿dª xq ̀ ÓfW_v ̀ wgnv‡̀ g Zj̈ bvAv G ̀ ÅB wfj v̈k ̧ g ã
_¡̀ ~W© Lfdvj gv‡A|(gv) •owAB M`¯‗ v`‡j bvAv G `ÅB wfj¨vk L_¨Ŭ Ë Bvh©Bg c~ wnBv `voj B‡g|
MdvegW? wj‡nŐ :4 Zj \v‡Åg †Bvj NBwV `gx ùvg `Ó vÙ j¤Ug †dGqv eo? 36, >4, 86, =6, 64, >:, 34, 6:, 34, 0:, 84, =:, 66, 34, 36, :4, =6, 66, 38, >:M° _Y¨‡B bvAv G `ÅB wT‡Å M`¯‗ v`j Bg|knvlvj?NAv‡j, f― eÂn _Y¨ ksA¨v ; 86 Nfs ùz dª _n _Y¨ ksA¨v ; :4
bvAv G `ÅB wTÅ bvAv `ÅB KWksA¨v
: 4 <
0 : <
= : 6 6 0
6 4 : 6 6 =
3 4 4 4 6 6 8 3
> 4 < : 08 4 6 :
† nvV ; :4
kevqB (Bfy)? =|6 Øvgv fyPvq =6
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NBwV w^wZVvo B¨vnwfªqvj `Ó Bvbjv
_… _xq Ll¨vq
†B‿dªxq `ÓfW_v g `wgnv`KFLPVZFP IC @FE]ZLA ]FEMFE@W
_Y¨ M`¯‗ v`j, KWksA¨v wj‡fbj •_wg Nfs †oA G jBbvg nvl¨‡n _Y¨‡B ksw ù Ù B‡g •fwbð¨ mz wV‡q
†_vov hvq| wBŬ Ë y _‡Y¨ g KvwW w_B •fwbð¨ Zvjvg Zj¨ †B‿dª xq nvj, †B‿dª xq `Ó fW_v G †B‿dª xq `Ó fW_vg`wgnv` Zvjv dgBvg| _‡Y¨g NBwV ksA¨vK_ nv‡jg kvev‡h¨ _vg LŬ Ë wj©we_ •fwbð¨ Nfs _z ojvn~ oB•fwb𨠆B‿dª xq `Ó fW_vg `wgnv` jvnB `Þw_g kvev‡h¨ Zvjv hvq|
N Ll¨vq `vS †b‡a wb ùvYx©gv
• †B‿dª xq `Ó fW_v G †B‿dª xq `Ó fW_vg `wgnv` f¨vA¨v Bg‡_ `vg‡f|
• †B‿dª xq `Ó fW_vg `wgnv`¸‡ovg fW© jv Bg‡_ `vg‡f|
• NBwV Lvd© b K‡ig `Ó‡qvZjxq ¸Wvfox f¨vA¨v Bg‡_ `vg‡f|
• †B‿dª xq `Ó fW_v `wgnv`¸‡ovg _z ojvn~ oB Lv‡ovTjv Bg‡_ `vg‡f|
• †B‿dª xq `Ó fW_v `wgnv`¸‡ovg ky wflv G Lky wflv fW© jv Bg‡_ `vg‡f|
• KvwWw_B K‡ig •fwbð¨ fv ln© vfox fW© jv Bg‡_ `vg‡ f|
• cvg Lv‡gvw`_ Ki G N‡dg `Ó ‡qvZjxq_v f¨vA¨v Bg‡_ `vg‡f| • wfcvZB nvjkn~ e wjW© q Bg‡_ `vg‡f|
0.4< †B‿dª xq `Ó fW_v G †B‿dª xq `Ó fW_vg `wgnv`@fetrla ]femfe`y & Kflsurfs ic @fetrla ]femfe`y
†B‿dª xq `Ó fW_v? †Bvj NBwV wj‡fbj fv _Y¨kvwg‡_ L‡jB¸‡ov nvj Yv‡B| Lvg NBwV nvj †B‡‿dª
Yv‡B| †B‡‿dª g nvjwV‡B †B‿dª xq nvj f‡o| †B‿dª xq nv‡jg T_z wd© ‡B wj‡fb‡jg fvBx nvj¸‡ovNBwÅ_ fv Ejxc~ _cv‡f YvB‡_ Tvq| †B‿dª xq nv‡jg wd‡B wj‡fb‡jg fvwB nvj¸‡ov NBwÅ_ fv
Ejxc~ _cv‡f YvBvg J‛\v fv `ÓfW_v‡B †B‿dª xq `Ó fW_v f‡o|
†B‿dª xq `Ó fW_vg `wgnv` ?
†Bvj NBwV wj‡fbj fv _Y¨kvwg‡_ L‡jB¸‡ov nvj Yv‡B| Lvg NBwV nvj †B‡‿dª Yv‡B|
†B‡‿dª g nvjwV‡B †B‿dª xq nvj f‡o| †B‿dª xq nv‡jg T_z wd© ‡B wj‡fb‡jg fvBx nvj¸‡ov NBwÅ_ fv
Ejxc~ _cv‡f YvB‡_ Tvq| †B‿dª xq nv‡jg wd‡B wj‡fb‡jg fvwB nvj¸‡ov NBwÅ_ fv Ejxc~_cv‡f
YvBvg J‛\v fv `Ó fW_v‡B †B‿dª xq `Ó fW_v f‡o| †h kBo KvwWw_B `wgnv‡`g kvev‡h¨ †Bvj
_‡Y¨g †B‿dª xq nvj wjW© q Bgv eq _v‡B †B‿dª xq `Ó fW_vg `wgnv` f‡o|
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`wgksA¨vj `ÓYn `Å
M‛Tnvl¨wnB `wgksA¨v j
6:
0.4: †B‿dª xq `Ó fW_vg `wgnv`¸‡ovg fW© jvMgs`uss Kflsurfs ic @fetrla ]femfe`y
†B‿dª xq `Ó fW_ vg `wgnv` 6 `ÓBvg| hYv
B. KvwWw_B Ki (Lrgthkftg` Kfle) A. Z¨vwnw_B Ki (Nfikftrg` Kfle)
K. _g» Ki (Hlrkieg` Kfle)
E. nl¨nv (Kfmgle)
I. `Ó TzgB (Kimf)
KvwWw_B Ki/†hvwZ_ Ki (Lrgthkftg` Kfle)? †Bvj _Y¨kvwg‡_ h_¸wo nvj Yv‡B _v‡dg
knwð‡B †nvV `dksA¨v Øvgv cvK B‡g †h nvj `vGqv hvq _v‡B H _Y¨kvwgg KvwWw_B Ki f‡o| Jev‡B LK Øvgv wTwû_ Bgv eq| _‡f To‡Bg wcw‡_ N‡B z,y,x J_¨vwd Øvgv `Ó Bvb Bgv eq|
L‡bªWxB… _ _‡Y¨g † ù ‡Å ? n‡j Bwg, †Bvj ToB x Ng e ksA¨B nvjkn~ e e x x ................., :< Nfs Mev‡dg KvwWw_B Ki x e‡o,
e
x x x x e
+++;
................:<
e
xe
g
g∜;; <
†bª wWB… _ _‡Y¨g † ù ‡Å? n‡j Bwg, †Bvj ToB x Ng e ksA¨B nvjkn~ e x
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†B‿dª xq `Ó fW_v
NBwV B¨vnwfªqvj w^wZVvo `Ó Bvbjv
60
L‡bªWxB… _ _‡Y¨g † ù ‡Å? n‡j Bwg, †Bvj ToB x Ng e ksA¨B Léj¨ ljv_¥B nvjkn~ e x
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`wgksA¨vj `ÓYn `Å
M‛Tnvl¨wnB `wgksA¨v j
6=
nl¨nv (Kfmgle)? †Bvj wj‡fbj fv _Y¨kvwgg nvj¸‡ov‡B MlŸ© fv wjnŐ¶‡n kvZv‡jvg `g †h nvjwV_Y¨kvwg‡B dy JwV knvj Ls‡b wfc° B‡g H nvjwV‡B M° _Y¨kvwgg nl¨nv f‡o| Jev‡B
f Øvgv
`Ó Bvb Bgv eq|n‡j Bwg, †Bvj _Y¨kvwg‡_ e ksA¨B nvj Lv‡\| NAj nl¨nv wjW©q Bg‡_ wjnŐ wowA_ wjqn Ljy kgW
Bg‡_ e‡f|
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†B‿dª xq `Ó fW_v
NBwV B¨vnwfªqvj w^wZVvo `Ó Bvbjv
66
ky _gvs, wj‡W© q nl¨nv, Kf ;
e
: _n `d + (
e
: +
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`wgksA¨vj `ÓYn `Å
M‛Tnvl¨wnB `wgksA¨v j
63
0.4= †B‿dªxq `ÓfW_v `wgnv`¸‡ovg _z ojvn~ oB Lv‡ovTjv@ikplrf ic thf Mgccfrfe`f Kflsurfs ic @fetrla ]femfe`y
ẁgksA v̈jwfd Wuaf Ng n‡_, NBwV Lvdb© nl¨B nvj / K‡ig wjnŐ wowA_ •fwbð¨ YvBv Lvfb¨B?
(g) Jevg kwSB G ky ¯ÿð ksÌv YvBv MwT_2(gg) Jev _Y¨kvwgg kBo nv‡jg M`g wjc©gbxo eGqv MwT_2
(ggg) Jev keZ‡fvl¨ G ke‡Z KWjvg M`‡hvKx eG qv MwT_2
(gv) Jev ke‡Z KvwWw_B G fxZKvwWw_B `wgKWjvg M`‡hvKx eGqv MwT_2
(v) Jev jny jv _vg_n¨ fv jnyjv wfTz ¨w_ Øvgv Bn `Ócvwf_ eGqv MwT_2
(vg) Jevg Tgn nvj Øvgv Bn `Ócvwf_ eGqv MwT_|
M`wgM° •fwbð¨kn~ e NBwV Lvdb© nl¨B nv‡jg nv`BvwS we‡k‡f f¨fñ_ eq| wj‡nŐ †B‿dª xq `Ó fW_vg
wfwcjŐ `wgnv`¸‡ovg n‡l¨ _zojvn~ oB Lv‡ovTjv Bgv eo √
KvwWw_B Ki Lvdb© nl¨B nv‡jg `Ó vq kf¸‡ov •fwb‡ð¨g LwlBvgx| Ng kwSB G ky ®ÿð ksÌv g‡q‡\|
Jev _Y¨kvwgg kBo nv‡jg M`g wjc©gbxo| Jev ke‡Z fy Pv hvq G ke‡Z KWjv Bgv hvq| N‡_
ke‡Z KvwWw_B G fxZKvwWw_B `Ó w¶qv `Ó ‡qvK Bgv hvq G ke‡Z KWjv Bgv hvq Nfs Jev jny jv
_vg_n¨ Øvgv Bn `Ócvwf_ eq wBŬ‘ KvwWw_B K‡ig `Ólvj Lky wflv eo NwV Tgn nvj Øvgv `Ó cvwf_ eq|
Z¨vwnw_B Ki _Y¨kvwgg kBo nv‡jg M`g wjc©gbxo| N‡_ ke‡Z KvwWw_B G fxZKvwWw_B `Ó w¶qv
`Ó ‡qvK Bgv hvq| Jev Tgn nvj Øvgv `Ó cvwf_ eq jv| NwV jny jv _vg_n¨ Øvgv Bn `Ó cvwf_ eq|
Z¨vwnw_B K‡ig `Ólvj Lky wflv eo Jev ke‡Z wjW© q Bgv hvq jv| Jev wjW© q Bg‡_ oKvwgd‡ng cvo
Ìvj YvBv Lvfb¨B|
_g» Ki _Y¨kvwgg kBo nv‡jg M`g wjc©gbxo| N‡_ ke‡Z KvwWw_B G fxZKvwWw_B `Ów¶qv`Ó‡qvK Bgv hvq| Jev Tgn nvj Øvgv Bn `Ócvwf_ eq wBŬ‘ _g» Ki keZ‡fvl¨ jq Nfs Jev
ke‡Z wjW©q Bgv hvq jv|
nl¨nv G `Ó TzgB McqJ keZ‡fvl¨ G ke‡Z wjW© q Bgv hvq| Jevgv Tgn nvj Øvgv `Ócvwf_ eq jv wBŬ‘
Ngv _Y¨kvwgg kBo nv‡jg M`g wjc©gbxo jq| Jevgv KvwWw_B G fxZKvwWw_B `wgKWjvg M`‡hvKx
jq| jnyjv _vg_n¨ Øvgv Ngv †fbx `Ócvwf_ eq|
M`‡gv° Lv‡ovTjv e‡_ †dAv hvq †h, KvwWw_B Ki Lvdb© nl¨B nv‡jg ¸g ã _¡̀ ~W© •fwb𨸇ovg
LwlBvgx Nfs Ng Lky wflv¸‡ov ky wflv¸‡ovg _z ojvq Lw_ jKj¨| _vJ KvwWw_B Ki‡B †B‿dª xq
`Ó fW_vg `wgnv`kn~ ‡eg n‡l¨ k‡f© vrB… ð `wg nv` fov hvq|
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†B‿dªxq `Ó fW_v
NBwV B¨vnwfªqvj w^wZVvo `Ó Bvbjv
6>
0.46 †B‿dª xq `Ó fW_v `wgnv`¸‡ovg ky wflv G Lky wflv]hf Kfrgts lem Mfkfrgts Kflsurfs ic @fetrla ]femfe`y
†B‿dª xq `Ó fW_vg `wgnv`¸‡ovg ky wflv G Lky wflv¸‡ov `―YB `―YBcv‡f Lv‡ovTjv Bgv e‡ov?
KvwWw_B K‡ig ky wflv? B) KvwWw_B Ki ke‡Z fy Pv hvq Nfs kwSB G ky ¯ÿð ksÌv Øvgv fy Pv‡jv hvq2A) NwV _Y¨kvwgg kBo nv‡jg M`g wjc© gbxo2 K) N‡_ ke‡Z KvwWw_B G fxZKvwWw_B `Ó w¶qv `Ó ‡qvK Bgv hvq2 E) NwV jny jv _vg_n¨ Øvgv Bn `Ófvwc_ eq2I) lvgvcy ° †Bvj ksA¨v éj¨ fv CWv_¥B e‡oG KvwWw_B Ki wjW©q Bgv hvq|
Kvw Ww_B K‡ig Lky wflv? B) KvwWw_B Ki `Ó vŬ Ë xq nvj Øvgv †fwb `Ó cvwf_ eq2 A) ¸WfvTB _‡Y¨g KvwWw_B Ki wjW© q Bgv hvq jv2K) wj‡fb‡jg †oA e‡_ KvwWw_B Ki wjW© ‡qg `Þw_ †jJ2 E) NB fv NBvwlB nvj LZvjv YvB‡o Jev wjW© q Bgv hvq jv|
Z¨vwnw_B K‡ig ky wflv? B) N‡B kwSB G ky ¯ÿð ksÌv Øvgv fy Pv‡jv hvq2 A) NwV kBo nv‡jg M`g wjc© gbxo2 K) NwV `Ó vŬ Ë xq nvj Øvgv Bn `Ócvwf_ eq2
E) NwV jny jv _vg_n¨ Øvgv Ay f NBVv `Ó cvwf_ eq jv|Z¨vwnw_B K‡ig Lky wflv?
B) NwV ke‡Z fy Pv hvq jv2 A) NwV wjW© q Bg‡_ oKvwgd‡ng `Ó ‡qvZj eq f‡o kB‡og `‡ ù wjW© q Bgv k¤¢ f jq2K) lvgvcy ° NB wV nvj b~j¨ fv wf‡Zvi ksA¨B nvj CWv_¥B e‡o Z¨vwnw_B Ki wjW©q Bgv hvq jv|
_g» K‡ig ky wflv? B) NwV kBo nv‡jg M`g wjc© gbxo2
A) evg, †fK G Ki wjW© ‡qg † ù ‡Å Jev cvo mo †dq2 K) Jev `ÓvŬ Ë xq nvj Øvgv Bn `Ócvwf_ eq2 E) N‡_ ke‡Z KvwWw_B G fxZKvwWw_B `Ó w¶qv `Ó ‡qvK Bgv hvq|
_g» K‡ig Lky wflv? B) Jev k‡eZ fy Pv hvq jv| A) _Y¨kvwgg kBo nvj Zvjv jv YvB‡o NJ Ki wjW© q Bgv hvq jv|K) wkwg‡Zg †Bvj gvwbg nvj éj¨ e‡o _g» Ki NJ wjW© q Bgv hvq jv|
nl¨nvg ky wflv? B) nl¨nv ke‡Z fyPv hvq Nfs ke‡Z wjW© q Bgv hvq2 A) Jev `ÓvŬ Ë xq nvj Øvgv `Ócvwf_ eq jv2K) Jev †o‡Ag kvevh¨ wjW© q Bgv hvq2 E) ¸WfvTB _‡Y¨g † ù ‡Å nl¨nv Lj¨vj¨ `wgnv` L‡` ù v cvo mo †dq|
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`wgksA¨vj `ÓYn `Å
M‛Tnvl¨wnB `wgksA¨v j
68
nl¨nvg Lky wflv? B) Jev kBo nv‡jg M`g wjc© g B‡g jv2 A) nl¨nv `gf_© x‡_ †Bvj KvwWw_B `wgKWjvg M`‡hvKx jq2 K) _‡Y¨g M`vdvj kwµ_ jv Bg‡o nl¨nv wjW© q Bgv hvq jv|
`Ó Tz g‡Bg ky wflv? B) `Ó Tz gB ke‡Z fyPv hvq Nfs ke‡Z wjW© q Bgv hvq2 A) Jev Tgn nvj Øvgv `Ófvwf_ eq jv2K) ¸WfvTB _‡Y¨g † ù ‡ÅG `Ó Tz gB wjW© q Bgv hvq2 E) Jev †oAwTÅ kvev‡h¨ wjW© q Bgv qvq|
`Ó Tz g ‡Bg Lky wflv? B) Jev kBo nv‡jg M`g wjc© g B‡g jv2
A) N‡_ LwlB fxZKvwWw_B `Ó w¶qv `Ó ‡qvK Bgv hvq jv2 K) _‡Y¨g †Bvj nvj `yWgvf― w jv EV‡o `ÓTz gB wjW© q Bgv BwSj2 E) Jevg jny jv wfTz ¨w_ LwlB eq|
0.43 KvwWw_B K‡ig •fwbð¨ fv ln© vfoxTripfrtgfs ic Lrgthkftg` Kfle
wj‡nŐ KvwWw_B K‡ig •fwbð¨ fv ln© vfox †dGqv e‡ov?
B. †Bvj _Y¨kvwgg ksA¨v¸‡ovg knwð ; `dksA¨v x KvwWw_B Ki2A. _Y¨ kvwgg `Ó w_wV nvj e‡_ KvwWw_B K‡ig f¨flv‡jg knwð éj¨2K. _Y¨ kvwgg `Ó w_wV nvj e‡_ KvwWw_B K‡ig f¨flv‡jg f‡K© g knwð ùz dª _n2 E. KvwWw_B Ki n~ o G nv`wjg M`g wjc© gbxo2I. KvwWw_B Ki _Y¨kvwgg `Ó ‡_¨BwV nv‡jg M`g wjc© gbxo2 T. dy wV To‡Bg ‡hvKmo fv wf‡qvKm‡og KvwWw_B Ki Mev‡dg wjZ wjZ KvwWw_B K‡ig
†hvKmo fv wf‡qvKm‡og knvj2
\. b ksA¨B _Y¨kvwgg kw¤§wo_ KvwWw_B Ki
b
b b
`
eee
xe xe xe x
+√√++
+√√√√++;
:<
:: cvg Lv‡gvw`_ fv ¸g ã_¡ `Ó d Ki G N‡dg `Ó‡qvZjxq_v^fgnhtfm Lrgthkftg` Kfle & Gkpirtle`f ic ^fgnhtfm Lrgthkftg` Kfle
cvg Lv‡gvw`_ Ki?
_Y¨kvwgg nvj¸‡ov f¨fev‡gg `vbv`vwb _v‡dg cvg fv ¸g ã _¡ ‡B f¨fevg B‡g †h Ki nvj †fg Bgv eq _v‡B cvg Lv‡gvw`_ Ki f‡o| cvg Lv‡gvw`_ Ki †nvV w_j `Ó Bvg| hYv √
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†B‿dª xq `Ó fW_v
NBwV B¨vnwfªqvj w^wZVvo `Ó Bvbjv
67
wj‡nŐ N‡dg wf¯ Ë vwg_ Lv‡ovTjv Bgv e‡ov?
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`wgksA¨vj `ÓYn `Å
M‛Tnvl¨wnB `wgksA¨v j
34
†bª wWB― _ _‡Y¨g † ù ‡Å?
T_zY© B, \g ; A + ` c
C ge
q
`
Þ√Þ
=
†hAv‡j, A ; g _n T_zY© B †bª wWg wjnŐ kxnv C` ; g _n T_zY© B †bª wWg `~ f© f_ © x †bª wW g ¶n‡ hvwZ_ KWksA¨vcq ; g _n T_zY© B †bª wWg KWksA¨v` ; g _n T_zY©B †bª wWg †bªwW f¨flvj|
dbnB (Mf`gaf)†Bvj _Y¨kvwgg nvj¸‡ov‡B FlŸ©¶n fv wjnŐ ¶n Ljy kv‡g kvZv‡jvg `g †h nvj¸‡ov H
_Y¨kvwg‡B knvj db cv‡K wfc° B‡g, †kJ nvj¸‡ovg `Ó ‡_¨Bw VJ eo NB NBwV dbnB| dbnB‡B Mg(g ;
-
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†B‿dª xq `Ó fW_v
NBwV B¨vnwfªqvj w^wZVvo `Ó Bvbjv
3<
†hAv‡j, A ; g _n b_nB †bª wWg wjnŐkxnvC` ; g _n b_nB †bª wW g `~ f©f_© x †bªw W g ¶n‡ hvwZ_ KWksA¨vc p ; g _n b_nB †bªwW g KWksA¨v
` ; g _n b_nB †bª wWg †bª wW f¨flvj|
Bw_`q M``vd¨ G _vg `ÓnvW Pikf ]hfirfk lem gts Triic
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`wgksA¨vj `ÓYn `Å
M‛Tnvl¨wnB `wgksA¨v j
3:
NAj, _Y¨kvwgg `Ó w_wV nvj e‡_ KvwWw_B K‡ig f¨flv‡jg knwð,
∜;
√e
g
gg x x c <
)(
; ∜ ∜√ x c x c ggg ; x E x √
∜ ;√∽ 4)( x x c gg .
.. KvwWw_B Ki e‡_ ksA¨v¸wog f¨flv‡jg knwð b~ j¨ | (`Ó nvwW_):| `Ó nvW Bg †h, KvwWw_B Ki n~ o G nv`wjg M`g wjc© gbxo|LYfv, `Ó nvW Bg †h, m `l x +; `Ó nvW ? L‡bªWxB… _ _‡Y¨g † ù ‡Å? n‡j Bwg, x To‡Bg e ksA¨B nvjkn~ e x
-
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†B‿dªxq `Ó fW_v
NBwV B¨vnwfªqvj w^wZVvo `Ó Bvbjv
30
fv, c g xg ; lc g + `c gmg
fv E
m c `
E
c l
E
x c ggggg ∜∜∜ +;
fv ` E
m c
E
E l x
gg
Þ+; ∜
... ` E
m c l x
gg Þ+; ∜ (`Ó nvwW_)| fv `m l x +; ... m `l x +; ky _gvs KvwWw_B Ki n~ o G nv`wjg M`g wjc© gbxo| (`Ó nvwW_)|
0| `Ó nvW Bg †h, _Y¨kvwgg `Ów_wV nvj e‡_ KvwWw_B K‡ig f¨flv‡jg f‡K© g knwð ùy dª _n| LYfv,
`Ó nvW Bg †h, ∜ ∜ √1√ :: )()( l x x x gg R L‡bªWxB… _ _‡Y¨g † ù ‡Å [ `Ó nvW Bg †h, ∜ ∜ √1√ :: )()( l x c x x c gggg R†bª wWB… _ _‡Y¨g † ù ‡Å [
L‡bªWxB… _ _‡Y¨g † ù ‡Å?
`Ó nvW? n‡j Bwg, x To‡Bg e ksA¨B nvjkn~ e x
-
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`wgksA¨vj `ÓYn `Å
M‛Tnvl¨wnB `wgksA¨v j
3=
†bª wWB… _ _‡Y¨g † ù ‡Å? Ó̀ nvW? n‡j Bwg, x To‡Bg e ksA¨B nvjkn~e x
-
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†B‿dª xq `Ó fW_v
NBwV B¨vnwfªqvj w^wZVvo `Ó Bvbjv
36
6|
-
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`wgksA¨vj Ó̀Yn `Å 33
>| dy wV Léj¨ ljv_¥B ksAvg † ù ‡Å `Ó nvW Bg †h, LK≦NK≦HK `Ó nvW? n‡j Bwg, x
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†B‿dªxq `Ó fW_v
NBwV B¨vnwfªqvj w^wZVvo `Ó Bvbjv
3>
8| dy JwV Léj¨ ljv_¥B ksA¨vg † ù ‡Å Ó̀ nvW Bg †h, LK.HK ; (NK):
LYfv, N HK LK ;.
Ó̀ nvW? n‡j Bwg, Léj¨ ljv_¥B ksA¨v dy JwV x
-
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`wgksA¨vj `ÓYn `Å
M‛Tnvl¨wnB `wgksA¨v j
38
:
e _n `d +
+ <:
e _n `d
----------------------------------------------------------------------------------------
:
:| Z¨vwnw_B Ki, ee x x xNK ....... :
-
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†B‿dª xq `Ó fW_v
NBwV B¨vnwfªqvj w^wZVvo `Ó Bvbjv
37
7| Ó̀Yn e ¯U vcvwfB ksA¨vg KvwWw_B Ki G nl¨nv knvj LY© vr:
-
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`wgksA¨vj `ÓYn `Å
M‛Tnvl¨wnB `wgksA¨v j
>4
KvwWw_B knk¨v G knvlvj
-
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75/242
†B‿dª xq `Ó fW_v
NBwV B¨vnwfªqvj w^wZVvo `Ó Bvbjv
><
knxBgW (
-
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76/242
`wgksA¨vj Ó̀Yn `Å>:
knxBgW )(g G )(ggg †hvK Bwgqv `vJ, 8
-
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77/242
†B‿dªxq `Ó fW_v
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>0
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:<
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::6=)64( : Þ√; ; :644 ‐ 744
;
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78/242
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>=
Lvfvg, 8.
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†B‿dª xq `Ó fW_v
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>6
3| Bw_`q ljv_¥B gvwbg KvwWw_B Ki 64 G Z¨vwnw_B Ki =4| gvwb¸‡ov‡B 6 Øvgv cvK Bgv e‡o cvKmo¸‡ovg KvwWw_B Ki G Z¨vwnw_B Ki wjW© q Bg|
knvlvj?
n‡j Bwg, †Bvj To‡Bg x Ng e ksA¨B nvjkn~ ee
x x √√√,,:<
KvwWw_B Ki 64:< ;+√√√√++
;e
x x x e
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66,
6
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j_z j KvwWw_B Ki ; e x x x e )666
( :< +√√√√++
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x x x e
6
:< +√√√√++
;
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e
x x xe:<
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;
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`wgksA¨vj `ÓYn `Å
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>| †Bvj To‡Bg Ki =6 Me vg `Ó w_wV nvj †Y‡B :4 wf‡qvK B‡g wf‡qvKmo‡B 6 Øvgv cvK Bg‡o j_z j To‡Bg Ki nvj B_ e‡f9
knvlvj? n‡j Bwg, †Bvj ToB x Ng e ksA¨B nvj x
-
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NBwV B¨vnwfªqvj w^wZVvo `Ó Bvbjv
>>
7| †Bvj To‡Bg `Ó w_wV nvj :64 wf‡qvK wd‡q wf‡qvKmo‡B e‡o n~ o To‡Bg Ki wjW© q Bg|
knvlvj? n‡j Bwg, †Bvj To‡Bg x Ng e ksA¨B nvjkn~ e e x x √√√√:< , Nfs Mev‡dg KvwWw_BKi x |
`Ó bŐn‡_,
-
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`wgksA¨vj Ó̀Yn `Å>8
Lvngv Zvwj, KvwWw_B Ki n~ o G nv`wjg M`g wjc© gbxo,u`l x +;
;
-
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NBwV B¨vnwfªqvj w^wZVvo `Ó Bvbjv
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Jev (
-
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84/242
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84
6 Zj \vÅ\vÅx Lv‡\| \vŇdg Ki j¤U g 84, \vÅx‡dg Ki j¤Ug >6 G kw¤§wo_Ki j¤U g >8 e‡o \vÅ G \vÅxg ksA¨v wjW© q Bg|
knvlvj ?
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⇚ ::66 ;e
⇚ 6
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∽ =6;e
∽ \vÅksA¨v, =6< ;e
∽ \vÅxksA¨v, 04=6>6: ;√;e
∽ wj‡W© q \vÅ G \vÅxksA¨v hYv¶‡n =6 G 04 Zj|
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85/242
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NBwV B¨vnwfªqvj w^wZVvo `Ó Bvbjv
8<
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86/242
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M‛Tnvl¨wnB `wgksA¨v j
8:
Lvngv Zvwj, kw¤§wo_ Ki,
:<
::
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87/242
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NBwV B¨vnwfªqvj w^wZVvo `Ó Bvbjv
80
kw¤§wo_ Ki,
:<
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M‛Tnvl¨wnB `wgksA¨v j
8=
kwSB Ki †f_j ; e
xg∜ ›
;
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89/242
†B‿dª xq `Ó fW_v
NBwV B¨vnwfªqvj w^wZVvo `Ó Bvbjv
86
ky _gvs u To‡Bg Z¨vwnw_B Ki,
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== xN;
∽ xN ;
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`wgksA¨vj `ÓYn `Å
M‛Tnvl¨wnB `wgksA¨v j
83
:0| B_¸wog ksA¨vg Z¨vwnw_B Ki =4 Mevg `Ó w_wV nvj‡B 6 Øvgv cvK B‡g `Ó vÙ nvj¸wog Z¨vwnw_B Ki B_9
knvlvj? n‡j Bwg, †Bvj To‡Bg x Ng e ksA¨B nvjkn~ e x
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91/242
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NBwV B¨vnwfªqvj w^wZVvo Ó̀ Bvbjv
8>
:=| hwd †Bvj ToB x Ng Z¨vwnw_B Ki
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`wgksA¨vj `ÓYn `Å
M‛Tnvl¨wnB `wgksA¨v j
88
lwg, T_zY© ksA¨vwV ; =
NK ;
-
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NBwV B¨vnwfªqvj w^wZVvo `Ó Bvbjv
87
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94/242
`wgksA¨vj `ÓYn `Å74
Z¨vwnw_B Ki,
NK ; ( <<
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; ( <<
0:
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95/242
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-
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70
04| Ó̀Yn 64 wV ¯U vcvwfB ksA¨vg Ki wjW© q Bg |knvlvj? Lvngv Zvwj, Ó̀Yn ¯U vcvwfB ksA¨vg Ki,
:
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99/242
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(e +
+
; 6 _n `d + (3 _n `d √ 6 _n `d) Þ 4.3
; : + (6 √ :) Þ 4.3 ; : + 0 Þ 4.3 ; 0.8
34 _n b_nB, T34 ;(e +
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`wgksA¨vj `ÓYn `Å
M‛Tnvl¨wnB `wgksA¨v j
73
0>| wj‡nŐ †Bvj NBwV Zy ‡_vg †dvBv‡j wfw¶_ Zy ‡_vg kvJ‡Zg KWksA¨v †dGqv e‡ov?
Zy _vg kvJZ
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NBwV w^wZVvo B¨vnwfªqvj `Ó Bvbjv
T_zY© Ll¨vq
wf¯Ë vg `wgnv`KFLPVZFP IC MGPTFZPGIE
†B‿dª xq `Ó fW_vg `wgnv` Øvgv Lvngv †Bvj NBwV _Y¨kvwgg nl¨Bnvj k¤ÿ‡B© lvgWv ovc Bg‡_ `vwg |
N‡ ù ‡Å Lvngv _Y¨kvwgg gvwb¸‡ovg wf¯ Ë ― w_ fv f¨vwÙ k¤U ‡Ñ †Bvj lvgWv `vJ jv| Nnj e‡_ `v‡g †hNBvwlB _Y¨kvwgg nl¨B nv j NBJ wBŬ Ë y gvwb¸‡ovg f¨vwÙ wcjŐ| †hnj ? 6,
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M‛T nvl¨wnB `wgksA¨vj - Ó̀Yn `Å
M‛Tnvl¨wnB `wgksA¨v j
78
MdvegW? wj‡nŐ L Nfs J dy wV _Y¨kvwgg nvj¸‡ovg wf¯ Ë v‡gg n‡l¨ _z ojv Bgv e‡ov| L J => 00
=0 :8
60 3064 66
6> ><
64; L x 64; J x
M`‡gv° _Y¨kvwg dyÖwV‡_ Ki knvj e‡oG _v‡dg wfj¨v‡kg KSj `Ó B… w_g n‡l¨ ky ¯ÿð `vY© B¨wfd¨nvj| BvgW L kvwgg wfwcjŐ nvj¸‡ov K‡ig Bv\vBvw\ Lf¯‗ vj B‡g wBŬ‘ J kvwgg nvj¸‡ov Ki†Y‡B L‡jB †fwb d~ ‡g Lf¯‗ vj B‡g| NJgƚ` _Y¨kvwgg † ù ‡Å wf Ë̄ v‡gg f¨fevg MrB… ð|wf Ë̄ vg `wgnv` (Kflsurfs ic Mgspfrsgie)? dy J fv _‡_vwlB wj‡fb‡j _z ojv Bg‡_ fv †Bvj wj‡fb‡jg †B‿dª xq nvj †Y‡B Mevg ksA¨v¸wo B_ fi fv B_ †\vV †kJ `vY© B¨ Ìv`B `wgnv`wVJ e‡ov wf¯ Ë vg `wgnv` LY© vr †h KvwWw_B `wgnv‡`g kvev‡h¨†Bvj wj‡fb‡jg †B‿dª xq nvj e‡_ Lj¨vj¨ nvj¸‡ovg f¨flvj wjW© q Bgv eq _v‡B wf¯ Ë vg `wgnv` f‡o|†hnj? `wgwn_ f¨flvj, wf‡cdvsB J_¨vwd| wf Ë̄ v g `wgnv‡`g `Ó Bvg‡cd? M‡Éb¨ G •fwbð¨K_ wdB †Y‡B wf¯ Ë vg `wgnv`‡B dy Jcv‡K cvK Bgv hvq| hYv ?
B. Lj‡` ù fv `gn wf Ë̄ vg `wgnv` (Ljsiautf kflsurfs ic mgspfrsgie) A. L‡`w ùB wf Ë̄ vg `wgnv` (Zfaltgvf kflsurfs ic mgspfrsgie)
(B) Lj‡` ù fv `gn wf Ë̄ vg `wgnv`? wf¯Ë v‡gg † h `wgnv` kn~e wj‡fb‡jg nl¨B nvj †Y‡B ksA¨v¸wog wf¯Ë …w_ LY©vr wj‡fb‡jg Lc¨Ŭ Ë gxW †cd `wgnv` B‡g _v‡dg‡B Lj‡` ù fv `gn wf¯Ë vg `wgnv` f‡o| `gn `wgnv`kn~e To‡Bg NB‡B `wgnv` Bgv eq| Jev NBwV kgo gvwb| NBB Lv‡\, nv`v eq|
(A) Lv‡`w ùB wf Ë̄ vg `wgnv`? wf Ë̄ v‡gg †h `wgnv`¸‡ov dy J fv _‡_vwlB wj‡fb‡jg wf¯ Ë … w_ _z ojvg Bv‡Z f¨fñ_ eq _v‡dg‡B Lv‡`w ùB wf Ë̄ vg `wgnv` f‡o| Lv‡`w ùB wf Ë̄ vg `wgnv`kn~ e keK, b_Bgv, Ljỳ v_ LvBv‡g `Ó Bvb Bgv eq| Ngv NBBny ° ksA¨v|
=.4: Lj‡` ù fv `gn wf¯Ë vg `w gnv‡`g `ÓBvg‡cd¸‡ov Lv‡ovTjv| Mgs`uss Ljsiautf Kflsurfs ic Mgspfrsgie
Lj‡` ù wf Ë̄ vg `wgnv`‡B Tvgcv‡K cvK Bgv hvq| hYv -
ѓ. `wgkg (Zlenf)ѓѓ. T_zY©B f¨flvj (\ulrtgaf Mfvgltgie)
ѓѓѓ. Ki f¨flvj (Kfle Mfvgltgie)
ѓv. `wgwn_ f¨flvj (Ptlemlrm Mfvgltgie)
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wf¯ ” vg `wgnv`
NBwV B¨vnwfªqvj w^wZVvo `Ó Bvbjv
77
ѓ) `wgkg (Zlenf)? `wgkg e‡ov _Y¨kvwgg kf‡T‡q keZ_n `wgnv`B| L‡bªWxB… _ _Y¨kvwgg† ù ‡Å †Bvj _Y¨kvwgg f― eÂn _Y¨ksA¨v G ùz dª _n _Y¨ksA¨vg f¨flvj‡B `wgkg f‡o|
`wgkg‡B Z Øvgv `Ó Bvb Bgv eq|
LY© vr A H x x √; †hnj? >,
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M‛T nvl¨wnB `wgksA¨vj - Ó̀Yn `Å
M‛Tnvl¨wnB `wgksA¨v j
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wf¯ ” vg `wgnv`
NBwV B¨vnwfªqvj w^wZVvo `Ó Bvbjv
6
@iauke√J 4 76 >4 84 >6 4; L x Nfs >4; J x
N‡ ù ‡Å L G J _Y¨kvwgg Ki knvj e‡oG _v‡dg KSj G `Ó B… w_g n‡l¨ ky ®ÿð `vY© B¨ wfd¨nvj| BvgW
Ki e‡_ L kvwgg wfwcjŐ nv‡jg wf¯ Ë … w_ L‡` ù vB… _ Bn Nfs J kvwgg nvj ‡̧ovg wf¯ Ë … w_ Ay f †fbx| gg. M‛T_g `h© v‡qg wfwcjŐ `wgkvswA¨B `Þw_g `wgnv`B we‡k‡f NwV f¨fñ_ eq| †hnj?
ks‡b ø a, wjc©gW, jnyjvqj, hYvY© _v hvTvJ `Ó c― w_ † ù ‡Å wf¯ Ë vg f¨fñ_ eq|
ggg. †Bvj BvgAvjvq Mr`vwd_ `‡W¨g hYvhY nvj wjqŬ¹ ‡W NwV f¨fñ_ eq|
gv. NwV †B‿dª xq nv‡jg hYvY© _v hvTvJ B‡g| †h _Y¨kvwgg wf¯ Ë vg h_ Bn _vg †B‿dª xq nvj¸wo _‡_v †fwb `Ó w_wjwl_¡ Bvgx|
v.
wf Ë̄ vg _Y¨kvwgg nvj¸wog kvnÍk¨_v `wgnv` B‡g| †h _Y¨kvwgg wf¯ Ë vg h_ †fwb _vg nvj¸wo _‡_v †fwb LkvnÍk¨`~W© |
=.4= NBwV Lvdb© wf¯Ë v‡gg ¸Wvfwo]hf Tripfrtgfs ic le Gmfla Kflsurfs ic Mgspfrsgie
NBwV Lvdb© wf Ë̄ vg `wgnv‡`g ¸Wvfox?
`wgksA¨vjwfd Wuaf-Ng n‡_ NBwV Lvdb© nl¨B nv‡jg †h kn¯ Ë ¸Wvfox YvBv Lvfb¨B NBwV Lvdb© wf Ë̄ vg `wgnv‡`g G †kJkf ¸Wvfox YvBv Lvfb¨B| LY© vr ,
• Jevg kwSB G ky ¯ÿð ksÌv YvBv MwT_|
• Jev _Y¨kvwgg kBo nv‡jg M`g wjc© gbxo|
• NVv keZ‡fvl¨ G ke‡Z KWjvg M`‡hvKx eGqv MwT_|
•
NVv ke‡Z KvwWw_B G fxZKvwWw_B `wgKWjvg M`‡hvKx eGqv MwT_| • Jev jny jv wfTz ¨w_ Øvgv Ay f †fbx `Ó cvwf_ eGqv MwT_ jq|
• NVv `Ó vwŬ Ë Bnvj fv Tgnnvj Øvgv Ay f †fwb `Ócvwf_ eGqv MwT_ jq|
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M‛T nvl¨wnB `wgksA¨vj - Ó̀Yn `Å
M‛Tnvl¨wnB `wgksA¨v j
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