Higher Secondary Level Statistics Book

8/15/2019 Higher Secondary Level Statistics Book

1/242

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


2/242

`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


3/242

Ll¨vq wffgW `― ýv js


4/242

_Â¡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


5/242

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`wÂ 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|


6/242

M‛T nvl¨wnB `wgksA¨vj-`ÓYn ̀ Å

NBwV B¨vnwfªqvj w^wZVvo `Ó Bvbjv

:


7/242

`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`vÂ 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 & ìwmfe, 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`ìrmgen 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 & ìwmfe 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

ìaaf`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`ìrmgen ti rflsieljaf stlemlrm ic l`ùrl`y, ìaaf`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 fÄ¨v `Ódvj Bgvg wfÌvj|


8/242



=

4‰ ............. J_¨vwd`wgksA¨vj jq| h_ù

W `h© Ŭ Ë

jv `Ó dÂ 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|


9/242



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‡Ébëxjcv‡f ksK― ex_ _Y¨ kwSB wkÞvŬ Ë wd‡_ fŸ© e‡_ `v‡g Nfs N lg‡Wg

_Y¨ †Bvj EVjvg `wg`~W© fW© jv wd‡_ fŸ© eq|

(vg) _‡Y¨g knZv_xq_v? `wgksA¨vjxq M`vÂ‡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`vÂ `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`vÂ‡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

ôv‡g `wgwn_ wB\y †ov‡Bg Lvq wj‡q KwS_ M`vÂ `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 wcwÂ‡_ 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|


10/242



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 wcwÂ 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 LÊ‡og 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‡\|


11/242



>


12/242



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 \vÅ‡d g Ki fqk Ljy kÑv‡j M° †bªWxB‡ ùg \vÅ‡d 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


13/242



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|


14/242

M‛T nvl¨wnB `wgksA¨vj-`ÓYn `Å



15/242

`wgksA¨vj, ToB G wfwcjŐ `Ó_x‡Bg lvgWv



16/242

M‛T nvl¨wnB `wgksA¨vj- Ó̀Yn `Å

wV v w v w w Vv ` vb v


17/242




18/242




19/242




20/242




21/242



; e` x x xj x x xl ee √+++√+++ )......()............( :<::

:

:

<

; ∜ ∜; ;

√√e

g

e

g

gg e` xj xl< <

:

; Z.H.P

∽ ∜;

√√e

g

gg `jxlx<

:

)( ; ∜ ∜; ;

√√e

g

e

g

gg e` xj xl< <

:

(`Ó nvwW_)

(gx) ∜;

+e

g

gg y x

<

)( ; ∜ ∜; ;

+e

g

e

g

gg y x

< <

`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<

:< ..........................

∜;

;+++∽e

g

ge y y y y<

:< ..........................

A.H.P ; ∜;

+e

g

gg y x<

)(

; )(......................)()( ee y x y x y x ++++++ ::


22/242




23/242

`wgksA¨vj, ToB G wfwcjŐ `Ó_x‡Bg lvgWv



24/242

M‛T nvl¨wnB `wgksA¨vj-`ÓYn `Å


:4

; ∜;

++++e

o

ok yk x x xe<

:< )......................(

; ∜ ∜; ;

+k

g

e

o

og yk xe< <

; P H ..

∽ ∜ ∜∜∜; ;; ;

+;+k

g

e

o

og

k

g

e

o

og yk xe y x<


25/242


M‛Tnvl¨wnB ẁgksA¨vj

:<

(xgv) ∜;

√e

g

g ` x<

)( ; ∜;

√e

g

g e` x<

`Ó nvW? n‡j Bwg, †Bvj ToB x-Ng e ksA¨B nvjkn~ e e x x ..................., :< Nfs ` NBwV lªãfB|

∜;

;+++∽e

g

ge x x x x<

:<..........................

A.H.P ; ∜;

√e

g

g ` x<

)(

; )(......................)()( ` x` x` x e √++√+√ :<

; )..............()...........( ``` x x x e +++√+++ :<

; ∜; √e

g

g e` xl<

; Z.H.P

∽ ∜;

√e

g

g ` x<

)( ; ∜;

√e

g

g e` xl

<

(`ÓnvwW_)

(xv) ∜;

√b

g

g jlx

<

:)( ; ∜ ∜; ;

+√b

g

b

g

gg bj xlj xl< <

::::

`Ó nvW? n‡j Bwg, †Bvj ToB x-Ng b ksA¨B nvjkn~ e b x x ..................., :< Nfs l G j dy wV lªãfB|

∜;

;+++∽b

g

gb x x x x<

:< ..........................

∜;

;+++∽b

g

gb x x x x<

::

:

:

<

: ..........................

A.H.P ; ∜;

√b

g

g jlx<

:)(

; )( ::

<

:: jljx xl gg

b

g

+√∜;

; )(.....................)()( ::::

:

:

:

::

<

:

<

:::: jljx xljljx xljljx xl b b +√+++√++√

; )...............()..........()...............( ::::<

:::

:

::

<

:: jjj x x xlj xl xl xl b b +++++++√+++

; :

<

::

:

:

<

:: bj xlj x x xl

b

g

gb +√+++ ∜;

).............(

; :


26/242

M‛T nvl¨wnB `wgksA¨vj-`ÓYn ̀ Å::

∜ ∜∜; ≤

√

+;

+++++++

+++++++;++++

+

++++

+++;

e

g g o

ggg

eeeee

ee

eee

e

e

x x x

x x x x x x x x

x x x x x x x x x

x x x x x

x x x x x

x x x x x

<

:


27/242


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`vÂ ksKÓ e Bgv| fv¯ Ë wfB

`‡ ù `wgksA¨vjxq wf‡b ø a‡Wg wcwÂ 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|


• _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|


28/242

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 wcwÂ‡_ _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?


29/242

_Y¨ ksKÓ e ksw³ÙBgW G M` ‗̄ v`j


:6

MdvegW?


30/242



: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 wcwÂ‡_ ¯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`wÂ ¯‗ 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|


31/242

_Y¨ ksKÓe ksw³ÙBgW G M`¯‗ v`j


:>

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|


32/242



: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|


33/242

_Y¨ ksKÓ e ksw³ÙBgW G M`¯‗v`j


: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 |


34/242



04

:.43 `ÓvYwnB G nvl¨wnB _Y¨ NBJ _Y¨Trgklry lem Pfìemlry Mltl lrf Jlsg`laay Plkf

†Bvj K‡faWvg Zj¨ kgvkwg _‡Y¨g Mr`wÂ¯‗ 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¨| ù 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 Pfìemlry 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|


35/242



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|


36/242



0:

A) `wgksA¨vwjB †oA? `wgksA¨vwjB M`vÂ‡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 wTÅ¸wo‡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 >


37/242



00

(A) knqwcwÂB †bªWxfÞBgW? kn‡qg `wgf_©‡jg kv‡Y kv‡Y †Bvj EVjv fv wfa‡q B_Vz Bz `wgf_© j eq _vg wcwÂ‡_ _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


38/242



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)


39/242

_Y¨ ksKÓ e ksw³ÙBgW G M` ‗̄ v`j


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 wcwÂ‡_ †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|

:.


40/242



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


41/242



0>

:., =, 8, 6, =, 3, :, 8, >, 0,


42/242



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?


43/242



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|


44/242



=4

:. 04-=4 >=4-=7


45/242



=<

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 ;


46/242



=:

†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


47/242



=0

:.


48/242



==

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-


49/242



=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 `ÓdÂ 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|


50/242



=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 _vwÂ¡ 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√


51/242



=>

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√


52/242



=8

:.<

6 >6

3 84

knvlvj? x L‡ ù kvo G y L‡ ù Mr`vdj fwk ‡q d ÔwTÅ LvuBv eo?


53/242



=7

A) f― ÂvBvg wTÅ (Tgf Mglnrlk)? †Bvj _Y¨kvwgg wfwcjŐ M`vdv‡jg Lvjỳ vw_B ev‡g NBwV f― Â‡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 dÂ 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


54/242



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 `Å‡Bg 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


55/242


_… _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•fwbð¨ †B‿dª xq `Ó fW_vg `wgnv` jvnB `Þw_g kvev‡h¨ Zvjv hvq|


• †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|


56/242

`wgksA¨vj `ÓYn `Å


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 wcwÂ‡_ 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


57/242

†B‿dª xq `Ó fW_v


60

L‡bªWxB… _ _‡Y¨g † ù ‡Å? n‡j Bwg, †Bvj ToB x Ng e ksA¨B Léj¨ ljv_¥B nvjkn~ e x


58/242



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|


59/242



66

ky _gvs, wj‡W© q nl¨nv, Kf ;

e

: _n `d + (

e

: +


60/242



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© •fwbð¨¸‡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|


61/242

†B‿dªxq `Ó fW_v


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|


62/242



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― wÂ 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 dÂ 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 √


63/242



67

wj‡nŐ N‡dg wf¯ Ë vwg_ Lv‡ovTjv Bgv e‡ov?


64/242



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 ;


65/242



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


66/242



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


67/242



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


68/242



3=

†bª wWB… _ _‡Y¨g † ù ‡Å? Ó̀ nvW? n‡j Bwg, x To‡Bg e ksA¨B nvjkn~e x


69/242



36

6|


70/242

`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


71/242



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


72/242



38

:

e _n `d +

+ <:

e _n `d

----------------------------------------------------------------------------------------

:

:| Z¨vwnw_B Ki, ee x x xNK ....... :


73/242



37

7| Ó̀Yn e ¯U vcvwfB ksA¨vg KvwWw_B Ki G nl¨nv knvj LY© vr:


74/242



>4

KvwWw_B knk¨v G knvlvj


75/242



><

knxBgW (


76/242

`wgksA¨vj Ó̀Yn `Å>:

knxBgW )(g G )(ggg †hvK Bwgqv `vJ, 8


77/242



>0

Lvngv Zvwj,

:<

:

:<

:

:< =)()( x x x x x x √+;√

::6=)64( : Þ√; ; :644 ‐ 744

;


78/242



>=

Lvfvg, 8.


79/242



>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

Z¨vwnw_B Ki ; =4)(<

:< ;√√√√ ee x x x

`Ó w_wV nvj‡B 6 Øvgv cvK B‡g `vJ,

66,

6

:< e x x x √√√√

j_z j KvwWw_B Ki ; e x x x e )666

( :< +√√√√++

;e

x x x e

6

:< +√√√√++

;

+√√√√++

e

x x xe:<

6

<

;


80/242



>3

>| †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


81/242



>>

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‡_,


83/242



>7

Jev (


84/242



84

6 Zj \vÅ\vÅx Lv‡\| \vÅ‡dg 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 ?

†dGqv Lv‡\,

>6:< ;+ee

n‡j Bwg,

\vÅ ksA¨v8;` x

Lvngv Zvwj,

:<

::6>6)>6()84(>8

⇚ >6

>6)>6>6(84>8

ee √Þ+;

⇚ >6

63:66>8

+; e

⇚ )>8>6(63:66 Þ;+e

⇚ 686463:66 ;+e

⇚ 63:668646 √;e

⇚ ::66 ;e

⇚ 6

::6;e

∽ =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|


85/242



8<


86/242



8:

Lvngv Zvwj, kw¤§wo_ Ki,

:<

::


87/242



80

kw¤§wo_ Ki,

:<

::


88/242

`wgksA¨vj Ó̀Yn `Å


8=

kwSB Ki †f_j ; e

xg∜ ›

;


89/242



86

ky _gvs u To‡Bg Z¨vwnw_B Ki,

eeu uuuN

<

:< )........................(;

ee x x x

<

:< )

=

........

=

.

=

(= ;

.

)=............=.=(

)(=

<

<

:<

e

ee x x x √√√√√;

ee

xN<

)=(

= ;

== xN;

∽ xN ;


90/242



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


91/242

†B‿dª xq `ÓfW_v

NBwV B¨vnwfªqvj w^wZVvo Ó̀ Bvbjv

8>

:=| hwd †Bvj ToB x Ng Z¨vwnw_B Ki


93/242



87


94/242

`wgksA¨vj `ÓYn `Å74

Z¨vwnw_B Ki,

NK ; ( <<

):8.=.:.< +√√√√ ee

; ( <<

0:


95/242



7<

:8|


96/242



7:

_g» Ki, H.K. ;


97/242



70

04| Ó̀Yn 64 wV ¯U vcvwfB ksA¨vg Ki wjW© q Bg |knvlvj? Lvngv Zvwj, Ó̀Yn ¯U vcvwfB ksA¨vg Ki,

:

.6 nvJo / E‿Vv| 0:| NBZj kvJ‡Bo Lv‡gvex _vg hvÅv`‡Yg Ó̀Yn 04 nvJo E‿Vvq =4 nvJo †f‡K, `gf_x© :6 nvJo

E‿Vvq 06 nvJo †f‡K G †ba :4 nvJo E‿Vvq 04 nvJo †f‡K Lw_¶n B‡g| _vg Ki‡fK B_9 knvlvj ? lwg,

Kw_‡fK ; g d~ g_¡ ; gw NAv‡j, >6:4:6040:< ;++;++ www

Lvngv Zvwj,

0

0

:

:

<

<

0:<

x

w

x

w

x

w

www K

++

++;

04:4

06:6

=404

>6

++

;

7

8=>6Þ;

; 06.:4 nvJo / E‿Vv|

NAv‡j,

,04

,06

,=4

0

:

<

;

;

;

:4

:6

04

0

:

<

;

;

;

w

w

w


98/242



7=

00| _z wn †_vnvg hvÅv`‡Y `Ó w_ E‿Vvq 34 nvJo †f‡K 744 nvJo †Vª ‡j, `Ó w_ E‿Vvq :6 nvJo †f‡K044 nvJo †j․Bvq, `Ó w_ E‿Vvq 064 nvJo †f‡K =44 nvJo wfnv‡j Nfs `Ó w_ E‿Vvq :6 nvJo†f‡K


99/242



76

06| 4)(<

;√∜;

e

g

gg b x c e‡o b Ng nvj B_9

knvlvj? n‡j Bwg, x To‡Bg e ksA¨B nvjkn~ e x (wf‡Zvi)

ky _gvs _… _xq T_zY© B, \0 ;(e++n dbnB, M> ;

(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 +


100/242



73

0>| wj‡nŐ †Bvj NBwV Zy ‡_vg †dvBv‡j wfw¶_ Zy ‡_vg kvJ‡Zg KWksA¨v †dGqv e‡ov?

Zy _vg kvJZ


101/242


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,


102/242

M‛T nvl¨wnB `wgksA¨vj - Ó̀Yn `Å


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)


103/242

wf¯ ” vg `wgnv`


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? >,


104/242




105/242

wf¯ ” vg `wgnv`


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|


106/242



8/15/2019 Higher Second

Higher Secondary Level Statistics Book

Documents