এসএস সি পদার্থবিজ্ঞান । প্রথম অধ্যায় । ভৌত রাশি ও পরিমাপ

cÖ_g Aa¨vq

†fŠZ ivwk I cwigvc

 

c`v_©weÁvb : weÁv‡bi †h kvLvq c`v_© I kw³ wb‡q Av‡jvPbv Kiv nq †mB kvLv‡K e‡j c`v_©weÁvb| c`v_©weÁv‡bi g~j jÿ¨ n‡”Q ch©‡eÿY, cixÿY I we‡køl‡Yi Av‡jv‡K e¯‘ I kw³i iƒcvšÍi I m¤úK© D`NvUb Ges cwigvYMZfv‡e Zv cÖKvk Kiv|

 

c`v_©weÁv‡bi µgweKvk : wLªóc~e© 625 †_‡K 212 wLªóvã ch©šÍ mgq‡K c`v_©weÁv‡bi cÖvPxbKvj ejv nq| G mg‡q †hme weÁvbx  c`v_©weÁvb weKv‡k Ae`vb iv‡Lb Zviv n‡jb

 

†_wjm (wLªóc~e© 624-569) : cÖvPxb wMÖK I †ivg mvgªv‡R¨ †_wjm m~h©MÖnY m¤úwK©Z fwel¨ØvYxi Rb¨ weL¨vZ wQ‡jb| wZwb †jvW‡÷v‡bi †PŠ¤^K ag© m¤ú‡K©I Rvb‡Zb|

 

wc_v‡Mvivm (wLªóc~e© 527-497) : weÁv‡bi BwZnv‡m GKwU ¯§iYxq bvg wc_v‡Mvivm| wZwb weÁvb, ag©, MwYZ I msMxZ, †flR weÁvb I wek¦ZË¡, kixi, gb I AvZ¥v mewKQy‡KB MvwYwZK m~‡Îi mvnv‡h¨ cÖKvk Ki‡Z †P‡qwQ‡jb| wZwb Av¸b, cvwb, gvwU I evqy-G PviwU †gŠ‡ji aviYv w`‡qwQ‡jb| eZ©gv‡b ev`¨hš¿ I msMxZ welqK †h †¯‹j i‡q‡Q Zv‡Z Zvi AvswkK Ae`vb i‡q‡Q|

 

†W‡gvwµUvm (wLªóc~e© 460-370) : wLª‡ói R‡b¥i PvikZ eQi Av‡M wMÖK `vk©wbK †W‡gvwµUvm cigvYyi cÖv_wgK aviYv †`b| 

 

AvwK©wgwWm (wLªóc~e© 287-212) : weL¨vZ wMÖK MwYZwe` AvwK©wgwWm wjfv‡ii bxwZ I Zi‡j wbgw¾Z e¯‘i Ici wµqvkxj EaŸ©gyLx e‡ji m~Î Avwe®‹vi K‡i avZzi †fRvj wbY©q Ki‡Z mg_© nb| wZwb †Mvjxq `c©‡Yi mvnv‡h¨ m~h©iwk¥ †K›`ªxf‚Z K‡i Av¸b aiv‡bvi †KŠkjI Rvb‡Zb|

 

Be‡b Avj nvB_vg (965-1039) I Avj nv‡Rb (965-1038) : Av‡jvK Z‡Ë¡i †ÿ‡Î Be‡b Avj nvB_vg I Avj nv‡R‡bi Ae`vb we‡kl D‡jøL‡hvM¨| Avj nv‡Rb U‡jwgi gZev‡`i we‡ivwaZv K‡ib Ges gZ cÖKvk K‡ib †h, e¯‘ †_‡K Av‡jv Avgv‡`i †Pv‡L Av‡m e‡jB Avgiv e¯‘‡K †`L‡Z cvB| cÖmviY m¤ú‡K© U‡jwgi ¯’~j m~Î m¤ú‡K© wZwb e‡jb †h, AvcZb †KvY cÖwZmiY †Kv‡Yi mgvbycvwZK GwU ïay ¶z`ª †Kv‡Yi †ejvq mZ¨|

 

Avj-gvmy`x (896-956) : Avj-gvmy`x cÖK…wZ BwZnvm wel‡q GKwU GbmvB‡K¬vwcwWqv †j‡Lb| G MÖ‡š’ DBÛwgj ev evqyK‡ji D‡jøL Av‡Q| eZ©gv‡b c„w_exi A‡bK †`‡k G evqyK‡ji mvnv‡h¨ Zwor kw³ Drcv`b Kiv n‡”Q|

 

ga¨hy‡M c`v_©weÁv‡bi weKvk : iRvi †eKb (1214-1294) wQ‡jb cixÿvg~jK ˆeÁvwbK c×wZi cÖe³v| Zuvi g‡Z, ch©‡eÿY I cixÿvi gva¨‡gB weÁv‡bi me mZ¨ hvPvB Kiv DwPZ|

wjDbv‡`©v `¨ wfw (1452-1519) : cvwLi Iov ch©‡eÿY K‡i D‡ovRvnv‡Ri GKwU g‡Wj ˆZwi K‡iwQ‡jb|

Wv. wMjevU© (1540-1603) : Pz¤^KZ¡ wb‡q M‡elYv I ZË¡ cÖ`vb K‡ib|

†mœj (1591-1626) : Av‡jvi cÖwZmi‡Yi m~Î Avwe®‹vi K‡ib|

nvB‡Mb (1626-1695): †`vj‡Ki MwZ ch©v‡jvPbv, Nwoi hvwš¿K †KŠk‡ji weKvk I Av‡jvi Zi½ZË¡ D™¢veb K‡ib|

ievU© ûK (1635-1703) : c`v‡_©i w¯’wZ¯’vcK a‡g©i AbymÜvb K‡ib|

fb ¸‡qwiK (1602-1686) : evqy cv¤ú Avwe®‹vi K‡ib|

†ivgvi (1644-1710) : e„n¯úwZi GKwU DcMÖ‡ni ch©‡eÿY K‡i Av‡jvi †eM cwigvc K‡ib|

†Kcjvi (1571-1630) : †mŠiRM‡Zi cÖPwjZ e„ËvKvi Kÿc‡_i cwie‡Z© Dce„ËvKvi Kÿc_ Kíbv K‡ib|

M¨vwjwjI (1564-1642) : miY, MwZ, Z¡iY, mgq BZ¨vw`i msÁv cÖ`vb I G‡`i g‡a¨ m¤úK© wbY©q K‡ib Ges e¯‘i cZ‡bi wbqg Avwe®‹vi I m„wZwe`¨vi wfwË ¯’vcb K‡ib|

m¨vi AvBR¨vK wbDUb (1642-1727) : ejwe`¨v I ejwe`¨vi weL¨vZ wZbwU m~Î Avwe®‹vi K‡ib| Av‡jvK, Zvc I kã weÁv‡bI Zuvi Ae`vb i‡q‡Q| MwY‡Zi bZzb kvLv K¨vjKzjvmI Zvi Avwe®‹vi|

 

Aóv`k I Ebwesk kZvãxi Avwe®‹vi I D™¢veb

n¨vÝ wµwðqvb I‡qi‡÷W (1777-1851) : Zwor cÖev‡ni †PŠ¤^K wµqv Avwe®‹vi K‡ib|

gvB‡Kj d¨viv‡W (1791-1867), †nbix (1797-1879) I †jÄ (1804-1865) : †PŠ¤^K wµqvi ZworcÖevn Drcv`b K‡i hvwš¿K kw³‡K Zwor kw³‡Z iƒcvšÍi cÖwµqv Avwe®‹vi K‡ib|

†Rgm K¬vK© g¨v·I‡qj (1831-1879) : Av‡jvi Zwor Pz¤^Kxq Z‡Ë¡i weKvk NUvb|

gvK©bx (1874-1937) : †eZvi hš¿ Avwe®‹vi K‡ib|

†e‡K‡ij (1852-1908) : BD‡iwbqv‡gi †ZRw¯ŒqZv Avwe®‹vi K‡ib|

ib‡Rb (1845-1923) : G·‡i Avwe®‹vi K‡ib|

g¨v· cø¨v¼ (1858-1947) : †Kvqv›Uvg ZË¡ cÖ`vb K‡ib|

Av‡b©÷ iv`vi‡dvW© (1871-1937) : cigvYy welqK wbDK¬xq ZË¡ cÖ`vb K‡ib|

AvjevU© AvBb÷vBb (1879-1955) : Av‡cwÿK ZË¡ cÖ`vb K‡ib|

bxjm †evi (1885-1962) : nvB‡Wªv‡Rb cigvYyi B‡jKUªb ¯Í‡ii aviYv †`b|

I‡Uv nvb (1879-1968) I †÷ªmg¨vb (1902-1980) : Zviv Avwe®‹vi K‡ib cigvYy wdkb‡hvM¨|

 

mf¨Zvi weeZ©‡b c`v_©weÁv‡bi Ae`vb : AvaywbK mf¨Zvi weeZ©‡b c`v_©weÁv‡bi Ae`vb Acwimxg| gvbemf¨Zvi weeZ©‡b weÁv‡bi †h Ae`vb, Zvi wecyj Ask G c`v_©weÁv‡bi Ae`vb| ˆ`bw›`b Rxe‡bi wewfbœ Avivg Av‡qk †_‡K ïiæ K‡i RvZxq Rxe‡b wewfbœ DbœwZ‡Z c`v_©weÁv‡bi Ae`vb Acwimxg| G gnvwek¦‡K nv‡Zi gy‡Vvq G‡b weeZ©‡bi aviv‡K Ae¨vnZ ivL‡Z c`v_©weÁv‡bi f‚wgKv AMÖMY¨|

 

†gŠwjK ivwk : †hme ivwk ¯^vaxb ev wbi‡cÿ †h¸‡jv Ab¨ ivwki Ici wbf©i K‡i bv eis Ab¨vb¨ ivwk G‡`i Ici wbf©i K‡i Zv‡`i †gŠwjK ivwk e‡j| gvc-†Rv‡Li †ÿ‡Î weÁvbxiv 7wU ivwk‡K †gŠwjK ivwk wn‡m‡e wPwýZ K‡i‡Qb| †hgb : 1. ˆ`N©¨, 2. fi, 3. mgq, 4. ZvcgvÎv, 5. ZworcÖevn, 6. `xcb ZxeªZv, 7. c`v‡_©i cwigvY|

 

jä ivwk : †h mKj ivwk †gŠwjK ivwki Ici wbf©i K‡i ev †gŠwjK ivwk †_‡K jvf Kiv hvq Zv‡`i jä ivwk e‡j| †eM, Z¡iY, ej, KvR, Zvc, wefe BZ¨vw`| 

cwigv‡ci GKK : †h Av`k© cwigv‡Yi mv‡_ Zzjbv K‡i †Kv‡bv †fŠZ ivwki cwigvY wbY©q Kiv nq Zv‡K cwigv‡ci GKK e‡j| wgUvi, wK‡jvMÖvg, †m‡KÛ BZ¨vw` cwigv‡ci GK‡Ki D`vniY|

 

Gm AvB (SI) Gi †gŠwjK GKKmg~n :

ˆ`‡N©¨i GKK wgUvi (m) : k~b¨¯’v‡b Av‡jv  †m‡K‡Û †h `~iZ¡ AwZµg K‡i Zv‡K 1 wgUvi (m) e‡j| 

f‡ii GKK wK‡jvMÖvg (kg) : d«v‡Ýi m¨v‡å‡Z B›Uvib¨vkbvj ey¨‡iv Ae I‡qUm& A¨vÛ †gRvi‡m iwÿZ cøvwUbvg-BwiwWqvg msKi avZzi ˆZwi GKwU wmwjÛv‡ii fi‡K 1 wK‡jvMÖvg (kg) e‡j| G wmwjÛviwUi e¨vm 3.9 cm Ges D”PZv 3.9 cm|

mg‡qi GKK †m‡KÛ (s) : GKwU wmwRqvg −133 cigvYyi 9 192 631 770 wU ¯ú›`b m¤úbœ Ki‡Z †h mgq jv‡M Zv‡K 1 †m‡KÛ (s) e‡j| 

ZvcgvÎvi GKK †Kjwfb (K) : cvwbi ˆÎa we›`yi ZvcgvÎvi   fvM‡K 1 †Kjwfb (K) e‡j|

Zwor cÖev‡ni GKK A¨vw¤úqvi (A) : k~b¨¯’v‡b 1 wgUvi `~i‡Z¡ Aew¯’Z Amxg ˆ`‡N©¨i Ges D‡cÿYxq e„ËvKvi cÖ¯’‡”Q‡`i `ywU mgvšÍivj mij cwievnxi cÖ‡Z¨KwU‡Z †h cwigvY Zwor cÖevn Pj‡j ci¯ú‡ii g‡a¨ cÖwZ wgUvi ˆ`‡N©¨ 2 × 10⁻⁷ wbDUb ej Drcbœ nq Zv‡K 1 A¨vw¤úqvi (A) e‡j|

`xcb ZxeªZvi GKK K¨v‡Ûjv (Cd) : K¨v‡Ûjv n‡”Q †mB cwigvY `xcb ZxeªZv hv †Kv‡bv Av‡jvK Drm GKwU wbw`©ó w`‡K 540 × 10¹² nvR© K¤úv‡¼i GKeY©x wewKiY wbtmiY K‡i Ges IB wbw`©ó w`‡K Zvi wewKiY ZxeªZv n‡”Q cÖwZ †÷‡iwWqvb Nb‡Kv‡Y  IqvU| 

c`v‡_©i cwigv‡Yi GKK †gvj : †h cwigvY c`v‡_© 0.012 wK‡jvMÖvg Kve©b−12 G Aew¯’Z cigvYyi mgvb msL¨K cÖv_wgK BDwbU (†hgb : cigvYy, AYy, Avqb, B‡jKUªb BZ¨vw` ev G¸‡jvi wbw`©ó †Kv‡bv MÖæc) _v‡K Zv‡K 1 †gvj (mol) e‡j|

 

gvÎv : †Kv‡bv †fŠZ ivwk‡Z Dcw¯’Z †gŠwjK ivwk¸‡jvi m~PK‡K ivwkwUi gvÎv e‡j|

†hgb : ej = fi × Z¡iY × |

ˆ`‡N©¨i gvÎv L, f‡ii gvÎv M, mg‡qi gvÎv T emv‡j e‡ji gvÎv cvIqv hv‡e|  ev, MLT⁻²|

wgUvi †¯‹j : cixÿvMv‡i ˆ`N©¨ cwigv‡ci me‡P‡q mij hš¿ n‡jv wgUvi †¯‹j| Gi ˆ`N©¨ 1 wgUvi ev 100 †mw›UwgUvi|

fvwb©qvi †¯‹j : mvaviY wgUvi †¯‹‡j Avgiv wgwjwgUvi ch©šÍ ˆ`N©¨ gvc‡Z cvwi| G †¯‹‡ji ¶z`ªZg fv‡Mi fMœvs‡ki  wbfz©j cwigv‡ci Rb¨ cÖavb †¯‹‡ji cv‡k †h †QvU Avi GKwU †¯‹j e¨envi Kiv nq Zv‡K fvwb©qvi †¯‹j e‡j|

fvwb©qvi aªæeK : cÖavb †¯‹‡ji ¶z`ªZg GK fv‡Mi †P‡q fvwb©qvi †¯‹‡ji GKfvM hZUzKz †QvU Zvi cwigvY‡K ejv nq fvwb©qvi aªæeK (Vernier Constant)| G‡K VC Øviv cÖKvk Kiv nq|

fvwb©qvi aªæeK, VC =  = 

¯øvBW K¨vwjcvm© : †h h‡š¿i mvnv‡h¨ †Mvj‡Ki e¨vm Ges AvqZb wbY©q Kiv hvq Zv‡K ¯øvBW K¨vwjcvm© e‡j| ¯øvBW K¨vwjcvm© GKwU DbœZ ai‡bi fvwb©qvi †¯‹j|

e¯‘i ˆ`N©¨, †PvO ev †ej‡bi D”PZv, duvcv b‡ji AšÍe©¨vm I ewne©¨vm, †Mvj‡Ki AvqZb wbY©q Z_v e¨vm, AvqZvKvi e¯‘i AvqZb, wmwjÛvi ev †PvO ev †ej‡bi D”PZv BZ¨vw` wbY©‡q ¯øvBW K¨vwjcvm© e¨eüZ nq|

¯Œz MR : †h h‡š¿ mg e¨vmv‡a©i GKwU ¯Œz _v‡K Zv‡K ¯Œz MR e‡j| Gi Aci bvg gvB‡µvwgUvi|

¯Œz M‡Ri mvnv‡h¨ wbgœwjwLZ KvR¸‡jv Kiv hvqÑ

Lye m~² ˆ`N©¨ gvcv hvq;

Zv‡ii e¨vm wbY©q Kiv hvq;

cv‡Zi cyiæZ¡ wbY©q Kiv hvq;

miæ †Pv‡Oi e¨vmva© wbY©q Kiv hvq|

 

jwNô MYb : ¯Œz M‡Ri e„ËvKvi †¯‹‡ji gvÎ GKfvM Nyiv‡j Zvi T-Gi cÖvšÍ ev ¯ŒzwU hZUzKz m‡i Av‡m Zv‡K ejv nq h‡š¿i jwNô MYb ev jwNôgvb| ¯Œz M‡Ri e„ËvKvi †¯‹jwU‡K GKevi Nyiv‡j

Gi hZUzKz miY N‡U Ges ˆiwLK †¯‹j eivei †h ˆ`N©¨ AwZµg K‡i Zv‡K H h‡š¿i †`Šo ev wcP e‡j| h‡š¿i wcP‡K e„ËvKvi †¯‹‡ji msL¨v Øviv fvM Ki‡j jwNô gvb cvIqv hvq|

myZivs, jwNô MYb = |

 

hvwš¿K ÎæwU : mwVKfv‡e cwigvc Kiv m‡Ë¡I h‡š¿i †h ÎæwUi Kvi‡Y †Kv‡bv e¯‘i mwVK cwigvY cvIqv hvq bv Zv‡K H h‡š¿i hvwš¿K ÎæwU e‡j| G‡K ± e Øviv cÖKvk Kiv nq|

 

¯øvBW K¨vwjcv‡m©i †ÿ‡Î : g~j †¯‹‡ji †Pvqvj I fvwb©qvi †¯‹‡ji †Pvqvj hLb †j‡M _v‡K ZLb mvaviYZ fvwb©qvi †¯‹‡ji k~b¨ `vM cÖavb †¯‹‡ji k~b¨ `v‡Mi mv‡_ wg‡j hvq| hw` fvwb©qvi †¯‹‡ji I g~j †¯‹‡ji k~b¨ `vM bv wg‡j Z‡e H h‡š¿ hvwš¿K ÎæwU i‡q‡Q e‡j g‡b Kiv nq| 

 

¯Œz M‡Ri †ÿ‡Î : e„ËvKvi †¯‹‡ji k~b¨ `vM hLb ˆiwLK †¯‹‡ji k~b¨ `v‡Mi mv‡_ bv wg‡j Z‡e a‡i wb‡Z n‡e h‡š¿ ÎæwU i‡q‡Q| G ÎæwU‡K hvwš¿K ÎæwU ejv nq|

hvwš¿K ÎæwU `yÕcÖKvi| h_v :  abvZ¥K I FYvZ¥K ÎæwU|

 

abvZ¥K ÎæwU : g~j †¯‹‡ji †Pvqvj I fvwb©qvi †¯‹‡ji †Pvqvj ci¯úi †j‡M _vK‡j hw` fvwb©qvi †¯‹‡ji k~b¨ `vM g~j †¯‹‡ji k~b¨ `v‡Mi Wvbw`‡K _v‡K Z‡e Zv‡K abvZ¥K ÎæwU e‡j| G‡ÿ‡Î mwVK cwigv‡ci Rb¨ AvcvZ cwigvc †_‡K hvwš¿K ÎæwU ev` w`‡Z nq| A_©vr mwVK cwigvc = AvcvZ cwigvc − abvZ¥K ÎæwU|

 

FYvZ¥K ÎæwU : g~j †¯‹‡ji †Pvqvj Ges fvwb©qvi †¯‹‡ji †Pvqvj ci¯úi †j‡M _vK‡j hw` fvwb©qvi †¯‹‡ji k~b¨ `vM g~j †¯‹‡ji k~b¨ `v‡Mi evg w`‡K _v‡K Z‡e Zv‡K FYvZ¥K ÎæwU e‡j| G‡ÿ‡Î AvcvZ cwigv‡ci mv‡_ hvwš¿K ÎæwU †hvM K‡i mwVK cwigvc cvIqv hvq| A_©vr mwVK cwigvc = AvcvZ cwigvc + FYvZ¥K ÎæwU|

 

Zzjv hš¿ : †Kv‡bv Aí wRwb‡mi fi m~²fv‡e cwigv‡ci Rb¨ †h hš¿ e¨eüZ nq Zv‡K Zzjv hš¿ e‡j| Zzjv hš¿ c`v_©we`¨v I imvq‡b j¨ve‡iUwi‡Z †Kv‡bv Aí wRwb‡mi fi m~²fv‡e cwigv‡ci Rb¨ e¨eüZ nq|

 

cÖkœ \ 1 \ Avgiv †Kb c`v_©weÁvb coeÑ G m¤ú‡K© GKwU cÖwZ‡e`b iPbv Ki|

DËi : weÁv‡bi PvweKvwV n‡jv c`v_©weÁvb| GwU weÁv‡bi GKwU †gŠwjK kvLv| Gi bxwZ¸‡jvB weÁv‡bi Ab¨vb¨ kvLvmg~‡ni wfwË ˆZwi K‡i‡Q| Avgiv c`v_©weÁvb coe KviYÑ

c`v_©weÁvb cÖK…wZi inm¨ D`NvUb K‡i : c`v_©weÁv‡bi M‡elYv cÖvK…wZK NUbv¸‡jv‡K fv‡jvfv‡e eyS‡Z Ges e¨vL¨v Ki‡Z mvnvh¨ K‡i Ges weÁv‡bi Ab¨vb¨ kvLvq Zvi cÖ‡qvM ¸i“Z¡c~Y© Ae`vb iv‡L| Dwbk kZ‡Ki †klv‡a© B‡jKUª‡bi Avwe®‹vi, B‡jKUªb gvB‡µv‡¯‹v‡ci D™¢veb ev e¯‘weÁvb I †Kvl-Rxewe`¨vq wec­e G‡b‡Q| GKw`‡K c`v_©weÁv‡b †hgb ZË¡ m„wó I MwY‡Zi cÖ‡qvM Av‡Q Aciw`‡K G‡Z e¨envwiK Dbœqb ev weKvk i‡q‡Q| imvqbweÁvb, f~-ZË¡weÁvb, †R¨vwZwe©Ávb, AvenvIqv weÁvb BZ¨vw` m¤ú‡K© †gŠwjK aviYv MVb| GQvov RxeweÁvb, mgy`ªweÁvb, g‡bvweÁvb I wPwKrmvweÁv‡b c`v_©weÁv‡bi c×wZ I hš¿cvwZi cÖPzi e¨envi i‡q‡Q|

c`v_©weÁvb cÖK…wZi wbqg¸‡jv eY©bv K‡i : Avgv‡`i GB cÖvK…wZK RMr ev c„w_ex KZ¸‡jv wbw`©ó wbqg †hgb wbDU‡bi gnvKl© m~Î, kw³i msi¶YkxjZv bxwZ BZ¨vw` †g‡b P‡j| c`v_©weÁvb c‡o cÖK…wZi wbqg¸‡jv m¤ú‡K© Ávb AR©b Ki‡Z cvwi|

c`v_©weÁv‡bi †gŠwjK m~θ‡jv Abymi‡Y cÖhyw³i DbœwZ N‡U : †Uwjwfkb Kx K‡i KvR K‡i, i‡KU Kx K‡i gnvk~‡b¨ D‡o, K…wÎg DcMÖn Kxfv‡e c„w_exi Pvicv‡k †Nv‡i, B›Uvi‡bU w`‡q Kxfv‡e gyn~‡Z© c„w_exi GK cÖvšÍ †_‡K Ab¨cÖv‡šÍ Ny‡i Avmv hvq, †gvevBj †dvb Kxfv‡e KvR K‡i, mve‡gwib Kxfv‡e cvwb‡Z Wz‡e _v‡K BZ¨vw` eyS‡Z n‡j c`v_©weÁv‡bi †gŠwjK m~θ‡jv Rvb‡Z nq| Gme cÖhyw³i D™¢ve‡bi g~‡j KvR Ki‡Q c`v_©weÁv‡b Avwe®‹…Z wbqgvewj|

c`v_©weÁvb Aa¨qb GKwU cÖK…ó gvbweK cÖwk¶Y : Kxfv‡e wPšÍv Ki‡Z nq, KviY `k©v‡Z nq, hyw³ w`‡Z nq, MwYZ‡K Kv‡R jvMv‡Z nq c`v_©weÁvb Zv Avgv‡`i †kLvq| GwU Avgv‡`i Kíbv‡K DÏxß K‡i Ges wPšÍvkw³i weKvk NUvq|

c`v_©weÁvb Avgv‡`i ch©‡e¶Y Ki‡Z †kLvq : Kx K‡i mwVK c×wZMZ ch©‡e¶Y Ki‡Z nq, c`v_©weÁvb cvV K‡i Zv Avgiv wkL‡Z cvwi|

 

cÖkœ \ 2 \ Òwesk kZvãx‡Z c`v_©weÁv‡bi we¯§qKi AMÖMwZ N‡UÓÑ D`vniYmn Gi mc‡¶ hyw³ `vI|

DËi : wesk kZvãx‡Z c`v_©weÁv‡bi we¯§qKi AMÖMwZ N‡U| G kZvãx‡Z g¨v· c­v¼ Avwe®‹vi K‡ib wewKiY msµvšÍ †Kvqv›Uvg ZË¡  Ges AvjevU© AvBb÷vB‡bi Av‡cw¶K ZË¡| wbDwK¬qvm †h wdkb‡hvM¨ Zv I‡Uv nvb I †÷ªmg¨vb wesk kZvãx‡ZB †ei K‡ib| XvKv wek¦we`¨vj‡qi cÖ‡dmi m‡Z¨›`ªbv_ emy c­¨v‡¼i †Kvqv›Uvg Z‡Ë¡i GKwU ï×Zi cÖgvY Dc¯’vcb K‡ib| c`v_©weÁvbx cÖ‡dmi Avãym mvjvg, †kjWb Møv‡kv Ges w÷‡fb IqvBbevM© GKxf‚Z †¶ÎZ‡Ë¡i †ejvq †gŠwjK ej¸‡jv‡K GKÎxKi‡Yi †¶‡Î ZvwoZ `ye©j ej Avwe®‹vi K‡i Amvgvb¨ Ae`vb iv‡Lb wesk kZvãx‡Z| wPwKrmvweÁ‡bi wewfbœ hš¿cvwZ Avwe®‹vi, †ivM wbivg‡qi †¶‡Î I wPwKrmv weÁv‡bi AMÖMwZ‡Z c`v_©weÁvb †i‡L‡Q ¸i“Z¡c~Y© Ae`vb| wesk kZvãx‡Z c`v_©weÁv‡bi Av‡iKwU ¸i“Z¡c~Y© AMÖMwZ gnvk~‡b¨ Awfhvb| A_©vr wesk kZvãx‡Z c`v_©weÁvb we¯§qKifv‡e GwM‡q hvq|

 

cÖkœ \ 3 \ (K) ivwk ej‡Z Kx eySvq?

(L) †gŠwjK ivwk I jä ivwki g‡a¨ cv_©K¨ wb‡`©k Ki|

DËi : 

(K) G †fŠZ RM‡Z hv wKQz cwigvc‡hvM¨ ZvB ivwk| †hgb : ˆ`N©¨, fi, mgq, †eM, Z¡iY, ej BZ¨vw`|

(L) †gŠwjK ivwk I jä ivwki g‡a¨ cv_©K¨ :

†gŠwjK ivwk	jä ivwk
1. †gŠwjK ivwk ¯^vaxb ev wbi‡c¶ Ab¨ ivwki Ici wbf©i K‡i bv|	1. jä ivwk †gŠwjK ivwki Ici wbf©ikxj|
2. †gŠwjK ivwki GKK B‡”Qg‡Zv wbe©vPb Kiv hvq|	2. jä ivwki GKK †gŠwjK ivwki Ici wbf©i K‡i wVK Ki‡Z nq|

 

cÖkœ \ 4 \ (K)GK‡Ki AvšÍR©vwZK c×wZ‡Z †Kvb †Kvb ivwk‡K †gŠwjK ivwk aiv n‡q‡Q?

(L) GB mKj ivwki GK‡Ki bvg Ki|

DËi : (K) GK‡Ki AvšÍR©vwZK c×wZ‡Z mvZwU ivwk‡K †gŠwjK ivwkiƒ‡c wPwýZ Kiv n‡q‡Q| ivwk¸‡jv n‡jv :

ˆ`N©¨ 2. fi 3. mgq 4. ZvcgvÎv 5. Zwor cÖevn 6. `xcb ZxeªZv 7. c`v‡_©i cwigvY

(L) ivwk   GKK (GmAvB)

1. ˆ`N©¨= wgUvi (m)

2. fi     =wK‡jvMÖvg (kg)

3. mgq   =†m‡KÛ (s)

4. ZvcgvÎv=     †Kjwfb (K)

5. Zwor cÖevn=  A¨vw¤úqvi (A)

6. `xcb ZxeªZv  =K¨v‡Ûjv (Cd)

7. c`v‡_©i cwigvY=     †gvj (mol)

 

cÖkœ \ 5 \ gvÎv ej‡Z Kx eyS?

DËi : †Kv‡bv †fŠZ ivwk‡Z Dcw¯’Z †gŠwjK ivwk¸‡jvi m~PK‡K ivwkwUi gvÎv e‡j| †hgb : ej = fi × Z¡iY

 

GLv‡b ˆ`‡N©¨i gvÎv L, f‡ii gvÎv M, mg‡qi gvÎv T emv‡j cvIqv hvq  [MLT⁻²]|

AZGe, ej F n‡j Gi gvÎv [F] = [MLT⁻²]|

⬤◼ Ávbg~jK cÖkœ I DËi ◼⬤

cÖkœ \ 1 \ m~h©MÖnY m¤úwK©Z fwel¨ØvYxi Rb¨ weL¨vZ †K?

DËi : †_wjm m~h©MÖnY m¤úwK©Z fwel¨ØvYxi Rb¨ weL¨vZ|

cÖkœ \ 2 \ cÖK…wZi BwZnvm m¤ú‡K© GKwU GbmvB‡K¬vwcwWqv †j‡Lb †K?

DËi : cÖK…wZi BwZnvm m¤ú‡K© GKwU GbmvB‡K¬vwcwWqv †j‡Lb Avj-gvmy`x|

cÖkœ \ 3 \ K¨vjKzjvm bvgK MwYZ e¨e¯’vi cÖeZ©b K‡ib †K?

DËi : K¨vjKzjvm bvgK MwYZ e¨e¯’vi cÖeZ©b K‡ib m¨vi AvBR¨vK wbDUb|

cÖkœ \ 4 \ cigvYy †h wdkb‡hvM¨ GwU cÖ_g Avwe®‹vi K‡ib †K ev Kviv?

DËi : cigvYy wdkb‡hvM¨ GwU cÖ_g Avwe®‹vi K‡ib weÁvbx I‡Uv nvb I †÷ªmg¨vb|

cÖkœ \ 5 \ Av‡jvi †eM cÖ_g †K wbY©q K‡ib?

DËi : 1675 mv‡j †Wbgv‡K©i †R¨vwZwe©Ávbx Ijd †ivgvi me©cÖ_g Av‡jvi †eM wbY©q K‡ib|

cÖkœ \ 6 \ wkí wec­e Kx?

DËi : Aóv`k kZvãxi ga¨fvM n‡Z Ebwesk kZvãxi ga¨fvM ch©šÍ weª‡U‡bi wk퇶‡Î eû ¸i“Z¡c~Y© cwieZ©b msNwUZ nq| G Af‚Zc~e© cwieZ©b‡K wkí wec­e bv‡g AwfwnZ Kiv nq|

cÖkœ \ 7 \ jä GKK Kx?

DËi : †hme ivwki GKK †gŠwjK ivwki GK‡Ki Ici wbf©i K‡i ev †gŠwjK ivwki GKK †_‡K jvf Kiv hvq Zv‡`i jä GKK e‡j| Nb‡Z¡i GKK  jä GKK|

cÖkœ \ 8 \ †gŠwjK GKK Kx?

DËi : †hme ivwki GKK G‡K A‡b¨i Ici wbf©i K‡i bv eis Hme ivwki GK‡Ki mvnv‡h¨ Ab¨vb¨ ivwki GKK MVb Kiv hvq †mme ivwki GKK‡K †gŠwjK GKK e‡j|

cÖkœ \ 9 \ c`v_©weÁv‡bi g~j j¶¨ Kx? 

DËi : c`v_©weÁv‡bi g~j j¶¨ n‡”Q ch©‡e¶Y, cix¶Y  we‡k­l‡Yi Av‡jv‡K e¯‘ I kw³i iƒcvšÍi I m¤úK© D`NvUb Ges cwigvYMZfv‡e Zv cÖKvk Kiv|

cÖkœ \ 10 \ wbDU‡bi ¯’vb Kv‡ji aviYvq gnvwek¦ Kx wb‡q MwVZ?

DËi : wbDU‡bi ¯’vb Kv‡ji aviYvq gnvwek¦ wÎgvwÎK ¯’vb I GKgvwÎK mgq wb‡q MwVZ|

cÖkœ \ 11 \ GmAvB c×wZ‡Z ˆ`‡N©¨i GKK wba©vi‡Y Av`k© wn‡m‡e Kx aiv nq?

DËi : k~b¨¯’v‡b Av‡jv  †m‡K‡Û †h `~iZ¡ AwZµg K‡i †mB `~iZ¡‡K ˆ`‡N©¨i GKK wba©vi‡Y Av`k© wn‡m‡e aiv nq|

cÖkœ \ 12 \ AvšÍR©vwZK c×wZ‡Z mg‡qi GKK wba©vi‡Y Av`k© wn‡m‡e Kx aiv nq?

DËi : GKwU wmwRqvg −133 cigvYyi 9192631770wU ¯ú›`b m¤úbœ Ki‡Z †h mgq jv‡M †mB mgq‡K mg‡qi GKK wba©vi‡Y Av`k© wn‡m‡e aiv nq|

cÖkœ \ 13 \ AvšÍR©vwZK c×wZ‡Z ZvcgvÎvi GKK †Kjwfb wba©vi‡Y Kx e¨envi Kiv nq?

DËi : cvwbi ˆÎawe›`yi ZvcgvÎvi  fvM‡K ZvcgvÎvi GKK †Kjwfb wba©vi‡Y e¨envi Kiv nq|

cÖkœ \ 14 \ GK A¨vw¤úqvi Kv‡K e‡j?

DËi : k~b¨¯’v‡bi 1 wgUvi `~i‡Z¡ Aew¯’Z Amxg ˆ`‡N©¨i Ges D‡c¶Yxq e„ËvKvi cÖ¯’‡”Q‡`i `ywU mgvšÍivj mij cwievn‡Ki cÖ‡Z¨KwU‡Z †h cwigvY Zwor cÖevn Pj‡j ci¯ú‡ii g‡a¨ cÖwZ wgUvi ˆ`‡N©¨ 2 × 10⁻⁷N ej Drcbœ nq Zv‡K GK A¨vw¤úqvi e‡j|

cÖkœ \ 15 \ GK K¨v‡Ûjv Kv‡K e‡j?

DËi : GK K¨v‡Ûjv n‡”Q †mB cwigvY `xcb ZxeªZv hv †Kv‡bv Av‡jvK Drm GKwU wbw`©ó w`‡K 540 × 10<sup>12</sup> nvR© K¤úv‡¼i GK eY©x wewKiY wbtmiY K‡i Ges H wbw`©ó w`‡K Zvi wewKiY ZxeªZv n‡”Q cÖwZ †÷‡iwWqvb Nb‡Kv‡Y  IqvU|

cÖkœ \ 16 \ GK †gvj Kv‡K e‡j?

DËi : †h cwigvY c`v‡_© 0.012 wK‡jvMÖvg Kve©b-12 G Aew¯’Z cigvYyi mgvb msL¨K cÖv_wgK BDwbU (†hgb : cigvYy, AYy, Avqb, B‡jKUªb BZ¨vw` ev G¸‡jvi wbw`©ó †Kv‡bv MÖ“c) _v‡K Zv‡K GK †gvj e‡j|

cÖkœ \ 17 \ wgUvi †¯‹j Kx?

DËi : cix¶vMv‡i ˆ`N©¨ cwigv‡ci me‡P‡q mij hš¿ n‡jv wgUvi †¯‹j| Gi ˆ`N©¨ 1 wgUvi ev 100 †mw›UwgUvi|

cÖkœ \ 18 \ ˆ`e ΓwU Kv‡K e‡j?

DËi : †Kv‡bv GKwU aª“e ivwk K‡qKevi cwigvc Ki‡j †h ΓwUi Kvi‡Y cwigvcK…Z gv‡b AmvgÄm¨ †`Lv hvq Zv‡K ˆ`e ΓwU e‡j|

cÖkœ \ 19 \ hvwš¿K ΓwU Kv‡K e‡j?

DËi : c`v_©weÁv‡b cix¶‡Yi Rb¨ Z_v gvc-†Rv‡Li Rb¨ Avgv‡`i h‡š¿i cÖ‡qvRb nq| †mB h‡š¿ hw` ΓwU _v‡K Zv‡K hvwš¿K ΓwU e‡j|

cÖkœ \ 20 \ e¨w³MZ ΓwU Kx?

DËi : ch©‡e¶‡Ki wb‡Ri Kvi‡Y cv‡V †h ΓwU Av‡m Zv‡K e¨w³MZ ΓwU e‡j|

cÖkœ \ 21 \ gvÎv Kx?

DËi : †Kv‡bv †fŠZ ivwk‡Z Dcw¯’Z †gŠwjK ivwk¸‡jvi m~PK‡K ivwkwUi gvÎv e‡j|

 

⬤◼ Abyavebg~jK cÖkœ I DËi ◼⬤

 

cÖkœ \ 1 \ †gŠwjK ivwk I jä ivwki cv_©K¨ e¨vL¨v Ki|

DËi : †hme ivwk ¯^vaxb ev wbi‡c¶ Ges †h¸‡jv Ab¨ ivwki Ici wbf©i K‡i bv eis Ab¨vb¨ ivwk G‡`i Ici wbf©i K‡i Zv‡`i †gŠwjK ivwk e‡j| Aciw`‡K, †hme ivwk †gŠwjK ivwki Ici wbf©i K‡i ev †gŠwjK ivwk †_‡K jvf Kiv hvq Zv‡`i jä ivwk e‡j|

†gŠwjK ivwk gvÎ mvZwU, †hLv‡b jä ivwki msL¨v AMwYZ| †gŠwjK ivwki gvÎv cÖKv‡k GKwUgvÎ wPý e¨envi Kiv nq, Aciw`‡K jä ivwki gvÎv cÖKv‡k GKvwaK wP‡ýi e¨envi cÖ‡qvRb nq|

cÖkœ \ 2 \ jä ivwk ej‡Z Kx †evSÑ e¨vL¨v Ki|

DËi : †hme ivwk †gŠwjK ivwki Ici wbf©i K‡i ev †gŠwjK ivwk †_‡K jvf Kiv hvq Zv‡`i‡K jä ivwk e‡j|

†hgb : Z¡iY =  = | 

Z¡iY ivwkwU `~iZ¡ I mgq GB `ywU †gŠwjK GKK †_‡K jvf Kiv hvq| ZvB Z¡iY GKwU jä ivwk|

cÖkœ \ 3 \ GK‡Ki ¸wYZK I Dc¸wYZK †Kb e¨envi Kiv nq e¨vL¨v Ki|

DËi : c`v_©weÁv‡bi eûmsL¨K k~b¨hy³ gvbmg~n mvaviYfv‡e †jLvi mgq Avgv‡`i mveavb _vK‡Z n‡e cÖwZ‡¶‡Î k~‡b¨i msL¨v wVKg‡Zv D‡j­L Kiv n‡q‡Q wKbv| wKš‘ GB msL¨vwU‡KB hw` Avgiv GK‡Ki DcmM© e¨envi K‡i wjwL, Zvn‡j A‡bK myweavRbK, msw¶ß I wbfz©jfv‡e †jLv m¤¢e nq| 

†hgb : 0.00001m ivwkwU‡K †jLv †h‡Z cv‡i 10ìm|

cÖkœ \ 4 \ e‡ji gvÎv MLT⁻² Ñ e¨vL¨v Ki|

DËi : e‡ji gvÎv = MLT⁻² =  = ×

myZivs ej ivwkwU fi, ˆ`N©¨ Ges mgq-G wZbwU †gŠwjK ivwki Ici wbf©i K‡i e‡j GwU jä ivwk Ges Gi GKK wbDUb =  

= kgms⁻²

cÖkœ \ 5 \ GKB ivwki GKvwaKevi cwigvcK…Z gv‡b AmvgÄm¨Zv Gov‡Z Kx Ki‡Z n‡e?

DËi : †Kv‡bv GKwU aª“e ivwk K‡qKevi cwigvc Ki‡j †h ΓwUi Kvi‡Y cwigvcK…Z gv‡b AmvgÄm¨Zv †`Lv †`q Zv n‡jv ˆ`e ΓwU| myZivs ˆ`e ΓwU‡K Kwg‡q Avb‡Z n‡j Z_v GKvwaKevi cwigvcK…Z gv‡b AmvgÄm¨Zv Gov‡Z cwigvcwU evi evi wb‡q G‡`i Mo wb‡Z nq|

cÖkœ \ 6 \ wbDUb jä GKK †Kb?

DËi : Avgiv Rvwb, e‡ji GKK = f‡ii GKK × 

ev, 1 wbDUb = ×

GLv‡b, ej GKwU jä ivwk hv wZbwU †gŠwjK ivwk fi, `~iZ¡ Ges mg‡qi mv‡_ m¤úwK©Z| fi, `~iZ¡ Ges mg‡qi GKK (†gŠwjK GKK) †_‡K e‡ji GKK wbY©q Kiv hvq| ZvB e‡ji GKK wbDUb GKwU jä GKK|

cÖkœ \ 7 \ gvÎv mgxKi‡Yi cÖ‡qvRbxqZv D‡j­L Ki|

DËi : c`v_©weÁv‡b gvÎv mgxKi‡Yi cÖ‡qvRbxqZv Acwimxg| †hme Kvi‡Y gvÎv mgxKi‡Yi cÖ‡qvRbxqZv i‡q‡Q wb‡P Zv D‡j­L Kiv n‡jv :

†h‡Kv‡bv †fŠZ ivwki GKK wbY©q Kiv hvq|

GKK‡K GK c×wZ †_‡K Ab¨ c×wZ‡Z iƒcvšÍi Kiv hvq|

wewfbœ ivwki mgxKiY MVb Kiv hvq|

†h‡Kv‡bv †fŠZ ivwki mgxKi‡Yi wbfz©jZv ev mZK©Zv hvPvB Kiv hvq|

†Kv‡bv †fŠZ mgm¨v mgvavb Kiv hvq|

cÖkœ \ 8 \ GmAvB (SI) GKK ej‡Z Kx †evSvq?

DËi : GmAvB GK‡Ki cy‡iv bvg International system of units| evsjvq ejv nq GK‡Ki AvšÍR©vwZK c×wZ| G International system ev AvšÍR©vwZK c×wZ‡K ms‡¶‡c †evSv‡Z SI (GmAvB) e¨envi Kiv nq|

ˆ`bw›`b KvRKg© I e¨emv evwY‡R¨i Kvi‡Y cÖvPxbKvj †_‡KB gvc-†Rv‡Li cÖPjb wQj| G gvc-†Rv‡Li Rb¨ wewfbœ ivwki ¯’vbxq ev GjvKvwfwËK eû GK‡Ki cÖPjb wQj| ˆeÁvwbK Z‡_¨i Av`vb-cÖ`vb I e¨emv evwY‡R¨i cÖmv‡ii Rb¨ mvivwe‡k¦ gvcІRv‡Li GKB iKg Av`‡k©i cÖ‡qvRb n‡q c‡o| G ZvwM‡` 1960 mvj †_‡K `ywbqv †Rvov wewfbœ ivwki GKB iKg GKK Pvjy Kivi wm×všÍ nq| GK‡Ki G c×wZ‡K ejv nq GK‡Ki AvšÍR©vwZK c×wZ ev ms‡¶‡c GmAvB (SI)|

cÖkœ \ 9 \ ¯Œz M‡Ri ΓwU e¨vL¨v Ki|

DËi : ¯Œzi gv_v hLb ¯’vqx KxjK ev mgZj cÖvšÍ ¯úk© K‡i ZLb e„ËvKvi †¯‹‡ji k~b¨ `vM ˆiwLK †¯‹‡ji k~b¨ `v‡Mi mv‡_  wg‡j  hvIqv  DwPZ|  hw` bv  wg‡j Zvn‡j eyS‡Z n‡e hvwš¿K ΓwU i‡q‡Q| e„ËvKvi †¯‹‡ji k~b¨ `vM hw` ˆiwLK †¯‹‡ji k~b¨ `v‡Mi wb‡P _v‡K Zvn‡j hvwš¿K ΓwU n‡e abvZ¥K (+e) Avi hw` e„ËvKvi †¯‹‡ji k~b¨ `vM ˆiwLK †¯‹‡ji k~b¨ `v‡Mi Dc‡i _v‡K Zvn‡j hvwš¿K ΓwU n‡e FYvZ¥K (−e)|

cÖkœ \ 10 \ hvwš¿K ΓwU ej‡Z Kx †evS?

DËi : ¯­vBW Kvwjcv‡m©i †¶‡Î, g~j †¯‹‡ji †Pvqvj I fvwb©qvi †¯‹‡ji †Pvqvj hLb †j‡M _v‡K ZLb mvaviYZ fvwb©qvi †¯‹‡ji k~b¨ `vM cÖavb †¯‹‡ji k~b¨ `v‡Mi mv‡_ wg‡j hvq| hw` fvwb©qvi †¯‹‡ji G g~j †¯‹‡ji k~b¨ `vM bv wg‡j Z‡e H h‡š¿ hvwš¿K ΓwU i‡q‡Q e‡j g‡b Kiv nq| Avevi ¯Œz M‡Ri †¶‡Î, e„ËvKvi †¯‹‡ji k~b¨ `vM hLb ˆiwLK †¯‹‡ji k~b¨ `v‡Mi mv‡_ bv wg‡j Z‡e a‡i wb‡Z n‡e h‡š¿ ΓwU i‡q‡Q| G ΓwU‡KB hvwš¿K ΓwU ejv nq|

cÖkœ \ 11 \ jwNô MYb ej‡Z Kx †evS?

DËi : ¯Œz M‡Ri e„ËvKvi †¯‹‡ji gvÎ GKfvM Nyiv‡j ¯ŒzwU hZUzKz m‡i Av‡m Zv‡K ejv nq h‡š¿i jwNô MYb ev jwNôgvb|

¯Œz M‡Ri mvnv‡h¨ cvV †bIqvi Av‡M jwNô gvb wbY©q Ki‡Z nq| e„ËvKvi †¯‹‡ji k~b¨ `v‡Mi mv‡_ ˆiwLK †¯‹‡ji k~b¨ `vM wgwj‡q wb‡Z nq| e„ËvKvi †¯‹jwU‡K GKevi Nyiv‡j Gi hZUzKz miY N‡U Ges ˆiwLK †¯‹j eivei †h ˆ`N©¨ AwZµg K‡i Zv‡K H h‡š¿i †`Šo ev wcP e‡j| h‡š¿i wcP‡K e„ËvKvi †¯‹‡ji msL¨v Øviv fvM Ki‡j jwNô gvb cvIqv hvq|

cÖkœ \ 12 \ †Kv‡bv ¯Œz M‡Ri jwNô MYb 0.01 wgwg ej‡Z Kx †evSvqÑ e¨vL¨v Ki|

DËi : †Kv‡bv ¯Œz M‡Ri jwNô MYb 0⋅01 wgwg ej‡Z †evSvq e„ËvKvi †¯‹‡ji gvÎ GK fvM Nyiv‡j Gi cÖvšÍ ev ¯ŒzwU 0.01 wgwg cwigvY m‡i Av‡m| G‡¶‡Î hš¿wUi wcP Ges e„ËvKvi †¯‹‡ji fvMmsL¨vi Abycv‡Zi gvb 0⋅01 wgwgi mgvb| 

myZivs e„ËvKvi †¯‹‡ji fvMmsL¨v 100 n‡j wc‡Pi gvb = 100 × 0⋅01 wgwg = 1 wgwg|

cÖkœ \ 13 \ fvwb©qvi aª“eK ej‡Z Kx †evSÑ e¨vL¨v Ki|

DËi : ¯­vBW K¨vwjcv‡m© cÖavb †¯‹‡ji ¶z`ªZg GK fv‡Mi †P‡q fvwb©qvi †¯‹‡ji GK fvM hZUzKz †QvU Zvi cwigvY‡K fvwb©qvi aª“eK e‡j| 

†hgb : fvwb©qv‡ii 10 fvM cÖavb †¯‹‡ji 9 ¶z`ªZg fv‡Mi mgvb n‡j fvwb©qvi cÖwZwU fv‡Mi ˆ`N©¨ = 0⋅9 wgwg Ges G‡¶‡Î fvwb©qvi aª“eK, VC =  wgwg = 0⋅1 wgwg = 0⋅01 †mwg|

 

cÖ_g Aa¨vq

†fŠZ ivwk I cwigvc

 

¸iæZ¡c~Y© enywbe©vPwb cÖ‡kœvËi

weÁv‡bi †Kvb kvLv c`v_© I kw³ wb‡q Av‡jvPbv K‡i?      (Abyaveb)

⬤ c`v_©weÁvb          L Dw™¢`weÁvb

M imvqb    N cÖvwYweÁvb 

c`v_©weÁvb‡K cÖavbZ KqwU kvLvq fvM Kiv n‡q‡Q?           (Ávb) 

K 7wU        L 9wU

⬤ 10wU       N 11wU

†jvW‡÷v‡bi Ô†PŠ¤^K ag©Õ m¤ú‡K© †K Rvb‡Zb?      (Ávb) 

⬤ †_wjm      L wc_v‡Mvivm 

M †W‡gvwµUvm         N A¨vwi÷vK©vm

cigvYyi cÖv_wgK aviYv †`b †K? (Ávb)

K wc_v‡Mvivm          ⬤ †W‡gvwµUvm

M Be‡b wmbv          N Avj nv‡Rb

avZzi †fRvj wbY©‡qi †KŠkj Avwe®‹vi K‡ib †K?     (Ávb)

K †_wjm     L A¨vwi÷vK©vm

M M¨vwjwjI ⬤ AvwK©wgwWm 

c`v_©weÁv‡bi g~j wfwË †Kvb bxwZ‡K ejv nq?       (Ávb)

⬤ kw³i msi¶YkxjZv bxwZ      L ej e„w×KiY bxwZ

M wjfv‡ii bxwZ       N AvwK©wgwW‡mi bxwZ

Av‡jvK Z‡Ë¡i †¶‡Î Kvi Ae`vb D‡j­L‡hvM¨?       (Ávb) 

K Avj wei“bx           L Avj gvmy`x 

⬤ Be‡b Avj nvB_vg   N iRvi †eKb

U‡jwgi gZev‡`i we‡ivwaZv K‡ib †K?    (Ávb)

⬤ Avj nv‡Rb           L Be‡b Avj nvB_vg

M U‡jwg     N Avj wei“bx

Avj gvmy`x GbmvB‡K¬vwcwWqv †j‡Lb †Kvb wel‡qi Ici?       (Ávb)

⬤ cÖK…wZi BwZnvm      L Bmjv‡gi BwZnvm 

M wMÖK mf¨Zvi BwZnvm         N †ivgvb mf¨Zvi BwZnvm

evqyK‡ji D‡j­L cvIqv hvq †Kvb eB‡q?    (Ávb)

K †R‡biv cøvbUvivg   ⬤ cÖK…wZi BwZnvm

M Avj wRei Iqvj gyKvwejv     N AwiwRb Ae w¯úwmm

cix¶vg~jK ˆeÁvwbK c×wZi cÖe³v †K? (Ávb)

K U‡jwg     ⬤ iRvi †eKb

M wjDbv‡`©v `¨ wfw  N ievU© ûK

wjDbv‡`©v `¨ wfw Kx wQ‡jb?    (Ávb)

K b„Z¨ wkíx L weÁvbx

M MwYZwe` ⬤ wPÎwkíx

Av‡jvi †eM cwigvc K‡ib †K?   (Ávb)

K ievU© e‡qj          L †Kcjvi

M M¨vwjwjI ⬤ †ivgvi

†K e„n¯úwZi GKwU DcMÖ‡ni MÖnY ch©‡e¶Y K‡i Av‡jvi †eM cwigvc K‡ib?        (Ávb)

K †Kcjvi   ⬤ †ivgvi

M M¨vwjwjI N Wv. wMjevU©

†KvcviwbKv‡mi †mŠi‡Kw›`ªK aviYvi MvwYwZK eY©bv †`b †K? (Ávb)

⬤ †Kcjvi    L UvB‡Kveªv‡ni

M †KvcviwbKvm        N wbDUb

e¯‘i cZ‡bi wbqg-Gi Avwe®‹vi‡Ki bvg Kx?         (Ávb)

⬤ M¨vwjwjI   L AvwK©wgwWm

M AvBb÷vBb         N wbDUb

m„wZwe`¨vi wfwË ¯’vcb K‡i †K? (Ávb)

K AvBb÷vBb         L U‡jwg 

M A¨vwi÷Uj           ⬤ M¨vwjwjI

miY, MwZ, Z¡iY, mgq BZ¨vw`i g‡a¨ m¤úK© ¯’vcb K‡ib †K?      (Ávb)

K wbDUb    ⬤ M¨vwjwjI

M wc_v‡Mvivm          N gnvexi

M¨vwjwjIi D™¢vweZ ˆeÁvwbK c×wZ‡K c~Y©Zvi iƒc cÖ`vb K‡ib †K?      (Ávb)

K †Kcjvi   L iRvi †eKb

⬤ wbDUb     N AvwK©wgwWm

Òc`v‡_©i AwefvR¨ GKK cigvYyÓÑ †K G aviYv †`b?         (Ávb)

K AvwK©wgwWm          L A¨vwi÷vK©vm

⬤ †W‡gvwµUvm          N iRvi †eKb 

ejwe`¨v Avwe®‹vi K‡ib †Kvb weÁvbx?      (Ávb)

K M¨vwjwjI L AvBb÷vBb

M g¨v· c­¨v¼         ⬤ wbDUb

M¨vwjwjI KZ mv‡j Rb¥MÖnY K‡ib?        (Ávb)

K 1442     L 1464

⬤ 1564      N 1674 

wb‡Pi †KvbwU wkí wec­‡e ¸i“Z¡c~Y© f‚wgKv cvjb K‡iwQj?       (D”PZi `¶Zv)

K evqyKj    L evqyev®ú

⬤ ev®úxq BwÄb         N BD‡iwbqvg

KZ mv‡j g¨v·I‡qj Av‡jvi ZvwoZ‡PŠ¤^K Zi½ ZË¡ cÖ`vb K‡ib?      (Ávb)

K 1831     L 1858

⬤ 1864      N 1884 

1896 mv‡j Zwor †PŠ¤^K Zi½ e¨envi K‡i AwaK `~i‡Z¡ †gvm©‡Kv‡W ms‡KZ cvVvb †K?      (Ávb)

K †nbwiL nvR©         L †jR

⬤ gvK©bx     N RM`xk P›`ª emy 

RM`xk P›`ª emy †Kvb †`‡ki weÁvbx wQ‡jb?         (Ávb)

K fviZ     L Pxb

⬤ evsjv‡`k  N BZvwj

†Kvqv›Uvg ZË¡ KLb Avwe®‹…Z nq?           (Abyaveb)

K Aóv`k kZvãx‡Z  L Ebwesk kZvãxi †k‡l

⬤ wesk kZvãxi ïi“‡Z N wesk kZvãxi †k‡l

†Kvqv›Uvg ZË¡ Avwe®‹vi K‡ib †K?          (Ávb)

K g¨v·I‡qj           L nvB‡Mb 

⬤ g¨v· c­¨v¼          N wbDUb 

Av‡b©÷ iv`vi‡dvW© cigvYy welqK †h ZË¡ cÖ`vb K‡ib Zvi bvg Kx?      (Ávb)

K iv`vi‡dvW© ZË¡      L †evi ZË¡ 

M †Kvqv›Uvg ZË¡       ⬤ wbDK¬xq ZË¡

nvB‡Wªv‡Rb cigvYyi B‡jKUªb ¯Í‡ii aviYv cÖ`vb K‡ib †K?   (Ávb)

K Rb Wvëb           L Av‡b©÷ iv`vi‡dvW© 

M †e‡K‡ij ⬤ wbjm †evi

wbDwK¬qvm wdkb‡hvM¨ GwU †h Avwe®‹vi K‡ibÑ       (Ávb)

K I‡Uv nvb I cø¨v¼  L †nbix I †÷ªmg¨vb

M †nbix I †jÄ       ⬤ I‡Uv nvb I †÷ªmg¨vb

m‡Z¨›`ªbv_ emy †Kvb wek¦we`¨vj‡qi cÖ‡dmi wQ‡jb? (Ávb)

K A·‡dvW© L K¨vwj‡dvwb©qv

M KjKvZv  ⬤ XvKv

c­¨v‡¼i †Kvqv›Uvg Z‡Ë¡i ï×Zi cÖgvY Dc¯’vcb K‡ib †K?   (Ávb)

K g¨v·I‡qj           L Ave`ym mvjvg 

M m‡Z¨›`ªbv_ `Ë     ⬤ m‡Z¨›`ªbv_ emy

m‡Z¨›`ªbv_ emyi ZË¡ Kx bv‡g cwiwPZ?     (Ávb)

K Rywj I Kzwi ZË¡     ⬤ †evm-AvBb÷vBb msL¨vqb

M emy ZË¡   N Av‡cw¶K ZË¡

ZvwoZ `ye©j ej Avwe®‹v‡ii Rb¨ †bv‡ej cyi¯‹vi †`Iqv nq KZ Rb‡K?       (Ávb)

K `yB        ⬤ wZb

M Pvi        N cuvP 

ZvwoZ `ye©j ej Avwe®‹v‡ii Rb¨ †bv‡ej cyi¯‹vi †`Iqv nq Dcgnv‡`‡ki †Kvb weÁvbx‡K?   (Ávb)

K P›`ª‡kLi igb       ⬤ Ave`ym mvjvg

M m‡Z¨›`ªbv_ emy      N m¨vi RM`xk P›`ª emy

igbcÖfve †Kvb †`‡ki weÁvbxi Avwe®‹vi? (Ávb)

⬤ fviZ      L cvwK¯Ívb

M Av‡gwiKv N  †¯úb

†Kvb kZvãx‡Z gnvk~b¨ Awfhvb cwiPvjbv Kiv nq? (Abyaveb)

K Ebwesk   ⬤ wesk

M GKwesk  N Aóv`k

AvenvIqvi c~e©vfvm `v‡b f‚wgKv ivL‡QÑ    (Abyaveb)

K †Uwjwfkb L †iwWI

⬤ K…wÎg DcMÖn         N AvBc¨vW

gvbyl Puv‡` c`vc©Y K‡i †Kvb kZvãx‡Z?   (Ávb)

K Aóv`k   L Ebwesk

⬤ wesk       N GKwesk

cvwLi Iov †`‡L D‡ovRvnv‡Ri g‡Wj ˆZwi K‡ib †K?         (Ávb)

K iRvi †eKb         ⬤ wjDbv‡`©v `¨ wfwÂ

M Igi ˆLqvg         N ivBU åvZ…Øq

cigvYyi cÖv_wgK aviYv †`b †K?  (Ávb)

K wbDUb    L †eKb

⬤ †W‡gvwµUvm          N wc_v‡Mvivm

avZzi †fRvj wbY©q Ki‡Z cÖ_g †K mg_©  jvf K‡ib?          (Ávb)

⬤ AvwK©wgwWm L A¨vwi÷Uj

M A¨vwi÷vK©vm        N wc_v‡Mvivm

†Kvb weÁvbx K¨vjKzjvm Avwe®‹vi K‡ib?   (Ávb)

K wc_v‡Mvivm          M AvBb÷vBb

⬤ wbDUb     N w÷‡db nwKs

nvB‡Wªv‡Rb cigvYyi B‡jKUªb ¯Í‡ii aviYv †`b †K? (Ávb)

K iv`vi‡dvW©           ⬤ wbjm †evi

M wW eªMwj  N †e‡K‡ij

†K cigvYy welqK wbDK¬xq ZË¡ cÖ`vb K‡ib?         (Ávb)

⬤ Av‡b©÷ iv`vi‡dvW©  L wbjm& †evi

M K¬vK© g¨v·I‡qj     N g¨v· c­¨v¼

†K wjfv‡ii bxwZ Avwe®‹vi K‡ib?          (Ávb)

⬤ AvwK©wgwWm L A¨vwi÷Uj

M wc_v‡Mvivm          N M¨vwjwjI

Av‡jvi Zwor Pz¤^Kxq Z‡Ë¡i weKvk NUvb †K?        (Ávb)

⬤ K¬vK© g¨v·I‡qj      K †nbwiL nvR©

M gvB‡Kj d¨viv‡W   N †nbix

me©cÖ_g †K Zwor‡Kvl Avwe®‹vi K‡ib?     (Ávb)

K mvBgb Ing         L ievU© wKikd

M Av‡jmv‡›`ªv †fvëv   ⬤ I‡qi‡÷W

fviZxq †Kvb weÁvbx c`v‡_©i ¶z`ªZg KYvi bvg †`b cigvYy? (Ávb) 

K KYv`     L Avh©fÆ

⬤ eivn wgwni           N gnvexi

Òch©‡e¶Y, cix¶Y Ges myk„•Ljfv‡e †fŠZ ivwki msÁv_© I G‡`i g‡a¨ m¤úK© wba©viY ˆeÁvwbK K‡g©i g~jwfwËÓ|Ñ Dw³wU Kvi?      (Ávb)

⬤ M¨vwjwjI   L wbDUb

M wc_v‡Mvivm          N U‡jwg

me©cÖ_g evqyK‡ji aviYv †`b †K?           (Ávb)

K Avj dvRvix         L AvwK©wgwWm

⬤ Avj gvmy`x N †Kcjvi

e¯‘i cZ‡bi wbqg I m„wZwe`¨vi wfwË ¯’vcb K‡ib †K?        (Ávb)

K wbDUb    ⬤ M¨vwjwjI

M AvwK©wgwWm          N †Kcjvi

weÁv‡b ¸i“Z¡c~Y© welq n‡jvÑ      (Abyaveb)

⬤ Ávb       L c×wZ

M `„wófw½ N cwiKíbv

Rvg©vb weÁvbx †mœj Avwe®‹vi K‡ibÑ        (Abyaveb)

K Av‡jvi cÖwZdj‡bi m~Π      L Av‡jvi Zi½ZË¡

⬤ Av‡jvi cÖwZmi‡Yi m~Π        N Av‡jvi †Kvqv›Uvg ZË¡

`ye©j wbDK¬xq ej Ges we`y¨r †PŠ¤^K ejØq‡K GKB e‡ji `ywU wfbœiƒc cÖgvY K‡ibÑ (Abyaveb)

K cÖ‡dmi mvjvg       L w÷‡fb IqvBbevM©

M †kjWb Møv‡kv       ⬤ Dc‡ii me

g¨v· c­¨v¼ n‡jbÑ     (Abyaveb)

⬤ †Kvqv›Uvg Z‡Ë¡i cÖwZôvZv     L Zwor Pz¤^K Z‡Ë¡i cÖwZôvZv

M Av‡cw¶K Z‡Ë¡i cÖwZôvZv    N Zi½ Z‡Ë¡i cÖwZôvZv

m~h©MÖnY m¤úwK©Z fwel¨ØvYxi Rb¨ weL¨vZ n‡jbÑ    (Abyaveb)

⬤ †_wjm      L wc_v‡Mvivm

M †KvcviwbKvm        N M¨vwjwjI

†K NUbv ev m‡Z¨i ch©‡e¶‡Yi Ici †ewk ¸i“Z¡ Av‡ivc Ki‡Zb?      (Abyaveb) 

⬤ d«vwÝm †eKb        L M¨vwjwjI

M A¨vwi÷Uj           N wbDUb

wesk kZvãx‡Z Avwe®‹…Z nq †KvbwU?        (Abyaveb)

K cøeZv      L GUg

M wjfvi bxwZ          ⬤ AvB‡mv‡Uvc

Av‡jvi Zwor Pz¤^Kxq Z‡Ë¡i weKvk NUvb †K?        (Abyaveb)

K †nbwiL nvR©         ⬤ †Rgm K¬vK© g¨v·I‡qj

M †jÄ       N gvB‡Kj d¨viv‡W

wc_v‡Mviv‡mi ev`¨hš¿ I msMxZ welqK †¯‹‡ji †h Ae`vbÑ     (cÖ‡qvM)

⬤ Zv‡ii K¤úb welqK           L Zv‡ii fi welqK

M Zv‡ii AvKl©Y welqK         N Zv‡ii cÖmviY welqK

AvwK©wgwWm †Mvjxq `c©‡Y m~‡h©i iwk¥ †K›`ªxf‚Z K‡i †KŠkj Avwe®‹vi K‡ibÑ         (cÖ‡qvM)

K we`y¨r Drcv`‡bi    ⬤ Av¸b aiv‡bvi

M Zvc Drcv`‡bi     N Av‡jv Drcv`‡bi

cigvYy wdkb‡hvM¨ Avwe®‹vi K‡i cvigvYweK †evgvi m~Pbv K‡ib cÖ_gÑ         (D”PZi `ÿZv)

K I‡Uv nvb  L †÷ªmg¨vb

M iv`vi‡dvW©          ⬤ I‡Uv nvb I †÷ªmg¨vb

Zi½ e¨envi K‡i AwaK `~i‡Z¡ †gvm©‡Kv‡W ms‡KZ cvVv‡bvi e¨e¯’v D™¢veb K‡i †eZvi †hvMv‡hv‡Mi Rb¥`vb K‡ibÑ      (Ávb)

⬤ gvK©bx     L †nbwiL nvR©

M K¬vK© g¨v·I‡qj     N gvB‡Kj d¨viv‡W

Avwe®‹vi−Avwe®‹vi‡Ki bvg n‡jvÑ  (cÖ‡qvM)

ev®úxq BwÄb − †Rgm IqvU

†Kvqv›Uvg ZË¡ − g¨v·cø¨v¼

G·‡i − i›U‡Rb

wb‡Pi †KvbwU mwVK?

K i I ii     L ii I iii

M i I iii    ⬤ i, ii I iii

wbDwK¬qvm wdDkb‡hvM¨ Avwe®‹v‡ii mv‡_ m¤úK© Av‡QÑ     (Abyaveb)

I‡Uv nvb

wbDUb

†÷ªmgvb

wb‡Pi †KvbwU mwVK?

K i I ii     L ii I iii

⬤ i I iii     N i, ii I iii

AvaywbK c`v_©weÁv‡b ¯’vb-Kv‡ji aviYvq cwieZ©b G‡b‡QÑ     (Abyaveb)

†evi ZË¡

†Kvqv›Uvg ZË¡

Av‡cwÿK ZË¡

wb‡Pi †KvbwU mwVK?

K i I ii     ⬤ ii I iii

M i I iii    N i, ii I iii

wbDU‡bi g‡ZÑ         (cÖ‡qvM)

¯’vb n‡”Q wÎgvwÎK

¯’v‡bi †Kv‡bv ïiæ ev †kl †bB

mg‡qi ïiæ Av‡Q ev †kl †bB

wb‡Pi †KvbwU mwVK?

⬤ i I ii      L ii I iii

M i I iii    N i, ii I iii

weÁvbx‡`i bv‡gi mv‡_ Avwe®‹v‡ii wgj †`Lv hvqÑ   (Abyaveb)

i›U‡Rb-G·‡i

†e‡K‡ij-†ZRw¯ŒqZv

g¨v· c­¨v¼-†Kvqv›Uvg ZË¡

wb‡Pi †KvbwU mwVK? 

K i I ii     L i I iii

M ii I iii   ⬤ i, ii I iii

†_wjm m¤ú‡K© mwVK Dw³ n‡jvÑ            (Abyaveb)

†_wjm m~h©MÖnY m¤úwK©Z fwel¨r evYx K‡i

†_wjm †jvW‡÷v‡bi †PŠ¤^K ag© m¤ú‡K© Rvb‡Zb

K¤úgvb Zv‡ii Ici †_wj‡mi KvR ¯’vqx Ae`vb †i‡LwQj

wb‡Pi †KvbwU mwVK?

⬤ i I ii      L i I iii

M ii I iii   N i, ii I iii

Av‡jvK Z‡Ë¡i †¶‡Î D‡j­L‡hvM¨ Ae`vb iv‡LbÑ     (Abyaveb)

Avj-gvmy`x

Avj nv‡Rb

Be‡b Avj nvB_vg

wb‡Pi †KvbwU mwVK?

K i I ii     ⬤ i I iii

M ii I iii   N i, ii I iii

·qv`k kZvãx †_‡K †lvok kZvãx ch©šÍ weÁv‡b Ae`vb iv‡LbÑ                (Abyaveb)

nvB‡Mb

iRvi †eKb

wjDbv‡`©v `¨ wfwÂ

wb‡Pi †KvbwU mwVK?

K i I ii     L i I iii

⬤ ii I iii    N i, ii I iii

wbDUb Zvi we¯§qKi cÖwZfvi Øviv Avwe®‹vi K‡ibÑ (Abyaveb)

ejwe`¨vi weL¨vZ wZbwU m~Î

m„wZwe`¨v

wek¦Rbxb gnvKl© m~Î

wb‡Pi †KvbwU mwVK?

K i I ii     ⬤ i I iii

M ii I iii   N i, ii I iii

ZvwoZ‡PŠ¤^K Zi‡½i gva¨‡g GK¯’vb †_‡K Ab¨¯’v‡b kw³ †cÖi‡Y m¶g nbÑ    (Abyaveb)

gvK©bx

K¬vK© g¨v·I‡qj

RM`xk P›`ª emy

wb‡Pi †KvbwU mwVK?

K i I ii     ⬤ i I iii

M ii I iii   N i, ii I iii

Ebwesk kZvãxi †k‡li w`‡K c`v_©weÁv‡b Amvgvb¨ Ae`vb iv‡LbÑ      (Abyaveb)

wbjm †evi 

†e‡K‡ij 

i›U‡Rb

wb‡Pi †KvbwU mwVK?

⬤ i I ii      L i I iii

M ii I iii   N i, ii I iii

Ò†evm-AvBb÷vBb msL¨vqbÓ Gi mv‡_ RwoZÑ      (Abyaveb)

m¨vi RM`xk P›`ª emy

A¨vjevU© AvBb÷vBb

m‡Z¨›`ªbv_ emy

wb‡Pi †KvbwU mwVK?

K i I ii     L i I iii

⬤ ii I iii    N i, ii I iii

ZvwoZ `ye©j ej Avwe®‹vi K‡ibÑ            (Abyaveb)

Ave`ym mvjvg

w÷‡fb IqvBbevM©

†kjWb M­v‡kv

wb‡Pi †KvbwU mwVK? 

K i I ii     ⬤ i I iii

M ii I iii   N i, ii I iii

Aóv`k kZvãxi ga¨fvM n‡Z Ebwesk kZvãxi ga¨fvM ch©šÍ Bsj¨v‡Û wkí wec­e msNwUZ nq| KviYÑ   (D”PZi `¶Zv)

†fŠZweÁv‡bi weKvk N‡U d‡j KvwiMwi †¶‡Î bvUKxq DbœwZ mvwaZ nq

weÁvbx‡`i M‡elYvjä wel‡qi mvnv‡h¨ wewfbœ hš¿cvwZi Avwe®‹vi nq

wkícwÊZiv weÁvb mvabvi †cQ‡b wewb‡qvM K‡ib

wb‡Pi †KvbwU mwVK?

K i I ii     L i I iii

M ii I iii   ⬤ i, ii I iii

cigvYyi wbDwK¬qvm AvwnZ _v‡KÑ            (Abyaveb)

K FYvZ¥Kfv‡e        L wbðjfv‡e

⬤ abvZ¥Kfv‡e         N wbi‡c¶fv‡e

wbDwK¬qvm Kx Øviv MwVZ?         (D”PZi `¶Zv)

K B‡jKUªb I †cÖvUb L B‡jKUªb I wbDUªb

M †cÖvUb I †evmb     ⬤ †cÖvUb I wbDUªb

B‡jKUªb wbDwK¬qv‡mi †Kv_vq †Nv‡i?       (Abyaveb)

K Dc‡i     L wb‡P

M †fZ‡i    ⬤ Pvicv‡k

ÔcigvYyi wbDwK¬qvm abvZ¥Kfv‡e AvwnZÕ GwU †Kvb kZ‡Ki Avwe®‹vi?     (Abyaveb)

K Ebwesk kZvãxi †k‡l        ⬤ wesk kZvãxi ïi“‡Z

M wesk kZvãxi †k‡l N GKwesk kZvãxi ïi“‡Z

c`v_©weÁv‡bi we¯§qKi AMÖMwZ N‡U †Kvb kZvãx‡Z?          (Ávb)

K Aóv`k kZvãx‡Z  ⬤ cÂ`k kZvãx‡Z

M wesk kZvãx‡Z      N Ebwesk kZvãx‡Z

cÖK…wZi †gŠwjK wbqg¸‡jv Avwe®‹vi †Kvb weÁv‡bi Ae`vb?     (Abyaveb)

⬤ c`v_©weÁvb          L †R¨vwZwe©`¨v

M RxeweÁvb           N f‚we`¨v

c`v_©weÁv‡bi cÖK…Z D‡Ïk¨ n‡”QÑ          (D”PZi `ÿZv)

cÖK…wZi inm¨ D`NvUb Kiv

cÖK…wZi wbqg¸‡jv Abyaveb Kiv

cÖvK…wZK NUbv¸‡jv e¨vL¨v Kiv

wb‡Pi †KvbwU mwVK? 

K i I ii     L i I iii

M ii I iii   ⬤ i, ii I iii

c`v_©weÁvb Avgv‡`iÑ (Abyaveb)

Kíbv‡K DÏxß K‡i

ch©‡e¶Y ¶gZv e„w× K‡i

wPšÍvkw³i weKvk NUvq

wb‡Pi †KvbwU mwVK? 

K i I ii     L i I iii

M ii I iii   ⬤ i, ii I iii

c`v_©weÁv‡bi c×wZ I hš¿cvwZ e¨envi Kiv nqÑ    (cÖ‡qvM)

wPwKrmvweÁv‡b

g‡bvweÁv‡b

ivóªweÁv‡b

wb‡Pi †KvbwU mwVK?

⬤ i I ii      L i I iii

M ii I iii   N i, ii I iii

†hme ivwk ¯^vaxb A_©vr Ab¨ ivwki Ici wbf©i K‡i bv Zv‡K Kx e‡j?      (Ávb)

K †hŠwMK ivwk         L gKi ivwk

M jä ivwk  ⬤ †gŠwjK ivwk

wb‡Pi †KvbwU jä ivwk?          (Abyaveb)

K fi        L `xcb ¶gZv

M ZworcÖevn           ⬤ NbZ¡

wb‡Pi †Kvb ivwkwU Ab¨ ivwki Ici wbf©ikxj?        (Ávb)

K ZvcgvÎv  ⬤ IRb

M Zwor cÖevn          N `xcb ¶gZv

cÖavbZ KqwU ivwk‡K †gŠwjK ivwk e‡j?    (Ávb)

⬤ 7wU        L 8wU

M 11wU      N 13wU

†KvbwU †gŠwjK ivwk bq?          (Ávb)

⬤ KvR       L c`v‡_©i cwigvY

M mgq      N fi

hv‡`i Rxeb †bB Zv‡`i m¤úwK©Z weÁvb‡K ejv nqÑ     (Abyaveb)

K c`v_©weÁvb          ⬤ †fŠZweÁvb

M RxeweÁvb           N imvqb weÁvb

†fŠZRM‡Z hv wKQy cwigvc Kiv hvq Zv‡K Kx e‡j? (Ávb)

K gvÎv       ⬤ ivwk 

M GKK     N fi

†h GKK †gŠwjK GKK †_‡K cÖwZcvw`Z n‡q‡Q Zv‡K Kx GKK ejv nq?           (Ávb) 

⬤ jä GKK            L wmwRGm GKK 

M GmAvB GKK       N †`kxq GKK 

mwVK mgxKiY †KvbwU?           (Abyaveb)

K ej = fi × Z¡iY    L ej = fi × 

⬤ ej = fi ×          N ej = fi × 

†KvbwU †gŠwjK ivwk?   (Abyaveb)

K NbZ¡      L AvqZb 

M ej        ⬤ fi

†Kvb ivwkwU Ab¨ ivwki Ici wbf©ikxj?    (Abyaveb)

K ZvcgvÎv  ⬤ IRb

M ZworcÖevn           N `xcb ¶gZv

wb‡Pi Z_¨¸‡jv j¶ KiÑ         (Abyaveb)

Zvc †gŠwjK ivwk

`xcb ZxeªZv †gŠwjK ivwk

Zwor cÖevn †gŠwjK ivwk

wb‡Pi †KvbwU mwVK? 

K i I ii     L i I iii

M ii I iii   ⬤ i, ii I iii

†gŠwjK ivwki AšÍfz©³ n‡jvÑ      (Abyaveb)

ˆ`N©¨, fi, c`v‡_©i cwigvc

mgq, ZvcgvÎv

Zwor cÖevn, `xcb ¶gZv

wb‡Pi †KvbwU mwVK? 

K i I ii     L i I iii

M ii I iii   ⬤ i, ii I iii

†gŠwjK ivwki Ici wbf©i K‡iÑ

kw³

Zwor cÖevn

KvR

wb‡Pi †KvbwU mwVK? 

K i I ii     ⬤ i I iii

M ii I iii   N i, ii I iii

wb‡Pi m~θ‡jv j¶ KiÑ          (Ávb)

ej = fi × Z¡iY

wbDUb = ×

ej = fi × 

wb‡Pi †KvbwU mwVK?

K i I ii     L i I iii

M ii I iii   ⬤ i, ii I iii

mg‡qi GKK wba©vi‡Y †Kvb †ZRw¯Œq c`v_© e¨envi Kiv nq?  (Ávb)

K BD‡iwbqvg          ⬤ wmwRqvg

M †iwWqvg   N †_vwiqvg

Av`k© f‡ii wmwjÛv‡ii e¨vm I D”PZv KZ?          (Ávb)

⬤ e¨vm 3⋅9 cm I D”PZv 3⋅9 cm    L e¨vm 3⋅9 cm I D”PZv 9⋅3 cm

M e¨vm 9⋅3 cm I D”PZv 3⋅9 cm   N e¨vm 9⋅3 cm I D”PZv 9⋅3 cm

m¨v‡å kniwU †Kvb †`‡k Aew¯’Z?          (Ávb)

K Bsj¨vÛ    ⬤ d«vÝ

M BZvwj     N Rvg©vwb

†gvj cwigv‡c †Kvb Kve©b e¨eüZ nq?     (Ávb)

K Kve©b-11           ⬤ Kve©b-12

M Kve©b-13           N Kve©b-14

†h Av`k© cwigv‡ci mv‡_ Zzjbv K‡i †fŠZ ivwk‡K cwigvc Kiv nq Zv‡K Kx e‡j?          (Ávb)

K cwigvc    L fi

M †gŠwjK ivwk         ⬤ cwigv‡ci GKK

wgUvi, wK‡jvMÖvg, †m‡KÛ BZ¨vw` wK‡mi D`vniY?  (Abyaveb)

K cwigv‡ci            ⬤ cwigv‡ci GK‡Ki

M ivwk                 N ˆ`N©¨, fi

`xcb ¶gZv †Kvb cÖKvi ivwk?   (Ávb)

K jä        ⬤ †gŠwjK

M wgkª       N †hŠwMK

wgUvi wK‡mi GKK?    (Ávb)

K f‡ii      L mg‡qi

⬤ ˆ`‡N©¨i    N ZvcgvÎvi

mg‡qi GKK Kx?       (Ávb)

K wgUvi      L wK‡jvMÖvg

⬤ †m‡KÛ    N †gvj

AvšÍR©vwZK c×wZ‡Z ZvcgvÎvi GKK Kx? (Ávb)

K Ryj        L wbDUb

M c¨vm‡Kj ⬤ †Kjwfb

AvšÍR©vwZK c×wZ‡Z Zwor cÖev‡ni GKK Kx?       (Ávb)

K †fvë      ⬤ A¨vw¤úqvi

M Ing      N †Kjwfb

`xcb ZxeªZvi GKK †KvbwU?     (Ávb)

K †Kjwfb  L A¨vw¤úqvi

⬤ K¨v‡Ûjv   N †gvj

AvšÍR©vwZK c×wZ‡Z c`v‡_©i cwigv‡Yi GKK Kx?   (Ávb)

K MÖvg        L wK‡jvMÖvg

⬤ †gvj       N cvDÛ

1 fm = KZ?          (cÖ‡qvM) 

K 10⁻¹¹F    L 10⁻¹¹m

M 10⁻¹¹s    ⬤ 10⁻¹⁵m

5 Em = KZ Ryj?    (cÖ‡qvM)

K 5 × 10¹² Ryj        L 5 × 10¹⁴ Ryj

M 5 × 10¹⁷ Ryj        ⬤ 5 × 10¹⁸ Ryj

AvšÍR©vwZK c×wZ‡Z (SI) f‡ii GKK †KvbwU?     (Ávb)

K MÖvg        ⬤ wK‡jvMÖvg

M †gvj      N cvDÛ

†Kv‡bv wKQyi cwigvY wbY©q Kiv‡K Kx ejv nq?       (Ávb)

⬤ cwigvc    L IRb M fi   N ej

10⁶ ÷ 10⁴ = KZ?      (cÖ‡qvM)

K 10¹⁰       L 10⁶

⬤ 10²        N 10

1 aW mgvb KZ IqvU?          (Ávb)

K 10^–12      ⬤ 10^–18

M 10^–24      N 10^–30

GK‡Ki AvšÍR©vwZK c×wZ‡K ms‡¶‡c Kx ejv nq?  (Ávb)

⬤ SI         L CGS

M MKS    N ISU

†Kvb mvj †_‡K `ywbqvRy‡o wewfbœ ivwki GKB iKg GKK Pvjy Kivi wm×všÍ nq?   (Ávb)

K 1965     L 1906 

⬤ 1960      N 1990 

GK wMMv KZ Ry‡ji mgvb?       (Ávb)

⬤ 10⁹ Ryj   L 10¹² Ryj

M 10⁶ Ryj  N 10^–9 Ryj

gvB‡µv A¨vw¤úqvi (ìA) = KZ?            (Ávb)

K 10⁶ A¨vw¤úqvi      L 10³ A¨vw¤úqvi

⬤ 10⁻⁶ A¨vw¤úqvi      N 10⁻⁹ A¨vw¤úqvi

†KvbwU jä GKK?     (Abyaveb)

K K¨v‡Ûjv  ⬤ wbDUb

M †Kjwfb  N A¨vw¤úqvi

10 wMMv Ryj Gi mwVK ms‡KZ †KvbwU?    (Ávb)

K 10 gj    L 10 Gj

M 10 gJ    ⬤ 10 GJ

GK‡Ki DcmM© e¨envi wb‡Pi †KvbwU mwVK?         (cÖ‡qvM)

K mmF    L muF

M ìnF      ⬤ pF

4 b¨v‡bv †m‡K‡Ûi mwVK ms‡KZ †KvbwU?            (Ávb)

K 4 NS    L 4 nS

⬤ 4 ns       N 4 Ns

AvšÍR©vwZK c×wZ‡Z †gŠwjK GKK †KvbwU?          (Abyaveb)

⬤ A¨vw¤úqvi L Ryj

M IqvU      N †fvë

†Kvb ivwk `ywUi GKK Awfbœ?    (Abyaveb)

K Zvc, ZvcgvÎv      ⬤ KvR, kw³

M KvR, ÿgZv        N kw³, ÿgZv

mg‡qi GKK wba©vi‡Y †Kvb †ZRw¯Œq c`v_© e¨envi Kiv nq?      (Abyaveb)

K †iwWqvg   L †cv‡jvwbqvg

⬤ wmwRqvg   N BD‡iwbqvg

†gŠwjK ivwki GKKmg~nÑ         (Abyaveb)

n‡Z n‡e AcwiewZ©Z

mn‡R cybiærcv`b Kiv hv‡e bv

Ab¨ GKK¸‡jvi Dci wbf©i K‡i bv

wb‡Pi †KvbwU mwVK?

K i I ii     L ii I iii

⬤ i I iii     N i, ii I iii

wb‡Pi m¤úK©¸‡jv jÿ Ki :      (Abyaveb)

1 †cUvwgUvi = 10¹⁵ m

1 wc‡KvwgUvi = 10⁻¹² m

1 b¨v‡bvwgUvi = 10⁻⁹ m

wb‡Pi †KvbwU mwVK?

K i I ii     L ii I iii

M i I iii    ⬤ i, ii I iii

†gŠwjK ivwkÑ (Abyaveb)

¯^vaxb

Ab¨ ivwki Dci wbf©i K‡i

Ab¨vb¨ ivwk Gi Dci wbf©i K‡i

wb‡Pi †KvbwU mwVK?

K i I ii     L ii I iii

⬤ i I iii     N i, ii I iii

`xcb ZxeªZviÑ          (Abyaveb)

GK‡Ki cÖZxK Cd

GmAvB GKK K¨v‡Ûjv

cÖZxK Iv

wb‡Pi †KvbwU mwVK?

K i I ii     L ii I iii

M i I iii    ⬤ i, ii I iii

wee„wZ¸‡jv jÿ KiÑ    (D”PZi `ÿZv)

fi cwigv‡c e¨eüZ msKi avZzi ˆZwi wmwjÛviwUi e¨vm 3⋅9 cm Ges D”PZv 3⋅9 cm

cvwbi ˆÎawe›`yi ZvcgvÎvi ⋅ fvM‡K GK †Kjwfb e‡j

wmwRqvg-133 cigvYy 1 †m‡K‡Û 9192631770wU ¯ú›`b m¤úbœ K‡i

wb‡Pi †KvbwU mwVK?

K i I ii     L i I iii

M ii I iii   ⬤ i, ii I iii

mg‡qi gvÎv n‡jvÑ     (Ávb)

K L         ⬤ T

M I          N O

ˆ`‡N©¨i gvÎv‡K Kx w`‡q cÖKvk Kiv nq?   (Ávb) 

K M        L T   

⬤ L          N F

ivwki gvÎv wb‡`©k Ki‡Z e¨envi Kiv nqÑ           (D”PZi `ÿZv)

K †iLv eÜbx                    L cÖ_g eÜbx

M wØZxq eÜbx                   ⬤ Z…Zxq eÜbx

†KvbwU e‡ji gvÎv mgxKiY?     (Abyaveb) 

K [ML²T⁻²]          L [ML²T⁻³]

M [MLT⁻¹]           ⬤ [MLT⁻²]

`xcb ZxeªZvi gvÎv †KvbwU?      (Ávb) 

K I          ⬤ J    

M L         N M

gvÎv mgxKi‡Yi mxgve×ZvÑ     (D”PZi `¶Zv)

gvÎv mgxKi‡Yi mvnv‡h¨ mKj †fŠZ mgm¨v mgvavb Kiv hvq bv

ejwe`¨v Qvov c`v_©weÁv‡bi Ab¨ †Kv‡bv kvLvq gvÎv mgxKiY e¨envi Kiv hvq bv

gvÎv mgxKi‡Yi mvnv‡h¨ †Kv‡bv ivwki GKK Rvbv hvq 

wb‡Pi †KvbwU mwVK?

⬤ i I ii      L i I iii

M ii I iii   N i, ii I iii

wb‡Pi Z_¨¸‡jv j¶ KiÑ         (Abyaveb)

ej cÖ‡qv‡M e¯‘i miY nq         

ej = fi × Z¡iY

e‡ji gvÎv mgxKiY [MLT⁻²]

wb‡Pi †KvbwU mwVK?

⬤ i I ii      L i I iii

M ii I iii   N i, ii I iii

wb‡Pi weeiY¸‡jv jÿ KiÑ       (Abyaveb)

Av‡cwÿK †iv‡ai GKK m, gvÎv mgxKiY [ML⁻³T³I⁻²]

Zwor ZxeªZvi GKK NC⁻¹, gvÎv mgxKiY [MLT⁻³I⁻¹]

ZvcaviY ÿgZvi GKK JK⁻¹, gvÎv mgxKiY [ML²T⁻²è⁻¹] 

wb‡Pi †KvbwU mwVK?

K i I ii     L i I iii

⬤ ii I iii    N i, ii I iii

wb‡Pi gvÎv¸‡jv j¶ KiÑ         (Abyaveb)

[F] = [MLT⁻²]

[a] = [LT⁻²]

[at²] = [L²]

wb‡Pi †KvbwU mwVK?

⬤ i I ii      L ii I iii

M i I iii    N i, ii I iii

¯Œz M‡Ri jwNô MYb 0⋅01 mm Ges e„ËvKvi †¯‹‡ji fvM msL¨v 100 n‡j, wcP KZ?       (cÖ‡qvM)

⬤ 1 mm    L 0⋅1 mm

M 0⋅01 cm         N 0⋅001 cm

GKwU ¯øvBW K¨vwjcv‡m© cÖavb †¯‹‡ji ¶z`ªZg GK N‡ii gvb 1mm I fvwb©qvi †¯‹‡ji fvMmsL¨v 20 n‡j GB †¯‹jwU w`‡q KZUzKz m~²fv‡e cwigvc Kiv hv‡e?      (cÖ‡qvM)

K 0⋅01 mn         L 0⋅005 mm

M 0⋅01 cm         ⬤ 0⋅005 cm

hvwš¿K ÎæwU k~b¨ GKwU ¯Œz M‡Ri e„ËvKvi fvM msL¨v x, jwNô MYb y Ges ¯Œyi wcP z n‡j wb‡Pi †KvbwU mwVK?  (D”PZi `ÿZv)

K x = yz   L y = zx

⬤ z = xy    N xyz = 1

GKwU `ʇK ¯øvBW K¨vwjcv‡m©i `yB †Pvqv‡ji gv‡S ivLvi d‡j cÖavb †¯‹j cvV I fvwb©qvi mgcvZb h_vµ‡g 4 cm I 7 cm cvIqv †Mj| fvwb©qvi aªæeK 0⋅1 mm n‡j `ÊwUi ˆ`N©¨ KZ?   (cÖ‡qvM)

⬤ 4⋅07 cm          L 4⋅7 cm

M 4⋅07 mm        N 4⋅7 mm

wgUvi †¯‹j e¨envi K‡i †KvbwU ch©šÍ mwVKfv‡e gvcv nq?      (Abyaveb)

⬤ wgwjwgUvi  L gvB‡µvwgUvi

M b¨v‡bvwgUvi         N †mw›UwgUvi

fvwb©qvi †¯‹j †K Avwe®‹vi K‡ib?           (Ávb)

K wc‡q‡i `¨ KzevZ©v   L †Rgm fvwb©qvi

⬤ wc‡q‡i fvwb©qvi      N wjI fvwb©qvi

wc‡q‡i fvwb©qvi †ckvq wQ‡jbÑ    (Ávb)

K wPwKrmK ⬤ MwYZwe`

M c`v_©we`¨v N cÖvwYweÁvbx

g~j †¯‹‡ji cvV 14 wgwg, fvwb©qvi aª“eK 0.1 wgwg Ges fvwb©qvi cvV 3 n‡j †gvU cvV KZ n‡e?           (cÖ‡qvM)

K 14⋅3 †mwg        L 1⋅43 wgwg

⬤ 14⋅3 wgwg         N 143 wgwg

fvwb©qvi †Kv‡bv `vM hw` cÖavb †¯‹‡ji †Kv‡bv `v‡Mi mv‡_ wg‡j hvq ev `v‡Mi me‡P‡q KvQvKvwQ _v‡K Z‡e H `vMB n‡eÑ   (Abyaveb)

K fvwb©qvi aª“eK       L hvwš¿K ΓwU

⬤ fvwb©qvi mgcvZb    N fvwb©qvi K¨vwjcvm©

cÖavb †¯‹j cvV m, fvwb©qvi mgcvZb V Ges fvwb©qvi aª“eK VC n‡j `‡Êi ˆ`N©¨ wbY©‡qi m~Î n‡eÑ    (D”PZi `ÿZv)

K L = M + VC    L L = MV + VC

M L = MVC + V  ⬤ L = M + V × VC

fvwb©qvi aª“eK‡K wb‡Pi †Kvb ms‡KZ Øviv cÖKvk Kiv nq?     (Ávb)

K L         ⬤ VC

M V         N M

duvcv b‡ji AšÍe©¨vm gvcv hvq †Kvb h‡š¿i mvnv‡h¨?   (Ávb)

K ¯Œz MR     L wgUvi †¯‹j

M fvwb©qvi †¯‹j        ⬤ ¯­vBW K¨vwjcvm©

GKwU wmwjÛv‡ii e¨vm wbY©‡qi †¶‡Î †Kvb hš¿ e¨envi Kiv nq?      (Ávb)

K wgUvi †¯‹j                     L fvwb©qvi †¯‹j

⬤ ¯­vBW K¨vwjcvm©      N †mw›UwgUvi †¯‹j

¯Œz M‡Ri mvnv‡h¨ wb‡Pi †KvbwUi e¨vmva© wbY©q Kiv nq?        (Ávb)

K †ej‡bi D”PZv

⬤ Zv‡ii e¨vmva©

M duvcv b‡ji AšÍe©¨vm

N duvcv b‡ji ewne©¨vm

¯Œz M‡Ri Uzwc T GKevi Nyiv‡j Gi hZUzKz miY N‡U Ges ˆiwLK †¯‹j eivei †h ˆ`N©¨ AwZµg K‡i Zv‡K Kx ejv nq?      (Ávb)

⬤ wcP        L jwNô MYb

M k~b¨ ΓwU  N wcQU ΓwU

e„ËvKvi †¯‹‡ji fvM msL¨v 50 n‡j jwNô MYb KZ? (cÖ‡qvM)

⬤ 0.02 wgwg L 0.04 wgwg

M 40 wgwg  N 50 wgwg

GKwU Zvi‡K GKwU ¯Œz M‡R ¯’vcb Kivi ci †h cvV cvIqv †Mj Zv n‡”Q ˆiwLK †¯‹j cvV 2 mm, e„ËvKvi †¯‹‡ji fvM msL¨v 30 Ges jwNô MYb 0.01 mm| ZviwUi e¨vm KZ?          (cÖ‡qvM)

K 1⋅6 mm          L 2⋅2 mm

⬤ 2⋅3 mm           N 3⋅4 mm

Lye Aí wRwb‡mi fi m~²fv‡e wbY©q Ki‡Z nqÑ      (Abyaveb)

K wbw³ Øviv ⬤ Zzjv hš¿ Øviv

M DfqwU Øviv          N ¯Œz MR Øviv

¶z`ª mgq e¨eavb cwigv‡ci Rb¨ †KvbwU e¨envi Kiv nq?     (Ávb)

⬤ ÷c IqvP L wi÷ IqvP

M †Uwej K¬K          N Iqvj K¬K

GKwU `ʇK ¯­vBW K¨vwjcv‡m© ¯’vc‡bi ci †h cvV cvIqv †Mj Zv n‡”Q cÖavb †¯‹j 2 cm, fvwb©qvi cvV 3 Ges fvwb©qvi aª“eK 1 mm `ÊwUi ˆ`N©¨ KZ?    (cÖ‡qvM)

K 2⋅03 cm         ⬤ 2⋅3 cm

M 2⋅03 mm        N 2⋅3 mm

fvwb©qvi aª“eK-Gi gvb KZ?      (Ávb)

⬤ 0⋅01 †mwg         L 1 wg

M 0⋅0001 wgwg     N 0⋅02 wgwg

¯Œz M‡Ri e„ËvKvi †¯‹‡ji k~b¨ `vM ˆiwLK †¯‹‡ji k~b¨ `v‡Mi wb‡P hvwš¿K ΓwU n‡eÑ        (Abyaveb) 

⬤ abvZ¥K    L FYvZ¥K

M wbi‡c¶  N  wbw³

cv‡Zi cyi“Z¡ wbY©‡q †KvbwU e¨envi Ki‡Z nq?        (Abyaveb)

K ¯­vBW K¨vwjcvm©     L fvwb©qvi †¯‹j

⬤ ¯Œz MR                N w¯cÖs wbw³

GKwU Zv‡ii ˆ`N©¨ 7.5 †mw›UwgUvi| †Kvb h‡š¿i mvnv‡h¨ `ª“Z I mnRfv‡e GB ˆ`N©¨ gvcv hv‡e?  (Abyaveb)

K ¯­vBW K¨vwjcvm©     L ¯Œz MR

⬤ wgUvi †¯‹j           N fvwb©qvi †¯‹j

wmwjÛv‡ii e¨vm gvcv †h‡Z cv‡i †Kvb h‡š¿i mvnv‡h¨?      (Abyaveb) 

K MR jvwV             ⬤ ¯­vBW K¨vwjcvm©

M fvwb©qvi †¯‹j        N wgUvi †¯‹j

ˆ`N©¨ gvcvi me‡P‡q mij hš¿Ñ   (Abyaveb)

K fvwb©qvi †¯‹j        ⬤ wgUvi †¯‹j

M ¯­vBW K¨vwjcvm©     N m‡bvwgUvi

†Kvb †¯‹‡ji mvnv‡h¨ wgwjwgUv‡ii fMœvsk mwVKfv‡e wbY©q Kiv hvq?      (Abyaveb)

K wgUvi †¯‹j          ⬤ fvwb©qvi †¯‹j

M m‡bvwgUvi N  jvwV

¯Œz M‡Ri †¶‡Î wcP‡K e„ËvKvi †¯‹‡ji msL¨v Øviv fvM Ki‡j wb‡Pi †KvbwU cvIqv hvq?     (Abyaveb)

K wcP        ⬤ jwNô MYb

M fvwb©qvi aª“eK       N hvwš¿K ΓwU

cÖavb †¯‹‡ji ¶z`ªZg 1 fv‡Mi ˆ`N©¨ s Ges fvwb©qv‡ii fvMmsL¨v n n‡j fvwb©qv‡ii aª“eK wbY©‡qi mwVK m~Î †KvbwU?     (cÖ‡qvM)

K              ⬤       

M sn        N s – n

¯Œz M‡Ri e„ËvKvi †¯‹‡ji fvM msL¨v 100 Ges h‡š¿i wcP 1 wgwg n‡j jwNô MYb KZ?        (cÖ‡qvM)

K 0⋅1 mm          ⬤ 0⋅01 mm

M 0⋅001 mm      N 0⋅0001 mm

wWwRUvj _vgv Nwoi wbfz©jZv cwigvc n‡jvÑ (Abyaveb)

− 0⋅01 s

+ 0⋅01 s

+ 0⋅1 s

wb‡Pi †KvbwU mwVK?

⬤ i I ii      L ii I iii

M i I iii    N i, ii I iii

fvwb©qvi aªæeK wbf©i K‡iÑ        (Abyaveb)

cÖavb †¯‹‡ji `vM KvUvi ˆewk‡ó¨i Ici

e„ËvKvi †¯‹‡ji `vM KvUvi ˆewk‡ó¨i Ici

fvwb©qvi †¯‹‡ji `vM KvUvi ˆewk‡ó¨i Ici

wb‡Pi †KvbwU mwVK?

K i I ii     L ii I iii

⬤ i I iii     N i, ii I iii

wb‡Pi Z_¨¸‡jv j¶ KiÑ         (D”PZi `ÿZv)

wgUvi †¯‹j ˆ`N©¨ cwigv‡ci RwUj †¯‹j

e¯‘i ˆ`N©¨ L = M + V × VC

¯­vBW K¨vwjcvm© e¨eüZ nq duvcv b‡ji AšÍe©¨vm I ewne©¨vm wbY©‡q

wb‡Pi †KvbwU mwVK? 

K i I ii     L i I iii

⬤ ii I iii    N i, ii I iii

fvwb©qvi †¯‹jÑ          (Abyaveb)

†mw›UwgUv‡ii fMœvsk gvc‡Z e¨eüZ nq

wc‡q‡i fvwb©qvi Avwe®‹vi K‡ib

wgUvi †¯‹‡ji mv‡_ e¨envi K‡i wgwjwgUv‡ii fMœvsk mwVKfv‡e wbY©q Kiv nq

wb‡Pi †KvbwU mwVK? 

K i I ii     L i I iii

⬤ ii I iii    N i, ii I iii

¯Œz M‡Ri mvnv‡h¨ wbY©q Kiv hvqÑ (Abyaveb)

Zv‡ii e¨vmva©

†QvU fi

†QvU ˆ`N©¨

wb‡Pi †KvbwU mwVK? 

K i I ii     ⬤ i I iii

M ii I iii   N i, ii I iii

Zzjvhš¿ e¨envi Kiv nqÑ          (Abyaveb)

c`v_©weÁv‡b

†R¨vwZwe©Áv‡b

imvq‡b

wb‡Pi †KvbwU mwVK? 

K i I ii     ⬤ i I iii

M ii I iii   N i, ii I iii

¯Œz M‡Ri wcP‡K e„ËvKvi †¯‹‡ji fvM msL¨v Øviv fvM Ki‡j cvIqv hvqÑ          (Ávb)

fvwb©qvi aª“eK

hvwš¿K ΓwU

jwNô MYb

wb‡Pi †KvbwU mwVK?

K i          L ii   

⬤ iii         N i I iii

¯­vBW K¨vwjcvm© Øviv wbY©q Kiv hvqÑ        (Abyaveb) 

e¯‘i fi

e¯‘i ˆ`N©¨ 

†Mvj‡Ki AvqZb 

wb‡Pi †KvbwU mwVK?

K i I ii     L i I iii

⬤ ii I iii    N i, ii I iii

†Kv‡bv ¯Œz M‡Ri ˆiwLK †¯‹‡ji cvV 2mm Ges e„ËvKvi †¯‹‡ji fvM msL¨v 30 n‡j H Ae¯’vq †Kv‡bv Zv‡ii e¨vm n‡eÑ (cÖ‡qvM)

2.30 mm

0⋅23 cm

15 mm

wb‡Pi †KvbwU mwVK?

⬤ i I ii      L ii    I iii

M i I iii    N i, ii I iii

¯­vBW K¨vwjcv‡m©i †¶‡Î cÖ‡hvR¨Ñ          (Ávb) 

L = M + V × VC

d = L + C × LC

M = L – V × VC

wb‡Pi †KvbwU mwVK?

K i I ii     L ii I iii

⬤ i I iii     N i, ii I iii

¯­vBW K¨vwjcv‡m©i e¨envi n‡jvÑ (D”PZi `¶Zv)

duvcv b‡ji AšÍe©¨vm wbY©‡q

duvcv b‡ji ewne©¨vm wbY©‡q

e¯‘i AvqZb wbY©‡q

wb‡Pi †KvbwU mwVK?

K i          L ii   

M i I ii     ⬤ i, ii I iii

GKwU Nb‡Ki evûi ˆ`N©¨ 6 cm Ges GKwU †Mvj‡Ki e¨vm 6 cm| G‡`i AbycvZ KZ?     (cÖ‡qvM)

K 1 t 2     L 2 t 1

⬤ 1⋅9 t 1 N 1 t 1⋅9

ˆ`N©¨wewkó GKwU wmwjÛv‡ii e¨vm KZ n‡j Gi AvqZb 4m³ n‡e?     (Ávb)

K 1 m      L 2 m

M 3 m      ⬤ 4 m

cwigv‡ci †¶‡Î Kq ai‡bi ΓwU _vK‡Z cv‡i?       (Ávb)

K 2          ⬤ 3

M 4          N 5

ˆ`e ΓwUi cÖZ¨vwkZ gvb KZ?    (Ávb)

K ⬤ 0    

M 1          N −1

hvwš¿K ΓwU KLb wbY©q Ki‡Z nq?          (Ávb)

⬤ cix¶v ïi“i Av‡M    L cix¶vi gv‡S

M cix¶vi †k‡l       N hš¿ †Kbvi mgq

ch©‡e¶‡Ki Kvi‡Y cv‡V †h ΓwU Av‡m Zv‡K Kx e‡j?          (Ávb)

K ˆ`e ΓwU  L k~b¨ ΓwU

M hvwš¿K ΓwU          ⬤ e¨w³MZ ΓwU

AvqZvKvi e¯‘i AvqZb wbY©‡q †KvbwU e¨envi Kiv nq?        (Ávb)

⬤ ¯­vBW K¨vwjcvm©      L ¯Œz MR

M Zzjv hš¿              N fvwb©qvi †¯‹j

Zv‡ii cÖ¯’‡”Q‡`i †¶Îdj wbY©‡qi m~Î †KvbwU?      (D”PZi `¶Zv)

K A = ðd² L A = ðd²

⬤ A = ðd² N A = ðd²

GKwU Zv‡ii e¨vm 4 cm n‡j Zv‡ii cÖ¯’‡”Q‡`i †¶Îdj KZ?      (cÖ‡qvM)

⬤ 3.1416 × 10⁻⁴m²  L 10⁻⁴m²

M 3.1416 × 10²m³  N 3.1416 × 10⁻²m²

wmwjÛvi ev †ej‡bi AvqZ‡bi †¶‡Î †KvbwU mwVK?      (Abyaveb)

K   ðr³     L   ðr²

⬤ ðr²h       N  ð²h

AvqZvKvi e¯‘i AvqZb wbY©‡qi m~Î †KvbwU?         (Abyaveb)

K ðr²       L ðr³

⬤ L × B × H           N L² × B × h

fvwb©qv‡ii k~b¨ `vM g~j †¯‹‡ji k~b¨ `v‡Mi evg cv‡k _vK‡j †Kvb ai‡bi ÎæwU n‡e?        (Abyaveb)

K abvZ¥K   ⬤ FYvZ¥K

M wbi‡cÿ  N ˆ`e ÎæwU

d e¨vm, L ˆ`N©¨wewkó †Kv‡bv wmwjÛv‡ii AvqZb wbY©‡qi m~Î †KvbwU?       (cÖ‡qvM) 

K  ðd²L    L   ðdL²

⬤  ðd²       N   ðd²L

fvwb©qv‡ii k~b¨ (0) `vM cÖavb †¯‹‡ji k~b¨ `v‡Mi Wvb cv‡k _vK‡j †Kvb ai‡bi ÎæwU n‡e?            (D”PZi `ÿZv) 

⬤ abvZ¥K

L FYvZ¥K

M abvZ¥K ev FYvZ¥K `y‡UvB n‡Z cv‡i

N abvZ¥K ΓwU n‡j AvcvZ cv‡Vi mv‡_ †hvM Ki‡Z n‡e

GKwU †Mvj‡Ki AvqZb ðr³, †MvjKwUi e¨vmva© 3 mm n‡j AvqZb KZ n‡e?     (D”PZi `ÿZv) 

K 113⋅04 cm 3              ⬤ 113⋅04 mm 3

M 11⋅304 m 3                N 123 mm 3

wb‡Pi m~θ‡jv j¶ Ki hv cÖPwjZ A_© †g‡b P‡jÑ   (Abyaveb) 

V = ðd³

A = ðd²

V = ðd²h

wb‡Pi †KvbwU mwVK?

K i I ii     L i I iii

M ii I iii   ⬤ i, ii I iii

GKwU AvqZvKvi e¯‘i AvqZb wbY©‡qi mgxKiY-     (Ávb)

AvqZb = ðr³ 

AvqZb = ˆ`N©¨ × cÖ¯’ × D”PZv 

AvqZb = ðr²h 

wb‡Pi †KvbwU mwVK?

K i          ⬤ ii     M i I ii          N i, ii I iii

wb‡Pi Z_¨¸‡jv j¶ KiÑ         (D”PZi `ÿZv)

Zv‡ii e¨vm D = L + C × LC

`‡Êi ˆ`N©¨ L = M + V × VC

wWwRUvj ÷cIqvP ± 0.1s ch©šÍ mwVK cvV w`‡Z _v‡K

wb‡Pi †KvbwU mwVK?  

⬤ i I ii      L i I iii

M ii I iii   N i, ii I iii

e¨w³MZ ÎæwU †`Lv †`q Ñ          (Abyaveb)

fvwb©qvi mgcvZb wbY©q Ki‡Z fzj Ki‡j

cÖavb †¯‹‡ji k~b¨ `vM fvwb©qvi †¯‹‡ji k~b¨ `v‡Mi mv‡_ bv wgj‡j

†`vj‡Ki †`vjbmsL¨v wbY©‡q fzj Ki‡j

wb‡Pi †KvbwU mwVK?  

K i I ii     ⬤ i I iii

M ii I iii   N i, ii I iii

Dw™¢‡`i e„w× †iKW© Kivi h‡š¿i bvg Kx?

K wmm‡gvMÖvd          ⬤ †µ‡¯‹vMÖvd

M w¯ú‡WvwgUvi         N A¨vwgUvi

†Kvb weÁvbx cÖgvY K‡ib †h, K¨vjwiK ej‡Z ev¯Í‡e wKQz †bB?

K mvwj©       L eUgwj

M Bb‡Rb nvDm       ⬤ KvD›U ivg‡dvW©

nvB‡Wªv‡Rb cigvYyi B‡jKUªªb ¯Í‡ii aviYv †`b †K?

K iv`vi‡dvW©           ⬤ wbjm †evi

M I‡Uv nvb N nvB‡Mb

¯’v‡bi R¨vwgwZK aviYv me©cÖ_g †K Dc¯’vcb K‡ib?

⬤ BDwK¬W    L M¨vwjwjI

M wbDUb    N Gwi÷Uj

†evmb Kx ai‡bi KYv?

K K…wÎg KYv

⬤ †gŠwjK KYv

M mn‡gŠwjK KYv

N RwUj KYv

AvaywbK ˆeÁvwbK c×wZi m~Pbv N‡U †Kvb weÁvbxi nv‡Z?   

K iRvi †eKb         L wbDUb

⬤ M¨vwjwjI   N AvBb÷vBb

Kvi eB‡q evqyK‡ji D‡jøL cvIqv hvq?

K U‡jgx     ⬤ Avj-gvmy`x

M Avj-nvwKg         N wMjevU©

Av‡cwÿK ZË¡ cÖ`vb K‡ib †K?

K g¨v·I‡qj           L g¨v· cø¨v¼

⬤ AvBb÷vBb          N m‡Z¨›`ªbv_ emy

wb‡Pi †Kvb weÁvbx ivwkqvi?

K †Rv‡md †nbwi

⬤ GBP. Gd. B. †jÄ

M gvB‡Kj d¨viv‡W

N wbDUb

wbDU‡bi g‡Z †KvbwUi ïiæ ev †kl bvB?

K kw³       L ÿgZv

M KvR      ⬤ ¯’vb

†KvbwU †gŠwjK ivwk?

⬤ fi         L ej

M miY       N †eM

wMMv b¨v‡bvi KZ ¸Y?

⬤ 10¹⁸ ¸Y   L 10⁹ ¸Y

M 10^-18 ¸Y  N 10⁶ ¸Y

1pF = KZ d¨vivW?

K 10¹²F     ⬤ 10^-12F

M 10⁹F     N 10^-18F

6733000000 msL¨vwU‡K ˆeÁvwbK cÖZx‡K cÖKvk Ki‡j Kx n‡e?     

⬤ 6⋅733 × 10⁹

L  67⋅33 × 10³

M 6⋅733 × 10⁶

N 6733 × 10⁶

wc_v‡Mvivm Ae`vb †i‡L‡Qb-

K¤úgvb Zv‡ii Dci

R¨vwgwZK Dccv‡`¨

cigvYyi MV‡b

wb‡Pi †KvbwU mwVK? 

⬤ i I ii     L i I iii

M ii I iii   N i, ii I iii