Aspect Physics 1

ASPECT PHYSICS cÖ_g cÎ †f․Z RMr I cwigvc 45 ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES SURVEY TABLE  Kx coe? †Kb coe? †Kv_v n‡Z coe? KZUzKz coe?  TOPICS MAGNETIC DECISION [hv co‡e] MAKING DECISION [†h Kvi‡Y co‡e] VVI For This Year DU JU RU CU GST Engr. HSC Written MCQ THEORY CONCEPT-01 weÁvb I c`v_©weÁv‡bi aviYv cÖ‡qvM I Avwe®‥v‡ii avcmg~n 10% 10% 10% 20% 10% - 10% - CONCEPT-02 c`v_©weÁv‡bi ¸iæZ¡c~Y© ivwkmg~n, Zv‡`i cÖZxK Ges gvbmg~n 80% 90% 80% 70% 70% - 30% - CONCEPT-03 KwZcq ¸iæZ¡c~Y© ivwki ms‡KZ, GKK Ges gvÎv 80% 90% 85% 60% 65% - 40% - CONCEPT-04 ¸iæZ¡c~Y© weÁvbxMY Ges Zv‡`i Avwe®‥vimg~n 20% 50% 30% 20% - - 5% - CONCEPT-05 •`N©¨ cwigv‡ci wKQz cÖPwjZ I b‡fvgÛjxq GKK 30% 30% 50% 40% 25% - 10% - CONCEPT-06 cwigv‡ci ÎæwUmg~n 20% 10% 30% 20% 30% - 10% - MvwYwZK cÖ‡qvM CONCEPT-01 fvwY©qvi aªæeK I jwNô MYb wbY©q msµvšÍ MvwYwZK cÖ‡qvM 15% 30% 50% 80% 50% 10% CONCEPT-02 ÎæwU msµvšÍ MvwYwZK cÖ‡qvM 30% 60% 80% 90% 85% 50% 25% CONCEPT-03 cwigv‡ci m~Îvejx msµvšÍ MvwYwZK cÖ‡qvM 15% 30% 30% 20% 30% - 10% - DU. = Dhaka University, JU. = Jahangirnagar University, RU. = Rajshahi University, CU = Chittagong University, GST = General, Science & Technology, Engr. = Engineering. STEP 1 mvRv‡bv me Z_¨ THEORY fwZ© †ivMxi c_¨ Concept 1 weÁvb I c`v_©weÁv‡bi aviYv, cÖ‡qvM I Avwe®‹v‡ii avcmg~n ✅ RMr: GB gnvwek^ Aw¯ÍZ¡kxj hv wKQz wb‡q MwVZ Zv‡K RMr e‡j| RMr‡K `yB †kÖwY‡Z fvM Kiv hvq- i. †f․Z RMr; ii. RxeRMr ✅ †f․ZRMr: c`v_© I kw³ wb‡q MwVZ cÖv‡Yi Aw¯ÍZ¡nxb RMr‡K †f․ZRMr e‡j| ✅ †f․ZRM‡Zi Dcv`vb: †f․ZRMr g~jZ PviwU Dcv`v‡bi mgš^‡q MwVZ- (K) ¯
vb, (L) Kvj ev mgq, (M) fi, (N) kw³| fv½‡bi ch©vqµg e¯‧ AYy cigvYy ¯
vqx I A¯
vqx KwYKv †KvqvK© kw³¸”Q| ✅ c`v‡_©i ag©: mvaviY ag© IRb, we¯Í…wZ, †iva, w¯
wZ¯
vcKZv we‡kl ag© KwVb c`v‡_©i w¯
wZ¯
vcKZv, `„pZv, f½yiZv; Zij c`v‡_©i c„ôUvb ev ZjUvb; Zij I evqexq c`v‡_©i mv›`ªZv ✅ c`v_©weÁv‡bi ev¯Íe cÖ‡qvM: welq e¨envi/cÖ‡qvM †iwWI 131I _vBi‡qW wµqv ch©‡eÿY, _vBi‡qW K¨vÝvi wPwKrmv| Zwor †P․¤^K Av‡ek †Rbv‡iUi, UªvÝdigvi| Zwor we‡kølY cÖwµqv Zwor cÖ‡jcb, Zwor gy`ªY, avZz wb®‥vkb, avZz weï×KiY| †jRvi iwk¥ gvbe‡`‡ni K¨vÝvi, MjeøvWvi I wKWwb †_‡K cv_i AcmviY| ÔXÕ iwk¥ ev ÔÕ iwk¥ g¨vwjMb¨v›U †Kvl aŸsm Kiv| †iwWI †Uwj‡¯‥vc Quasars I Pulsars Avwe®‥v‡i Gi Ae`vb Av‡Q| †iwWI 137Cs wbDwK¬K Gwm‡Wi MVb Rvb‡Z mnvqZv K‡i| BD‡Uwib K¨vÝvi wPwKrmv| µgUv †`‡L bvI: aviYv AbyKí ¯^xKvh© ZË¡ m~Î bxwZ mgxKiY Abywm×všÍ mn‡R g‡b ivLvi Dcvq: auvavi Avm‡i wm×v_© ‡Zvgv‡K mKj bxwZ mg~n AbymiY Ki‡Z n‡e aviYv AbyKí ¯^xKvh© ZË¡ m~Î bxwZ mgxKiY Abywm×všÍ †fŠZ RMr I cwigvc PHYSICAL WORLD AND MEASUREMENT cÖ_g cÎ 01 Aa¨vq c„ôv 45

46 An Exclusive Parallel Text Book of Physics ASPECT PHYSICS ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ✅ c`v‡_©iweÁv‡bi KwZcq welq: bvg msÁv D`vniY aviYv/cÖZ¨q (Concept) †Kvb wKQz m¤ú‡K© mwVK Dcjwä ev †evaMg¨Zv n‡jv H welq m¤ú‡K© aviYv| †Kvb aviYv n‡jv †Kv‡bv fvebv ev wPšÍvaviv ev †Kv‡bv mvaviY AwfgZ| Zv‡ci aviYv n‡jv Zvc GK cÖKvi kw³ hv †Kvb e¯‧‡Z cÖ‡qvM Ki‡j ZvcgvÎv e„w× cvq Ges eR©b Ki‡j n«vm cvq| AbyKí (Hypothesis) †Kvb wKQz m¤ú‡K© AbymÜv‡bi †h AbywgZ wm×všÍ †bIqv nq Zv‡K AbyKí e‡j| A¨v‡fv‡M‡Wªvi AbyKí| ¯^xKvh© (Postulates) †Kvb MvwYwZK g‡Wj ev m~Î cÖwZôv Kivi j‡ÿ¨ hw` wKQz c~e©kZ© ¯^xKvi K‡i †bIqv nq, Z‡e H c~e©kZ©mg~n‡K ¯^xKvh© e‡j| AvBb÷vB‡bi we‡kl Av‡cwÿK ZË¡ `ywU †g․wjK ¯^xKv‡h©i Dci cÖwZwôZ| c`v_©weÁvbx bxjm& †evi Zuvi cigvYy g‡W‡ji wfwË wn‡m‡e wZbwU ¯^xKvh© cÖ`vb K‡ib| bxwZ (Principle) †hme mvaviY m~Î weÁvb ev c`v_©weÁv‡bi wfwË Zv‡`i ejv nq bxwZ| †hmKj cÖvK…wZK mZ¨ mivmwi ¯úófv‡e cÖgvY Kiv hvq Ges IB m‡Z¨i mvnv‡h¨ A‡bK cÖvK…wZK NUbv‡K cÖgvY Kiv hvq Zv‡K bxwZ e‡j| Wcjv‡ii bxwZ| nvB‡Rbev‡M©i AwbðqZv bxwZ| Zi‡½i DcwicvZb bxwZ| ZË¡ (Theory) cixÿv-wbixÿvi Øviv cÖgvwYZ AbyKí‡K ZË¡ e‡j| †Kvb wKQz e¨vL¨vi Rb¨ †h AvbyôvwbK wPšÍvaviv, fve ev aviYv Zv‡K ZË¡ e‡j| AvBb÷vB‡bi Av‡cwÿK ZË¡| WviDB‡bi weeZ©b ZË¡| cø¨v‡¼i †Kvqv›Uvg ZË¡| m~Î (Law) hLb †Kv‡bv ZË¡ A‡bK cixÿv-wbixÿvi mvnv‡h¨ cÖgvwYZ nq Ges g~j K_v¸‡jv GKwU Dw³i gva¨‡g cÖKvk Kiv nq ZLb Zv‡K •eÁvwbK m~Î e‡j| †Kvb wbw`©ó kZ© ev Ae¯
vq me mgq Kx NU‡e Zvi eY©bv n‡jv m~Î| M¨vwjwjIi cošÍ e¯‧i m~Î| wbDU‡bi MwZ m~Î| wbDU‡bi gnvKl© m~Î| REAL TEST ANALYSIS OF PREVIOUS YEAR QUESTIONS STEP 01 ANALYSIS OF DU-7 Clg QUESTION 01. wb‡Pi †KvbwU wPivqZ ejwe`¨vq †g․wjK ivwk bq? [DU-7Clg.A.19-20] A. mgq B. fi C. `ªæwZ D. •`N©¨ S C info ‣`N©¨, fi I mgq wPivqZ ejwe`¨vi †g․wjK ivwk| STEP 02 ANALYSIS OF GST QUESTION PART A Analysis of General University Question KU 01. mbvZbx ejwe`¨vq †Kvb `ywU‡K aªæe aiv nq? [KU. 14-15] A. ¯
vb I Kvj B. ¯
vb I `ªæwZ C. `ªæwZ I Kvj D. ¯
vb I Z¡iY Ans A PART B Analysis of Science & Technology Question MBSTU 01. †Mvjxq Z‡ji e¨vmva© wbY©‡qi Rb¨ †KvbwU e¨eüZ nq? [MBSTU-A, Set-2 19-20] A. ¯øvBW‡Kwjcvm© B. †ù‡ivwgUvi C. ¯…zMR D. gvB‡µvm‡Kvc S B info †ù‡ivwgUv‡ii mvnv‡h¨ †Mvjxq Z‡ji eµZvi e¨vmva© wbY©q Kiv nq| HSTU 01. AvšÍR©vwZK c`v_© weÁvb el© †KvbwU? [HSTU. 15-16] A. 1905 B. 2005 C. 1955 D. †KvbwUB bq Ans A STEP 03 ANALYSIS OF MEDICAL & DENTAL QUESTION MAT 01. wb‡Pi †KvbwU‡Z c`v_©we`¨v jä Ávb wPwKrmv we`¨vq cÖ‡qvM Kiv nq bv? [MAT; 19-20] A. Ultrasound B. Biometric attendance C. X-ray D. Magnetic Resonance Imaging S B info c`v_©we`¨vjwä Ávb wPwKrmvwe`¨vq †hme †ÿ‡Î cÖ‡qvM Kiv nq X-ray, Magnetic Resonanc Imaging, Ultrasound, CT Scan, Positron Enuming, Tomography cÖf…wZ| 02. ‘LASER’ Gi c~Y© iƒc Kx? [MAT; 19-20] A.Light Augmentation by Stimulated Emission of Radiation B. Light Amplification by Stimulated Emission of Rays C. Light Amplification by Stimulated Emission of Radiation D.Light Amplification by Stimulated Emission of Electromagnetic Radiation Ans C 03. c`v_©we`¨vi AvIZvq Av‡m bv †KvbwU? [MAT; 19-20] A. Electromagnetism B. Astronomy C. Thermodynamics D. Anthropometry S D info c`v_©we`¨vi AvIZvf~³ welqmg~n: ejwe`¨v (Mechanics) ZvcMwZwe`¨v (Thermodynamics) ZvcweÁvb (Heat) ‡R¨vwZwe`¨v (Astronomy) kãweÁvb (Sound) B‡jKUªwb· (Electronomics) Av‡jvKweÁvb (Light) Av‡cwÿKZv (Relativity) Pz¤^KweÁvb (Magnetism) wbDwK¬q c`v_©weÁvb (Nuclear Physics) ZworweÁvb (Electricity) †Kvqv›Uvg c`v_©weÁvb (Quantum Physics) Zwor Pz¤^KweÁvb (Electromanetism) DAT 01. webv cÖgv‡Y †Kvb wKQz †g‡b †bIqv‡K e‡j- [DAT. 19-20; RU. 2016-17; iv.†ev. 2016; wm.†ev. 2015] A. aviYv B. ¯^xKvh© C. bxwZ D. ZË¡ S B info welq msÁv aviYv †Kv‡bv wKQz m¤ú‡K© mwVK Dcjwä ev †evaMg¨Zv| ¯^xKvh© webv cÖgv‡Y †Kv‡bv wKQz †g‡b wb‡q hyw³ ev wee„wZ cÖ`vb| bxwZ †hme mvaviY m~Î weÁv‡bi wfwË| ZË¡ cixÿv-wbixÿv Øviv cÖgvwYZ AbyKí|

ASPECT PHYSICS cÖ_g cÎ †f․Z RMr I cwigvc 47 ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES STEP 04 ANALYSIS OF HSC BOARD QUESTION 01. GKwU Av`k© ev hyw³c~Y© AvPiY wfwË hvi mv‡c‡ÿ Ab¨vb¨ welq Zzjbv, wePvi we‡kølY I cwigvc Kiv nq Zv‡K wK e‡j? [iv. †ev. 2016] A. m~Î B. bxwZ C. AbyKí D. ¯^xKvh© Ans B 02. cixÿv Øviv cÖgvwYZ AbyKí‡K e‡j [P. †ev. 2016] A. bxwZ B. ¯^xKvh© C. m~Î D. ZË¡ Ans D 03. †Kv‡bv wKQz e¨vL¨vi Rb¨ †h AvbyôvwbK wPšÍvaviv Zv‡K e‡j [Kz. †ev. 2016] A. ¯^xKvh© B. ZË¡ C. AbyKí D. m~Î Ans B Concept 2 c`v_©weÁv‡bi ¸iæZ¡c~Y© ivwkmg~n, Zv‡`i cÖZxK Ges gvbmg~n Name Symbol Value with unit Name Symbol Value with unit k~b¨ gva¨‡g Av‡jvi †eM c = (00) –1 3 108ms1 d¨viv‡W aªæeK F 96500C Ak^ ÿgZv H.P 1hp = 746W = 550ft-lbs1 cø¨vsK aªæeK h 6.6310–34Js AwfKl©R Z¡iY g 9.8ms2 = 980cms2 = 32fts2 wWivK aªæeK ħ = h 2 1.05510–34Js gnvKl©xq aªæeK G 6.673 10–11 Nm2 kg2 B‡j±ª‡bi K¤úUb Zi½‣`N©¨ c 2.426 10–12m f~-c„‡ô gyw³‡eM Ve 11.2kms1 ‡cÖvU‡bi K¤úUb Zi½‣`N©¨ cp 1.321 10–15m c„w_exi fi Me 6 1024kg wiWevM© aªæeK RH 1.097 107m 1 c„w_exi e¨vmva© Re 6.4 106m GK Kzix curie 3.7 1010decay/s m~‡h©i fi Ms 2 1030kg ‡evi e¨vmva© r1/0 0.53 A B¯úv‡Zi Bqs ¸YvsK Ys 2 1011Nm2 †evi g¨vM‡bUªb R 9.274 10–24Am2 cqmb AbycvZ 1 < 0.5 ‡÷dvb-‡evëRg¨vb aªæeK 5.67 108Wm2 k 4 M¨vm aªæeK/mve©Rbxb M¨vm aªæeK R 8.314 Jmol1 k 1 fxb aªæeK b 2.9 10–3mK ‡evëRg¨vb aªæeK k 1.38 1023JK1 k~b¨¯
v‡bi Zwor †f`b‡hvM¨Zv 0 8.854 10–12 C 2N 1m 2 A¨v‡fv‡M‡Wªv msL¨v NA 6.023 1023mol1 k~b¨¯
v‡bi †P․¤^K cÖ‡ek¨Zv 0 4 10–7TmA1 B‡j±ªb †fvë eV 1.610–19J K¤úUb Zi½‣`N©¨/ K¤úUb aªæeK h m0C 2.455 10–12m GK cvigvYweK fi amu 1.6610–27kg ‡evi cÖ_g Kÿc‡_i kw³ E1 –13.6eV wbðj B‡j±ª‡bi fi me 9.110–31kg wbDwK¬qvm aªæeK ro 1.4 Fermi = 1.4 10–15m †iwWqvb c 57.3 nvej aªæe‡Ki hyw³m½Z gvb H 17kms1 per million light year wbðj †cÖvU‡bi fi mp 1.6710–27kg ‡gMv cvi‡mK MPC 3.084 1019km wbðj wbDUª‡bi fi mn 1.67510–27kg 1Astronomical Unit AU 1.495 108 km B‡j±ª‡bi PvR© e 1.60210–19C 1 X-ray Unit X.U 10–13m ✅ ivwk cwigvc‡Ki wewfbœ hš¿: welq h‡š¿i bvg welq h‡š¿i bvg evqyi Pvc cwigvcK hš¿ e¨v‡ivwgUvi wbDwK¬qv‡mi kw³ Kv‡R jvMv‡bvi hš¿ wiq¨v±i DòZv ev ZvcgvÎv cwigvcK hš¿ _v‡g©vwgUvi f~wgK¤ú gvcvi hš¿ wmm‡gvMÖvd/wi±vi †¯‥j evqy‡Z Rjxq ev‡®úi cwigvY cwigvcK hš¿ nvB‡MÖvwgUvi M¨v‡mi Pvc wbY©qKvix hš¿ g¨v‡bvwgUvi M¨vmxq c`v‡_©i IRb wbY©qKvix hš¿ A¨v‡ivwgUvi cvZjv cv‡Zi cyiæZ¡ I eµZvi e¨vmva© †ù‡ivwgUvi †eM cwigvcK hš¿ †fjv‡UvwgUvi `ªæwZ cwigvcK hš¿ w¯ú‡WvwgUvi Zi‡j wbgw¾Z †Kvb e¯‧i IRb cwigvcK hš¿ D`w¯
wZ wbw³ †Mvj‡Ki e¨vm cwigvc, †gvUv Zvi, †MvjK BZ¨vw`i e¨vm ¯øvBW K¨vwjcvm© `~ieZ©x e¯‧i Zvc wbY©qKvix hš¿ cvB‡ivwgUvi i³ Pvc wbY©qKvix hš¿ wùM‡gvb¨v‡bwgUvi D”PZv gvcvi hš¿ AwëwgUvi †h cv‡Îi Zwor we‡kølY Kiv nq †fvëvwgUvi †fv‡ëR cwigvcK hš¿ †fvëwgUvi we`y¨r cÖevn cwigvcK hš¿ A¨vwgUvi k‡ãi K¤úv¼ wbY©‡qi hš¿ m‡bvwgUvi evqexq c`v‡_©i cøeZv wbY©qKvix hš¿ e¨v‡iv‡¯‥vc m~²Zv‡ii e¨vm ¯…z MR evZv‡mi †eM wbY©qKvixhš¿ A¨v‡bv‡gvwgUvi we‡kl Z_¨ : ¯…z MR Øviv me©wb¤œ cwigvc Kiv hvqÑ h‡š¿i b~¨bv¼ (0.01mm) ¯œvBW K¨vwjcvm© Øviv b~¨bZg gvcv hvqÑ 0.01mm fvwb©qvi †¯‥j w`‡q me©wb¤œ wgwjwgUvi GKK ch©šÍ gvcv hvq

48 An Exclusive Parallel Text Book of Physics ASPECT PHYSICS ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES REAL TEST ANALYSIS OF PREVIOUS YEAR QUESTIONS STEP 01 ANALYSIS OF JU QUESTION 01. †fjv‡UvwgUvi Øviv cwigvcb Kiv nq- [JU. 17-18] A. Z¡iY B. †eM C. g›`b D. fi‡eM Ans B 02. †Kv‡bv e„‡Ëi e¨vmv‡a©i mgvb e„Ë Pvc e„‡Ëi †K‡›`ª †h †KvY Drcbœ K‡i Zv‡K e‡j- [JU. 15-16; RU. 15-16] A. 1 †iwWqvb B. 0.5 †iwWqvb C. 2 †iwWqvb D. 2.5 †iwWqvb Ans A STEP 02 ANALYSIS OF RU QUESTION 01. cvZjv cv‡Zi cyiæZ¡ Ges eµZ‡ji e¨vmva© cwigvc Kivi h‡š¿i bvg wK? [RU. 17-18] A. †ù‡ivwgUvi B. ¯øvBW K¨vwjcvm© C. ¯…z MR D. fvwb©qvi †¯‥j Ans B 02. GKwU AwZ my² Zv‡ii e¨vm †Kvb hš¿wU w`‡q cwigvc Ki‡e? [RU. 15-16] A. ¯øvBW K¨vwjcvm© B. ¯…z-MR C. ‡ù‡ivwgUvi D. me KqwU Øviv Ans B 03. ¯…z-MR Øviv b~¨bZg KZ `~iZ¡ gvcv hv‡e? [RU. 14-15] A. 1mm B. 0.01 mm C. 0.1 mm D. h‡š¿i b~¨bv¼ Ans D 04. ¯øvBW K¨vwjcvm© Øviv b~¨bZg KZ `~iZ¡ gvcv hvq? [RU. 14-15] A. 1 mm B. 0.01 mm C. 0.1 mm D. fvwb©qvi aªæeK Ans B STEP 03 ANALYSIS OF GST QUESTION PART B Analysis of Science & Technology Question HSTU 01. wi±vi †¯‥j w`‡q wK gvcv nq? [HSTU. 15-16] A. f~-K¤úb Avkvi c~‡e©i mZK©Zv B. evqyi Pvc C. f~-Py¤^‡Ki ZxeªZv D. f~wgK‡¤úi ZxeªZv Ans D PSTU 01. †h h‡š¿i mvnv‡h¨ Zwor kw³‡K hvwš¿K kw³‡Z Ges hvwš¿K kw³‡K Zwor kw³‡Z iæcvšÍwiZ Kiv hvq Zv‡K wK e‡j? [PSTU. 17-18] A. Zwor hš¿ B. Wvqbv‡gv C. Zwor †gvUi D. k~b¨ Ans A 02. †m․i‡Kvl GKwUÑ [PSTU. 17-18] A. A¨vbvjM hš¿ B. wWwRUvj hš¿ C. B‡jKUªwbK hš¿ D. GKwU •e`y¨wZK †gvUi Ans C STEP 04 ANALYSIS OF MEDICAL & DENTAL QUESTION MAT 01. 1 (GK) wKD‡mK cvwbi Nbdj KZ wjUvi? [MAT; 19-20] A. 28.517 B. 28.717 C. 28.917 D. 28.317 S D info wKD‡mK n‡jv cvwb cÖev‡ni GKK| GK †m‡K‡Û GK NbdzU ev 28.317 wjUvi cvwb cÖevwnZ n‡j Zv‡K GK wKD‡mK e‡j| 02. fvwb©qvi †¯‥j w`‡q me©wb¤œ KZ GKK ch©šÍ gvcv nq? [MAT. 18-19] A. wgwjwgUvi B. b¨v‡bvwgUvi C. gvB‡µvwgUvi D. †mw›UwgUvi Ans A DAT 01. f~wgK¤ú gvcvi h‡š¿i bvg Kx? [DAT. 16-17] A. w¯ú‡WvwgUvi B. nvB‡WªvwgUvi C. _v‡g©vwgUvi D. wmm‡gvMÖvd Ans D AFMC 01. gnvKl©xq aªæe‡Ki gvb KZ? [AFMC. 2020-21] A. 6.67 1011 Nm2 kg–2 B. 4.67 10–11 Nm2 kg–2 C. 6.67 10–11 Nm2 kg–2 D. 6.67 10–13 Nm2 kg–2 S C info 6.67 10–11 Nm2 kg–2 wbDU‡bi gnvKl© m~Îvbymv‡i, F = G m1m2 d 2 myZivs, GKK f‡ii `ywU e¯‧KYv GKK `~iZ¡ †_‡K †h e‡j ci¯úi‡K AvKl©Y K‡i Zvi gvb‡K gnvKlx©q aªæeK e‡j| gvÎv: [L3M –1T –2 ]; GKK: Nm2 kg–2 wnmve K‡i †`Lv †M‡Q 1 kg f‡ii `ywU e¯‧‡K 1m `~‡i ¯
vcb Ki‡j Zv‡`i AvKl©Y ej 6.67 10–11N G = 6.67 10–11 Nm2 kg–2 STEP 05 ANALYSIS OF HSC BOARD QUESTION 01. GKwU ¯…zM‡Ri jwNô aªæe‡Ki gvb 0.01mm| GwU Øviv b~¨bZg KZ †ea gvcv hv‡e? [iv.†ev. 2019] A. 1mm B. 0.10mm C. 0.01mm D. 0.001mm Ans C 02. GKwU m~² Zv‡ii e¨vm †Kvb hš¿wU w`‡q cwigvc Ki‡e? [iv.†ev. 15-16] A. ¯øvBW K¨vwjcvm© B. ¯…zMR C. †ù‡ivwgUvi D. me KqwU Øviv Ans B Concept 3 KwZcq ¸iæZ¡c~Y© ivwki ms‡KZ, GKK Ges gvÎv ✅ †f․Z ivwk I GKK : ivwki msÁv †f․Z RM‡Z hv wKQz cwigvc Kiv hvq Zv‡K Avgiv ivwk ewj| cÖKvi‡f` (i) †g․wjK ivwk; (ii) †h․wMK/jä ivwk D`vniY †g․wjK ivwk: •`N©¨, fi, mgq, ZvcgvÎv, †KvY, we`y¨r cÖevngvÎv, `xcb gvÎv, c`v‡_©i cwigvY BZ¨vw`; †g․wjK ivwk g‡b ivLvi mnR †K․kj: mZZv †fv‡ii `xc w`ev‡jv‡K m Z Zv †fv‡ii `x c w`ev‡jvK mgq Zwor cÖevn ZvcgvÎv fi `xcb ZxeªZv c`v‡_©i cwigvY ‣`N©¨ ✅ (‡g․wjK ivwk I Zv‡`i GKK): ivwk Gm.AvB GKK GK‡Ki ms‡KZ 1. •`N©¨ (Length) wgUvi (meter) m 2. fi (Mass) wK‡jvMÖvg (kilogram) kg 3. mgq (Time) †m‡KÛ (second) s 4. ZvcgvÎv (Temperature) †Kjwfb (kelvin) k 5. `xcb ZxeªZv (Luminous intensity) K¨v‡Ûjv (candela) cd 6. c`v‡_©i cwigvb †gvj (mole) mol 7. Zwor cÖevn A¨vw¤úqvi (ampere) A ◈ wØgvwÎK †KvY: †iwWqvb * wÎgvwÎK †KvY : †÷wiwWqvb

ASPECT PHYSICS cÖ_g cÎ †f․Z RMr I cwigvc 49 ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ✅ wewfbœ †f․Z ivwki ms‡KZ, GKK I gvÎv: bvg Terminology Gm.AvB GK‡K (evsjv bvg) GKK gvÎv †eM, `ªæwZ velocity, speed wgUvi/‡m‡KÛ ms–1 LT–1 Z¡iY acceleration wgUvi/‡m‡KÛ2 ms–2 LT–2 fi ‡eM momentum wK‡jvMÖvg-wgUvi/†m‡KÛ kgms–1 MLT–1 ej force wbDUb kgms–2 MLT–2 KvR, kw³ work, energy Ryj (j) N.m ML2T –2 ¶gZv power IqvU (w) J.s–1 ML2T –3 NbZ¡ density wK‡jvMÖvg/wgUvi 3 kgm–3 ML–3 Pvc pressure c¨vm‡Kj (Pa) Nm–2 ML–1T –2 Zvc Heat Ryj (j) N.m ML2T –2 Zvc aviY ¶gZv Heat capacity Ryj/‡Kjwfb J.k–1 ML2T –2 – 1 Av‡cw¶K Zvc Specific heat Ryj/wK‡jvMÖvg ‡Kjwfb J.kg–1 k –1 L 2T –2 – 1 Zvc cwievnKZ¡ Thermal conductivity IqvU/wgUvi-‡Kjwfb wm–1 k –1 MLT–3 – 1 `xcb ZxeªZv Luminous intensity K¨v‡Ûjv cd J Av‡jvK d¬v· Luminous flux jy‡gb cd.sr J Zwor ZxeªZv electric intensity wbDUb/Kzj¤^ N.C–1 MLT–3 I –1 Zwor wefe electric potential †fvë J.C–1 ML2T –3 I –1 Zwor PvjK kw³ electromotive force †fvë J.C–1 ML2T –3 I –1 †iva resistance Ing () V.A–1 ML2T –3 I –2 Av‡cw¶K ‡iva specific resistance IÕg- wgUvi - m ML3T –3 I –2 cwievnxZv conductance wm‡gÝ V.A–1 M –1L –2 T 3 I 2 cwievnKZ¡ conductivity cÖwZ IÕg- cÖwZ wgUvi –1 – m –1 M –1L –3 T 3 I 2 `xcb ÿgZv illumination jv· lm.m–2 JL–2 mv›`ªZvsK viscosity wbDUb-†m‡KÛ/wgUvi2 Nsm–2 ML–1T –1 c„ôUvb Surface tension wbDUb/wgUvi Nm–1 MT –2 cxob Stress wbDUb/wgUvi2 Nm–2 ML–1T –2 gnvKl©xq aªæeK Gravitational constant wbDUb-wgUvi2 /†KwR2 Nm2 kg–2 M –1L 3 T –2 ✅ †g․wjK GKK : 3wU •`‡N©¨i GKK (m) f‡ii GKK (kg) mg‡qi GKK (sec.) ✅ GKBgvÎv mgxKiY wewkó ivwk : ivwk gvÎv ivwk gvÎv KvR, kw³, Zvc, UK©/e‡ji åvgK, ؇›Øi åvgK ASPECT SPECIAL: ejvB‡qi e‡ji åvgK fvB UvKv UK© †`q ؇›Øi åvgK kw³ kw³ KvKv‡K KvR ML2T –2 †K․wYK fi‡eM I cø¨v¼ aªæeK ML2T –1 cxob, Pvc, w¯
wZ¯
vcK ¸Yv¼ ML–1T –2 •iwLK fi‡eM I e‡ji NvZ MLT–1 K¤úv¼, †K․wYK †eM, †e‡Mi bwZgvÎv T –1 c„ôkw³, c„ôUvb, w¯ús aªæeK MT–2 Z¡iY, gnvKl©xq cÖvej¨ LT –2 REAL TEST ANALYSIS OF PREVIOUS YEAR QUESTIONS STEP 01 ANALYSIS OF DU QUESTION 01. hw` A=BnC m Ges A, B I C Gi gvÎv h_vµ‡g, LT, L2T –1 Ges LT2 nq Z‡e n I m Gi gvb n‡e- [DU. 17-18] A. 2/3, 1/3 B. 2, 3 C. 4/5, –1/5 D. 1/5, 3/5 S D info A=BnC m LT= (L 2 T –1 ) n .(LT 2 ) m = L 2n + m T –n+2m So, 2n+ m=1 & –n +2m = 1 , n = 1/5; m = 3/5 02. wb‡Pi †KvbwU †g․wjK GKK? [DU. 16-17] A. Coulomb B. Ampere C. Volt D. Ohm Ans B STEP 02 ANALYSIS OF RU QUESTION 01. wb‡Pi †KvbwU †g․wjK GKK? [RU. Sinovac, Set-1. 20-21] A. Kzj¤^ B. A¨vw¤úqvi C. †fvë D. In&g S B info Zwor cÖev‡ni GKK A¨vw¤úqvi| hv GKwU †g․wjK GKK| A_©vr †g․wjK ivwkmg~‡ni GKKB †g․wjK GKK| 02. †g․wjK GKK n‡jv- [RU. 18-19] (i) wK.MÖv., wgUvi I †m‡KÛ (ii) †m‡KÛ I †fvë (iii) †Kjwfb, K¨v‡Ûjv I wbDUb wb‡Pi †KvbwU mwVK? A.i B. ii C. i,iii D. i, ii,iii Ans A 03. †Kvb&wU †g․wjK ivwk bq? [RU. 17-18] A. ZvcgvÎv B. fi C. ‣`N©¨ D. †eM Ans D 04. [ML–1T –2 ] gvÎv mgxwKiYwU Kvi? [RU. 15-16] A. ÿgZv B. MwZkw³ C. c„ôUvb D. cxob Ans D STEP 03 ANALYSIS OF CU QUESTION 01. †KvbwU †g․wjK ivwk bq? [CU-A, Set-4. 20-21] A. Zwor wefe B. ZvcgvÎv C. Av‡jvi ZxeªZv D. c`v‡_©i cwigvY S A info ZvcgvÎv, Av‡jvi ZxeªZv, c`v‡_©i cwigvY n‡jv †g․wjK ivwk|

50 An Exclusive Parallel Text Book of Physics ASPECT PHYSICS ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES 02. wb‡Pi †KvbwU jä ivwk? [CU-A, 19-20, DU. Tech. 20-21] A. K¤úv¼ B. fi C. mgq D. ZvcgvÎv S A info fi, mgq I ZvcgvÎv †g․wjK ivwk| 03. GK‡Ki mwVK µg †KvbwU? [CU-A, 19-20, RU. 20-21; Xv.†ev. 2016] A. cvi‡mK > G¨vs÷ªg > †gMvwgUvi > Av‡jvK eQi B. cvi‡mK > Av‡jvK eQi > †gMvwgUvi > G¨vs÷ªg C. Av‡jvK eQi > G¨vs÷ªg > †gMvwgUvi > cvi‡mK D. G¨vs÷ªg > cvi‡mK > Av‡jvK eQi > †gMvwgUvi S B info 1 cvi‡mK (pc) = 3.083 × 1013 km = 3.26 ly 1 Av‡jvK eQi = 9.42 × 1012 km 1 †gMvwgUvi = 106m. 1 G¨vs÷ªg = 10–10 m 04. †KvbwU f~wg ivwk (Base quantity) bq? [CU. 13-14] A. fi B. mgq C. •`N©¨ D. NbZ¡ E. ZvcgvÎv Ans D STEP 04 ANALYSIS OF GST QUESTION PART A Analysis of Science & Technology Question SUST 01. †eM, Z¡iY, ej, KvR, ÿgZv I kw³i gvÎv h_vµ‡g- [SUST. 10-11; HSTU. 12-13; MBSTU. 11-12] A. LT–1 , LT–2 , MLT2 , ML2T –2 , ML2T –3 , MLT–2 B. LT–1 , LT–2 , MLT2 , ML2T –2 , ML2T –3 , ML2T –2 C. LT–1 , LT–2 , MLT–2 , ML2T –2 , MLT–3 , ML2T –2 D. LT–1 , LT–2 , MLT–2 , ML2T –2 , ML2T –3 , ML2T –2 Ans D 02. †Kvb gvÎvwU mwVK? [SUST. 05-06] A. NbZ¡ ML3 B. fi‡eM MLT3 C. ÿgZv MLT1 D. Pvc ML–1T 2 Ans A 03. wb‡Pi †KvbwU SI GKK bq? [SUST. 04-05] A. K B. J C. erg D. A Ans C JUST 01. wb‡Pi †Kvb `ywUi gvÎv GKB? [JUST. 12-13] A. UK© I kw³ B. ej I KvR RoZvi C. †K․wYK fi‡eM I Z¡iY D. åvgK I ÿgZv Ans A MBSTU 01. wb‡Pi †KvbwU kw³i gvÎv? [MBSTU. 13-14] A. ML3T –2 B. ML2T –2 C. MLT2 D. ML2T –1 Ans B 02. RoZvi åvg‡Ki gvÎv wK? [MBSTU. 13-14; HSTU. 12-13] A. [ML2 ] B. [ML] C. [M2L] D. [M2L 2 ] Ans A 03. Impulse of force ev e‡ji Nv‡Zi gvÎv mgxKiY †KvbwU? [MBSTU. 12-13] A. [MLT–2 ] B. [MLT–1 ] C. MLT–3 D. [ML2T –2 ] S B info Ft = mv = kgms–1 [Ft] = [MLT–1 ] HSTU 01. U‡K©i gvÎv mgxKiY †KvbwU? [HSTU. 10-11] A. MLT–2 B. ML–1T –1 C. MLT–1 D. ML2T –2 Ans D STEP 05 ANALYSIS OF ENGINEERING & BUTex QUESTION RUET 01. e‡ji gvÎv mgxKiY †KvbwU? [RUET. 12-13] A. [MLT–2 ] B. [MLT] C. [MLT–1 ] D. [MLT–3 ] E. [MLT–4 ] Ans A STEP 06 ANALYSIS OF MEDICAL & DENTAL QUESTION MAT 01. Pv‡ci SI GKK †KvbwU? [MAT; 19-20] A. CmHg B. Pascal C. cmH2O D. mmHg S B info Pv‡ci SI GKK pascal ev Nm2 Ges gvÎv mgxKiY [ML1T 2 ] Pv‡ci Ab¨vb¨ GKK n‡jv atm, tor, bar, mmHg, cmHg cÖf…wZ| 02. fi‡e‡Mi gvÎv mgxKiY wb‡Pi †KvbwU? [MAT. 17-18] A. [MLT–1 ] B. [MLT–2 ] C. [ML2T] D. [ML2T -2 ] Ans A DAT 01. wb‡Pi †Rvo¸‡jvi g‡a¨ †KvbwUi gvÎv (dimension) GKB? [DAT. 2020-21] A. KvR I kw³ B. ej I KvR C. ej I UK© D. KvR I ÿgZv S A info KvR I kw³ Df‡qi gvÎv ML2T –2 KviY, KvR n‡jv kw³i GKwU iƒc| STEP 07 ANALYSIS OF HSC BOARD QUESTION 01. e„ËvKvi †¯‥‡ji c~Y© N~Y©b msL¨v M, e„ËvKvi †¯‥‡ji AwZwi³ fvM msL¨v N Ges jwNô MYb Lc n‡j †¯‥‡ivwgUv‡ii mvnv‡h¨ h wbb©‡qi m~Î †KvbwU? [Xv.†ev. 2019] A. h = M + Lc B. h = M N + Lc C. h = M wcP + Lc D. h = M wcP+ N + Lc Ans D 02. Pvc GKwU †h․wMK ivwk| Gi Gm. AvB. GKK n‡”Q- [iv. †ev. 2017] A. cvm‡Kj B. wbDUb/wgUvi2 C. WvBb/†mwg.2 D. A I B DfqB S D info Pvc Gi SI GKK Pa/Nm–2 , C.G.S GKK dyne cm–2 Ges F.P.S GKK ℓbft–1 s –2 03. †g․wjK ivwk n‡jvÑ [w`.†ev. 2017] i. Zwor cÖevngvÎv ii. c`v‡_©i cwigvY iii. `xcb ZxeªZv wb‡Pi ‡KvbwU mwVK? A. i I ii B. ii I iii C. i I iii D. i, ii I iii Ans D 04. Av‡jvKel© wK‡mi GKK? [h. †ev. 2016] A. mgq B. `~iZ¡ C. Z¡iY D. †eM Ans B 05. wb‡Pi †KvbwUi GKK Ab¨ wZbwUi GKK n‡Z wfbœ? [Kz. †ev. 2017] A. NbZ¡ AvqZb †eM B. fi‡e‡Mi cwieZ©‡bi nvi C. Bqs Gi w¯
wZ¯
vcK ¸YvsK †ÿÎdj D. fi AwfKl©R Z¡iY Ans A 06. c`v‡_©i cwigv‡Yi Gm AvB GKK n‡jvÑ [Kz.†ev.2015; e.†ev. 2016] A. A¨vw¤úqvi B. K¨v‡Ûjv C. †gvj D. wK‡jvMÖvg Ans C 07. wb‡Pi †KvbwU jä ivwk? [wm.†ev. 2019] A. NbZ¡ B. fi C. ZvcgvÎv D. mgq Ans A 08. wb‡Pi †KvbwU ‣`‡N©¨i S.I GKK? [wm. †ev. 2017] A. †mw›UwgUvi B. gvBj C. wgUvi D. dzU Ans C 09. †g․wjK GKK n‡jv [wm. †ev. 2016] i. wgUvi I †Kjwfb ii. †m‡KÛ I A¨vw¤úqvi iii. K¨v‡Ûjv I †gvj wb‡Pi †KvbwU mwVK? A. i I ii B. i I iii C. ii I iii D. i, ii I iii Ans D 10. †Kvb `ywU †f․Z RM‡Zi Dcv`vb? [e. †ev. 2016] A. mgq I Z¡iY B. fi I ¯
vb C. ¯
vb I †eM D. fi I ZvcgvÎv S B info ¯
vb, Kvj, fi †f․Z RM‡Zi Dcv`vb| Concept 4 ¸iæZ¡c~Y© weÁvbxMY Ges Zv‡`i Avwe®‹vimg~n weÁvbx Avwe®‥vi/gZvgZ mgqKvj wMÖK `vk©wbK cx_v‡Mvivm c„w_ex †Mvj e‡j gZ †`b| wLª÷c~e© 500 A‡ã †W‡gvwµUvm cigvYy AwefvR¨ (Atomas) wKš‧ wesk kZvãxi weÁvbxiv †`Lv‡jb cigvYy wefvR¨| wZwb c`v‡_©i AwefvR¨ GK‡Ki bvg †`b cigvYy| wLª÷c~e© 400 A‡ã

ASPECT PHYSICS cÖ_g cÎ †f․Z RMr I cwigvc 51 ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES weÁvbx Avwe®‥vi/gZvgZ mgqKvj wMÖK weÁvbx AvwK©wgwWm wjfvi, cyj Pvjbvi m~Î Avwe®‥vi K‡ib Ges Amg KwVb e¯‧i NbZ¡ wbY©‡qi m~Î Avwe®‥vi K‡ib| †Mvjxq `c©Y e¨envi K‡i m~h© iwk¥i mvnv‡h¨ Av¸b aiv‡bvi †K․kj †ei K‡ib| wjfv‡ii bxwZ I D`w¯
wZwe`¨vi m~Î Avwe®‥vi K‡ib| wLª÷c~e© 200 A‡ã wMÖK †R¨vwZwe©` wnccviPvm© c„w_ex †_‡K Puv‡`i `~iZ¡ I AvKvi wbY©q K‡ib| wLª÷c~e© 100 A‡ã †cvj¨v‡Ûi †R¨vwZwe©` †Kcjvi MÖ‡ni MwZ msµvšÍ wZbwU m~Î cÖ`vb K‡ib| †Kvcvwb©Kvm Gi †m․i‡Kw›`ªK Z‡Ë¡i aviYv †_‡K wZwb e‡jb, MÖn¸‡jv Dce„ËvKvi Kÿc‡_ Nyi‡Q| 1543 wLª÷v‡ã BZvjxq weÁvbx M¨vwjwjI AvaywbK •eÁvwbK c×wZi m~PbvKvix| miY, MwZ, Z¡iY, mgq BZ¨vw`i msÁv cÖ`vb I G‡`i g‡a¨ m¤úK© wbY©q K‡ib| e¯‧i cZ‡bi wbqg Avwe®‥vi I w¯
wZwe`¨vi wfwË ¯
vcb K‡ib| nvej †Uwj‡¯‥vc w`‡q MÖ‡ni MwZ ch©‡eÿY K‡ib| Ôm~h©‡K †K›`ª K‡i c„w_ex †Nv‡iÕ-Gi gZev` mg_©b K‡ib| ÔThe Law of MotionÕ iPbv K‡ib| †h․wMK AYyexÿYhš¿ I †Uwjwfkb Avwe®‥vi K‡ib| 1600 wLª÷v‡ã Bs‡iR weÁvbx Wv. wMjevU© c„w_exi Pz¤^KZ¡ Avwe®‥vi I K¤úv‡mi e¨envi m¤ú‡K© aviYv †`b| 1600 wLª÷v‡ã †eøBR c¨vm‡Kj evqy I Zi‡ji Pvc wb‡q M‡elYv K‡ib| 1600 wLª÷v‡ã Bs‡iR weÁvbx wbDUb ejwe`¨vi wZbwU weL¨vZ m~Î cÖwZcv`b K‡ib; AcwUKm& bvgK eB †j‡Lb; 1687 mv‡j Zvi wek^ bw›`Z MÖš
 Philosophiae Naturalis Principia Mathematica cÖKvwkZ nq †hLv‡b wZwb me©Rbxb gnvKl© m~Î I MwZi wZbwU m~Î cÖ`vb K‡ib; wZwb Av‡jvi KwYKv Z‡Ë¡i cÖe³v; MwZi mgxKiY gnvKl© m~Î, Av‡jvi eY©vwji KYv ZË¡ Avwe®‥vi K‡ib; MwY‡Zi bZzb kvLv K¨vjKzjvm Avwe®‥vi K‡ib| †j‡Ýi m~Î cÖeZ©b K‡ib Ges cÖwZdjK †Uwj‡¯‥vc Avwe®‥vi K‡ib| mß`k kZvãxi gvSvgvwS (1665-1755) †_wjm m~h©MÖnY m¤úwK©Z fwel¨r evYxi Rb¨ weL¨vZ| †Kvcvwb©Kvm †m․i‡Kw›`ªK Z‡Ë¡i aviYv †`b| †Rgm IqvU ev®ú BwÄb Avwe®‥vi iRvi †eKb cixÿvg~jK •eÁvwbK c×wZi cÖe³v| Ugvm Bqs wØ-wPo cixÿv I Av‡jvi e¨wZPvi Avwe®‥vi| c`v‡_©i w¯
wZ¯
vcKZv Avwe®‥vi| gvB‡Kj d¨viv‡W Avwe®‥vi K‡ib †h, GKwU cÖej †P․¤^K‡ÿ‡Îi cÖfv‡e mgeZ©b Zj Ny‡i hvq (d¨viv‡W wµqv)| cÖ_g Wvqbv‡gv •Zwi K‡ib| †P․¤^K‡ÿÎ Øviv Zwor cÖevn m„wó Kiv hvq| we`y¨r †P․¤^K †ÿÎZË¡ cÖ`vb K‡ib| †W‡gvwµUvm c`v‡_©i AwefvR¨ GK‡Ki aviYv †`b Ges Gi bvg †`b cigvYy| U‡jwg me©cÖ_g f~-†Kw›`ªK ZË¡ Dc¯
vcb K‡ib| g¨v·I‡qj me©cÖ_g AvYweK †eM eÈb m¤ú‡K© ZË¡ †`b| wZwb †`Lvb †h, Av‡jv GK cÖKvi ZvwoZ †P․¤^K Zi½| fv¯‥ivPvh© = 22 7 wbY©q K‡ib| †¯œj Av‡jvi cÖwZmiY| ievU© e‡qj M¨v‡mi Pvcxq m~Î †`b| Avj LyRv›`x MÖn, bÿ‡Îi `~iZ¡ wbY©‡qi hš¿, †m·U¨v›U hš¿ Avwe®‥vi| g¨v· cø¨v¼ K…òe¯‧i wewKiY m¤ú‡K© ¸iæZ¡c~Y© ZË¡ cÖYqb| †Kvqv›Uvg/†ZRKbvev` ZË¡ †`b e¨vKewW †¯úKUªvg Gi kw³i eÈb e¨vL¨v K‡ib| A¨vjevU© AvBb÷vBb 1905 mv‡j Av‡cwÿKZvi we‡kl ZË¡ cÖKvk K‡ib| g¨v· cø¨v‡¼i †Kvqv›Uvg ZË¡‡K m¤úªmvwiZ K‡ib| Av‡jv‡K Zworwµqvi e¨vL¨v cÖ`vb Ges Av‡jvi †Kvqv›Uvi bvg †dvUb †`b| iv`vi‡dvW© †cÖvUb Avwe®‥vi K‡ib| 1919 wLªóv‡ã ✅ wewfbœ ZË¡ I cÖeZ©K : weÁvbx ZË¡ weÁvbx ZË¡ wbDUb KYv ZË¡ nvB‡Mbm Zi½ ZË¡ g¨v· cøv¼ †Kvqv›Uvg ZË¡ g¨v·I‡qj Zwor-Pz¤^K Zi½ ZË¡

52 An Exclusive Parallel Text Book of Physics ASPECT PHYSICS ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES REAL TEST ANALYSIS OF PREVIOUS YEAR QUESTIONS STEP 01 ANALYSIS OF DU QUESTION 01. †cÖvUb KZ mv‡j †K Avwe®‥vi K‡ib? [DU. 13-14] A. 1932, P¨vWDBK B. 1919, iv`vi‡dvW© C. 1932, iv`vi‡dvW© D. 1911, iv`vi‡dvW© Ans B STEP 02 ANALYSIS OF JU QUESTION 01. Av‡jvi †Kvqv›Uvg bvg †dvUb †`b †K? [JU. 14-15] A. g¨v· cø¨v¼ B. wMjevU© jyBm C. AvjevU© AvBb÷vBb D. ‡KvbwUB bq Ans C STEP 03 ANALYSIS OF RU QUESTION 01. Av‡jvi KwYKv Z‡Ë¡i cÖe³v †K? [RU. 17-18] A. Ugvm Bqs B. wbDUb C. AvjevU© AvBb÷vBb D. g¨v· cø¨v¯‥ Ans B 02. †Kvqv›Uvg Z‡Ë¡i RbK †K? [RU. 17-18] A. g¨v·I‡qj B. cø¨v¼ C. cøv›U D. nvB‡Mb Ans B 03. †Kvb weÁvbx K¨vjKzjvm Avwe®‥vi K‡ib? [RU. 16-17] A. AvBb÷vBb B. M¨vwjwjI C. Ugvm Bqs D. wbDUb Ans D 04. c`v_©weÁv‡b 2016 mv‡j †bv‡ej cyi¯‥v‡ii Aa©vsk cvb- [RU. 16-17] A. ‡WwfW _vD‡mj B. wcUvi wnMm C. ZvKvAvwK KvwRZv D. gvB‡Kj K÷viwjrm Ans A 05. †Kvb weÁvbxi g‡Z ÔGKwU KYvi Ae¯
vb I fi‡eM GKB mv‡_ Rvbv Am¤¢e? [RU. 16-17] A. nvB‡RbevM© B. `¨ eªMjx C. g¨v·I‡qj D. g¨v· cøvsK Ans A 06. †Kvb weÁvbx Av‡jv‡Ki e¨wZPvi Avwe®‥vi K‡ib? [RU. 15-16] A. Ugvm Bqs, 1980 B. jW© iv`vi‡dvW©, 1911 C. AvjevU© AvBb÷vBb, 1920 D. g¨v· cø¨v¯‥, 1925 Ans A 07. m~‡h©i iwk¥ †K›`ªxf~Z K‡i Av¸b R¡vjv‡bvi †KŠkj Rvb‡Z †Kvb weÁvbx? [iv.we.-15-16] A. _gvm Bqs B. AvwKwgwWm C. M¨vwjwjI D. g¨v· cø¨v¼ Ans B STEP 04 ANALYSIS OF GST QUESTION PART A Analysis of General University Question IU 01. cvwLi Dov ch©‡eÿY K‡i D‡ovRvnv‡Ri g‡Wj •Zwi K‡ib †K? [B.we.-15-16; Xv. †ev. 2017] A. †Rgm IqvU B. wµwðqvb C. wjIbv‡`©v `v wfw D. Avj nv‡Rb Ans C PART B Analysis of Science & Technology Question SUST 01. eøvKewW †¯úKUªv‡gi kw³i eÈb †K e¨vL¨v Ki‡Z †c‡iwQ‡jb? [SUST. 06-07] A. †evi B. g¨v· cø¨v¼ C. wWevB D. AvBb÷vBb Ans B PSTU 01. †Kvb weÁvbx †Kvqv›Uvg Z‡Ë¡i aviYv‡K m¤úªmvwiZ K‡ib? [PSTU. 17-18] A. Michael Faraday B. Albert Einstein C. Max Planck D. Newton Ans B STEP 05 ANALYSIS OF MEDICAL & DENTAL QUESTION MAT 01. ÒMÖn ¸wji MwZc_ Dce„ËvKviÓÑ ZË¡wU †K Avwe®‥vi K‡i‡Qb? [MAT. 19-20] A. †Kcjvi B. U‡jwg C. wc_v‡Mvivm D. M¨vwjwjI Ans A 02. †Kvb •eÁvwbK me©cÖ_g m~h©‡Kw›`ªK †m․iRM‡Zi aviYv cÖ`vb K‡ib? [MAT. 18-19, HSC Board.2018] A. †Kcjvi B. U‡jwg C. †W‡gvwµUvm D. †Kvcvwb©Kvm Ans D STEP 06 ANALYSIS OF HSC BOARD QUESTION 01. wb¤œwjwLZ †Kvb weÁvbx †Kvqv›Uvg Z‡Ë¡i aviYv‡K m¤úªmvwiZ K‡ib? [w`. †ev. 2016] A. gvB‡Kj d¨viv‡W B. AvjevU© AvBb÷vBb C. g¨v· cøvsK D. wbDUb Ans B Concept  5 •`N©¨ cwigv‡ci wKQz cÖPwjZ I b‡fvgÛjxq GKK ✅ •`‡N©¨i ÿz`ª GKK: 1 gvB‡µvb () 104 †mwg. 10–6 wgUvi 1 G·‡i BDwbU (X..) 10–11 †mwg. 10–13 wgUvi 1 wgwjgvB‡µvb (m) 107 †mwg. 10–9 wgUvi 1 gvB‡µvwgUvi (m) 10–4 †mwg. 10–6 wgUvi 1 G¨vs÷ªg ( A) 108 †mwg. 10–10 wgUvi 1 dvwg© 10–13 †mwg. 10–15 wgUvi ✅ •`‡N©¨i e„nr GKK: 1 †gMvwgUvi (Mm) = 108 †mwg. = 106 wgUvi 1 G¨v‡÷ª‡bvwgK¨vj BDwbU (AU) = 1.496 108 wK‡jvwgUvi = 9.2696 107 gvBj 1 Av‡jvK ermi (ly) = GKeQ‡i Av‡jv‡Ki AwZµvšÍ `~iZ¡ = 9.42 1015 wgUvi = 5.865 1012 gvBj = 9.42 1012km 1 cvi‡mK (pc) = 3.083 1013 wK‡jvwgUvi = 3.26 ly 1 GKK cvigvYweK fi (a.m.u) = 1.66 10–27 wK‡jvMÖvg 1 M¨vjb = 4.54 10–3m 3 ✅ `‡ki m~PK: †Wwm 10–1 †mw›U 10–2 wgwj 10–3 gvB‡µv 10–6 b¨v‡bv 10–9 wc‡Kv 10–12 †dg‡Uv 10–15 A¨v‡Uv 10–18 †n‡±v 102 wK‡jv 103 wgwiqv 104 †gMv 106 wMMv 109 †Uiv 1012 †cUv 1015 G·v 1018

ASPECT PHYSICS cÖ_g cÎ †f․Z RMr I cwigvc 53 ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ✅ •`N©¨ 1 Bw = 2.54 cm = 2.5 × 104 micron 1 m = 39.37 inch = 3.28 feet; 1 mile = 1760 MR; 5280 feet = 1609.76m = 1.61 km 1 km = 0.62 mile fi 1 kg = 2.2046/lb (cvDÛ) 1 †gwUªK Ub = 1000 kg 1 Ub = 2240 lb = 1016 kg AvqZb 1m3 = 1000L = 1000dm3 1 L = 1 dm3 = 1000mL = 1000cm3 1 M¨vjb (UK) = 4.546L = 277 inch3 KvR 1 erg = 10–7 J; 1 J = 107 erg; 1 ft – poundal = 4.2 105 erg; 1 gm – cm = 980 erg; 1 ft – 1b = 1.356 J; 1 kg – m = 9.8 Joule kw³i GKK 1 joule = 1 Nm = 107 dyne.cm = 107 erg; 1ppm = 1mg/L; 1 eV(B‡jKUªb †fvë) = 1.6 10–19J ÿgZvi GKK 1 watt = 621 lumen; 1 HP = 746 watt 1 HP = 550 lb ft s1 REAL TEST ANALYSIS OF PREVIOUS YEAR QUESTIONS STEP 01 ANALYSIS OF DU QUESTION 01 . 1 watt mgvb KZ Lumen? [DU. 13-14] A. 550 B. 620 C. 600 D. 621 Ans D STEP 02 ANALYSIS OF JU QUESTION 01. b¨v‡bv eySvq †KvbwU? [JU-A, Set-A. 19-20] A. 10–6 B. 10–9 C. 10–12 D. 10–15 S B info 1 gvB‡µvb = 10–6 m ; 1 b¨v‡bvwgUvi = 109m ; 1 wc‡Kv = 10–12m ; 1 †dg‡Uv = 10–15 m 02. GK †dg‡UvwgUvi- [JU-A, Set-D. 19-20] A. 10–18m B. 10–15m C. 10–12m D. 10–9 m S B info 1 A¨v‡Uv = 10–18 ; 1 ‡dg‡Uv = 1015m ; 1 wc‡Kv = 10–12 ; 1 b¨v‡bv = 10–9 m 03. `‡ki †Kvb DcmM©wU me‡P‡q †QvU? [JU-H, Set-1. 19-20] A. †dg‡Uv B. A‡Uv C. b¨v‡bv D. †R‡Þv S D info 1 A¨v‡Uv = 1018 ; 1 †dg‡Uv = 10–15; 1 b¨v‡bv = 10–9 ; 1 †R‡Þv = 10–21 04. 20kg-m †K Joule G cÖKvk Ki| [JU. 17-18] A. 199J B. 196J C. 200J D. 188J S B info 20kg-m = 20 9.8 = 196J 05. 3 wbDUb‡K cvDÛv‡j cÖKvk Ki| [JU. 17-18] A. 25.6972 B. 26.6972 C. 21.6972 D. 30.6972 S C info 1 wbDUb = 7.2324 cvDÛvj 3 wbDUb = 7.2324 3 = 21.6972 cvDÛvj 06. 1ft-cvDÛvj = [JU. 17-18] A. 0.05214J B. 0.04214J C. 0.06214J D. 0.03214J S B info Avgiv Rvwb, 1J = 23.73 ft pdl 1 ft pdl = 1 23.73 = 0.04214J STEP 03 ANALYSIS OF RU QUESTION 01. GK Bw mgvb? [RU. 17-18] A. 2.54 104 gvBµb B. 2.54 105 gvBµb C. 2.54 10–4 cm D. †KvbwUB bq Ans A 02. 1 ppm = ? [RU. 15-16] A. 1mg/L B. 0.1 mg/L C. 10 mg/L D. 106 mg/L Ans A 03. 1 atto second n‡”Q- [RU. 12-13] A. 10–18 S B. 10–15 S C. 10–12 S D. 10–9 S Ans A STEP 04 ANALYSIS OF CU QUESTION 01. wc‡Kv (p) †KvbwU? [CU. 15-16; wm.†ev.15; w`.†ev.15; Kz.†ev.15] A. 1012 B. 109 C. 109 D. 1012 E. 1011 Ans D STEP 05 ANALYSIS OF GST QUESTION PART A Analysis of General University Question IU 01. G·v (hvi ms‡KZ E) GK‡Ki KZ ¸Y? [IU. 17-18] A. 109 B. 1012 C. 1015 D. 1018 Ans D BRUR 01. GK †Uiv wgUvi mgvb KZ? [BRU. 16-17] A. 109 wgUvi B. 1012 wgUvi C. 1015 wgUvi D. 1018wgUvi Ans B JKKNIU 01. 1 B‡qvUªvwgUvi = KZ? [JKKNIU-B, Set-3, 19-20] A. 1013 m B. 1018 m C. 1020 m D. 1024 m Ans D PART B Analysis of Science & Technology Question SUST 01. AvbygvwbK KZ wgUvi `~i‡Z¡i g‡a¨ mej wbDwK¬q ej Kvh©Ki? [SUST-B, 19-20] A. 10–15 B. 10–8 C. 10–10 D. 10–5 E. 10–20 S A info kw³kvjx wbDK¬xq ej AwZ ÿz`ª `~iZ¡ 10–15 m Gi g‡a¨ wµqvkxj| G `~i‡Z¡i evB‡i G e‡ji gvb k~b¨| MBSTU 01. 1 Mpc = ? [MBSTU. 15-16] A. 3.084 1019 km B. 3.84 109 km C. 3.84 1019 km D. 3.084 109 km Ans A BSMRSTU 01. Av‡jvKel© wK‡mi GKK? [BSMRSTU-B, 19-20] A. `ªæwZi B. `~i‡Z¡i C. mg‡qi D. Av‡jvi †e‡Mi S B info GK Av‡jvK el© = 9.42 1015 m = 9.42 1012 km. 02. GK b¨v‡bvwgUvi mgvb KZ wgUvi? [BSMRSTU. 16-17] A. 10–8m B. 10–7m C. 10–14m D. 10–9m Ans D HSTU 01. GK U‡b KZ †K.wR.? [HSTU. 16-17] A. 1016 B. 1610 C. 1160 D. 1000 S A info 1 Ub = 2,240 cvDÛ = 2240 453.6 1000 kg = 1016kg STEP 06 ANALYSIS OF MEDICAL & DENTAL QUESTION MAT 01. 1 (GK) wKD‡mK cvwbi Nbdj KZ wjUvi? [MAT. 19-20] A. 28.517 B. 28.717 C. 28.917 D. 28.317 Ans D DAT 01. GK eQ‡i Av‡jv KZ `~iZ¡ AwZµg K‡i? [DAT. 17-18, HSC.B.2018; Kz.†ev.-2015] A.9.41012km B.9.71012km C. 9.41018 km D. 9.61012km Ans A

54 An Exclusive Parallel Text Book of Physics ASPECT PHYSICS ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES AFMC 01. 1 gvBj I 1 wK‡jvwgUv‡ii g‡a¨ cv_©K¨ KZ wgUvi? [AFMC. 2020-21; MAT. 2019-20] A. 507 B. 609 C. 709 D. 1000 S B info 1 mile = 1609 m Ges 1km = 1000 m 1mile – 1 km = 609 m STEP 07 ANALYSIS OF HSC BOARD QUESTION 01. wb‡Pi †KvbwU 1GHz I 1 MHz Gi Abycv‡Zi mgvb? [P.†ev.-2015] A. 109 B. 106 C. 103 D. 10–3 S C info 1G Hz = 109 Hz, 1 MHz = 106 Hz AbycvZ = 109 106 = 103 02. me©v‡cÿv †QvU GKK †KvbwU? [Kz.†ev. 2019] A. wgwjgvB‡µvb B. A¨vs÷ªg C. G·-†i BDwbU D. A‡UvwgUvi S C info 1Å = 10–10 m, 1milimicron = 1007 × 10–9 m 1 X-ray unit = 1.002 × 10–13 m, 1 Atto = 10–18 m Concept  6 cwigv‡ci ÎæwUmg~n ✅ cwigv‡c cuvP ai‡bi ÎæwU we`¨gvb: (i) hvwš¿K ÎæwU (ii) ch©‡eÿYg~jK/e¨w³MZ ÎæwU (iii) G‡jv‡g‡jv/AwbqwgZ ÎæwU (iv) cybive„wËK/wbqwgZ ÎæwU (v) jwNô MYb ÎæwU| ✅ cwigv‡ci ÎæwU mg~n: cybivq hš¿wU ch©‡eÿ‡Y G‡jv| cybivq hš¿wU ch©‡eÿ‡Y G‡jv cybive„wËK ÎæwU hvwš¿K ÎæwU ch©‡eÿYg~jK ÎæwU G‡jv‡g‡jv ÎæwU ✅ hvwš¿K ÎæwU wewfbœ ai‡bi n‡Z cv‡i: k~b¨ ÎæwU wcQU/e¨vKjvk ÎæwU †j‡fj/Abyf~wgK ÎæwU cÖavb †¯‥‡ji k~b¨`vM hw` fvwb©qvi/e„ËvKvi †¯‥‡ji k~b¨ `v‡Mi mv‡_ bv wg‡j Z‡e k~b¨ ÎæwU nq| †Kvb h‡š¿i ¯…z ÿq n‡q hvevi d‡j Dfq w`‡K miY mgvb nq bv| G ai‡bi ÎæwU‡K wcQU ÎæwU e‡j| hš¿ ‡j‡fj/mgvb bv K‡i wb‡j †h ÎæwU nq Zv‡K †j‡fj ÎæwU e‡j| ¯øvBW K¨vwjcvm©, fvwb©qvi †¯‥j, ¯…z MR †ù‡ivwgUv‡i G ÎæwU †`Lv hvq| GKB w`‡K Nywi‡q Nywi‡q cvV wb‡j G ÎæwU `~i nq| D`vniY: bvU, ¯…z BZ¨vw`| †P․¤^Kgvb U¨vb‡R›U M¨vjfv‡bvwgUvi, AYyexÿY Ges `~iexÿY hš¿ BZ¨vw` †ÿ‡Î G ÎæwU †`Lv hvq| ✅ hvwš¿K ÎæwU g‡b ivLvi †K․kj: kvcjv kv c jv k~b¨ ÎæwU wcQU ÎæwU †j‡fj ÎæwU ◈ ch©‡eÿYRwbZ ÎæwU g‡b ivLvi †K․kj: j¤^v e¨w³‡`i cwi‡ek ch©‡eÿY ÿgZv my›`i: j¤^v e¨w³‡`i cwi‡ek ch©‡eÿY ÿgZv my›`i j¤^b ÎæwU e¨w³MZ ÎæwU cwi‡ekMZ ÎæwU cÖvšÍ-`vM ÎæwU m~PK ÎæwU ✅ G‡jv‡g‡jv ÎæwU: G ÎæwU cwieZ©bkxj| †ekx †ekx cvV wb‡q Zv Mo K‡i G ÎæwU cwinvi Kiv hvq| ✅ cybive„wËK ÎæwU: cixÿ‡Yi KvR I hš¿cvwZi ÎæwUi Kvi‡Y G ÎæwU nq| wgUvi weª‡Ri cÖvwšÍK ÎæwU, †cv‡UbwkIwgUv‡ii cÖvwšÍK ÎæwU, ¯…zM‡Ri k~b¨ ÎæwU GB ÎæwUi D`vniY, G ÎæwU cwinv‡ii Rb¨ wewfbœ Ae¯
vq cixÿYwU evievi Ki‡Z n‡e| cybive„wËK ÎæwU g‡b ivLvi †K․kj : M‡Ri c‡i wgUvi ¯…zM‡Ri k~b¨ ÎæwU †cv‡UbwkIwgUv‡ii cÖvwšÍK ÎæwU wgUvi eªx‡Ri cÖvwšÍK ÎæwU ✅ jwNô MYb ÎæwU: wbqwgZ Ges AwbqwgZ Dfq‡ÿ‡Î G ÎæwU †`Lv hvq| wKQz †¯‥‡ji jwNó MYb: (A) wgUvi †¯‥j0.1cm; (B) ¯øvBW K¨vwjcvm© 0.01cm; (C) ¯…z-MR ev †ù‡ivwgUvi 0.001cm G QvovI cig ÎæwU, †gvU ÎæwU, Av‡cwÿK ÎæwU, kZKiv ÎæwU, AvbycvwZK ÎæwUI †`Lv hvq| REAL TEST ANALYSIS OF PREVIOUS YEAR QUESTIONS STEP 01 ANALYSIS OF JU QUESTION 01. cwigv‡ci m~PK ÎæwU wK ai‡bi ÎæwU? [JU-H, Set-1. 19-20] A. hvwš¿K ÎæwU B. ch©‡eÿYRwbZ ÎæwU C. e¨e¯
vMZ ÎæwU D. G‡jv‡g‡jv ÎæwU S B info ● hvwš¿K ÎæwU: k~b¨ ÎæwU, wcQb ÎæwU, †j‡fj ÎæwU ● ch©‡eÿYg~jK ÎæwU: j¤^b ÎæwU, e¨w³MZ ÎæwU, cwi‡ekMZÎæwU, cÖvšÍ`vM ÎæwU, m~PK ÎæwU| STEP 02 ANALYSIS OF CU QUESTION 01. ch©‡eÿ‡Ki `„wói w`K cwieZ©‡bi mv‡_ jÿ¨ e¯‧i AvcvZ cwieZ©b RwbZ cwigv‡ci ÎæwU ‡K e‡jÑ [CU. 18-19] A. cÖvšÍ `vM ÎæwU B. m~PK ÎæwU C. j¤^b ÎæwU D. e¨w³MZ ÎæwU Ans C

ASPECT PHYSICS cÖ_g cÎ †f․Z RMr I cwigvc 55 ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES STEP 03 ANALYSIS OF MEDICAL & DENTAL QUESTION AFMC 01. Parallax Error †Kvb ai‡bi µwU? [AFMC. 2020-21] A. e¨w³MZ µwU B. hvwš¿K µwU C. AwbqwgZ ÎæwU D. wbqwgZ ÎæwU S A info ch©‡eÿYg~jK ev e¨w³MZ ÎæwU: ch©‡eÿ‡Ki ch©‡eÿ‡bi fzj Ges mwVK g~j¨q‡bi Afv‡e G ÎæwU cwijwÿZ nq| G‡K ch©‡eÿY ÎæwU e‡j| ch©‡eÿY ÎæwU wewfbœ fv‡e n‡Z cv‡i| †hgbe¨w³MZ ÎæwU : G ÎæwU `~i Kiv m¤¢e bv| cÖvšÍ `vM ÎæwU : `xN©w`b e¨env‡ii d‡j cÖv‡šÍi `vM ÿ‡q †M‡j G ÎæwU †`Lv hvq| j¤^b ÎæwU/ `„wóåg ÎæwU/ Parallax error : Pÿzi Ae¯
vb 90 K‡i †i‡L G ÎæwU `~i Kiv hvq| m~PK ÎæwU : Av‡jvK †e‡Â G ÎæwU †`Lv hvq| cwi‡ekMZ ÎæwU : ZvcgvÎv, Av`ªZv cwieZ©‡bi d‡j G ÎæwU †`Lv hvq| STEP 04 ANALYSIS OF HSC BOARD QUESTION 01. †Kv‡bv GKwU ivwki cÖK…Z gvb I cwigvcK…Z gv‡bi cv_©K¨‡K †Kvb ai‡bi ÎæwU e‡j? [Xv.†ev. 2019] A. Av‡cwÿK ÎæwU B. cig ÎæwU C. mvgwMÖK ÎæwU D. cybive„wËK ÎæwU Ans B 02. cybive„wËK ÎæwU †KvbwU? [Xv.†ev.-2015] A. ¯…z †M‡Ri k~b¨ ÎæwU B. `„wóåg ÎæwU C. AwbqwgZ ÎæwU D. mvgwMÖK ÎæwU Ans A 03. ch©‡eÿ‡Ki Kvi‡Y cv‡V †h ÎæwU Av‡m Zv‡K ejv nq- [P. †ev.; w`. †ev. 2019] A. •`e ÎæwU B. k~b¨ ÎæwU C. hvwš¿K ÎæwU D. j¤^b ÎæwU Ans D 04. Av‡cwÿK ÎæwU I kZKiv ÎæwUi g‡a¨ m¤úK©Ñ [P.†ev. 2015] A. kZKiv ÎæwU = Av‡cwÿK ÎæwU 100 B. kKZiv ÎæwU = Av‡cwÿK ÎæwU 100% C. Av‡cwÿK ÎæwU = kZKiv ÎæwU 100 D. Av‡cwÿK ÎæwU = kZKiv ÎæwU 100% S B info Av‡cwÿK ÎæwU = cÖK…Z gvb ̶ cwigvcK…Z gvb cÖK…Z gvb Av‡cwÿK ÎæwU‡K kZKivq cÖKvk Ki‡j kZKiv ÎæwU e‡j| 05. wb‡Pi †Kvb ÎæwU ïay ¯…z RvZxq h‡š¿ _v‡K? [P.we. 2015] A. e¨w³MZ ÎæwU B. wbqwgZ ÎæwU C. wcQU ÎæwU D. †j‡fj ÎæwU Ans C 06. ch©‡eÿYRwbZ ÎæwU †KvbwU? [w`.†ev.2019; h.†ev.2019] A. wcQU ÎæwU B. †j‡fj ÎæwU C. G‡jv‡g‡jv ÎæwU D. j¤^b ÎæwU Ans D 07. †j‡fj ÎæwU †Kvb h‡š¿i cwigv‡ci Rb¨ cÖ‡hvR¨? [h. †ev. 2017] A. ¯…zMR B. wgUvi †¯‥j C. D`w¯
wZ wbw³ D. †ù‡ivwgUvi Ans C 08. cwigv‡ci h_v_©Zv Kvi mv‡_ m¤úwK©Z? [h. †ev. 2017] i. ÎywUi ii. h‡š¿i iii. fy‡ji wb‡Pi †KvbwU mwVK? A. i I ii B. ii I iii C. i I iii D. i, ii I iii Ans D 09. cwigv‡c abvZ¥K I FYvZ¥K Dfq cÖKvi ÎywU nq †Kvb Kvi‡Y? [e. †ev. 2016] A. h‡š¿i B. cwi‡ekMZ C. ZË¡xq D. e¨w³MZ Ans D 10. wbw³i mvnv‡h¨ fi cwigv‡c †Kvb ÎæwU cwinvi Kiv hvq? [e. †ev. 2015] A. wcQU ÎæwU B. †j‡fj ÎæwU C. k~b¨ ÎæwU D. ch©‡eÿY ÎæwU Ans B STEP 2 mg„× †ewmK MvwYwZK cÖ Ö‡qvM (MATH) kU©KvU †UKwbK Concept 1 fvwY©qvi aªæeK I jwNô MYb wbY©q msµvšÍ MvwYwZK cÖ‡qvM FORMULA 01. fvwb©qvi aªæeK: fvwb©qvi aªæeK (V.C) = s n = g~j †¯‥‡ji ÿz`ªZg GK fv‡Mi ÿz`ªZg •`N©¨ 1(mm) fvwY©qvi †¯‥‡ji fvMmsL¨v 02. jwNô MYb (L.C) = cxP (e„ËvKvi †¯‥‡ji GKevi N~Y©‡b •iwLK miY) e„ËvKvi †¯‥‡ji fvM msL¨v CONCEPTUAL MATH MEx 01 GKwU fvwY©qvi K¨vwjcv‡m©i fvwY©qvi †¯‥‡j 50wU fvM Av‡Q, hv cÖavb †¯‥‡ji 49 fv‡Mi mv‡_ wg‡j hvq| fvwY©qvi aªæeK KZ? [cÖwZ cm G cÖavb †¯‥‡j 20wU fvM] VC = 1 20 50 cm = 10–3 cm = 10–3 104 = 10 MEx 02 GKwU K¨vwjcv‡m©i cÖavb †¯‥‡ji ÿz`ªZg GK N‡ii gvb 1mm Ges fvwb©qvi †¯‥‡ji 10 Ni cÖ`vb †¯‥‡ji 9 N‡ii mgvb| H †¯‥‡ji fvwb©qvi aªæeK KZ? fvwb©qvi aªæeK = 1 9 10 = 0.1 NOW START PRACTICE 01. GKwU †ù‡ivwgUv‡ii †MvjvKvi †¯‥j 100wU `v‡M mgvbfv‡e wPwýZ Kiv Av‡Q Ges †MvjvKvi †¯‥‡ji GKevi c~Y© AveZ©‡b •iwLK †¯‥j 0.01cm GwM‡q hvq| †ù‡ivwgUv‡ii jwNô aªæeK wbY©q Ki| 02. GKwU ¯øvBW K¨vwjcv‡m©i cÖavb †¯‥‡ji ¶z`ªZg GK N‡ii gvb 1mm Ges fvwb©qvi †¯‥‡ji 30 Ni cÖavb †¯‥‡ji 29 N‡ii mgvb| H †¯‥‡ji fvwb©qvi aªæeK n‡e03. 1mm wcPwewkó GKwU ‡ù‡ivwgUv‡ii e„ËvKvi ‡¯‥‡ji fvM msL¨v 50 †ù‡ivwgUv‡ii jwNô MYb KZ? NOW PRACTICE SOLVE : 01. GLv‡b •iwLK †¯‥‡ji ÿz`ªZg fv‡Mi gvb = 0.01cm; †MvjvKvi †¯‥‡ji †gvU cvV msL¨v = 100 L.C. = 0.01 100 cm = 10–4 cm 02. fvwb©qvi aªæeK = 1 – 29 30 = 1 30 = 0.033mm 03. jwNó Mbb = h‡š¿i cxP e„ËvKvi †¯‥‡ji fvM msL¨v = 1mm 50 = 0.02mm

56 An Exclusive Parallel Text Book of Physics ASPECT PHYSICS ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES REAL TEST ANALYSIS OF PREVIOUS YEAR QUESTIONS STEP 01 ANALYSIS OF DU QUESTION 01. GKwU ¯øvBW K¨vwjcv‡m©i cÖavb †¯‥‡ji ¶z`ªZg GK N‡ii gvb 1mm g~j †¯‥‡ji 99 fvM fvwb©qvi †¯‥‡ji 100 fv‡Mi mgvb| fvwb©qvi aªæe‡Ki gvb KZ? [DU. 11-12; JnU. 11-12; HSTU. 15-16] A. 0.01 B. 0.001 C. 0.1 D. 0.0001 S A info fvwb©qvi aªæeK = 1 – 99 100 = 1 100 = 0.01 STEP 02 ANALYSIS OF RU QUESTION 01. GKwU ¯øvBW K¨vwjcv‡m©i cÖavb †¯‥‡ji ¶z`ªZg GK N‡ii gvb 1mm Ges fvwb©qvi †¯‥‡ji 20 Ni cÖavb †¯‥‡ji 19 N‡ii mgvb| H †¯‥‡ji fvwb©qvi aªæeK n‡e- [RU. 18-19, 15-16] A. 0.5 mm B. 0.01 mm C. 0.05 mm D. 0.1 mm S C info fvwb©qvi aªæeK = 1 – 19 20 = 1 20 = 0.05mm STEP 03 ANALYSIS OF CU QUESTION 01. GKwU fvwb©qvi K¨vwjcv‡m©i fvwb©qvi †¯‥‡j 50 wU fvM Av‡Q hv cÖavb †¯‥‡ji 49 fv‡Mi mv‡_ wg‡j hvq| fvwb©qvi aªæeK KZ? †`qv Av‡Q, cÖwZ †m.wg. G cÖavb †¯‥‡j 20wU fvM| [CU. 18-19] A. 100m B. 1000m C. 10m D. 1m S C info Vc = 1 20 50cm = 1 10–3 cm = 10m STEP 04 ANALYSIS OF GST QUESTION PART A Analysis of General University Question JKKNIU 01. GKwU ¯…zM‡Ri e„ËvKvi ‡¯‥‡ji fvM msL¨v 100 Ges wcP Gi gvb 1mm n‡j, jwNó aªæe‡Ki gvb KZ? [JKKNIU-B, Set-3, 19-20] A. 0.01 mm B. 0.001 cm C. 100 mm D. A I B DfqB jwNó aªæeK = cxP e„ËvKvi †¯‥‡ji fvM msL¨v = 0.1cm 100 = 0.001cm. PART B Analysis of Science & Technology Question SUST 01. GKwU ¯…z M‡Ri e„ËvKvi †¯‥‡ji fvM msL¨v 50 Ges e„ËvKvi †¯‥jwU m¤ú~Y© GKevi Nyiv‡j GKwU •iwLK †¯‥j eivei 0.5mm •`N©¨ AwZµg K‡i, ¯…zMRwUi jwNô MYb KZ mm? [SUST. 12-13] A. 0.001 B. 0.01 C. 0.05 D. 0.1 E. 0.5 S B info jwNô MYb = 0.5 50 = 0.01 BSMRSTU 01. GKwU †ù‡ivwgUv‡ii jwNô aªæe‡Ki gvb 0.01 mm n‡j Gi Øviv ÿz`ªZg †h †ea gvcv m¤¢e Zv njÑ [BSMRSTU-C, 19-20] A. 0.1 mm B. 0.01 mm C. 1.0 mm D. 0.05 mm Ans B STEP 05 ANALYSIS OF ENGINEERING & BUTex QUESTION BUET 01. GKwU ¯øvBW K¨vwjcv‡m©i cÖavb †¯‥‡ji 39 fvM fvwY©qvi †¯‥‡ji 40 fv‡Mi mgvb| cÖavb †¯‥‡ji GK fv‡Mi 1.00mm| fvwY©qvi aªæeK KZ? [BUET. 16-17; KUET. 06-07; DU. 01-02] A. 0.010mm B. 0.020mm C. 0.025 mm D. 0.100mm S C info v.c. = 40 – 39 40 = 0.025 m STEP 06 ANALYSIS OF HSC BOARD QUESTION 01. GKwU ¯…zM‡Ri jwNô aªæe‡Ki gvb 0.01mm| GwU Øviv b~¨bZg KZ †ea gvcv hv‡e? [iv.†ev. 2019] A. 1mm B. 0.10mm C. 0.01mm D. 0.001mm S C info †Kvb h‡š¿i mvnv‡h¨ b~¨bZg †h cwigvc †bIqv m¤¢e Zv‡K H h‡š¿i jwNó MYb ev aªæeK e‡j| L.C = wcP e„ËvKvi †¯‥‡ji fvM msL¨v 02. ‡ù‡ivwgUv‡ii e„ËvKvi †¯‥‡ji †gvU fvM msL¨v 50| †¯‥jwU‡K GK cvK Nyiv‡j •iwLK †¯‥‡j miY nq 0.5 mm| jwNô MYb KZ? [P. †ev. 2016] A. 0.01 mm B. 0.01 cm C. 0.25 mm D. 0.50 mm S A info L.C. = 0.5 50 = 0.01 mm Concept 2 ÎæwU msµvšÍ MvwYwZK cÖ‡qvM FORMULA 01. Av‡cwÿK ÎæwU = e – x 02. kZKiv ÎæwU = e – x 100% 03. AvbycvwZK ÎæwU = cÖK…Z gvb – cÖvß gvb cÖK…Zgvb 100% 04. cig ÎæwU = cÖK…Zgvb – cÖvß gvb| ASPECT SPECIAL: % AvqZb ÎæwU = 3 × % •`N©¨ ÎæwU % †ÿÎdj ÎæwU = 2 × % •`N©¨ ÎæwU % cwiwa ÎæwU = % •`N©¨ ÎæwU •`N©¨ ÎæwUi cwie‡Z© e¨vm ev e¨vmva© ÎæwU _vK‡jI GKB m~Î cÖ‡hvR¨ n‡e| Model Example01 †Mvj‡Ki e¨vmva© r = (5.3 0.1)m n‡j AvqZb wbY©‡qi kZKiv ÎæwU KZ? General Rules [Written] 3 in 1 Shortcut Tricks & Tips [MCQ] (i) r r 100% = 0.1 5.3 100% = 1.886% V = 4 3 r 3 ; v v = 3 r r = 3 1.886% = 5.66% 0.1 5.3 3 100% = 5.66%

ASPECT PHYSICS cÖ_g cÎ †f․Z RMr I cwigvc 57 ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES Model Example02 GKwU †Mvj‡Ki e¨vmva© cwigv‡c 1.2% fzj n‡j H †Mvj‡Ki AvqZb cwigv‡c kZKiv KZ fzj n‡e? General Rules [Written] 3 in 1 Shortcut Tricks & Tips [MCQ] †Mvj‡Ki AvqZb, V = 4 3 R 3 ev, V R 3 AvqZ‡b AvbycvwZK ÎæwU, V V = 3R R = 3 1.2% = 3.6% AvqZb cwigv‡ci kZKiv ÎæwU = (3 1.2)% = 3.6% NOW START PRACTICE 01. wmwjÛv‡ii D”PZv h = (1 0.1)m Ges e¨vmva© r = (.5 0.025)m n‡j AvqZb wbY©‡qi ÎæwU kZKivq KZ? 02. GKwU e„‡Ëi e¨vmva© (2.5 0.2)cm n‡j Gi †ÿÎdj cwigv‡ci kZKiv ÎæwU KZ? NOW PRACTICE SOLVE : 01. V = r 2 h; v v = 2. r r + h h = 2. 0.025 0.5 + 0.1 1 100% = 20% 02. e„‡Ëi e¨vmva© R = 2.5 cig ÎæwU R = 0.2; †ÿÎdj A = R 2 ; †ÿÎd‡ji kZKiv ÎæwU = 2 0.2 2.5 100% = 16% REAL TEST ANALYSIS OF PREVIOUS YEAR QUESTIONS STEP 01 ANALYSIS OF JU QUESTION 01. GKwU †Mvj‡Ki cwigvc¨ e¨vmva© (2.5 0.2) cm n‡j Gi AvqZb cwigv‡ci kZKiv ÎæwU KZ? [JU-A, Set-A. 19-20, 16-17,MBSTU. 16-17, KU. 19-20; Xv.†ev. 2015,P. †ev. 2015] A. 0.08% B. 0.24% C. 8% D. 24% S D info V = 4 3 R 3 V R 3 AvqZb cwigv‡c kZKiv ÎæwU, V V = 3 R R × 100% = 3×0.2 2.5 × 100% = 24% 02. V=4/3 r 3 mgxKi‡b r Gi gvb cwigv‡c hw` 2% ÎæwU nq Z‡e V wbY©‡qi ÎæwU KZ n‡e? [JU. 16-17; wm. †ev. 2016] A. 1% B. 6% C. 5% D. 2% S B info ASPECT SPECIAL: AvqZb cwigv‡ci kZKiv ÎæwU = (3 2)% = 6% 03. 10m •`N©¨ cwigv‡c ÎæwUi cwigvc 10cm n‡j ÎæwUi nvi KZ? [JU. 16-17] A. 0.01% B. 0.1% C. 1% D. 10% S C info 10cm = 0.1m ÎæwUi nvi = ÎæwUi cwigvY cÖK…Z gvb 100% = 0.1 10 100% = 1% 04. mij †`vj‡Ki GKwU cixÿvq †Kvb ¯
v‡bi AwfKl©R Z¡iY 10ms –2 cvIqv †M‡j kZKiv ÎæwU KZ? H ¯
v‡b AwfKl©R Z¡i‡bi cÖK…Zgvb 9.81ms–2 | [JU. 16-17,MBSTU. 19-20; iv. †ev. 2019] A. 1.93% B. –19% C. 19% D. 19.36% S A info kZKiv ÎæwU = 10 – 9.81 10 100% = 0.19 10 100% = 1.9% STEP 02 ANALYSIS OF RU QUESTION 01. GKwU †Mvj‡Ki e¨vmva© cwigvc Kiv n‡jv R| R = (10 0.2) n‡j Gi AvqZ‡bi kZKiv µwU KZ? [RU. Moderna, Set-2. 20-21] A. 1% B. 2% C. 4% D. 6% S D info V V = 3 R R V V = 3 0.2 10 = 0.06 [V = 4 3 R 3 ] AZGe, kZKiv ÎæwU = 0.06 100% = 6% 02. c`v_©weÁvb j¨ve‡iUwi‡Z mij †`vj‡Ki mvnv‡h¨ g-Gi gvb wbY©q Ki‡Z wM‡q 9.78 ms2 cvIqv †Mj| g-Gi cÖK…Z gvb 9.81 ms2 n‡j cÖvß gv‡bi kZKiv ÎæwU n‡eÑ [RU. Sinovac, Set-1. 20-21] A. 30% B. 3% C. 0.3% D. 0.03% S C info kZKiv ÎæwU = 9.87 – 9.78 9.81 100% = 0.3% 03. GKwU †Mvj‡Ki e¨vmva©, R cwigvc Kiv nj| R= (10 0.1) n‡j, Gi AvqZ‡bi kZKiv ÎæwU KZ? [RU. 17-18, JUST. 19-20; w`. †ev. 2017] A. 1% B. 3% C. 5% D. 0.001% S B info AvqZ‡bi kZKiv ÎæwU = 3 0.1 10 100% = 3% 04. GKwU `‡Ûi cwigvcK…Z •`N©¨ 25cm Ges cÖK…Zgvb 20cm n‡j, cwigv‡ci kZKiv ÎæwU KZ? [RU. 17-18] A. 20% B. 15% C. 10% D. 25% S A info kZKiv ÎæwU = 25 – 20 25 100 = 20% 05. GKwU e„‡Ëi e¨vmva© (2.5 0.2)cm n‡j Gi †ÿÎdj cwigv‡ci kZKiv ÎæwU KZ? [RU. 16-17] A. 0.08% B. 0.16% C. 8% D. 16% S D info †ÿÎd‡ji kZKiv ÎæwU = 2 0.2 2.5 100% = 16% 06. GKwU †Mvj‡Ki e¨vmva© cwigv‡c 1.2% fzj Ki‡j, H †Mvj‡Ki AvqZ‡b kZKiv KZ fzj n‡e? [RU. 15-16, DU. 7Clg-A: 20-21] A. 8.6% B. 6.6% C. 5.6% D. 3.6% S D info AvqZ‡b kZKiv ÎæwU = 3 R R = 31.2% = 3.6% STEP 03 ANALYSIS OF DU-7 Clg QUESTION 01. GKwU †Mvj‡Ki e¨vmva© cwigv‡Y 1.5% fzj n‡j H †Mvj‡Ki AvqZb cwigv‡c kZKiv KZ fzj n‡e? [DU. 7Clg-A: 16-17] A. 1.5% B. 4.5% C. 3.37% D. 3.0% S B info AvqZ‡b kZKiv ÎæwU = 3 R R = 31.5% = 4.5% STEP 04 ANALYSIS OF GST QUESTION 01. GKwU †Mvj‡Ki e¨vmva© (2.0 0.1) m a‡i c„ôZ‡ji †ÿÎdj wnmve Ki‡j kZKiv ÎæwU KZ? [GST-A. 20-21] A. 5 B. 10 C. 15 D. 20 S B info †ÿÎd‡ji kZKiv ÎæwU = 2r r × 100 = 2×0.1 2 × 100 = 10 PART A Analysis of General University Question KU 01. GKwU `‡Ûi cwigvcK…Z •`N©¨ 100 cm Ges cÖK…Z gvb 100.4 cm n‡j Gi cwigv‡ci kZKiv ÎæwU KZ? [KU. 17-18] A. 0.0398 B. 0.398 C. 0.4 D. 0.4016 S C info kZKiv ÎæwUi nvi = x x y 100% = 100 0.4 100% = 0.4%

58 An Exclusive Parallel Text Book of Physics ASPECT PHYSICS ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES PART B Analysis of Science & Technology Question SUST 01. GKwU e„ËvKvi PvKwZi cwigvc¨ e¨vmv&a© R = 5.0 0.1 n‡j †ÿÎd‡ji kZKiv ÎæwU KZ? [SUST. 17-18] A. 1% B. 3% C. 4% D. 5% S C info ‡ÿÎd‡ji kZKiv ÎæwU = 2 0.1 5 100% = 4% JUST 01. †iva R = (V/I); †fv‡ë‡Ri cwigvc¨ cvV (10 0.2) †fvë Ges cÖev‡ni cwigvc¨ cvV (5 0.2) A¨vw¤úqvi| †iva cwigv‡c kZKiv ÎæwU KZ? [JUST-B, 19-20] A. 2% B. 4% C. 6% D. 12% S C info †iva cwigv‡c kZKiv ÎæwU = 0.2 10 + 0.2 5 ×100% = 6% STEP 05 ANALYSIS OF MEDICAL & DENTAL QUESTION MAT 01. GKwU `‡Ûi cwigvcK…Z •`N©¨ 10cm Ges cÖK…Zgvb 10.40 cm n‡j, cwigv‡ci kZKiv ÎæwU KZ? [MAT. 18-19] A. 4% B. 3.6% C. 3.84% D. 0.4% S C info kZKiv ÎæwU = 10.40–10 10.40 100 = 3.86% STEP 06 ANALYSIS OF HSC BOARD QUESTION 01. †Kv‡bv †Mvjxq Z‡ji eµZvi e¨vmva© wbY©q Kivi Rb¨ †Kvb mgxKiYwU e¨eüZ nq? [iv.†ev. 2017; h.†ev. 2015; P.†ev. 2017; IU. 17-18] A. R = d h + h 2 B. R = d 2 2 + h 2 C. R = d 2 6h + h 2 D. R = d 2 12 + h 2 d S C info †Kvb †Mvjxq Zj †h †Mvj‡Ki Ask, †mB †Mvj‡Ki e¨vmva©‡K H †Mvjxq Z‡ji eµZvi e¨vmva© e‡j| eµZvi e¨vmva©, R = d 2 6h + h 2 d = †ù‡ivwgUv‡ii †h‡Kvb `yB cv‡qi ga¨ewZ© Mo `~iZ¡| h = eµZ‡ji c„ô‡K ¯úk© Kiv‡Z hZUzKz Dc‡i ev wb‡P bvgv‡Z nq| h = M × wcP + N × LC 02. Av‡cw¶K ÎæwU I kZKiv ÎæwUi g‡a¨ m¤úK©- [P. †ev. 2015] A. kZKiv ÎæwU = Av‡cw¶K ÎæwU 100 B. Av‡cw¶K ÎæwU = kZKiv ÎæwU 100 C. kZKiv ÎæwU = cig ÎæwU 100 D. Dc‡ii ‡Kv‡bvwUB bq S A info kZKiv ÎæwU = cig ÎæwU cÖK…Z gvb 100% = Av‡cw¶K ÎæwU 100% Dc‡ii wb‡`©kbvi Av‡jv‡K 03 I 04 bs cÖ‡kœi DËi `vI : †Kvb e¯‧i fi (100kg 2%) Ges AvqZb (10m3 3%)| 03. H e¯‧i Nb‡Z¡i kZKiv ÎywU KZ? [h. †ev. 2017] A. 10 B. 5 C. 0.5 D. 0.1 S B info GLv‡b, m = 100 × 2% = 2 kg V = 10 × 3% = 0.3 m3 Nb‡Z¡i kZKiv ÎæwU = M M + V V ×100% = 2 100 + 0.3 10 ×100% 04. H e¯‧wUi Nb‡Z¡i cig ÎywUi mwVK gvb †KvbwU? [h. †ev. 2017] A. 5kgm-3 B. 5gmm-3 C. 0.5gm-3 D. 0.5kgft-3 S C info = 5 100 = 5 100 = 5 100 m V = 5 100 × 100 10 = 0.5 kgm–3 05. †Kv‡bv †Mvj‡Ki e¨vmv‡a©i cÖK…Z gvb 3 cm Ges cwigvc¨ gvb 2.98 cm| †MvjKwUi AvqZb cwigv‡c kZKiv ÎæwU KZ? [e. †ev. 2017] A. 0.02 B. 0.066% C. 0.66% D. 2% S D info kZKiv ÎæwU = 3 – 2.98 3 × 3 × 100% = 0.66% × 3 = 2% Concept 3 cwigv‡ci m~Îvejx msµvšÍ MvwYwZK cÖ‡qvM FORMULA 01. †Mvj‡Ki m~Î: c„ôZ‡ji †ÿÎdj = 4r 2 02. †ù‡ivwgUv‡ii eµZvi e¨vmva©, R = d 2 6h + h 2 03. †Mvj‡Ki AvqZb, V = 4 3 r 3 04. wmwjÛv‡ii AvqZb, V = r 2 l 05. cvB‡ci cÖ¯
‡”Q‡`i †ÿÎdj, A = r 2 = d 2 2 = 1 4 d 2 CONCEPTUAL MATH MEx 01 GKwU wmwjÛv‡ii •`N©¨ 7 22 wgUvi| hw` Dnvi AvqZb 16m 3 nq Zvn‡j Dnvi e¨vm KZ n‡e? wmwjÛv‡ii AvqZb, r 2 l; r 2 l= 16 22 7 .r2 7 22 = 16 r 2 = 16 r = 4 e¨vm, d = 2r = 2 4 = 8m NOW START PRACTICE 01. GKwU †ù‡ivwgUv‡ii `yB cv‡qi `~iZ¡ d = 24 mm Ges h = 48mm cixÿYxq eµZvi e¨mva© KZ? NOW PRACTICE SOLVE : 01. R = d 2 6h + h 2 = (24) 2 6 × 46 + 48 2 = 2 + 24 = 26 mm

ASPECT PHYSICS cÖ_g cÎ †f․Z RMr I cwigvc 59 ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES REAL TEST ANALYSIS OF PREVIOUS YEAR QUESTIONS STEP 01 ANALYSIS OF JU QUESTION 01. GKwU wmwjÛv‡ii •`N©¨ 7 22 wgUvi| hw` Dnvi AvqZb 4m3 nq, Zvn‡j Dnvi e¨vm KZ n‡e? [JU. 14-15; MAT. 14-15] A. 1m B. 4m C. 22 7 m D. 2m S B info r 2 h = 4 ev, 22 7 r. 7 22 = 4 ev, r 2 = 4 ev, r = 2 e¨vm d = 2r = 22 = 4m STEP 02 ANALYSIS OF CU QUESTION 01. mxmvi NbZ¡ 12 gm/cc| GKwU mxmv B‡Ui fi 15 kg Ges Gi AvqZb 10 cm 5cm 4 cm| GwU [CU-A, Set-2. 19-20] A. 25% †_‡K 50% ch©šÍ Lvwj B. 75% Gi †ekx Lvwj C. 0% †_‡K 25% ch©šÍ Lvwj D. 50% †_‡K 75% ch©šÍ Lvwj S C info AvqZb, V = 10 5 4 = 200cm3 200cm3 AvqZ‡b fi = 15000gm 1cm3 AvqZ‡b fi = 15000 200 100cm3 AvqZ‡b fi = 15000 100 200 = 7500 1 100 = 75% Lvwj _v‡K 0% †_‡K 25% ch©šÍ STEP 03 ANALYSIS OF HSC BOARD QUESTION 01. e„ËvKvi †¯‥‡ji c~Y© N~Y©b msL¨v M, e„ËvKvi †¯‥‡ji AwZwi³ fvM msL¨v N Ges jwNô MYb Lc n‡j †¯‥‡ivwgUv‡ii mvnv‡h¨ h wbY©‡qi m~Î †KvbwU? [Xv.†ev. 2019] A. h = M + Lc B. h = M N + Lc C. h = M wcP + Lc D. h = M wcP+ N + Lc Ans D 02. cÖavb †¯‥j cvV M, fvwb©qvi cvV V Ges fvwb©qvi aªyeK VC n‡j •`N©¨, L wbY©‡qi m~Î [wm. †ev. 2016] A. L = M+VC B. L = MV + VC C. L = MVC+V D. L = M + V VC Ans D SAQ Short Answer Questions WRITTEN PART BAQ Broad Answer Questions 01. GKwU †Mvj‡Ki cwigvc¨ e¨vmva©, R = 5.3 0.1m n‡j AvqZb kZKiv ÎæwU wbY©q Ki| Solve Avgiv Rvwb, †Mvj‡Ki AvqZb V = 4R 3 3 GLv‡b, R = 5.3m cig ÎæwU, R = 0.1 AvqZ‡bi Av‡cwÿK ev AvbycvwZK ÎæwU, V V = 3R R = 3 0.1 5.3 = 0.3 5.3 AZGe, AvqZ‡b kZKiv ÎæwU = V V 100% = 5.7% 02. †Kvb †Mvj‡Ki e¨vmva wbY©‡q 0.3% ÎæwU nq| H †Mvj‡Ki †ÿÎdj wbY©‡q m‡e©v”P kZKiv KZ ÎæwU n‡Z cv‡i? Solve †Mvj‡Ki †ÿÎdj, A = 4r 2 †h‡nZz 4 aªæe c`, myZivs 4 wbY©‡q †Kv‡bv ÎæwU n‡e bv| myZivs †ÿÎd‡j wbY©‡q AbycvwZK ÎæwU = A A 100% = 2 r r 100% = 2 0.3% = 0.6% 03. gvÎv we‡ePbvq †`LvI †h, Fs = 1 2 mu2 mgxKiYwU mwVK| Solve evgcÿ, Fs = [MLT–2 ] [L] = [ML2T –2 ] Wvbcÿ, 1 2 mv2 = [M] [LT–1 ] 2 = [ML2T –2 ] 1 2 mu2 = [M] [LT–1 ] 2 = [ML2T –2 ] gvÎv we‡ePbvq mgxKiYwU mwVK| GLv‡b, s-Gi gvÎv = [L] F-Gi gvÎv = [MLT–2 ] m-Gi gvÎv = [M] u-Gi gvÎv = [LT–1 ] v-Gi gvÎv = [LT–1 ] 04. evwà GKw`b cixÿvMv‡i †ù‡ivwgUv‡i mgZj †KvP ‡cø‡Ui D”PZvi Mo cvV 0.1m Ges DËj †j‡Ýi D”PZvi Mo cvV 1.24m †cj| h‡š¿ wZb cv‡qi Mo `~iZ¡ 40mm| (K) †jÝwUi eµZvi e¨vmva© wbY©q Ki; (L) †jÝwU DËj bv n‡q AeZj n‡j eµZvi e¨vmv‡a©i †Kv‡bv cwieZ©b n‡e Kx-gZvgZ `vI| Solve Avgiv Rvwb, (K) eµZvi e¨vmva© R = d 2 6h + h 2 = 0.57m (L) AeZj †j‡Ýi Rb¨, eµZvi e¨vmva© R = d 2 6h + h 2 = 0.57m GLv‡b, DËj †j‡Ýi †ÿ‡Î, d = 40 mm = 0.04m h = 1.24 m 1m = 1.14m AeZj †j‡Ýi †ÿ‡Î, d = 40mm = 0.04m h = 0.1m – 1.24m = – 1.14 m = 1.14m [FYvZ¥K wPý wb‡Pi w`‡K miY‡K eySvq] †jÝwU DËj ev AeZj hvB †nvK DÏxcKwUi eµZvi e¨vmva© GKB n‡e| 05. hw` A = BnC m Ges A, B I C Gi gvÎv h_vµ‡g, LT, L2T –1 Ges LT2 nq Z‡e n I m Gi gvb KZ n‡e? Solve A = BnC m LT = (L2T –1 ) n . (LT2 ) m = L2n+m T –n+2m So, 2n+ m=1 & –n +2m = 1 , n = 1/5; m = 3/5 06. GKwU e„‡Ëi e¨vmva© (1.5 0.2)cm n‡j †ÿÎdj cwigv‡ci kZKiv ÎæwU KZ? Solve See Concept-2 07. GKwU ¯øvBW K¨vwjcv‡mi cÖavb †¯‥‡ji ÿz`ªZg GK N‡ii gvb 1mm Ges fvwb©qvi †¯‥‡ji 10 Ni cÖavb †¯‥‡ji 9 N‡ii mgvb H †¯‥‡ji fvwb©qvi aªæeK KZ? Solve See Concept-1 08. GKwU ¯…z M‡Ri e„ËvKvi †¯‥‡ji fvM msL¨v 20 Ges e„ËvKvi †¯‥jwU m¤ú~Y© GKevi Nyiv‡j GKwU †¯‥j eivei 0.2mm •`N©¨ AwZµg K‡i, ¯…zMRwUi jwNô MYb KZ mm? Solve See Concept-1 09. GKwU `‡Ûi cwigvcK…Z •`N©¨ 15cm Ges cÖK…Z gvb 15.5cm n‡j cwigv‡ci kZKiv ÎæwU KZ? Solve See Concept-2

60 An Exclusive Parallel Text Book of Physics ASPECT PHYSICS ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES STEP 3 mKj cvV¨eB‡qi NCTB QUESTIONS ANALYSIS cÖkœ e¨vLvmn mgvavb cÖkœ 01. ¯^Ztwm× ev ¯^xKvh© Kx? [Bm&nvK, Avwgi] A. MvwYwZK hyw³ B. ‡Kv‡bv aviYv ev ZË¡ C. ‣eÁvwbK cix¶vq cÖvgwYZ D. cix¶‡Yi mvi-ms‡¶c Ans A 02. cigvYyi mg¯Í ab Avavb Ges fi Gi †K‡›`ª Aew¯’Z-GB ZË¡ †K Dc¯’vcb K‡ib? [Bm&nvK, Avwgi] A. iv`vi‡dvW© B. M¨vwjwjI C. AvBb÷vBb D. g¨v· cø¨v¼ Ans A 03. Òfi I kw³ mgZzj¨Ó- ‡Kvb weÁvbxi AwfgZ? [Bm&nvK, Avwgi] A. wbDUb B. M¨vwjwjI C. AvBb÷vBb D. d¨viv‡W Ans C 04. ‡Kvb e¯‧ n‡Z kw³i wewKiY wbiew”Qbœ fv‡e N‡U bv ÑÑÑ GB Z‡Ë¡i cÖe³v ‡K? ev †Kvqv›Uvg Z‡Ë¡i RbK †K? [Bm&nvK, Avwgi] A. jW© iv`vi‡dvW© B. AvjevU© AvBb÷vBb C. g¨v· cø¨v¼ D. gvB‡Kj d¨viv‡W Ans C 05. AwbqwgZ ÎæwU Kx ai‡bi ÎæwU? [Bm&nvK, Avwgi] A. hvwš¿K ÎæwU B. e¨w³MZ ÎæwU C. A I B Dfq ai‡bi ÎæwU D. Dc‡ii †Kv‡bvwUB bq Ans C 06. hw` υ = `ªæwZ, r = e¨vmva© Ges g = AwfKl©R Z¡iY nq, Zvn‡j wb‡¤œi †Kvb ivwkwU gvÎvnxb? [Bm&nvK, Avwgi] A. υ 2 r g B. υ 2 g r C. υ 2 rg D. υ 2 rg Ans D 07. GKwU Av`k© ev hyw³c~Y© AvPiY wfwË hvi mv‡c‡ÿ Ab¨vb¨ welq Zzjbv, wePvi we‡kølY I cwigvc Kiv nq Zv‡K Kx e‡j? [Bm&nvK, Avwgi] A. m~Î B. bxwZ C. AbyKí D. ¯^xKvh© Ans B 08. Av‡jvKel© Kx‡mi GKK? [Bm&nvK, Avwgi] A. mgq B. `~iZ¡ C. Z¡iY D. †eM Ans B 09. cixÿv Øviv cÖgvwYZ AbyKí‡K e‡j- [Bm&nvK, Avwgi] A. bxwZ B. ¯^xKvh© C. m~Î D. ZË¡ Ans C 10. ch©‡eÿY I cixÿvi gva¨‡gB weÁv‡bi me mZ¨ hvPvB Kiv DwPZgZev`wU †Kvb weÁvbxi? [Bm&nvK, Avwgi] A. †_wjm B. iRvi †eKb C. M¨vwjwjI D. wbDUb Ans C 11. GKwU `‡Ûi cwigvcK…Z •`N©¨ 10 cm Giƒc cÖK…Z gvb 10.40 cm n‡j cwigv‡ci kZKiv ÎæwU KZ? [Bm&nvK, Avwgi] A. 4% B. 3.84% C. 0.398% D. 0.04% S B info kZKiv ÎæwU = 10.40 – 10 10.40 × 100% = 3.84% 12. hw` L, C I R h_vµ‡g ¯^Kxq Av‡ekv¼ aviKZ¡ I †iva m~wPZ K‡i, Z‡e K¤úv‡¼i gvÎv †h ivwkwUi gvÎv Øviv m~wPZ n‡e Zv n‡jv- [Bm&nvK, Avwgi] A. RL B. CL C. 1 LC D. RC Ans C 13. GKwU ¯øvBW K¨vwjcv‡m©i fvwb©qvi †¯‥‡ji n fvM g~j †¯‥‡ji (n – 1) fv‡Mi mv‡_ wg‡j hvq| g~j †¯‥‡j 1 fv‡Mi gvb 1 mm| h‡š¿i fvwb©qvi aªæeK KZ? [Bm&nvK, Avwgi] A. x mm B. (n – 1) mmC. 1 n + 1 mm D. 1 10 n mm Ans D 14. R †iv‡ai ga¨ w`‡q I cÖevngvÎv t mgq a‡i cÖevwnZ n‡j Drcbœ Zvc, H = 1 2Rt| I, R Ges t cwigv‡c ÎæwU h_vµ‡g 3%, 1% Ges 2% n‡j Drcbœ Zvc cwigv‡c ÎæwU KZ? [Bm&nvK, Avwgi] A. 8% B. 4% C. 6% D. 9% S D info H = I2RT cwigv‡c ÎæwU, H H = 2 I I + R R + T T = 2×3% + 1% + 2% = 9% 15. `ywU †iv‡ai gvb, R1 = (8 0.5) Ges R2 (12 0.5) | †iva¸wj‡K †kÖwY mgevq hy³ Ki‡j kZKiv ÎæwUmn Zzj¨ †iva KZ? [Bm&nvK, Avwgi] A. 20 5% B. 20 6.25% C. 20 5% D. 20 10% S C info R = R1 + R2 = (8 0.5) + (12 0.5) = (20 1) R R = 1 20 × 100% = 5% R = (20 5%) 16. cwigv‡ci h_v_©Zv Kvi mv‡_ m¤úwK©Z? [Bm&nvK, Avwgi] i. ÎæwUi ii. h‡š¿i iii. fz‡ji wb‡Pi †KvbwU mwVK? A. i I ii B. ii I iii C. i I iii D. i, ii I iii Ans A 17. Av‡cw¶K ÎæwU I kZKiv ÎæwUi g‡a¨ m¤úK©- [Bm&nvK, Avwgi] A. kZKiv ÎæwU = Av‡cw¶K ÎæwU 100 B. Av‡cw¶K ÎæwU = kZKiv ÎæwU 100 C. kZKiv ÎæwU = cig ÎæwU 100 D. ‡Kv‡bvwUB bq S A info kZKiv ÎæwU = cig ÎæwU cÖK…Z gvb 100%= Av‡cw¶K ÎæwU 100% 18. GKRb wkÿv_x© GKwU wmwjÛv‡ii e¨vmva© wbY©‡qi Rb¨ 0.001 cm jwNô MY‡bi GKwU ¯…z MR e¨envi Kij| Zvi cÖvß djvd‡ji me©vwaK mwVK gvb †KvbwU? [Zcb, AvwRR] A. 1.4 cm B. 1.41 cm C. 1.402 cm D. 1.4021 cm Ans C 19. GKwU †ù‡ivwgUv‡ii e„ËvKvi †¯‥‡ji fvM msL¨v 50| e„ËvKvi †¯‥jwU GKevi Nyiv‡j GwU •iwLK †¯‥j eivei 1 mm `~iZ¡ AwZµg K‡i| †ù‡ivwgUviwUi jwNô MYb n‡e- [Zcb, AvwRR] A. 0.2 cm B. 0.02 cm C. 0.002 cm D. 0.0002 cm S C info LC = p n = 1 50 = 0.02 mm = 0.002 cm 20. GKxf~Z cvigvYweK fi GKK (u) n‡”Q- [Zcb, AvwRR] i. 12 6C Gi f‡ii 1 12 ii. 16 8O Gi f‡ii mgvb iii. 1.66 × 10–27 kg wb‡Pi †KvbwU mwVK? A. i I ii B. i I iii C. ii I iii D. i, ii I iii Ans B 21. gvB‡µvI‡qf Drc‡bœi hš¿ wb‡q KvR Kivi mgq c‡K‡Ui PK‡jU M‡j †h‡Z †`‡L gvB‡µvI‡qf I‡fb •Zwii K_v fv‡eb †K? [Zcb, AvwRR] A. g¨v·I‡qj B. gvB‡Kj d¨viv‡W C. cvwm© †¯úbmvi D. g¨v· cø¨v¼ Ans C 22. GK †UivwgUvi mgvb KZ? [Zcb, AvwRR] A. 109 m B. 1012 m C. 1015 m D. 1018 m Ans B 23. ¯…z ÿq nIqvi d‡j h‡š¿ †h ÎæwUi D™¢e nq Zv‡K Kx e‡j? [Zcb, AvwRR] A. j¤^b ÎæwU B. m~PK ÎæwU C. wcQU ÎæwU D. †j‡fj ÎæwU Ans C 24. x = 3u3 n‡j x wbY©‡qi AvbycvwZK ÎæwU KZ? [Zcb, AvwRR] A. u u B. 3u u C. (u) 3 u D. 3 u u 3 S B info x = 3u3 Ax x = 3. u u 25. AwfKl©R Z¡iY wbY©‡qi Rb¨ Avgiv ivwkgvjv cvB g = 4 2 ℓ T 2 | g wbY©‡qi AvbycvwZK ÎæwU wbY©‡qi ivwkgvjv n‡e- [Zcb, AvwRR] A. g g = ℓ ℓ B. g g = 4ℓ ℓ – 8T T C. g g = ℓ ℓ + T T 2 D. g g = ℓ ℓ – T T 2 S A info g = 4 2 ℓ T 2 g g = ℓ ℓ + 2 T T g g = ℓ ℓ 26. Av‡jv m¤úwK©Z me©‡kl gZev` †KvbwU? [Zdv¾j, gwnDwÏb] A. KYv B. Zi½ C. †Kvqv›Uvg D. ZvwoZ †P․¤^K Ans C 27. †KvbwU †g․wjK is bq- [Mwb, mykvšÍ] A. jvj B. njy` C. bxj D. meyR Ans B 28. Òc`v‡_©i cZ‡bi MwZ Zvi IR‡bi Dci wbf©i K‡iÓ Ges ÒAv‡jv ¯^”Q gva¨‡gi wfZi w`‡q PjvPj K‡iÓ G `ywU wm×všÍ me©cÖ_g †K MÖnY K‡ib? [Mwb, mykvšÍ] A. wbDUb B. †Kvcvwb©Kvm C. Gwi÷Uj D. †RvnvÝ ¸‡UbevM© Ans C 29. me weÁv‡bi †P‡q me‡P‡q †g․wjK weÁvb †KvbwU? [†gvK‡Q` m¨vi] A. imvqb B.ev‡qvjwR C. c`v_©we`¨v D. g‡bvweÁvb Ans C

ASPECT PHYSICS cÖ_g cÎ †f․Z RMr I cwigvc 61 ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES 30. Drmvn, †gav Ges eyw×gËvi mv‡_ RwoZ- [†gvK‡Q` m¨vi] A. mvwnZ¨ B. weÁvb C. msMxZ D. `k©b Ans B 31. wPivqZ/K¬vwmK¨vj c`v_©weÁvb cÖ‡hvR¨ nq- [†gvK‡Q` m¨vi] A. AYyex¶wYK RMr/ gvB‡µv¯‥wc RMr B. g¨v‡µv¯‥wcK RMr C. DfqB D. ej‡Z cv‡i bv Ans B 32. c`v_©weÁvb n‡”Q - [†gvK‡Q` m¨vi] A. cixw¶Z weÁvb B. cwigvcMZ weÁvb C. me‡P‡q †g․wjK weÁvb D. Dc‡ii me¸‡jv Ans D 33. m~h© †_‡K c„w_ex‡Z Av‡jv Avm‡Z KZ mgq jv‡M? [†gvK‡Q` m¨vi] A. 8 Av‡jvKel© B. 8 †m‡KÛ C. 8 wgwbU D. 8 N›Uv S C info s = 1.47 1011 m, v = 3 108 ms-1 ,s = vt t = 490s 8min10sec 3 10 1.47 10 v s 8 11 34. e¨vKj¨vm µwUi D`vniY †KvbwU ? [†gvK‡Q` m¨vi] A. cybive„wËK fyj B. cwi‡ekMZ fzj C. G‡jv‡g‡jv fzj D. mgwóMZ fzj Ans A 35. jwNô ¸iæZ¡c~Y© wdMvi (Significant figure) Gi c‡ii AsK¸‡jv A_©nxb ‡Kb? [†Mvjvg m¨vi] A. †QvU nIqvq B. g~j gv‡bi `kgvsk nIqvq C. eo msL¨v ‡jLv AmyweavRbK nIqvq D. Awbf©i‡hvM¨ nIqvq Ans D wb‡Pi Aby‡”Q`wU co Ges 36 I 37 bs cÖ‡kœi DËi `vI: [cÖvgvwbK m¨vi] 1mm wcPwewkó GKwU ‡ù‡ivwgUv‡ii e„ËvKvi ‡¯‥‡ji fvM msL¨v 50| 3wU cv‡qi g‡a¨ 2wU cv‡qi ga¨eZ©x `~iZ¡¸‡jv 7.1cm, 7.0cm, 7.0cm hš¿wUi mvnv‡h¨ cwigvc K‡i GKwU eµZ‡ji D”PZv cvIqv ‡Mj 8cm. 36. †ù‡ivwgUv‡ii jwNô MYb KZ? [cÖvgvwbK m¨vi] A. 0.05mm B. 0.5mm C. 0.02mm D. 0.2mm S C info jwNó Mbb = h‡š¿i cxP e„ËvKvi †¯‥‡ji fvM msL¨v = 0.02mm 50 1mm 37. Z‡ji eµZvi e¨vmva© KZ? [cÖvgvwbK m¨vi] A. 5.3cm B. 0.50cm C. 4.9cm D. 5.03cm S D info †ù‡ivwgUv‡ii cv‡qi ga¨eZ©x Mo `~iZ¡, cm 7.03cm 3 7.1 7 7 d ; eµZ‡ji D”PZv, h = 8 cm eµZvi e¨vmva©, d 2 6h + h 2 = (7.03) 2 6 8 + 8 2 = 5.03cm 38. MÖ‡ni MwZ msµvšÍ mwVK aviYv me©cÖ_g ‡`b ‡K? [cÖvgvwbK m¨vi] A. †Kvcvwb©Kvm B. A¨vwi÷Uj C. U‡jwg D. wbDUb Ans A 39. Av‡jvi •ØZ ag© Avwe®‥vi K‡ib- [igv m¨vi] A. AvjevU© AvBb÷vBb B. g¨v· cø¨vsK C. AvBR¨vK wbDUb D. _gvm Bqs Ans A 40. wb‡Pi ‡Kvb welqwU c`v_©weÁv‡bi mv‡_ IZ‡cÖvZfv‡e RwoZ? [kvgmyi m¨vi] A. †Ljvayjv B. MwYZ C. `k©b D. mvwnZ¨ I ms¯‥…wZ Ans B 41. weªwUk BwÄwbqvwis c×wZ‡Z ‡g․wjK ivwk ej, •`N©¨ Ges mgq‡K h_vµ‡g F, L Ges T gvÎv aiv nq, Zvn‡j f‡ii gvÎv ‡KvbwU? [kvgmyi m¨vi] A. FL–1T 2 B. FL–1T –1 C. FLT–2 D. FL–1T –2 S A info Avgiv Rvwb, F = ma Avevi, S = 1 2 at2 m = F a a = 2S t 2 ej, •`N©¨ I mgq‡K F, L I T gvÎv aiv nq, f‡ii gvÎv = F T 2 L =FL–1T 2 STEP 4 MCQ CONCEPT TEST WRITTEN cÖkœ 01. SI c×wZ‡Z kw³i GKKA. wbDUb B. IqvU C. Ryj D. †fvë 02. GKwU ¯…z-MR n‡Z msL¨v-m~PK cvV 0.0016 0.00005 cvIqv †Mj| †Kvb Dw³wU mZ¨? A.mwVK Aï×Zv n‡e 5% B.AvswkK Aï×Zv n‡e 5 ×10-5 C. AvswkK Aï×Zv n‡e 15 16 D.Aï×Zvi nvi n‡e 3% 03. GKwU e¯‧i fi I `ªæwZ cwigv‡c h_vµ‡g 2% Ges 3% µwU n‡jv| fi I `ªæwZ cwigv‡ci mvnv‡h¨ MwZkw³ cwigvc Ki‡j µwU KZ n‡e? A. 4% B. 6% C. 8% D. 12% 04. GKwU gvcb h‡š¿i fvwb©qvi aªæe‡Ki gvb 0.1mm n‡j H hš¿ Øviv KZ ÿz`ªZg •`N¨© wbLyuZfv‡e gvcv hv‡e? A. 0.0001m B. 0.001m C. 0.01m D. 0.1m 05. ch©‡eÿYRwbZ µwU †KvbwU? A. wcQU ÎæwU B. †j‡fj ÎæwU C. G‡jv‡g‡jv ÎæwU D. j¤^b ÎæwU 06. †Kv‡bv wKQz e¨vL¨vi Rb¨ AvbyôvwbK wPšÍv aviv‡K wK e‡j? A. ¯^xKvh© B. ZË¡ C. AbyK¤ú D. m~Î 07. hw` †Kv‡bv †Mvj‡Ki cwigvcK…Z e¨vmva© nq R = 5.3 0.1 cm Zvn‡j †Mvj‡Ki AvqZb wbY©‡q ÎæwUi cwigvY KZ? A. 6.7% B. 7.5% C. 7.8% D. 5.7% 08. m~h©‡K gnvwe‡k¦ w¯
i †K›`ª we‡ePbv Ki‡j AvKv‡ki e¯‧mg~‡ni GKwU mnR eY©bv †`Iqv n‡q‡Q- Dw³wU †Kvb weÁvbxi? A. K¨v‡fwÛ‡mi B. wbDU‡bi C. †Kcjv‡ii D. †Kvcvwb©Kv‡mi 09. wb‡¤œi †Kvb ÎæwU ïay ¯…z RvZxq h‡š¿i _v‡K? A. e¨w³MZ ÎæwU B. wbqwgZ ÎæwU C. wcQU ÎæwU D. †j‡fj ÎæwU 10. †Kvb eµZ‡ji e¨vmva© wbY©‡qi Rb¨ †Kvb hš¿ e¨envi nqA. ¯øvBW K¨vwjcvm© B. ¯…MR C. †ù‡ivwgUvi D. wgUvi †¯‥j 11. wb‡Pi †KvbwU †g․wjK GKK? A. Ryj B. wbDUb C. †Kjwfb D. IqvU 12. cigvYy welqK wbDwK¬q ZË¡ †K cÖ`vb K‡ib? A. iv`vi‡dvW© B. g¨v· cøv¼ C. nvej D. bxjm †evi 13. K…ò e¯‧i wewKiY e¨vL¨vq kw³i †Kvqv›Uvg bxwZ cÖ_g e¨envi K‡ibA. gvB‡Kj d¨viv‡W B. jW© iv`vi‡dvW© C. g¨v· cø¨v¼ D. AvjevU© AvBb÷vBb 14. 10 m •`N©¨ cwigv‡c ÎæwUi cwigvY 10 cm n‡j ÎæwUi nvi KZ? A. 0.01% B. 0.1% C. 1% D. 10% 15. GK K¨v‡Ðjv `xcb ZxeªZv Av‡jvK Dr‡mi gvb cÖwZ †÷‡iwWqvb Nb‡Kv‡Y KZ? A. 1 386 IqvU B. 1 683 IqvU C. 386 IqvU D. 683 IqvU 16. GK cvi‡mK KZ Av‡jvK e‡l©i mgvb? A. 3.26 B. 3.36 C. 3.46 D. 3.56 17. k~b¨¯
v‡b Av‡jv 1 299792458 sec-G †h `~iZ¡ AwZµg K‡i Zv‡K Kx e‡j? A. GK wgUvi B. GK wK‡jvwgUvi C. GK dzU D. GK Av‡jvK el© 18. GKwU `‡Ûi cwigvcK…Z •`N©¨ 10cm Ges cÖK…Zgvb 10.40cm n‡j, cwigv‡ci kZKiv ÎæwU KZ? A. 4% B. 3.6% C. 3.64% D. 0.4% 19. GKwU e„ËvKvi PvKwZi cwigvc¨ e¨vmva© R = 5.0 0.1 n‡j †ÿÎd‡ji kZKiv ÎæwU KZ A. 1% B. 3% C. 4% D. 5% 20. GKwU ¯øvBW K¨vwjcv‡m©i cÖavb †¯‥‡ji ¶z`ªZg GK N‡ii gvb 1mm Ges fvwb©qvi †¯‥‡ji 20 Ni cÖavb †¯‥‡ji 19 N‡ii mgvb| H †¯‥‡ji fvwb©qvi aªæeK n‡eA. 0.5 mm B. 0.01 mm C. 0.05 mm D. 0.1 mm OMR SHEET 07. 14. 01. 08. 15. 02. 09. 16. 03. 10. 17. 04. 11. 18. 05. 12. 19. 06. 13. 20. A B C D A B C D A B C D A B C D A B C D A B C D A B C D A B C D A B C D A B C D A B C D A B C D A B C D A B C D A B C D A B C D A B C D A B C D A B C D A B C D

62 An Exclusive Parallel Text Book of Physics ASPECT PHYSICS ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES WRITTEN PART 21. GKwU †ù‡ivwgUvi Øviv GKwU KvP cv‡Zi cyiæZ¡ cwigvc Ki‡Z wM‡q •iwLK cvV 1 wg.wg., mgcvZb cvV 25 Ges jwNô ¸Yb 0.001 mm cvIqv †Mj| Zvn‡j Kv‡Pi cyiæZ¡ KZ? DËi:....................................................................................... 22. AvBb÷vB‡bi Av‡cwÿKZvi we‡kl ¯^xKvh©¸‡jv AbyKí bq †Kb e¨vL¨v Ki| DËi:....................................................................................... 23. GKwU ‡ù‡ivwgUv‡ii 3wU cv‡qi g‡a¨ 2wU cv‡qi ga¨eZ©x `~iZ¡¸‡jv 5cm, 5cm, 5cm| hš¿wUi mvnv‡h¨ cwigvc K‡i GKwU eµZ‡ji D”PZv cvIqv †Mj 5cm. Z‡ji eµZvi e¨vmva© KZ? DËi:....................................................................................... 24. cošÍ e¯‧i †ÿ‡Î A¨vwi÷Uj I M¨vwjwjIi aviYv †Kgb? DËi:....................................................................................... 25. GKwU ¯…z-M‡Ri •iwLK †¯‥‡ji cvV cvIqv †Mj 4cm Ges e„ËvKvi †¯‥j cvV cvIqv †Mj 37| ¯…y-MRwU jwNô aªæeK 0.02mm n‡j cÖK…Z cvV KZ? DËi:....................................................................................... 26. GKwU ¯…z-MR n‡Z msL¨v-m~PK cvV 0.0016 0.00005 cvIqv †Mj| †Kvb Dw³wU mZ¨? DËi:....................................................................................... 27. GKwU e¯‧i fi I `ªæwZ cwigv‡c h_vµ‡g 2% Ges 3% µwU n‡jv| fi I `ªæwZ cwigv‡ci mvnv‡h¨ MwZkw³ cwigvc Ki‡j µwU KZ n‡e? DËi:....................................................................................... 28. GKwU gvcb h‡š¿i fvwb©qvi aªæe‡Ki gvb 0.1mm n‡j H hš¿ Øviv KZ ÿz`ªZg •`N¨© wbLyuZfv‡e gvcv hv‡e? DËi:....................................................................................... 29. 10m •`N©¨ cwigv‡c ÎæwUi cwigvY 10cm n‡j ÎæwUi nvi KZ? DËi:....................................................................................... 30. GKwU ¯…z MR Gi e„ËvKvi †¯‥j m¤ú~Y© GK cvK Nyi‡j •iwLK †¯‥j eivei 0.5 mm •`N©¨ AwZµg K‡i| e„ËvKvi †¯‥‡ji fvM msL¨v 50 n‡j, ¯…z M‡Ri jwNô MYb KZ? DËi:....................................................................................... MCQ ANSWER ANALYSIS WRITTEN cÖkœ bs DËi e¨vL¨v 01 C e‡ji GKK = wbDUb, ÿgZvi GKK = IqvU; wefe cv_©‡K¨i GKK = †fvë, Zwor PvjK e‡ji GKK = †fvë; 1W = 1Js–1 , 1V = 1Jc–1 02 D Aï×Zvi nvi= = 3.125% 3% 03 C Ek= 2 1 mv2 ; lnEk = ln 2 1 + lnm + 2 1nv k k E dE = m dm + v 2dv =0.02+2×0.03=0.08=8% 04 B fvwb©qvi aªæe‡Ki gvb 0.1mm Ve = s = Ve n = 0.1 10–3 ×10=0.001m 05 D 06 B 07 D V V = 3R R × 100% = 3 × 0.1 5.3 × 100% = 5.7% 08 D 09 C 10 C 11 C 12 A 13 C 14 C 15 B 16 A 17 A 18 C 19 C 20 C 21 cyiæZ¡ = •iwLK cvV + (mgcvZb jwNô ¸Yb| = 1 + (250.001)mm = 1.025mm = 0.1025 cm 22 Av‡cwÿKZvi we‡kl ¯^xKvh©¸‡jv AvBb÷vBb hLb w`‡qwQ‡jb ZLb wZwb ZvwË¡K cÖgvY w`‡Z cvi‡jI e¨envwiK †Kv‡bv cÖgvY w`‡Z cv‡ibwb| e¨envwiK cÖgv‡Yi Rb¨ Zv‡K eûKvj A‡cÿv Ki‡Z n‡qwQj, 1925 mv‡j msNwUZ m~h©MÖnY ch©šÍ| ZvB Av‡cwÿKZv m¤úwK©Z Zvi we‡kl ¯^xKvh©¸‡jv AbyKí bq| 23 †ù‡ivwgUv‡ii cv‡qi ga¨eZ©x Mo `~iZ¡, d = 5 + 5 + 5 3 cm = 5cm; eµZ‡ji D”PZv, h = 8 cm; eµZvi e¨vmva©, d 2 6h + h 2 = (5) 2 6 5 + 5 2 = 3.33cm 24 A¨vwi÷U‡ji aviYv wQj, DuPz †Kv‡bv RvqMv †_‡K e¯‧ †Q‡o w`‡j KZ `ªæZ co‡e Zv wbf©i K‡i IR‡bi Ici| fvix e¯‧ ZvovZvwo co‡e, nvjKv e¯‧ ax‡i co‡e| M¨vwjwjIi aviYv wQj, GK †m‡K‡Û e¯‧ hZ`yi co‡e `yB †m‡K‡Û co‡e Pvi¸Y| wZb †m‡K‡Û e¯‧wU bq ¸Y `~i‡Z¡ co‡e| Gfv‡e mg‡q mv‡_ `~i‡Z¡i e‡M©i gvb evo‡e| 25 cÖK…Z cvV,L = L1 + C L.C. = 4 + 37 0.02 10 = 4.074 cm 26 Aï×Zvi nvi= 100% 0.0016 0.00005 = 3.125% 3% 27 Ek= 2 1 mv2 ; lnEk = ln 2 1 + lnm + 2 1nv k k E dE = m dm + v 2dv =0.02+2×0.03=0.08=8% 28 fvwb©qvi aªæe‡Ki gvb 0.1mm Ve = n s s = Ve n = 0.1 10–3 ×10=0.001m 29 x – y = 10cm = 0.1m; x = 10m ÎæwUi nvi = x – y x 100% = 0.1 10 100% = 1% 30 C = wcP e„ËvKvi †¯‥‡ji fvi msL¨v 0.01mm 50 0.5mm 100% 0.0016 0.00005 n s

ASPECT PHYSICS cÖ_g cÎ †f±i 63 ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES SURVEY TABLE  Kx coe? †Kb coe? †Kv_v n‡Z coe? KZUzKz coe?  TOPICS MAGNETIC DECISION [hv co‡e] MAKING DECISION [†h Kvi‡Y co‡e] VVI For This Year DU JU RU CU GST Engr. HSC Written MCQ THEORY CONCEPT-01 †f±i ivwki aviYv, •ewkó¨ Ges ¸iæZ¡c~Y© m~Îmg~n 20% 10% 10% 10% 100% - 20% - CONCEPT-02 †f±‡ii cÖKvi‡f` 30% 40% 35% 30% 40% - 20% - CONCEPT-03 †f±i ivwki ¸Yb 60% 70% 65% 70% 60% - 20% - CONCEPT-04 Acv‡iUi, †MÖwW‡q›U, WvBfvi‡RÝ, Kv‡j©i aviYv I ¸iæZ¡c~Y© Z_¨vewj 30% 20% 25% 30% 30% - 30% MvwYwZK cÖ‡qvM CONCEPT-01 GKK †f±i msµvšÍ MvwYwZK cÖ‡qvM 70% 80% 75% 70% 70% 60% 80% CONCEPT-02 jwä msµvšÍ MvwYwZK cÖ‡qvM 85% 85% 80% 75% 80% 70% 90% CONCEPT-03 †b․Kv msµvšÍ MvwYwZK cÖ‡qvM 90% 90% 85% 80% 75% 80% 90% CONCEPT-04 e„wó msµvšÍ MvwYwZK cÖ‡qvM 70% 80% 75% 80% 65% 80% 70% CONCEPT-05 ga¨eZ©x †KvY msµvšÍ MvwYwZK cÖ‡qvM 90% 85% 80% 70% 70% 90% 70% CONCEPT-06 A‡ÿi mv‡_ †KvY wbY©q msµvšÍ MvwYwZK cÖ‡qvM 85% 80% 80% 75% 75% 88% 80% CONCEPT-07 `ywU †f±i ci¯úi j¤^ msµvšÍ MvwYwZK cÖ‡qvM 80% 80% 70% 70% 70% 70% 75% CONCEPT-08 `ywU †f±i ci¯úi mgvšÍivj msµvšÍ MvwYwZK cÖ‡qvM 85% 85% 75% 80% 80% 75% 75% CONCEPT-09 WU ¸Yb, µm ¸Yb I †ÿÎdj msµvšÍ MvwYwZK cÖ‡qvM 70% 85% 70% 60% 60% 60% 80% CONCEPT-10 Awf‡ÿc I Dcvsk msµvšÍ MvwYwZK cÖ‡qvM 70% 75% 60% 65% 70% 70% 70% CONCEPT-11 WvBfvi‡RÝ, †MÖwW‡q›U, Kvj© msµvšÍ MvwYwZK cÖ‡qvM 60% 50% 40% 30% 40% 30% 60% DU. = Dhaka University, JU. = Jahangirnagar University, RU. = Rajshahi University, CU = Chittagong University, GST = General, Science & Technology, Engr. = Engineering. STEP 1 mvRv‡bv me Z_¨ THEORY fwZ© †ivMxi c_¨ Concept 1 †f±i ivwki aviYv, •ewkó¨ Ges ¸iæZ¡c~Y© m~Îmg~n ✅ ivwk: c`v‡_©i †h me ‡f․Z •ewkó¨ cwigvc Kiv hvq Zv‡`i‡K ivwk e‡j| ✅ ivwk‡K w`K wbf©iZv Abymv‡i `yB fv‡M fvM Kiv hvq| h_v: (i) w`K ivwk ev †f±i ivwk (ii) Aw`K ivwk ev †¯‥jvi ivwk ◈ w`K ivwk ev †f±i ivwki D`vniYmg~n: Òf‡e me wcÖIZg fv‡m Uzwbi wZZv †cÖ‡gÓ f fi‡eM wcÖ cÖvej¨ fv åvgK †e †eM I IRb ‡m mv›`ªZv ¸Yv¼ †cÖ c„ôUvb m miY Z Z¡iY/Zwor cÖevn (cÖevngvÎv) Uywbi UK© †g gnvKl©xq cÖvej¨ e ej/e‡ji NvZ g g›`b wZZv Zwor‡ÿÎ [Note:] mKj cÖKvi cÖvej¨ I åvgK w`K ivwk| e¨wZµg-RoZvi åvgK| GwU †¯‥jvi ivwk| ✅ †¯‥jvi ivwk I †f±i ivwki cv_©K¨ †¯‥jvi ivwk †f±i ivwk †¯‥jvi ivwki ïay gvb Av‡Q wK¯‧ w`K †bB| †f±i ivwki gvb I w`K DfqB Av‡Q| mvaviY MvwYwZK wbq‡g †hvM, we‡qvM, ¸Y, fvM Kiv hvq| mvaviY MvwYwZK wbq‡g †hvM, we‡qvM, ¸Y, fvM Kiv hvq bv| ïay gv‡bi cwieZ©‡b cwiewZ©Z nq| gvb A_ev w`K A_ev Df‡qi cwieZ©‡b cwiewZ©Z nq| `yBwU †¯‥jvi ivwki †KvbwUi gvb k~b¨ bv n‡j G‡`i ¸Ydj k~b¨ nq bv| `yBwU †f±i ivwki †Kvb GKwUi gvb k~b¨ bv n‡jI G‡`i †f±i ¸Ydj k~b¨ n‡Z cv‡i| `yBwU †¯‥jvi ivwki ¸Y‡b me©`v †¯‥jvi ivwk cvIqv hvq| `yBwU †f±i ivwki ¸Ydj GKwU †f±i ivwk A_ev GKwU †¯‥jvi ivwk n‡Z cv‡i| ✅ GKwU †¯‥jvi ivwki mv‡_ GKwU †f±i ivwki †hvM m¤¢e bq| †f±i VECTOR cÖ_g cÎ 02 Aa¨vq c„ôv 63

64 An Exclusive Parallel Text Book of Physics ASPECT PHYSICS ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ✅ R¨vwgwZK c×wZ‡Z †f±i ivwki †hv‡Mi 5wU m~Î: (i) mvaviY m~Î (ii) wÎfzR m~Î (iii) eûfzR m~Î (iv) mvgvšÍwiK m~Î (v) Dcvsk m~Î| ◈ †f±i †hvRb g‡b ivLvi mnR m~Î: Dmv eû wÎfzR G‡K‡Q D mv eû wÎfzR G‡K‡Q Dcvsk m~Î mvaviY m~Î, mvgvšÍwiK m~Î eûfzR m~Î wÎfzR m~Î m~Î wee„wZ wÎf~R m~Î hw` GKwU wÎfy‡Ri `ywU mwbœwnZ evû Øviv gvb I w`‡K GKB µ‡g `ywU †f±i‡K cÖKvk Kiv nq Zvn‡j Z…Zxq evû Øviv wecixZ µ‡g H †f±i؇qi jwä wb‡`©k K‡i| eûf~R m~Î `yB-Gi AwaK †f±i ivwki †ÿ‡Î †f±i ivwk¸‡jv‡K GKB µ‡g mvwR‡q cÖ_g †f±i ivwki cv`we›`y Ges †kl †f±i ivwki kxl©we›`y †hvM Ki‡j †h eûfzR cvIqv hvq Gi †kl evûwU wecixZµ‡g †f±i ivwk¸‡jvi jwäi gvb I w`K wb‡`©k K‡i| mvgšÍwiK m~Î hw` mvgšÍwi‡Ki `ywU mwbœwnZ evû Øviv gvb I w`‡K `ywU †f±i‡K cÖKvk Kiv nq Z‡e H we›`y n‡Z AswKZ mvgšÍwi‡Ki KY© †f±i؇qi jwä wb‡`©k K‡i| ✅ †f±i †hv‡Mi K‡qKwU m~Î: †f±‡ii wewbgq m~Î: A + B = B + A †f±‡ii ms‡hvM m~Î: ( A + B) + C = A + ( B + C) †f±‡ii eÈb m~Î: m ( A + B) = m A +m B REAL TEST ANALYSIS OF PREVIOUS YEAR QUESTIONS STEP 01 ANALYSIS OF DU QUESTION 01. ( A + B) + C = A + ( B + C) GwU †f±i- [DU. 12-13] A. wewbgq m~Î B. ms‡hvM m~Î C. eÈb m~Î D. ‡KvbwUB bq Ans B 02. wb‡Pi †Kvb wPÎwU mgxKiYwU mwVK fv‡e Dc¯’vcb K‡i? [DU. 11-12] A. R Q P B. R Q R C. R Q P D. R Q P Ans C 03. wb‡Pi wP‡Î P , Q Ges R GB wZbwU †f±i ivwk‡K †`Lv‡bv n‡q‡Q| wPÎ †_‡K wbY©q Kiv hvq †h- [DU. 04-05] Q R P A.P – Q – R = 0 B. P + Q – R = 0 C. B. P + Q + R = 0 D. B. P – Q + R = 0 Ans A STEP 02 ANALYSIS OF JU QUESTION 01. wb‡Pi †KvbwU †f±i ivwk? [JU-A, Set-A. 19-20] A. AvqZb B. Pvc C. †ÿÎdj D. KvR S C info †ÿÎdj GKwU †f±i ivwk Ges Pvc, AvqZb, KvR †¯‥jvi ivwk| 02. †KvbwU †f±i ivwk? [JU. 13-14] A. `yiZ¡ B. AvqZb C. kw³ D. mib Ans D STEP 03 ANALYSIS OF RU QUESTION 01. †KvbwU †¯‥jvi ivwk? [RU. 09-10] A. IRb B. Z¡ib C. Zwor wefe D. Zwor cÖvej¨ Ans C 02. †f±i‡K †f±i Øviv ¸Y Ki‡j ¸Ydj nq- [RU. 09-10] A. †¯‥jvi B. †f±i C. KL‡bv †¯‥jvi, KL‡bv †f±i D. aªæeK Ans C STEP 04 ANALYSIS OF GST QUESTION PART A Analysis of General University Question KU 01. †Kvb mgq GKB we›`y‡Z wµqviZ wZbwU mgZjxq †f±i ivwk‡K †Kvb wÎfy‡Ri wZbwU evû Øviv GKB µ‡g wb‡`©k Ki‡j G‡`i jwä- [KU. 09-10] A. Kg n‡e B. †ekx n‡e C. k~Y¨ n‡e D. †Kvb cwieZ©b n‡e bv Ans C IU 01. Zj ev Z‡ji †¶Îdj- [IU. 14-15] A. †¯‥jvi ivwk B. Aw`K ivwk C. †f±i ivwk D. †g․wjK ivwk Ans C PART B Analysis of Science & Technology Question SUST 01. a Aw`K ivwk Ges A w`K ivwk n‡j wb‡Pi †KvbwU A_©c~Y© bq? [SUST. 2000-01] A. aA B. a + A C. A/a D. aA.A Ans B MBSTU 01. †KvbwU w`K ivwk? [MBSTU. 2015-16] A. •e`y¨wZK wefe B. KvR C. ¯^Kxq Av‡ek ¸bvsK D. †P․¤^K cÖvej¨ Ans D 02. wb‡Pi †KvbwU †¯‥jvi ivwk bq- [MBSTU. 2014-15] A. KvR B. ¶gZv C. kw³ D. ej Ans D PSTU 01. †KvbwU †¯‥jvi (Aw`K ivwk)? [PSTU. 2014-15] A. miY B. ‣`N©¨ C. ‡eM D. ej Ans B 02. †¯‥jvi ivwk †Kvb¸wj? [PSTU. 2014-15] A. ¶gZv, KvR, †eM B. kw³, Z¡iY, ¶gZv C. KvR, †eM, kw³ D. KvR, kw³, ¶gZv Ans D STEP 05 ANALYSIS OF MEDICAL & DENTAL QUESTION MAT 01. wb‡Pi †KvbwU †f±‡ii wewbgq m~Î- [MAT. 18-19] A. P (Q + R ) = P .Q + P .R B. P + Q = Q + P C. (P + Q ) + R = P +(Q + R ) D. P + Q = P .Q Ans B R P Q

ASPECT PHYSICS cÖ_g cÎ †f±i 65 ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES 02. wb‡Pi †KvbwU †¯‥jvi ivwk- [MAT. 09-10] A. Zwor wefe B. Zwor cÖvej¨ C. †eM D. fi‡eM Ans A 03. wb‡¤œi †KvbwU †f±i ivwki we‡qvR‡bi m~Î bq? [MAT. 04-05] A. mvavib B. mgvšÍivj C. mvgšÍwiK D. Dcvsk Ans B 04. †¯‥jvi ivwki †ejvq †KvbwU mwVK bq? [MAT. 03-04, 08-09, 13-14] A. †¯‥jvi ivwki †hvM, we‡qvM, ¸Y, mvaviY MvwYwZK wbq‡g Kiv hvq B. gv‡bi cwieZ©b n‡j †¯‥jvi ivwki cwieZ©b nq C. `ywU ‡¯‥jvi ivwki †KvbwUi gvb ïb¨ bv n‡jI G‡`i ¸bdj ïb¨ n‡Z cv‡i D. `ywU †¯‥jvi ivwki ¸Ydj GKwU †¯‥jvi ivwk Ans C 05. †KvbwU mZ¨ bq? [MAT. 01-02] A. G GKwU mve©Rbxb aªæeK B. Pvc GKwU w`K ivwk C. ‡fvë Pv‡R©i GKK D. K¨v‡_vW iwk¥ FbvZ¡K Kbv enb K‡i| S C info ‡fvë= wef‡ei GKK, Kzj¤^ = Pv‡R©i GKK DAT 01. †KvbwU †f±i ivwki (Vector quantity) D`vniY bq? [DAT. 2020-21] A. †eM B. Z¡iY C. `ªæwZ D. ej S C info `ªæwZ GKwU †¯‥jvi ivwk| †¯‥jvi ivwk: ‣`N©¨, fi, mgq, RbmsL¨v, ZvcgvÎv, Zvc, •e`y¨wZK wefe, `ªæwZ, KvR, AvqZb, NbZ¡, `~iZ¡, kw³ BZ¨vw`| †f±i ivwk: miY, †eM, Z¡iY, g›`b, ej, IRb, fi‡eM, †K․wYK fi‡eM, UK©, Zwor‡ÿÎ BZ¨vw`| STEP 06 ANALYSIS OF HSC BOARD QUESTION 01. N~Y©biZ e¯‘i †ÿ‡Î, cÖhy³ ej I Ae¯’vb †f±‡ii ga¨eZ©x †KvY n‡jÑ [Xv.‡ev 2021] i. = 180 n‡j N~Y©bej m‡e©v”P n‡e ii. = 0 n‡j N~Y©bej me©wb¤œ n‡e iii. = 90 n‡j N~Y©bej m‡e©v”P n‡e wb‡Pi †KvbwUmwVK? A. i I ii B. ii I iii C. i I iii D. i, ii I iii Ans B 02. DÏxc‡Ki Av‡jv‡K †KvbwU mwVK? [Xv. †ev. 2017] A. L + N − M = 0 B. L + N + M = 0 C. L + N − M = 0 D. M + N − L = 0 Ans D 03. †¯‥jvi ivwki D`vniY- [w`.‡ev 2021] A. KvR B. ej C. UK© D. †K․wYK fi‡eM Ans A 04. DÏxc‡Ki ABC Gi †ÿ‡Î †KvbwU mwVK? [w`.‡ev. 2019] A. − = B. − = C. + = D. − = Ans B 05. †¯‥jvi ivwk n‡”Q- [h. †ev. 2016] i. kw³ ii. miY iii. wefe wb‡Pi †KvbwU mwVK? A. i I ii B. i I iii C. ii I iii D. i, ii I iii Ans B 06. wb‡Pi †KvbwU †¯‥jvi ivwk? [Kz. †ev. 2017] A. e‡ji åvgK B. †K․wYK fi‡eM C. †K›`ªgyLx ej D. RoZvi åvgK Ans D 07. wPÎvbymv‡i †KvbwU mwVK?[wm. †ev. 2019; w`. †ev. 2019; Xv. †ev. 2017; w`. †ev. 2016] B A C R Q P A. R = P + Q B. P = R + Q C. Q = R + P D. P + Q + R = 0 Ans B 08. wb‡Pi †KvbwU †f±i ivwk? [wm. †ev. 2015] A. cxob B. weK…wZ C. mv›`ªZv D. c„ô kw³ Ans A 09. wb‡Pi †KvbwU †¯‥jvi ivwk? [g.‡ev 2021] A. AwfKl©xq fi B. KvR C. UK© D. †K․wYK fi‡eM Ans B 10. mgvb †f±‡ii •ewkó¨- [e.‡ev 2021] i. mgRvZxq ivwk ii. gvb mgvb iii. w`K GKB w`‡K wb‡Pi †KvbwU mwVK? A. i I ii B. ii I iii C. i I iii D. i, ii I iii Ans D 11. wb‡Pi †KvbwU †f±i ivwk? [e. †ev. 2015] A. cxob B. weK…wZ C. mv›`ªZv D.c„ôkw³ Ans A Concept 2 †f±‡ii cÖKvi‡f` VECTOR TERMS DEFINITION ¯^vaxb ‡f±i Free vector †Kvb †f±i ivwki cv`we›`y ‡Kv_vq n‡e Zv hw` B”QvgZ cQ›` Kiv hvq, Z‡e †mB †f±i‡K ¯^vaxb †f±i e‡j| mxgve× ‡f±i Localised Vector †Kv‡bv †f±‡ii cv`we›`y hw` B”QvgZ cQ›` Ki‡Z bv †`Iqv nq Z‡e †mB †f±i‡K mxgve× †f±i e‡j| k~b¨ †f±i Null Vector GKwU †f±‡ii m~Pbv we›`y I cÖvšÍ we›`y hw` wg‡j hvq Z‡e Zv‡K k~b¨ †f±i e‡j| G †f±‡ii gvb k~b¨ I w`K Awbw`©ó| k~b¨ †f±i Qvov Ab¨vb¨ mKj †f±i‡K mwVK (Proper) †f±i e‡j| Ae¯
vb ‡f±i Position vector cÖm½ KvVv‡gvi g~j we›`yi mv‡c‡¶ ‡Kvb we›`yi Ae¯
vb †h ‡f±‡ii mvnv‡h¨ wbY©q ev wb‡`©k Kiv nq Zv‡K Ae¯
vb †f±i e‡j| GwU‡K e¨vmva© †f±iI e‡j| miY †f±i Displacement vector •iwLK ev mij c‡_ ‡Kvb we›`yi AwZµvšÍ `~iZ¡‡K miY †f±i e‡j| mwVK †f±i Proper Vector †h me †f±‡ii gvb k~b¨ bq Zv‡`i‡K mwVK †f±i ev Ak~b¨ †f±i e‡j| GKK †f±i Unit Vector †h †f±‡ii gvb GK GKK Zv‡K GKK †f±i e‡j| = A | A| wecÖZxc †f±i Reciprocal Vector `ywU mgvšÍivj †f±i GKwU AciwUi ¸YvZ¥K wecixZ n‡j Zv‡K wecÖZxc †f±i e‡j| †hgb: A = 3 i Ges B = 1 3 i; A I B wecÖZxc|

66 An Exclusive Parallel Text Book of Physics ASPECT PHYSICS ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES VECTOR TERMS DEFINITION mgZjxq †f±i Co-planar Vector `yB ev Z‡ZvwaK †f±i GKB Z‡j KvR Ki‡j Zv‡K mgZjxq †f±i e‡j| G‡ÿ‡Î, A . ( ) B C = 0 wecixZ ev FY †f±iOpposite or Negative Vector wecixZ w`‡K wµqviZ `ywU mgRvZxq †f±‡ii gvb mgvb n‡j Zv‡`i‡K G‡K Ac‡ii wecixZ ev FY †f±i e‡j| mgvb †f±i Equal Vector `ywU †f±‡ii gvb I w`K GKB n‡j Zv‡`i mgvb †f±i ejv nq| `ywU mgvb †f±‡ii Avw` we›`yAvjv`v n‡Z cv‡i| †m‡ÿ‡Î AwšÍg we›`yI Avjv`v n‡e| †cvjvi †f±i Polar Vector e¯‧i N~Y©‡bi m‡½ hy³ bq Ggb †f±i‡K †cvjvi †f±i e‡j| D`vniY: ej, fi‡eM, miY, MwZ‡eM BZ¨vw`| Aÿxq †f±i Axial Vector †h mg¯Í †f±i †Kv‡bv bv †Kv‡bv cÖKvi N~Y©‡bi m‡½ m¤úwK©Z Ges hv‡`i †K N~Y©‡bi mgvšÍivj †iLv Øviv cÖKvk Kiv nq, Zv‡`i‡K Aÿxq †f±i e‡j| D`vniY: UK©, †K․wYK †eM, †K․wYK fi‡eM BZ¨vw`| REAL TEST ANALYSIS OF PREVIOUS YEAR QUESTIONS STEP 01 ANALYSIS OF JU QUESTION 01. `yB ev Z‡ZvwaK †f±i GKB Z‡j KvR Ki‡j Zv‡K e‡j| [JU. 15-16] A. GKK †f±i B. mg‡iL †f±i C. mgZjxq †f±i D. ¯
vbxq †f±i Ans C STEP 02 ANALYSIS OF CU QUESTION 01. X Z Z‡j GKwU we›`yi Ae¯’vb †f±i †KvbwU? [CU-A, Set-2. 19-20] A. B. r = x i + y j C. D. S C info r = y j + z k YZ mgZj; r = x i + y j XY mgZj; r = x i + z k ZX mgZj; r = x i + y j + z k XYZ mgZj| 02. gvb k~b¨ bq G iKg GKwU †f±i‡K Zvi gvb w`‡q fvM Ki‡j wK cvIqv hvq? [CU. 2015-16] A. bvj †f±i B. Ae¯
vb †f±i C. GKK †f±i D. mgZjxq †f±i E. mgvšÍivj †f±i Ans C STEP 03 ANALYSIS OF GST QUESTION PART A Analysis of General University Question KU 01. g~j we›`y mv‡c‡¶ Ab¨ †Kvb we›`yi Ae¯’vb wbY©‡qi Rb¨ †h †f±i e¨envi Kiv nq Zv‡K e‡j- [KU. 10-11] A. GKK †f±i B. bvj †f±i C. k~b¨ †f±i D. Ae¯
vb †f±i Ans D JKKNIU 01. mgRvZxq `yB ev Z‡ZvwaK †f±i hw` GKB w`‡K wµqv K‡i, Z‡e Zv‡`i‡K †f±i e‡j| [JKKNIU-B, Set-3, 19-20] A. mxgve× B. m`„k C. mgvb D. mg‡iL S B info mggv‡bi `yB ev Z‡ZvwaK †f±i GKB w`‡K wµqv Ki‡j Zv‡`i mgvb †f±i e‡j| mggv‡bi bv n‡j Zviv m`„k †f±i| STEP 04 ANALYSIS OF MEDICAL & DENTAL QUESTION MAT 01. wb‡Pi †Kvb †f±‡ii w`K wbw`©ó bq? [MAT. 17-18; Kz.†ev. 2017] A. wecÖZxc ‡f±i B. k~b¨ †f±i C. mgvb †f±i D. wecixZ †f±i Ans B 02. wb‡Pi †KvbwU †f±‡ii cÖKvi‡f` bq? [MAT. 06-07] A. FY †f±i B. mgvb †f±i C. mgZjxq †f±i D. ab †f±i Ans D DAT 01. †Kvb †f±‡ii kxl©we›`y I cv`we›`y GKB n‡j †f±iwU n‡e wb‡Pi †KvbwU? [DAT. 17-18; Xv.†ev. 2016] A. e¨vmva© †f±i B.m`„k †f±i C. bvj †f±i D. mg‡iL †f±i Ans C STEP 05 ANALYSIS OF HSC BOARD QUESTION 01. †f±‡ii WU¸Yb †g‡b P‡j- [P.‡ev 2021] i. wewbgq m~Î ii. eÈb m~Î iii. ms‡hvM m~Î wb‡Pi †KvbwU mwVK? A. i I ii B. i I iii C. ii I iii D. i, ii I iii Ans D 02. mgvb †f±‡ii •ewkó¨- [P.‡ev 2021] i. mgRvZxq ivwk ii. gvb mgvb iii. w`K GKB w`‡K wb‡Pi †KvbwU mwVK? A. i I ii B. ii I iii C. i I iii D. i, ii I iii Ans D 03. P I Q ci¯ú‡ii wecixZ †f±i n‡j- [P. †ev. 2015] A. P + Q = 0 B. P . Q = 0 C. P Q = 0 D. A I B DfqB mwVK Ans A 04. Amg gv‡bi Ges wecixZgyLx mgRvZxq `ywU †f±i‡K e‡j- [w`.‡ev 2021] A. wecixZ †f±i B. wecÖZxc †f±i C. wem`„k †f±i D. m`„k †f±i Ans C 05. A. B = 0 n‡j wb‡Pi †Kvb wPÎwU mwVK? [Kz.‡ev 2021] A. B. C. D. B A A B B A A B S C info – A . – B = 0 n‡j †f±iØq ci®úi j¤^ nq| 06. A = 2B n‡j A I B Gi †f±i `ywU- [Kz. †ev. 2017] A. m`„k B. wem`„k C. mg‡iL D. B I C DfqB Ans D 07. A I B †K wecÖZxc †f±i ejv nq hLbÑ [Kz. †ev. 2016] A. A = 4i I B = 1 4 i B. A = 4i I B = 8i C. A = 8i I B = 4i D. A = 4i I B = 4i Ans A 08. Gi gvb 0 †_‡K 90 ch©šÍ e„w× Kiv n‡j vx Ges vy Gi gv‡bi Kxiƒc cwieZ©b n‡e? [Kz. †ev. 2016] vx vy vx vy A. Kg‡e evo‡e B. evo‡e Kg‡e C. evo‡e evo‡e D. Kg‡e Kg‡e Ans A 09. ‡f±i wb‡`©kK †iLvskwUi Avw` we›`y I †klwe›`y hw` wg‡k hvq Zvn‡j Zv‡K Kx †f±i e‡j? [wm.‡ev 2021] A. ¯^vaxb B. m`„k C. mgvb D. k~b¨ Ans D 10. A = 5 i n‡j Gi wecÖZxc †f±i wb‡Pi †KvbwU? [g.‡ev 2021] A. –5 i B. 1 5 i C. 5 1 i D. 1 5 i Ans B r yj zk ˆ ˆ r xi zk ˆ ˆ r xi yj zk ˆ ˆ ˆ

ASPECT PHYSICS cÖ_g cÎ †f±i 67 ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES Concept 3 †f±i ivwki ¸Yb †¯‥jvi ev WU ¸Yb `ywU †f±i ivwki WU ¸Yb GKwU †¯‥jvi ivwk mg‡K․wYK GKK †f±img~‡ni ¸Ydj: i ˆ .i ˆ = j ˆ .j ˆ = k ˆ .k ˆ = 1; i ˆ .i ˆ = 1.1cos0 = 1; i ˆ .j ˆ = j ˆ .k ˆ = k ˆ .i ˆ = 0 ; i ˆ .j ˆ = 1.1 cos90 = 0 GKwU †f±‡ii gv‡bi eM© cvIqv hvq, A_v©r, A . A = A2 WU ¸Yb wewbgq m~Î †g‡b P‡j| A_©vr A. B = B. A P . Q = PQcos †f±i؇qi ga¨eZ©x †KvY = cos–1 A. B AB †f±i ev µm ¸Yb `ywU †f±i ivwki µm ¸Yb GKwU †f±i ivwk mg‡K․wYK GKK †f±img~‡ni ¸Ydj : i ˆ i ˆ = j ˆ j ˆ = k ˆ k ˆ = 0; i ˆ j ˆ = k ˆ ; k ˆ i ˆ = j ˆ ; j ˆ k ˆ = i ˆ ; j ˆ i ˆ = k ˆ ; i ˆ k ˆ = –j ˆ ;k ˆ j ˆ = –i ˆ GKwU †f±‡ii gv‡bi eM© k~b¨ nq, A_v©r, A A = A2 = 0 µm ¸Yb wewbgq m~Î †g‡b P‡j bv| A_©vr A B = – B A P Q = PQsin = sin1 A B | | A B A B = 0; when = 0˚; – A B = 0; when = 180˚ A = – B n‡j A B =0 KviY = 180˚ mgZ‡ji Dci j¤^ GKK †f±i, = A B | A B| A B = C Ges B A = D n‡j C Ges D Gi ga¨eZ©x †KvY 180˚ A . ( A B) = 0 Ges B . ( A B) = 0 KviY A B Gi mv‡_ Df‡qB j¤^ †f±i ¸Y‡bi gvb Øviv mvgvšÍwi‡Ki ‡¶Îdj wb‡`©k Kiv nq| A I B mvgvšÍwi‡Ki evû n‡j †¶Îdj = | | A B Ges KY© n‡j †ÿÎdj = 1 2 | A B| when | | A + B = | | A – B then = 90˚ When A. B = | A B| then = 45 * | A. B| 2 + | A B| 2 = A2B 2 ✅ †¯‥jvi ¸Ydj I †f±i ¸Ydj cv_©K¨: †f±i ¸Ydj †¯‥jvi ¸Ydj 1. †f±i ¸Yb GKwU †f±i ivwk| WvbnvwZ ¯…z-Gi wbqg n‡Z Gi w`K cvIqv hvq| 1. †¯‥jvi ¸Yb GKwU †¯‥jvi ivwk Gi †Kvb w`K †bB| 2. †f±i ¸Y‡bi gvb ivwk؇qi gv‡bi Ges AšÍfz©³ ¶z`ªZg †Kv‡Yi sine Gi ¸Yd‡ji mgvb| 2. †¯‥jvi ¸Y‡bi gvb ivwk؇qi gv‡bi Ges AšÍfz©³ ¶z`ªZg †Kv‡Yi cosine Gi ¸Yd‡ji mgvb| 3. †f±i ¸Ydj wewbgq m~Î gv‡b bv| 3. †¯‥jvi ¸Ydj wewbgq m~Î gv‡b| 4. †f±i `ywU ci®úi mgvšÍivj n‡j †f±i ¸Yb k~b¨ nq| 4. †f±i `ywU ci®úi j¤^ n‡j †¯‥jvi ¸Yb k~b¨ nq| 5. D`vniY: i. mvgvšÍwi‡Ki †ÿÎdj `ywU †f±‡ii µm ¸Yd‡ji gv‡bi mgvb| ii. UK©, = r F = rF sin, †hLv‡b Ae¯
vb †f±i r Ges cÖhy³ ej F iii. †K․wYK †eM ( ) Gi †f±i MvwYwZK cÖKvk n‡jv v = r iv. †K․wYK fi‡eM, L = r P 5. D`vniY: i. KvR W = F. S = Fs cos ; ii. w¯
wZkw³; w = mgh iii. •e`y¨wZK wefe; v = w q ✅ we‡kl †ÿÎmg~n: †¯‥jvi ¸Ydj †f±i ¸Ydj hw` = 0 nq, Z‡e P. Q = PQ cos0 = PQ. hw` = 0 nq, Z‡e R = P Q = PQ sin 0 = 0 hw` = 90 nq, Z‡e P. Q = PQ cos90 = 0. hw` = 90 nq, Z‡e R = P Q = PQ sin 90 = PQ hw` = 180 nq, Z‡e P. Q = PQ cos180 = –PQ. hw` = 180 nq, Z‡e R = P Q = PQ sin 180 = 0 REAL TEST ANALYSIS OF PREVIOUS YEAR QUESTIONS STEP 01 ANALYSIS OF DU QUESTION 01. A = – B n‡j, A B Gi gvb †ei Ki- [DU. 05-06, JU. 13-14, IU. 12-13] A. – A 2 B. 0 C. – B 2 D. 1 S B info A B = – B B = B.B sin 180 = 0 STEP 02 ANALYSIS OF JU QUESTION 01. | | A + B = | | A – B n‡j †f±i A I B Gi †¶Î| [JU. 15-16,DU. 7Clg. 20-21] A. A + B= 0 B. A . B = 0 C. A = B D. †KvbwUB bq S B info | A + B | = | A – B | | A| 2 + | B| 2 + 2ABcos = | A| 2 + | B| 2 – 2ABcos 4ABcos = 0 cos = 0 = cos90 = 90

68 An Exclusive Parallel Text Book of Physics ASPECT PHYSICS ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES 02. `ywU †f±‡ii WU ¸Ydj kyb¨ n‡j, †f±i؇qi ga¨eZx© †KvY- [JU. 13 -14; KU. 10-11] A. 0 B. 30 C. 90 D. 60 Ans C STEP 03 ANALYSIS OF RU QUESTION 01. †Kvb †f±iwU x-A‡ÿi mv‡_ mgvšÍivj? [RU. Sinovac, Set-1. 20-21] A. ( ) i × j × i B. ( ) i × j × k C. ( ) i × j × j D. ( ) k × j × k S C info ( ) i × j × j = k j = – i hv x A‡ÿi Dci Aew¯
Z GKwU GKK †f±i hv H A‡ÿiB mgvšÍivj| 02. wewbgq m~Î †g‡b P‡j bv- [RU. 15-16] A. ‡f±i ivwki WU ¸bb B. ‡f±i ivwki µm ¸bb C. ‡f±i ivwki †hvM D. ‡Kv‡bvwUB bq Ans B 03. ( ˆ k ˆ j )+ ( ˆ j ˆ k ) = Gi gvb KZ? [RU. 13-14] A. ˆ j B. 0 C. ˆ i D. ˆk S B info ˆ k ˆ j + ˆ j ˆ k = – ˆ i ˆ i = 0 04. A B = C n‡j C . A KZ? [RU. 12-13] A. | | A|| C B. C A C. 0 D. †KvbwUB bq| S C info A B = C ; A_©vr C †f±i A Ges B Df‡qi mv‡_ j¤^| Zvn‡j C . A = CAcos90 = 0 STEP 04 ANALYSIS OF CU QUESTION 01. A Ges B †f±iØq KLb A.B = –AB n‡e? [CU-A, Set-1. 20-21,MBSTU. 15-16] A. †f±iØiq mgvšÍivj Ges GKB w`‡K B. †f±iØiq mgvšÍivj wKš‧ wecixZgyLx C. †f±iØq ci¯úi j¤^ D. †KvbwUB bq S B info A.B = AB cos 180 = –AB A_©vr A Ges B †f±iØq ci¯úi mgvšÍivj Ges wecixZgyLx| 02. hw` C = A × B I D = B × A nq, Z‡e C I D Gi ga¨eZ©x †Kv‡Yi gvb KZ? [CU-A, Set-2. 20-21] A. 90 B. 0 C. 180 D. 45 S C info C = A × B = – ( B × A ) = – D; A_©vr C Ges D ci¯úi mgvb Ges wecixZgyLx (180)| 03. wb‡¤œi †KvbwU mwVK DËi? [CU-A, Set-3. 20-21] A. j × k = – i B. j × k = i C. j × k = 1 D. j × k = 0 S B info †f±i ¸Y‡bi wbqvgvbymv‡i, i. P × Q = – Q × P ii. i × i = j × j = k × k = 0 iii. i × j= k = – ( j × i) iv. j × k = i = – ( k j) 04. hw` | A – B|= | A + B| nq ZLb A Ges B Gi ga¨eZx© †KvY n‡e- [CU. 18-19; KU. 12-13] A. 0 B. 3 C. 4 D. 2 Ans D 05. A = ˆ i, B = ˆ j, C = ˆk nq Z‡e A . ( B C) = ? [CU. 14-15] A. 0 B. 1 C. 2 D. –1 E. –2 S B info A = ˆ i, B = ˆ j, C = ˆk A ( B C) = i.( ˆ j ˆk) = i.i = 1 06. ˆ k ( ) ˆ i + ˆ j Gi gvb KZ? [CU. 11-12] A. 2 B. 4 C. 0 D. 6 E. 1 S C info ˆk( ) ˆ i + ˆ j = ˆk. ˆ i + ˆk. ˆ j = 0 + 0 = 0 STEP 05 ANALYSIS OF GST QUESTION PART A Analysis of General University Question JnU 01. A I B `ywU †f±i ivwk n‡j †KvbwU mwVK? [JnU. 15-16] A. A B = B A B. – A B = B A C. ‡KvbwUB bq D. A I B DfqB Ans B 02. GKK †f±i (Unit vector) Gi †¶‡Î †Kvb gvbwU mwVK? [JnU. 13-14] A. ˆ i ˆ i = 1 B. ˆ i ˆ j = 0 C. ˆ i ˆ j = ˆk D. ˆ i ˆ i = –1 Ans C 03. A , B , I C wZbwU †f±i ivwk n‡j Ges C = A B n‡j C Gi w`K n‡e- [JnU. 12-13, 14-15] A. A eivei B. B eivei C. A I B Gi mgZ‡ji j¤^ eivei D. A I B Gi mgZj eivei Ans C 04. GKwU mvgvšÍwi‡Ki †¶Îdj- [JnU. 11-12] A. | | A B B. |A.B| C. AB D. †KvbwUB bq Ans A 05. A I B †f±‡ii j¤^ eivei GKK ‡f±‡ii ivwkgvjv- [JnU. 10-11] A. = | | A B A B B. = A B | | A B C. = A B | | A . B D. = A . B | | A . B Ans B BRUR 01. `ywU †f±i ivwki jwäi m‡e©v”P I me©wb¤œ gvb mgvb nB‡j, †f±i ؇qi ga¨eZ©x †Kvb KZ n‡e? [BRU. 12-13] A. 0 B. 90° C. 80° D. 60° Ans B JKKNIU 01. †¯‥jvi ¸Y‡bi D`vniY †KvbwU? [JKKNIU-B, Set-3, 19-20] A. KvR B. ej C. UK© D. †K․wYK fi‡eM S A info †f±‡ii ¸Y‡bi †ÿ‡Î: KvR, W = F . s ; UK©, = r F ; †K․wYK fi‡eM, L = r P ; •iwLK †eM, v = r PART B Analysis of Science & Technology Question SUST 01. ‣iwLK †eM v, ‡K․wbK †eM Ges Ae¯’vb †f±i r n‡j wb‡Pi †KvbwU mwVK? [SUST. 06-07] A. = r v B. v = r C. v = r D. r = v Ans B BSMRSTU 01. `yBwU †f±i ci¯úi j¤^ n‡j Zv‡`i †f±i ¸Yd‡ji gvbÑ [BSMRSTU-H, 19-20] A. Amxg nq B. k~b¨ nq C. m‡e©v”P nq D. me©wb¤œ nq S C info A B = AB sin90˚ = AB ; ci¯úi mgvšÍivj n‡j A B = 0 PUST 01. †KvbwU mwVK? [PUST-A, 19-20] A. – A – B = – 0 When – A – B B. | – A – B| = AB sin C. – A. – B = 0 When – A || – B D. – A – B = – – B – A S D info – A – B = – 0 When – A || – B ; |– A – B| = AB sin – A. – B = 0 When – A – B ; – A – B = – – B – A

ASPECT PHYSICS cÖ_g cÎ †f±i 69 ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES STEP 06 ANALYSIS OF HSC BOARD QUESTION 01. ( j + k) × k = ? [Xv.‡ev 2021] A. l B. i C. j D. k Ans B 02. wP‡Îi A I B †f±i `ywUiÑ [Xv.†ev. 2019] i. WU ¸Yb wewbgq m~Î †g‡b P‡j ii. µm ¸Yb wewbgq m~Î †g‡b P‡j iii. µm ¸Yb wewbgq m~Î †g‡b P‡j bv wb‡Pi †KvbwU mwVK? A. i I ii B. i I iii C. ii I iii D. i, ii I iii Ans B 03. `ywU †f±‡ii µm ¸bdj m¤ú‡K© ejv hvqÑ [iv.‡ev. 2019] i. µm ¸Ydj GKwU †f±i ivwk ii. µm ¸Yd‡ji w`K †f±iØq †h mgZ‡j Zvi j¤^ eivei iii. µm ¸Ydj wewbgq m~Î †g‡b P‡j A. i I ii B. ii I iii C. i I iii D. i, ii I iii Ans A 04. `ywU m`„k¨ †f±i I hw` GKB mg‡q GKB we›`y‡Z wµqv K‡i Zvn‡jÑ [iv.‡ev. 2019] i. A. B = 0 ii. A × B = 0 iii. | | A + | | B = A + B wb‡Pi †KvbwU mwVKÑ A. i I ii B. i I iii C. ii I iii D. i, ii I iii Ans C 05. |A B | 2 = wb‡Pi †KvbwU? [iv. †ev. 2017] A. A2B 2 – (A . B)2 B. A2B 2 – 2A . B C. A2B 2 – 2 AB sin D. A2B 2 – 2AB cos S A info |A B | 2 = |ABsin| 2 = A2B 2 sin2 |A B | 2 = |ABcos| 2 = A2B 2 cos2 |A B | 2 + |A B | 2 = A2B 2 (sin2 + cos2 ) |A B | 2 = A2B 2 – |A B | 2 06. + . Gi gvb n‡eÑ [P.‡ev. 2019] A. B. C. 0 D. 1 Ans C 07. wP‡Îi †f±i؇qi †¯‥jvi MyYbÑ [P. †ev. 2015] A. A. B = AB cos B. A B= AB sin C. A B= AB sin ^ n D. A. B = sin Ans A 08. AvqZ GKK †f±‡ii †ÿ‡Î †KvbwU mwVK? [w`. †ev. 2015] A. i ˆ .j ˆ = i ˆ .k ˆ = k ˆ . i ˆ = 0 B. i ˆ .i ˆ = j ˆ .j ˆ = k ˆ .k ˆ = 1 C. i ˆ i ˆ = j ˆ j ˆ = k ˆ k ˆ = 0 D. me¸‡jv mwVK Ans D 09. e¨vmva© †f±i I cÖhy³ e‡ji †f±i ¸Yb‡K e‡j- [Kz. †ev. 2017] A. RoZvi åvgK B. UK© C. †K․wYK fi‡eM D. PµMwZi e¨vmva© Ans B 10. wb‡Pi †KvbwU †¯‥jvi ¸Yd‡ji ag©? [wm.‡ev 2021] A. GKB †f±i‡K `yevi wb‡j ¸Ydj k~b¨ nq B. ci¯úi j¤^ `ywU †f±‡ii ¸Ydj k~b¨ nq C. ci¯úi mgvšÍivj `ywU †f±‡ii ¸Ydj k~b¨ nq D. GKB †f±i‡K `yevi wb‡j ga¨eZ©x †KvY k~b¨ nq Ans B 11. j ( j k) = ? [g.‡ev 2021] A. 0 B. i C. k D. – k Ans D S D info j ( j k) = j × i = – k 12. †f±‡ii WU¸Y †g‡b P‡j- [e.‡ev 2021] i. wewbgq m~Î ii. eÈb m~Î iii. ms‡hvM m~Î wb‡Pi †KvbwU mwVK? A. i I ii B. i I iii C. ii I iii D. i, ii I iii Ans D 13. A B = ? [e. †ev. 2015] A. AB cos B. AB sin C. B A D. B A Ans C 14. ej F I miY r DfqB †f±i ivwk n‡j G‡`i †¯‥jvi ¸Yd‡j Kx ivwk Drcbœ n‡e? [e.‡ev 2021] A. ÿgZv B. kw³ C. KvR D. UK© Ans C Concept 4 Acv‡iUi, †MÖwW‡q›U, WvBfvi‡RÝ, Kv‡j©i aviYv Ges ¸iæZ¡c~Y© Z_¨vejx ✅ †f±i †hvR‡bi `„óvšÍ: †b․Kvi MwZ, PjšÍ Mvwo‡Z cošÍ e„wó, cvwLi DÇqb| ✅ †f±i wefvR‡bi `„óvšÍ: ¸Y Uvbv †b․Kv, jb †ivjvi Gi MwZ, mvB‡K‡ji µvs‡Ki wµqv, mij †`vjK, cv‡q nvUv| ✅ ‡f±‡ii †hvR‡bi Rb¨ e„wó‡Z PjšÍ Mvwoi mvg‡bi KuvP wf‡R hvq wcQ‡bi KuvP bq| ✅ `yB ev Z‡ZvwaK †f±i †hvM K‡i GKwU bZzb †f±i cvIqv hvq G‡K jwä e‡j| ✅ `ywU †f±i wecixZ w`‡K wµqv Ki‡j jwäi gvb me©wb¤œ nq| ✅ `ywU †f±i GKB w`‡K wµqv Ki‡j jwäi gvb m‡e©v”P nq| ✅ me©wb¤œ mg‡q b`x cvi n‡Z n‡j b`xi cÖ¯
 eivei †b․Kv Pvjv‡Z nq| ✅ `ywU mggv‡bi †f±‡ii jwäi gvb G‡`i †h †Kvb GKwU †f±‡ii mgvb n‡j AšÍfz©³ †KvY 120˚ n‡e| ✅ w`K †KvmvBb: GKwU †f±i A hw` abvZ¥K X, Y I Z A‡ÿi mv‡_ h_vµ‡g , Ges †KvY Drcbœ K‡i Zvn‡j cos, cos Ges cos †K w`K †KvmvBb ejv nq| †h‡Kv‡bv †f±‡ii w`K †KvmvBb¸‡jvi e‡M©i mgwó me©`v 1 nq| A_©vr, cos2 + cos2 + cos2 = 1 ✅ jwäi gv‡bi †iÄ : Rmin R Rmax ✅ `ywU mggv‡bi ej 180 †Kv‡Y wµqv Ki‡j ej؇qi jwäi ïb¨ n‡e ✅ Rmax = P + Q [ = 0 ev GKB w`‡K]; Rmin = P Q [ = 180 ev wecixZ w`‡K] ✅ 2 i + 2 j †f±iwU xy mgZ‡j Aew¯
Z ; 2 j + 2 k †f±iwU yz mgZ‡j Aew¯
Z ; 2 i + 2 k †f±iwU zx mgZ‡j Aew¯
Z ✅ AvYyf~wgK w`‡K e‡ji Dcvsk Fcos Ges Dj¤^ w`‡K Dcvsk Fsin

70 An Exclusive Parallel Text Book of Physics ASPECT PHYSICS ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES jb †ivjvi jb †ivjvi‡K ‡Vjv A‡c¶v Uvbv mnRZi| jb †ivjvi †Vjvi mgq Uvbv A‡cÿv IRb †ewk nq 2Fsin Fcos jb †ivjvi‡K mvg‡bi w`‡K wb‡q hvq| Fsin Dcvs‡ki Rb¨ jb †ivjvi †Vjvi A‡cÿv Uvbv mnR| †Vjvi †ÿ‡Î AvcvZ IRb = w + F sin Uvbvi †ÿ‡Î AvcvZ IRb = w F sin †b․Kvi ¸YUvbv Fcos †b․Kv‡K mvg‡bi w`‡K wb‡q hvq| ¸Y hZ j¤^v nq ZZ Kg nq Ges †b․Kv `ªæZ mvg‡b GwM‡q hvq| Fsin Dcvs‡ki Rb¨ †b․Kv cv‡oi w`‡K hvq hv •eVv Øviv Dckg Kiv nq| wKQz cÖ‡qvRbxq kZ© `ywU †f±i j¤^ nIqvi kZ© A. B = 0 `ywU †f±i mgvšÍivj nIqvi kZ© A B = 0 wZbwU †f±i ( A, B , C) mgZjxq nIqvi kZ©- A.( B C) = 0 AN~Y©bkxjZvi I msiÿYkxjZvi kZ©, V = 0 [Kvj© k~b¨] mwjb‡q‡Wi kZ©, . V = 0 ✅ †h MvwYwZK wµqv GKwU ivwk‡K Ab¨ ivwk‡Z iƒcvšÍwiZ K‡i Zv‡K Acv‡iUi e‡j| †hgb: , log, , d dx ✅ Acv‡iUi n‡”Q GK ai‡bi MvwYwZK wb‡`©k| ivwk ivwki cÖK…wZ •ewkó¨ I Zvrch© †MÖwW‡q›U †f±i ivwk i. †MÖwW‡q›U n‡jv wewfbœ A‡ÿi mv‡c‡ÿ †Kv‡bv †¯‥jvi dvsk‡bi Xvj| ii. †¯‥jvi ivwki †MÖwW‡q›U Gi gvb IB †¯‥jvi ivwki me©vwaK e„w×i nv‡ii mgvb| WvBfvi‡RÝ †¯‥jvi ivwk i. WvBfvi‡R‡Ýi gva¨‡g GKwU †f±i †ÿ·K †¯‥jvi †ÿ‡Î iƒcvšÍi Kiv hvq| ii. gvb abvZ¥K n‡j, Zij c`v‡_©i AvqZb e„w× cvq, Nb‡Z¡i n«vm N‡U| Avi, gvb FYvZ¥K n‡j AvqZ‡bi ms‡KvPb N‡U, NbZ¡ e„w× cvq| iii. gvb k~b¨ n‡j, AvMZ I wbM©Z d¬v· mgvb nq| A_©vr, . V = 0. ZLb IB †f±i †ÿ·K mwjbqWvj (Solenoidal) e‡j| Kvj© †f±i ivwk i. Gi gvb H †ÿ‡Î GKK †ÿ‡Îi Rb¨ me©vwaK †iLv Bw›UMÖv‡ji mgvb I N~Y©‡bi mv‡_ m¤úwK©Z| ii. Kv‡j©i gva¨‡g cÖvß †f±iwUi gvb N~Y©b A‡ÿi mv‡c‡ÿ †K․wYK †e‡Mi wظY nq| A_©vr | V| =2 iii. †Kv‡bv †f±i †ÿ‡Îi Kvj© Gi bwZgvÎv (gradient) k~b¨| A_©vr ( V) =0 A_©vr †f±‡ii w`K H †ÿ‡Îi Awfj¤^ eivei wµqv K‡i| iv. †Kvb †f±‡ii Kvj© k~b¨ n‡j †f±iwU AN~Y©bkxj Ges msiÿYkxj nq| A_©vr V = 0 n‡j V AN~Y©bkxj nq| ◈ †MÖwW‡q›U, WvBfvi‡RÝ Kvj© g‡b ivLvi mnR †K․kj: WvBfvi‡RÝ Kvj© †MÖwW‡q›U WvBfvi‡RÝ Kvj© bigvj ¸Yb WU ¸Yb µm ¸Yb ◈ †f±i Acv‡iU‡ii Aci bvg b¨vejv ( ) | m¨vi n¨vwgjUb GwU D™¢veb K‡ib| = d dx ^ i + d dy ^ j + d dz ^ k REAL TEST ANALYSIS OF PREVIOUS YEAR QUESTIONS STEP 01 ANALYSIS OF JU QUESTION 01. †f±i wefvR‡bi `„óvšÍ †KvbwU? [JU. 13-14] A. ¸YUvbv †b․Kvi MwZ B. cvwLi DÇqb C. PjšÍ Mvwo‡Z cošÍ e„wó D. Mvwoi MwZ Ans A 02. GKwU Li‡¯ªvZv b`x me‡P‡q Kg mg‡q cvi n‡Z GKwU †b․Kvi †Kvb w`‡K hvIqv DwPZ? [JU. 12-13] A. opposite shore B. somewhat upstream C. somewhat downstream D. None Ans A 03. `ywU †f±i wecixZ w`‡K wµqviZ _vK‡j jwäi gvb n‡e- [JU. 11-12] A. me©vwaK B. k~b¨ C. me©wbgœ D. †KvbwUB bq Ans C STEP 02 ANALYSIS OF RU QUESTION 01. †Kvb †f±i ivwki Kvj© (Curl) k~b¨ n‡j †f±iwU †Kgb n‡e? [RU-C, Set-1. 19-20] A. N~Y©bkxj I AmsiÿYkxj B. N~Y©bkxj I msiÿYkxj C. AN~Y©bkxj I msiÿYkxj D. AN~Y©bkxj I AmsiÿYkxj S C info WvBfvi‡RÝ k~b¨ n‡j †f±iwU mwjbqWvj| STEP 03 ANALYSIS OF GST QUESTION PART A Analysis of General University Question KU 01. d dx ( ) K U = ? [KU. 10-11] A. d K dx d U dx B. d K dx. U d U dx. K C. d K dx U + K d U dx D. d K dx + U + K + d U dx. K S C info AšÍixKi‡bi m~Î: d dx ( ) K U = d k dx U + k d U dx CoU 01. `yBwU †f±i ivwk ci¯úi mgvšÍivj n‡j †KvbwU mwVK? [CoU. 11-12, 13-14] A. A B = 0 B. A. B= 0 C. | | A | | B = 0 D. | | A , | | B = 0 Ans A

ASPECT PHYSICS cÖ_g cÎ †f±i 71 ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES IU 01. •iwLK †e‡Mi Kvj© †K․wYK †e‡Mi KZ ¸Y? [IU-D, 19-20] A. 2 B. 3 C. 4 D. 9 Ans A S A info •iwLK †e‡Mi Kvj© †K․wYK †e‡Mi wظY| 02. Ae¯’v‡bi mv‡c‡¶ †Kv‡bv †¯‥jvi †¶‡Îi m‡e©v”P cwieZ©‡bi nvi H †¶‡Îi- [IU. 15-16] A. wWdv‡iw݇qkb B. ‡Wj C . WvBfvi‡RÝ D. †MÖwW‡q›U Ans D 03. †f±i wefvR‡bi †ÿ‡Î Dcvsk¸‡jvi jwä- [IU. 14-15] A. AskK B. jwä Dcvsk C. g~j †f±i D. jwä †f±i Ans C 04. gvbyl‡K mvg‡b Pj‡Z mvnvh¨ K‡i- [IU. 12-13] A. Dj¤^ Dcvsk B. Avbyf~wgK Dcvsk C. (Dj¤^-Abyf~wg) Dcvsk D. ‡KvbwU bq Ans B 05. `yBwU mggv‡bi ej KZ wWMÖx †Kv‡Y wµqv Ki‡j ej؇qi jwä k~b¨ n‡e- [IU. 12-13] A. 0° B. 90° C. 120° D. 180° Ans D 06. `ywU †f±i ivwk jwäi gvb m‡ev©”P n‡j Zv‡`i ga¨eZ©x †Kvb n‡e [IU. 10-11] A. 900 B. 00 C. 450 D. 1800 Ans B BRUR 01. b~¨bZg KZwU Amg †f±i n‡j Zv‡`i jwäi gvb k~b¨ n‡e? [BRUR. 13-14] A. 2 B. 3 C. 4 D. 4 Gi AwaK Ans B PART B Analysis of Science & Technology Question MBSTU 01. GKwU †f±i †ÿ‡Î A AN~Y©bkxj n‡e hw`? [MBSTU-C, Set-2 19-20] (i) ▽. A = 0 (ii) ▽ A = 0 (iii) ▽ A 0 wb‡Pi †KvbwU mwVK? A. i B. ii C. iii D. i I ii S B info †f±i †ÿÎ A AN~Y©bkxj Ges msiÿYkxj n‡e hw` ▽ A = 0; †f±i †ÿÎ A mwjbqWvj n‡e hw` ▽. A = 0 02. P Ges Q GB `ywU †f±i mgvšÍivj nIqvi kZ© †KvbwU? [MBSTU. 14-15] A. P. Q = 0 B. P Q = 0 C. P. Q = 1 D. P Q = 1 Ans B PUST 01. GKwU †b․Kv jwM w`‡q MwZkxj Ki‡Z n‡j wb‡Pi †Kvb ivwk †b․Kv‡K mvg‡bi w`‡K GwM‡q wb‡q hv‡e? [PUST-A, 19-20] A. jwM KZ…©K cÖhy³ e‡ji Dj¤^ Dcvsk B. cÖwZwµqv e‡ji Dj¤^ Dcvsk C. jwM KZ…©K cÖhy³ e‡ji Avbyf~wgK Dcvsk D. cÖwZwµqv e‡ji Avbyf~wgK Dcvsk S D info cÖwZwµqv e‡ji Avbyf~wgK Dcvs‡ki Rb¨ cvwL Dovi mgq mvg‡bi w`‡K GwM‡q hvq Ges muvZvi KvUvi mgq gvbyl mvg‡bi w`‡K GwM‡q hvq| HSTU 01. `ywU †f±i KZ †Kv‡Y wµqvkxj n‡j me©wbgœ jwä cvIqv hv‡e? [HSTU. 14-15] A. 0° B. 90° C. 180° D. 270° Ans C STEP 04 ANALYSIS OF MEDICAL & DENTAL QUESTION MAT 01. Scalar quantity Ges magnitude of gradient Gi g‡a¨ m¤úK©wU njÑ [MAT. 2020-21] A. Disproportional B. Proportional C. Equal D. Opposite S C info GKwU †¯‥jvi ivwki †MÖwW‡q›U GKwU †f±i ivwk| †f±i ivwki magnitude †¯‥jvi ivwki cwieZ©‡bi m‡e©v”P nv‡ii mgvb| STEP 05 ANALYSIS OF HSC BOARD QUESTION 01. mwjbqWvj n‡jv- [P. †ev. 2017; Kz. †ev. I h. †ev. 2015] A. V = 0 B. . V = 0 C. = 0 D. = 0 Ans B 02. †KvbwU †¯‥jvi ivwk? [w`. †ev. 2016] A. MÖ¨vwW‡q›U B. WvBfvi‡RÝ C. Kvj© D. miY Ans B 03. GKwU †f±i †ÿÎ B AN~Y©bkxj n‡e hLb- [h. †ev. 2019] A. B = 0 B. B 0 C. . B 0 D. A I B Ans A 04. †Kv‡bv †f±i †ÿ‡Îi WvBfvi‡RÝ k~b¨ n‡j D³ †f±i †ÿÎwU n‡e- [h. †ev. 2016] A. mwjbqWvj B. AN~Y©bkxj C. †Wj Acv‡iUi D. N~Y©bkxj Ans A 05. V= 0 n‡jÑ V [Kz. †ev. 2016] i. ‡Kv‡bv c`v‡_© AvMZ I wbM©Z d¬v· mgvb nq ii. Zij Ams‡KvPbxq nq iii. ‡f±i †ÿÎwU mwjbqWvj wb‡Pi †KvbwU mwVK? A. i I ii B. i I iii C. ii I iii D. i, ii I iii Ans D 06. ‡Kv‡bv †f±‡ii WvBfvi‡Rj n‡jvÑ [e.‡ev. 2019] A. ‡f±i ‡ÿÎ B. ‡¯‥jvi ‡ÿÎ C. H †f±‡ii bwZgvÎv D. AN~Y©kxj Ans B 07. †¯‥jvi dvskb‡K †f±i ivwk‡Z iƒcvšÍi K‡i- [e. †ev. 2016] A. µm ¸Yb B. WU ¸Yb C. †MÖwW‡q›U D. WvBfvi‡RÝ Ans C STEP 2 mg„× †ewmK MvwYwZK cÖ Ö‡qvM (MATH) kU©KvU †UKwbK Concept 1 GKK †f±i msµvšÍ MvwYwZK cÖ‡qvM FORMULA GKK †f±i: 01. †Kvb †f±‡ii w`‡K GKK †f±i = ‡f±i gvb 04. †Kvb †f±‡ii mgvšÍivj w`‡K GKK †f±i = ‡f±i gvb 02. A I B Gi jw×i mgvšÍivj w`‡K GKK †f±i = A + B | | A + B 05. A I B Gi mgZ‡ji Dci j¤^ GKK †f±i = A B | | A B 03. A= x i + y j + z k n‡j | A| = x 2 + y2 + z2

72 An Exclusive Parallel Text Book of Physics ASPECT PHYSICS ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES CONCEPTUAL MATH MEx 01 R = 4ˆ i – 6 ˆ j + 12ˆk n‡j Gi mgvšÍivj GKK †f±i †KvbwU? R = 4ˆ i – 6 ˆ j + 12ˆk |R| = (4) 2 + (– 6) 2 + (12) 2 = 196 = 14 mgvšÍivj w`‡K GKK †f±i = 4 14 ˆ i – 6 14 ˆ j + 12 14 ˆk = 2 7 ˆ i – 3 7 ˆ j + 6 7 ˆk NOW START PRACTICE 01. A i k ˆ ˆ Ges B i j ˆ ˆ †f±i؇qi Awfj¤^ w`‡K GKK †f±i n‡e| 02. P I Q we›`yi Ae¯’vb †f±i h_vµ‡g P i j k Ges Q 2 i 3 j 2 k.PQ †f±i wbb©q Ki| NOW PRACTICE SOLVE : 01. A = ˆ i – ˆk Ges B = ˆ i + ˆ j A B = ˆ i 1 1 ˆ j 0 1 ˆk –1 0 ˆ i – ˆ j + ˆk, hvi gvb = (1) 2 + (–1) 2 +(1) 2 = 3. Zv‡`i j¤^ w`‡K GKK †f±i = ˆi 3 – ˆj 3 + kˆ 3 02. P = i + j + k Ges Q = 2 i + 3 j – 2 kn‡j PQ ‡f±i Gi gvb n‡e, PQ = Q – P = ) ˆ ˆ ˆ ( ˆ 2i ˆ 3 ˆ j 2k i j k = i j k ˆ ˆ 2 ˆ 3 REAL TEST ANALYSIS OF PREVIOUS YEAR QUESTIONS STEP 01 ANALYSIS OF JU QUESTION 01. A = 3 i + 2 j – 6 k †f±i ivwkwUi gvb KZ? [JU-A, Set-E. 20-21] A. 7 B. 18 C. 12 D. 6 S A info | A| = 3 2 + 22 + (–6) 2 = 49 = 7 02. 3i – 4j + 12k †f±iwUi gvb KZ? [JU. 18-19] A. 8 B. 11 C. 13 D. 18 S C info 9 + 16 + 144 = 169 = 13 STEP 02 ANALYSIS OF RU QUESTION 01. xy Z‡ji mgvšÍivj Ges 2i – 2j + 6k Gi mv‡_ mg‡Kv‡Y Aew¯’Z GKK †f±i †KvbwU? [RU. 18-19] A. i + j 2 B. k 2 C. i + j 44 D. i + j 2 2 S A info awi, †f±iwU (ai + bj ), hv xy mgZ‡ji mgvšÍivj| Avevi, (ai + bj ) . (2i – 2j + 6k ) = 0 GLb, 2a – 2b = 0 a = b a(i + j ) 2a = i + j 2 STEP 03 ANALYSIS OF CU QUESTION 01. †f±i A = 2 i – j + 2 k Gi mgvšÍivj GKK †f±i †KvbwU? [CU-A, Set-4. 20-21] A. 2 9 i – 1 9 j – 2 9 k B. 2 3 i – 1 3 j + 2 3 k C. 2 5 i – 1 5 j + 2 5 k D. i – j + k S B info A Gi mgvšÍivj GKK †f±i a = A |A| = 2 i – j + 2 k (2 2 ) + (–1) 2 + 22 = 2 3 i – 1 3 j + 2 3 k STEP 04 ANALYSIS OF DU-7 Clg QUESTION 01. †Kv‡bv GKwU KYv A(3,5,7) we›`y †_‡K B(5,6,7) ¯’vbvšÍwiZ n‡j KYvwUi miY †f±i KZ? [DU. 7Clg-A: 20-21] A. i+ j+7 k B. 2 i+ 2 j+ k C. 2 i+ j D. 8 i + 11 j+14 k S C info S = OB – OA = (5 – 3) i + (6 – 5) j + (7 – 4) k = 2 i + j STEP 05 ANALYSIS OF GST QUESTION PART A Analysis of General University Question JnU 01. †f±i A = 2ˆ i + 4ˆ j – 5 ˆk Ges B = ˆ i + 2ˆ j + 3ˆk †`Iqv Av‡Q| Zvn‡j | A + B| †ei Ki- [JnU. 08-09] A. 3 B. 6 C. 7 D. 9 S C info A = 2ˆ i + 4ˆ j – 5 ˆk Ges B = ˆ i + 2ˆ j + 3ˆk A + B = 3ˆ i + 6ˆ j – 2 ˆk | A + B| = (3) 2 +(6) 2 + (–2) 2 = 9 + 36 + 4 = 49 = 7 KU 01. R = 4ˆ i – 6 ˆ j + 12ˆk n‡j Gi mgvšÍivj GKK †f±i †KvbwU? [KU. 10-11] A. 2 7 ˆ i – 3 7 ˆ j + 6 7 ˆk B. 2 ˆ i – 3 ˆ j + 6ˆk C. ˆ i – ˆ j + 2ˆk D. 8 ˆ i – 12ˆ j + 24ˆk S A info R = 4ˆ i – 6 ˆ j + 12ˆk |R| = (4) 2 + (– 6) 2 + (12) 2 = 196 = 14 mgvšÍivj w`‡K GKK †f±i = 4 14 ˆ i – 6 14 ˆ j + 12 14 ˆk = 2 7 ˆ i – 3 7 ˆ j + 6 7 ˆk 02. F1 = 2ˆ i + 4ˆ j – 5 ˆk Ges F2 = ˆ i + 2ˆ j + 3ˆk. F1 I F2 Gi jwä †f±‡ii mgvšÍivj †f±iwU wbY©q Ki| [KU. 04-05] A. 7 B. 10 C. 8 D. 6 S A info jwä F = F1 + F2 = 2ˆ i + 4ˆ j – 5 ˆk + ˆ i + 2ˆ j + 3ˆk = 3 ˆ i + 6ˆ j – 2 ˆk Gi jwä †f±‡ii mgvšÍivj †f±i | F| = 3 2 + 62 + (– 2) 2 = 49 = 7

ASPECT PHYSICS cÖ_g cÎ †f±i 73 ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES BU 01. 1 2 ˆ i + 1 2 ˆ j + bˆk GKK ‡f±‡i b Gi gvb KZ? [BU. 15-16] A. 1 2 B. 1 C. 1 2 D. 1 4 S C info 1 2 ˆ i + 1 2 ˆ j + bˆk Gi gvb = 1 1 2 2 + 1 2 2 + (b 2 ) = 1 ev, 1 4 + 1 4 + b2 = 1ev, b 2 = 1 – 1 2 ev, b 2 = 1 2 ev, b = 1 2 PART B Analysis of Science & Technology Question BSMRSTU 01. †f±i coscosi + cossinj + sink GKwUÑ [BSMRSTU-B, 19-20] A. k~b¨ †f±i B. GKK †f±i C. aªæe †f±i D. †KvbwUB bq S B info †f±iwUi gvb = (cos cos) 2 + (cos sin) 2 + sin2 = cos2 (cos2 + sin2 ) + sin2 = cos2 + sin2 = 1 GwU GKK †f±i| DU Technology 01. A = 2 i +4 j – 5 k Ges B = i+ 2 j + 3 k | A I B Gi jw× †f±‡ii mgvšÍivj GKK †f±iwU n‡jv- [DU-Tech. 2020-21] A. 3 7 i + 6 7 j + 2 7 k B. 3 7 i + 6 7 j – 2 7 k C. – 3 7 i + 6 7 j + 2 7 k D. 3 7 i – 6 7 j + 2 7 k S B info jw× †f±i R = A + B = (2 i + 4 j – 5 k) + ( i + 2 j + 3 k) = 3 i + 6 j – 2 k jw× †f±‡ii mgvšÍivj GKK †f±i, r = R | R| = 3 i + 6 j – 2 k 3 2 + 62 + (–2) 2 = 3 7 i + 6 7 j + 2 7 k STEP 06 ANALYSIS OF HSC BOARD QUESTION wb‡Pi DÏxcKwU co Ges cÖ‡kœi DËi `vI: P = 2 i + j + k Ges Q = i + 2 j – 2 k 01. P I Q Gi jwäi mgvšÍivj GKK †f±i †KvbwU? [Xv.‡ev 2021] A. 1 2 i + 1 2 j – 1 2 k B. 3 19 i + 3 19 j – 1 19 k C. 1 3 i + 1 3 j – 1 9 k D. 3 19 i + 3 19 j – 1 19 k S B info P + Q = 3 i + 3 j k jwäi mgvšÍivj GKK †f±i = 3 19 i + 3 19 j – 1 19 k 02. XZ mgZ‡j 3i + 5j + 4k †f±‡ii •`N©¨ KZ GKK? [Xv. †ev. 2017] A. 5 B. 34 C. 41 D. 12 S A info 3i + 5j + 4k Gi XZ Z‡j Dcvsk: 3i + 4k | •`N©¨ = |3i + 4k | = 3 2 + 42 = 5 03. ^ i Ges ^ j †h Z‡j Aew¯’Z †mB Z‡ji Dci j¤^ GKK †f±i n‡jvÑ [Xv. †ev. 2015] A. ( ^ j ^ k) B. ( ^ i ^ j) C. ( ^ k ^ i) D. ( ^ i ^ k) Ans B 04. P I Q Gi ¯’vbv¼ (3, 2, 1) Ges (3, 4, 5) PQ Gi gvb KZ? [iv. †ev. 2017] A. 29 B. 20 C. 56 D. 6 29 S B info PQ¯¯ = OQ¯¯ – OP¯¯ OQ¯¯ = 3i ˆ – 4j ˆ + 5k ˆ OP¯¯ = 3i ˆ – 2j ˆ + k ˆ = (3 – 3) i ˆ + (–4 + 2) j ˆ + (5 – 1) k ˆ = –2j ˆ + 4k ˆ |PQ| = (–2) 2 + (4) 2 = 20 05. wb‡Pi †KvbwU GKK †f±i wb‡`©k K‡i? [iv. †ev. 2015] A. ^ a = A A B. ^ a = A A C. ^ a = A A D. a = A A Ans C 06. ‡Kv‡bv †f±i Ges Gi GKK †f±‡ii ga¨eZx© †Kv‡Yi gvb KZ?[P.‡ev. 2019] A. 180 B. 90 C. 45 D. 0 Ans D 07. A I B Gi GKK †f±i a -Gi ga¨eZx© †KvY- [P. †ev. 2019, 2015] A. 0 B. 45 C. 90 D. 180 Ans A Concept 2 jwä msµvšÍ MvwYwZK cÖ‡qvM FORMULA 01. R = P 2 + Q2 + 2PQcos ; Rmax = P + Q [ = 0 ev GKB w`‡K]; Rmin = P Q [ = 180 ev wecixZ w`‡K]; R = P 2 + Q2 [ = 90] jwäi w`K tan = Qsin P + Qcos ; R hvi mv‡_ †KvY Ki‡e †mwU p Gi ¯
v‡b em‡e P Q R Q P 02. = 90 n‡j 2 2 R P Q Ges =tan-1 P Q 05. P 2Q Ges jwä eivei wµqv Ki‡j = 120 03. P Q n‡j R P 2 Ges = 90 06. = 90 n‡j, Rmax 2 + Rmin 2 = 2R2 04. P Q R n‡j = 120 Ges 2 07. jwäi †iÄ Rmin R Rmax ASPECT SPECIAL: P = Q n‡j n‡j jwä, R = 2p cos 2 Ges ga¨eZ©x †KvY, = 2

74 An Exclusive Parallel Text Book of Physics ASPECT PHYSICS ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES Model Example01 `ywU †f±i ivwki cÖ‡Z¨KwUi gvb 7 GKK| Giv ci¯úi 120 †Kv‡Y GKB mv‡_ †Kv‡bv we›`y‡Z wµqvkxj| G‡`i jwäi gvb KZ n‡e? General Rules [Written] 3 in 1 Shortcut Tricks & Tips [MCQ] R 2 = P2 + Q2 + 2PQ cos R 2 = P2 + P2 + 2P.P . cos [∵ P = Q] R 2 = 2P2 + 2P2 cos = 2P2 (1 + cos) = 2P2 1 + cos2. 2 = 2P2 . 2cos2 2 R 2 = 4P2 cos2 2 R = 2P cos 2 = 2 7 cos 120 2 R = 7 GKK| R = 2P cos 2 = 2 7 cos60 R = 7 GKK A_©vr, hw` `ywU †f±‡ii gvb mgvb nq Ges ga¨eZ©x †KvY 120 nq Zvn‡j jwä †f±‡ii mgvb nq| [P = Q = R n‡j, = 120] Model Example02 `ywU w`K ivwki cÖ‡Z¨KwUi gvb 10 GKK Ges ga¨eZ©x †KvY 900 n‡j, jwä KZ? General Rules [Written] 3 in 1 Shortcut Tricks & Tips [MCQ] R = P 2 + Q2 + 2PQ cos 102 + 102 + 2×10×10 Cos900 = 100 + 100 14.14 GKK R = P 2 = 10 2 = 14.14 GKK hLb, P = Q Ges = 900 Model Example03 `ywU w`K ivwki e„nËg jwä 14 GKK Ges ÿz`ªZg jwä 2 GKK | ejØq ci¯úi j¤^fv‡e wµqv Ki‡j jwä KZ? General Rules [Written] 3 in 1 Shortcut Tricks & Tips [MCQ] P + Q = 14 P + Q = 14 P – Q = 2 P – Q = 2 2P = 16 2Q = 12 P = 8 Q = 6 Avgiv Rvwb, R = P 2 + Q2 + 2PQ Cos 8 2 + 62 + 2×8×6 Cos900 100 10 GKK R 2 max + R2 min = 2R2 per [ = 900 n‡j] 142 + 22 = 2R2 per Rper = 10 GKK NOW START PRACTICE 01. 5N I 10N gv‡bi `ywU ej GKwU KYvi Dci Av‡ivwcZ n‡j †Kvb ejwU KYvwUi Dci jwä ej n‡Z cv‡i bv? 02. `ywU w`K ivwki e„nËg jwä 14 GKK Ges ÿz`ªZg jwä 2 GKK| ejØq ci¯úi j¤^fv‡e wµqv Ki‡j jwä KZ? 03. GKwU e¯‘‡K 50 N ej Øviv c~e©w`‡K Ges 20 N ej Øviv cwðg w`‡Ki mv‡_ 600 †Kvb K‡i `wÿY w`‡K Uvbv nj| jwä e‡ji gvb I w`K KZ? 04. `ywU e‡ji jwäi m‡e©v”P gvb 17. ejØq j¤^fv‡e wµqv Ki‡j jwäi gvb 13. jwäi me©wb¤œ gvb KZ? 05. `ywU mgvb e‡ji jwäi gvb ej ؇qi ¸Yd‡ji eM©g~‡ji mgvb| ej؇qi ga¨eZ©x †KvY KZ? 06. 2i – j + k Ges 2i + j – k †f±i `yBwUi jwä gvb I w`K KZ? NOW PRACTICE SOLVE : 01. Rmin R Rmax: Rmax = (5 + 10N = 15N, Rmin = 10~5 = 5N myZivs jwä, 15N n‡Z cv‡i Ges 5N n‡Z cv‡i Ges 15N I 5N Gi ga¨eZ©x †h †Kvb ej n‡Z cv‡i| Z‡e 5N Gi Kg ev 15N Gi †ewk n‡Z cvi‡e bv| 02. R 2 max + R2 min = 2R2 per [ = 900 n‡j] 142 + 22 = 2R2 per Rper = 10 GKK 03. jwä, R 2 = (50 2 + (20 2 + 2.50.20. cos 1200 ev, R = 43.58N Ges tan = 20sin120 50 + 20cos120 = 23.40 Ans. 04. Rmax 17 , Rp 13, ? Rmin R 2 max + R2 min = 2R2 p ev, R 2 min = 2R2 p – R 2 max = 2(13)2 – (17)2 = 49 Rmin = 7 05. P = Q n‡j R = P.P = P P = Q = R = 120 06. jwä = 4i jwä gvb = 4 2 = 4 Ges w`K X Aÿ eivei KviY i GKK †f±i| REAL TEST ANALYSIS OF PREVIOUS YEAR QUESTIONS STEP 01 ANALYSIS OF DU QUESTION 01. wZbwU †f±i, a, b I c, hv‡`i gvb h_vµ‡g 4, 3 Ges 5, †hvM Ki‡j k~b¨ nq A_©vr a + b + c = 0| Zvn‡j | c ( a b) Gi gvb n‡jv- [DU. 18-19] A. 12 B. 60 C. 25 D. 15 S B info | c( a b)|= c(absin90 | = | abc sin90 | = abc 345=60 D‡jøL¨, 3, 4, 5 wc_v‡Mvwiqvb Îqx| 02. `ywU mggv‡bi †f±i GKwU we›`y‡Z wµqvkxj| G‡`i jwäi gvb †h‡Kv‡bv GKwU †f±‡ii gv‡bi mgvb| †f±i `ywUi ga¨eZx© †Kv‡Yi gvb KZ? [DU. 18-19, 99-00; CU. 12–13; JU. 10–11; RU. 10-11, 15-16; BU. 15-16; MBSTU. 14-15] A. 0 B. 90 C. 120 D. 180 S C info P = p 2 + p2 + 2.p.p cos cos = –1 2 = 120

ASPECT PHYSICS cÖ_g cÎ †f±i 75 ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES 03. †f±i A , B I C Gi gvb h_vµ‡g 12, 5 I 13 Ges | I †f±i؇qi ga¨eZx© †Kv‡Yi gvb KZ? [DU. 17-18 ; BUET. 06-07] A. 2 B. 3 C. 4 D. 6 S A info AšÍf‚©³ †KvY, = 2 ev, 90˚ n‡j, R = P 2 + Q 2 122 + 52 = 13, A I B †f±i؇qi ga¨eZx© †Kv‡Yi gvb 2 A C B 04. 5N Ges 10N gv‡bi `ywU ej GKwU KYvi Dci Av‡ivwcZ n‡j, wb‡¤œi †Kvb ejwU KYvwUi Dci jwä ej n‡Z cv‡i bv? [DU. 17-18, 06-07] A. 5N B. 10N C. 15N D. 20N S D info ej؇qi m‡e©v”P gvb, Rmax= P + Q = 15 N; 20N ejwU KYvwUi Dci jwä ej n‡Z cv‡i bv| Rmin = PQ = 5N 05. `yBwU e‡ji jwä 40 N. ej `ywUi g‡a¨ †QvU ejwUi gvb 30 N Ges GwUi jwä †QvU e‡ji j¤^ eivie wµqv K‡i| eo ejwUi gvb KZ? [DU. 10-11; CU. 15-16] A. 40N B. 45N C. 50N D.60N O A C B Q R P S C info 1g ej P= ?; 2q ej Q=30N; jwä, R = 40N 2q ej jwäi mv‡_ mg‡Kv‡Y AvbZ| e„nËgej, P = (40) 2 + (30) 2 ev, P=50N 06. P = ˆ i + 2ˆ j – 2 ˆk Ges Q =3ˆ i + 2ˆ j +2 3 ˆk †f±i `yBwU GKwU we›`y‡Z ci¯úi j¤^fv‡e wµqvkxj| G‡`i jwä †f±‡ii w`K ( PGi mv‡c‡¶ ) KZ ? [DU. 08-09] A. 20 B. 59 C. 70 D. 90 S B info |P| = 1 2 + 2 2 + (–2) 2 = 3 Ges |Q| = 3 2 + 22 + (2 3) 2 = 5 P Gi w`‡K w`K, tan = Q P = 5 3 ev, = 59 STEP 02 ANALYSIS OF JU QUESTION 01. GKwU e¯‘‡K 50N ej Øviv cwðg w`‡K Ges 20N ej Øviv DËi w`‡K Uvbv n‡”Q| jwä e‡ji gvb KZ n‡e? [JU. 18-19] A. 53.85N B. 63.85N C. 43.85N D. 50.85N S A info F = 502 + 202 = 53.85N 02. 20 N Ges 60 N gv‡bi `ywU †f±i ivwki ga¨Kvi †KvY 30| ivwk `ywUi jwäi gvb KZ n‡e? [JU. 2015-16; RU. 2013-14] A. 67.96 N B. 77.96 N C. 87.96 N D. 57.96 N S B info R = 202 + 602 + 2 20 60 cos30 = 77.96 03. `ywU w`K ivwki cÖ‡Z¨KwUi gvb 10 GKK| G‡`i jwäi gvb 102 GKK n‡j Zv‡`i ga¨eZ©x ‡KvY KZ? [JU. 13-14] A. 0 B. 60 C. 90 D. 120 S C info cÖ‡Z¨KwU ivwki gvb = P; ga¨eZx© †KvY = 90 Zvn‡j jwä R = P 2 STEP 03 ANALYSIS OF RU QUESTION 01. 8 GKK I 4 GKK gv‡bi `yBwU mw`K ivwki ga¨eZ©x †KvY 120| ivwk `yBwUi jwä gvb KZ GKK? [RU. 15-16] A. 43 B. 33 C. 53 D. 35 S A info jwäi gvb, R = P 2 + Q2 + 2PQ cos = 8 2 + 42 2.8.4 cos120 = 4 3 02. 7 I 5 gv‡bi `yÔwU mw`K ivwki we‡qvM d‡ji gvb 2 n‡j Zv‡`i AšÍf©y³ †Kv‡Yi gvb KZ ? [RU. 14 -15] A. /2 B. /4 C. D. 2 S C info R = P Q e‡j = 180° = 03. O we›`y‡Z †f±i P I †f±i Q wµqvkxj| G‡`i jwä †f±i R| †f±i P I †f±i Q Gi ga¨eZx© †KvY | †f±i R I †f±i P ga¨eZx© †KvY | = 1800 n‡j, = 1800 n‡e hLb- [RU. 11-12] A. P > Q B. Q > P C. Q = P D. ‡KvbwUB bq S B info jwä, R = Q P Q > P Q P R STEP 04 ANALYSIS OF CU QUESTION 01. `yÕwU mggv‡bi †f±i GKwU we›`y‡Z wµqvkxj| Zviv ci¯úi 240 †Kv‡Y wµqv K‡i| Dnv‡`i jwäi w`K- [CU. 11-12] A. 180 B. 90 C. 120 D. 240 E. 360 S C info = 2 = 240 2 = 120 [P = Q n‡j = 2 ] 02. `ywU †f±i ivwki cÖ‡Z¨KwUi gvb 7 GKK| Giv ci¯úi 1200 †Kv‡Y GKB mv‡_ †Kvb we›`y‡Z wµqvkxj| G‡`i jwäi gvb n‡e? [CU. 07-08, RU. 14-15] A. 8 GKK B. 7 GKK C. 9 GKK D. 10 GKK E. 6 GKK S B info hw` P = Q n‡j Ges = 120 nq| Zvn‡j R = P/Q myZivs R = 7 GKK STEP 05 ANALYSIS OF GST QUESTION PART A Analysis of General University Question BRUR 01. GKB we›`y‡Z wµqviZ `ywU †f±‡ii gvb mgvb| G‡`i ga¨eZ©x †Kvb Ges G‡`i jwä †h †Kvb GKwU †f±‡ii mv‡_ †Kvb Drcbœ Ki‡j, I Gi m¤ú©K n‡e- [BRUR. 12-13] A. 2 B. = 3 2 C. = 2 D. = Ans C PART B Analysis of Science & Technology Question JUST 01. 2A I A †f±iØq ci¯ú‡ii m‡½ GKwU wbw`©ó †Kv‡Y AvbZ| cÖ_g †f±i‡K wظY Ki‡j jwäi gvb wZb¸Y e„w× nq| †f±i؇qi AšÍeZx© †KvY KZ? [JUST-A, Set-Ka 19-20] A. 180˚ B. 90˚ C. 45˚ D. 0˚ S A info R 2 = 4A2 + A2 + 2.2A. A cos R 2 = 5A2 + 4A2 cos .......... (i) Avevi, 9R2 = 16A2 + A2 + 2.4A. A cos 9R2 = 17A2 + 8A2 cos GLb, (i × 9 – ii) K‡i cvB, 28A2 + 28A2 cos = 0 cos = –1 = 180°. A B

76 An Exclusive Parallel Text Book of Physics ASPECT PHYSICS ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES 02. N›Uvq 40 km †e‡M c~e©w`‡K Pjgvb GKwU Mvoxi PvjK N›Uvq 40 3km †e‡M GKwU UªvK‡K DËi w`‡K Pj‡Z †`Lj| UªvKwU †Kvb w`‡K Pj‡Q?[JUST. 14-15] A. 20 B. 30 C. 40 D. 50 E. 60 S B info tan = 40 40 3 = 1 3 = 30 STEP 06 ANALYSIS OF ENGINEERING & BUTex QUESTION BUET 01. A = 2 ˆ i + 2 ˆ j + ˆ k Ges B = 6 ˆ i – 3 ˆ j + 2 ˆ k n‡j B eivei A Gi Awf‡¶c n‡e? [BUET. 09-10] A. 8 7 B. 8 3 C. 3 8 D. 7 8 S A info B = 6 ˆ i – 3 ˆ j + 2 ˆ k B eivei A †f±‡ii Awf‡¶c = A. B |B| = 12 – 6 + 2 (6) 2 + (–3) 2 + (2) 2 = 8 7 KUET 01. `ywU †f±i ivwki cÖ‡Z¨KwUi gvb 5 GKK| Zviv GKB we›`y‡Z ci®úi 120° †Kvb wµqv K‡i| Zv‡`i jwäi gvb KZ? [KUET. 12-13; RUET. 09-10] A. 5 unit B. 0 unit C. 25 unit D. 15 unit E. None S A info P = Q = R n‡j, = 120 myZivs jwä, R = 5 unit STEP 07 ANALYSIS OF HSC BOARD QUESTION wb‡Pi DÏxcKwU co Ges cÖ‡kœi DËi `vI: P = 2 i + j + k Ges Q = i + 2 j – 2 k 01. †f±i؇qi jw× gvb KZ? [Xv. †ev 2021] A. 19 B. 6 C. 9 D. 19 S A info R = P + Q = 3 i + 3 j k myZivs jwäi gvb |R| = 3 2 + 32 + ( 1) 2 = 19 02. P I Q Gi jw× me©wb¤œ gvb †KvbwU? [Xv.‡ev 2021] A. | P| +| Q| B. P × Q C. P. Q D. | P| –| Q| Ans D 03. A I B Gi wecixZ †f±‡ii jwäi gvb- [iv. †ev. 2016] A. 0 B. 1 C. A D. 2A Ans A 04. wb‡Pi wP‡Îi Av‡jv‡K |A | + B = ? [P. †ev. 2017] A. 15.81 N B. 14 N C. 13.23 N D.11.23N S C info cÖkœ A¯ I B¯ †f±‡ii w`K †`qv bv _vKvq A¯ †K X A‡ÿi 60˚ †Kv‡Y Ges B¯ †K X A‡ÿi wecixZ a‡i Avgiv cvB, (A¯ + B¯) = A 2 + B2 + 2ABcos = (15) 2 + (10) 2 + 2×10×15cos(150 – 60˚) = 13.23 N 05. GKwU UªvK VT †e‡M C c~e© w`‡K Ges GKwU Kvi VC †e‡M cwðg w`‡K MwZkxj n‡j Uªv‡Ki mv‡c‡ÿ Kv‡ii Av‡cwÿK †eM KZ? [h.‡ev. 2019] A. (VT + VC) B. (VT – VC) C. (VC – VT) D. ( ) Ans A 06. `yBwU †f±‡ii gvb mgvb| wb‡Pi †Kvb Ae¯’v‡b G‡`i jw× GKwU †f±‡ii gv‡b 3 ¸Y n‡e? [wm.‡ev 2021] A. 0 B. 45 C. 60 D. 90 S C info P = Q n‡j, R = 2pcos 2 3P = 2P cos 2 cos 2 = 3 2 2 = 30 = 60 07. = − − n‡j, Gi gvb KZ? [wm.‡ev. 2019] A. 3 B. 3 C. 1 D. -1 S B info | P| = 1 2 + (–1) 2 + (–1) 2 = 3 08. wb‡¤œv³ wP‡Î `ywU †f±i A I B Gi cÖ‡Z¨‡Ki gvb 5 GKK| Zv‡`i g‡a¨Kvi †KvY 60| A − B wbY©q Ki| [wm. †ev. 2017] A. 0 B. 5 GKK C. 7.07 GKK D. 8.66 GKK S B info | A – B| = 5 2 + 52 + 2.5.5 cos120˚ = 25 = 5 09. mggv‡bi `ywU e‡ji jwäi gvb Zv‡`i †h †Kv‡bv GKwUi A‡a©K n‡j ej `ywUi ga¨eZx© †KvY KZ? [e. †ev. 2017] A. 28.90 B. 41.40 C. 138.6 D. 151.04 S D info †h‡Kvb GKwU mge‡ji w`‡K ej¸‡jv Dcvsk mgxK…Z K‡i cvB, P 2 cos 2 = P + P cos [mgvb e‡ji jwä AšÍfz©³ †KvY‡K mgwØLwÛZ K‡i] 1 2 cos 2 = 1 + cos = 2cos2 2 = 2cos–1 1 4 = 151.04˚ 10. F = 5i + 2j 3k GB ej †f±iwUi XZ Z‡j gvb KZ GKK? [mKj †evW©. 2014] A. 13 B. 29 C. 34 D. 38 S C info XZ Z‡j gvb = 5 2 + (–3) 2 = 34 Concept 3 †bŠKv msµvšÍ MvwYwZK cÖ‡qvM 01. †mvRv cvivcvi: jwä, R = v 2 – u 2 02. = cos–1 –u v 04. t = d R = d v 2 – u 2 03. t = d R = d vsin 05.AvovAvwo cvivcvi: R = u 2 + v2 + 2uv cos †¯ªv‡Zi AbyK~j, u + v †¯ªv‡Zi cÖwZK~j, v – u R = jwä; d = b`xi cÖ¯
; t = b`x ci nIqvi mgq u = †¯ªv‡Zi †eM; v = †b․Kvi †eM FORMULA

ASPECT PHYSICS cÖ_g cÎ †f±i 77 ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES Model Example01 †¯ªvZ bv _vK‡j †h mvZviæ 4 km/h †e‡M mvZvi KvU‡Z cv‡ib, 2km/h †e‡M mij‡iLv eivei cÖevwnZ b`xi Icv‡i wVK wecixZ we›`y‡Z †cu․Qv‡Z mvZviæ‡K KZ †Kv‡Y mvZvi KvU‡Z n‡e? General Rules [Written] 3 in 1 Shortcut Tricks & Tips [MCQ] GLv‡b, = 900 †¯ªv‡Zi †eM, P = 2 km/h ; mvZviæi †eM, Q = 4 km/h ‡¯ªvZ I mvZviæi ga¨eZ©x †KvY, = ? Avgiv Rvwb, tan = Q sin P + Q cos tan 900 = 4 sin 2 + 4 cos 1 0 = 4 sin 2 + 4 cos 2 + 4 cos = 0 4 cos = – 2 cos = – 1 2 = cos–1 (– 1 2 ) = 1200 ASPECT SPECIAL: mvZviæi †eM ev †b․Kvi †eM †¯ªv‡Zi †e‡Mi wظY n‡j Ges b`xi Icv‡i wecixZ we›`y ej‡j, | Ges P = Q nq, R = 2P cos 2 CONCEPTUAL MATH MEx 01 †Kv‡bv GKwU b`x‡Z GKwU †b․Kv †mªv‡Zi AbyK‚‡j NÈvq 24 gvBj Ges cÖwZK‚‡j N›Uvq 4 gvBj P‡j| †b․KvwU‡K †Kvb w`‡K Pvjv‡j †mvRv Aci cv‡o †c․uQv‡e? P + Q = 24, P – Q = 4 P=14, Q = 10, cos = – 10 14 = 135 NOW START PRACTICE 01. ‡Kvb GKwU b`x‡Z GKwU `uv‡oi †b․Kvi †eM †¯ªv‡Zi AbyK~‡j N›Uvq 18 km Ges cÖwZKzj N›Uvq 6km| †b․KvwU‡K †Kvb w`‡K Pvjbv Ki‡j Zv †mvRv Aci cv‡i †c․Qv‡e Ges †b․KvwU KZ †e‡M Pj‡e? 02. GKRb †jvK †mªvZnxb Ae¯’vq 100m cÖk¯Í GKwU b`x 4 wgwb‡U †mvRv‡mvwR mvZwo‡q cvi n‡Z cv‡i| wKš‘ †mªvZ _vK‡j †mB GKB c‡_ 5 wgwb‡U G‡K AwZµg Ki‡Z cv‡i| †mªv‡Zi MwZ‡eM †ei Ki| 03. GKwU b`xi ‡¯ªv‡Zi †eM 6 ms–1 , 9 ms–1 †e‡Mi GKwU †b․Kv‡K H b`x‡Z †Kvb w`‡K Pvjv‡j GwU †mvRv Aci cv‡k †cu․Qv‡e? †b․Kvi jwä †eM KZ? 04. †mªvZ bv _vK‡j GKRb muvZviæ NÈvq 4 km †e‡M muvZvi KvU‡Z cv‡i| NÈvq 2 km †e‡M mij‡iLv eivei cÖevwnZ GKwU b`xi Gcvi †_‡K Icv‡ii wVK wecixZ we›`y‡Z †h‡Z n‡j muvZviæ‡K †Kvb w`‡K muvZvi KvU‡Z n‡e? 05. b`x‡Z †mªvZ 3kmh–1 †e‡M cÖevwnZ n‡”Q| GKRb gvwS †mªv‡Zi mv‡_ 300 †KvY K‡i 4 kmh–1 †e‡M †b․Kv Pvjv‡”Q| b`xwU 2km PIov n‡j GK Zxi †_‡K iIbv n‡q Aci Zx‡i †cu․Qv‡Z gvwSi KZ mgq jvM‡e? 06. GKwU b`x‡Z †mªvZ 1kmh–1 ‡e‡M cÖevwnZ n‡”Q| GKRb gvwS †mªv‡Zi mv‡_ 300 †Kv‡Y 3 kmh–1 †e‡M †b․Kv Pvjv‡”Q| b`xwU 0.5km PIov n‡j GK Zxi †_‡K iIqvbv n‡q Ab¨ Zx‡i †cu․Qv‡Z KZ mgq jvM‡e? 07. †mªv‡Zi AbyK‚‡j †b․Kv †eM 12kmh–1 Ges †mªv‡Zi cÖwZK‚‡j †b․Kvi †eM 8kmh–1 n‡j (i) †mvRv Aci cv‡o †c․uQ‡Z †b․Kvi KZ mgq jvM‡e? (ii) Aci cv‡o †c․Qv‡Z me©wbgœ KZ mgq jvM‡e? (hLb b`xi cÖ¯’ 2km) NOW PRACTICE SOLVE : 01. cos = – v u = 12 6 = – 2 1 = cos1200 ev =1200 , V= 2 2 v u = 2 2 12 6 =6 3 =10.39kmh-1 02. b`xi cÖk¯Í d = 100m ‡¯ªvZ bv _vK‡j mvZviæi †eM v = 100 4 = 25m/min †mªvZ _vK‡j, †eM, A_©vr jwä‡eM w = 100 5 =20m/min †mªv‡Zi †eM u = v 2 – w 2 u = 252 – 202 = 625 – 400 = 225= 15m/min [ïaygvÎ †mvRvmywR AwZµg Kivi †ÿ‡Î] 03. cos = – †¯ªv‡Zi †eM †b․Kvi †eM = cos–1 – 6 9 cos–1 – 2 3 (Ans) jwä, R = (eo gvb) 2 – (†QvU gvb) 2 9 2 – 6 2 = 45 = 6.71 ms–1 04. = cos –1 – u v = cos –1 – 2 4 = 120˚ muvZviæ‡K †mªv‡Zi mv‡_ 120˚ †Kv‡Y muvZvi w`‡Z n‡e| 05. b`x cvi n‡Z cÖ‡qvRbxq mgq = b`xi we¯Ívi we¯Ívi eivei †b․Kvi †e‡Mi Dcvsk = 2 4sin30 = 1hr 06. b`x cvi n‡Z mgq jvM‡e, t = b`xi cÖk¯ÍZv †b․Kvi †e‡Mi Dj¤^ Ask = 0.5 3sin30 ev, t = 0.5 3 0.5 = 1 3 NÈv = 60 3 = 20min 07. AbyK‚‡j, u+v=12 kmh-1 ; cÖwZK‚‡j, v–u = 8 kmh-1†b․Kvi †eM,v =10 kmh-1†mªv‡Zi †eM,u=2 kmh-1 (i) b`x cvi n‡Z cÖ‡qvRbxq mgq, t = d v 2 – u 2 = 2 102 – 2 2 = 0.204h = 734.85 sec; (ii) cvivcv‡ii b~¨bZg mgq, tmin = d u = 2 10 = 0.2h = 720 sec

78 An Exclusive Parallel Text Book of Physics ASPECT PHYSICS ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES STEP 01 ANALYSIS OF GST QUESTION PART A Analysis of Science & Technology Question 01. myigv b`x‡Z †mªv‡Zi †eM 3 km.h–1 | GK e¨w³ 5 km.h–1 †e‡M †b․Kv Pvjv‡Z mÿg| b`xi cÖ¯’ 0.5 km| †mªv‡Zi m‡½ KZ wWwMÖ †Kv‡Y †b․Kv Pvjv‡j †m 12 min G b`xi Aci cv‡i GKwU wbw`©ó Nv‡U †c․uQv‡Z cvi‡e? [SUST-B, 19-20] A. 30 B. 50 C. 45 D. 59 E. 35 S A info d = 0.5km ; t = 12 min = 12 60 = 0.2h t = d vsin = sin1 d vt = sin1 0.5 0.2 5 = 30 STEP 02 ANALYSIS OF ENGINEERING & BUTex QUESTION 01. GKwU BwÄb PvwjZ †b․Kvi †eM 14km/hr | b`xi cÖ¯’ 12.125km n‡j b`xwUi AvovAvwo cvwo w`‡Z KZ mgq jvM‡e? †mªv‡Zi †eM 7km/hr| [CUET. 14-15] A. 1.25 hr B. 1 hr C. 1 2 hr D. None of them S B info t = S h 2 – v 2 = 12.125 142 – 7 2 = 1.00053 1hr. STEP 03 ANALYSIS OF MEDICAL & DENTAL QUESTION 01. GKwU b`x‡Z †mªv‡Zi †eM 5Kmh–1 GKwU †b․Kvi †eM 10Kmh–1 †mªv‡Zi mv‡_ KZ wWMÖx †Kvb K‡i †b․Kv Pvjv‡j †b․KvwU Aci cv‡i wVK †mvRv‡mvwR †c․Qv‡e? [MAT. 05-06] A. 120° B. 150° C. 130° D. 100° S A info †mªv‡Zi †eM = 5Kmh–1 Ges ‡b․Kvi †eM =10Kmh–1 hvnviv ci®úi wظb| †KvY = 120° STEP 04 ANALYSIS OF HSC BOARD QUESTION 01. GKRb gvwS †¯ªv‡Zi wecix‡Z O we›`y‡Z iwk †eu‡a Abyf~wg‡Ki mv‡_ †Kv‡Y †b․KvwU‡K T e‡j mvg‡bi w`‡K Uvb‡Q| iwki •`N©¨ OA n‡j [Xv. †ev. 2016] i. nvj Øviv T cos cÖkwgZ nq ii. iwk¥i •`N©¨ OB n‡j †b․Kv A‡cÿvK…Z `ªyZ Pj‡e iii. Tsin Gi gvb †ewk Kg n‡j ‡b․Kv mvg‡bi w`‡K †ewk MwZkxj n‡e wb‡Pi †KvbwU mwVK? A. i I ii B. i I iii C. ii I iii D. i, ii I iii Ans C 02. †mªvZhy³ b`x‡Z me©wb¤œ mg‡q Icv‡i †h‡Z †mªv‡Zi mv‡_ wKfv‡e †b․Kv Pvjbv Ki‡Z n‡e? [h. †ev. 2017] A. 45 B. 60 C. 90 D. 120 Ans C DÏxcKwU c‡o wb‡Pi cÖkœwUi DËi `vI : [h. †ev. 2015] GKwU Lv‡ji AB Ges CD `ywU mgvšÍivj Zxi| †b․Kvi O we›`y n‡Z F1 Ges F2 gv‡b ej cÖ‡qv‡M `y'Rb e¨w³ MyY Uvb‡Q| 03. F1 I F2 †f±i؇qi jwäi gvb KZ? A. 10.22 B. 10.52 C. 11.22 D. 11.52 S C info F1 + F2 = 5i ˆ + j ˆ + 10k ˆ | F1 + F2| = 5 2 + 12 + 102 = 11.2 Concept 4 e„wó msµvšÍ MvwYwZK cÖ‡qvM 01. e„wó f~wgi mv‡_ †h †KvY •Zwi K‡i, tan = j¤^ f~wg = j¤^ eivei miY/†eM/Z¡iY/ej f~wg eivei miY/†eM/Z¡iY/ej (Dj‡¤^i mv‡_ †KvY n‡j f~wgi mv‡_ †KvY = 90 ) gvbyl I e„wói ga¨eZ©x †KvY tan = gvby‡li †eM e„wói †eM [†Kv‡bv w`K D‡jøL¨ bv _vK‡j Dj¤^ Gi mv‡_ †KvY K‡i QvZv aie|] Model Example01 GKRb mvB‡Kj Av‡ivnx mgZj iv¯Ívi Dci w`‡q KZ †e‡M Pj‡j 8 ms–1 †e‡Mi e„wói †dvUv Zvi Mv‡q 450 †Kv‡Y co‡e? General Rules [Written] 3 in 1 Shortcut Tricks & Tips [MCQ] GLv‡b, e„wói †eM Q = 8ms–1 mvB‡K‡ji †eM P = ? = 450 = 900 tan = Q sin P + Q cos tan 450 = 8 sin 900 P + 8 cos900 1 = 81 P + 80 1 = 8 P P = 8 ms–1 tan = gvby‡li †eM e„wói †eM tan 450 = 8 P P = 8 ms–1 REAL TEST ANALYSIS OF PREVIOUS YEAR QUESTIONS SUST CUET MAT FORMULA

ASPECT PHYSICS cÖ_g cÎ †f±i 79 ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES CONCEPTUAL MATH MEx 01 3ms–1 †e‡M †`․ovevi Kv‡j GKRb e¨w³ 3ms-1 †e‡M j¤^fv‡e cwZZ e„wói m¤§yLxb n‡jv| e„wó n‡Z i¶v †c‡Z n‡j Zv‡K KZ †Kv‡Y QvZv ai‡Z n‡e? tan = gvby‡li †eM e„wói †eM ev, = 450 NOW START PRACTICE 01. e„wói †dvUv Lvov wb‡Pi w`‡K 5ms–1 †e‡M co‡Q| GKRb †jvK e„wói g‡a¨ 2ms-1 †e‡M nvU‡Q| (i) KZ †Kv‡Y QvZv ai‡Z n‡e?(ii) e„wói †dvUvi jwä †eM KZ? 02. 4ms–1 †e‡M †`․‡o hvevi Kv‡j GKRb e¨w³ 3ms–1 †e‡M j¤^fv‡e cwZZ e„wói m¤§yLxb n‡jv| e„wó n‡Z i¶v †c‡Z n‡j Zv‡K KZ †Kv‡Y QvZv ai‡Z n‡e? NOW PRACTICE SOLVE : 01. (i) Djø‡¤^i mv‡_ †Kv‡Y QvZv ai‡Z n‡j, = tan–1 u v = tan–1 2 5 = 2148; (ii) e„wói jwä †eM, R = v 2 + u 2 = 2 2 + 52 = 5.39 ms–1 02. = tan–1 u v = tan–1 3 4 = 36.870 †Kv‡Y QvZv ai‡Z n‡e| STEP 01 ANALYSIS OF JU QUESTION 01. †mv‡nj mvB‡K‡j K‡i evwo hvw”Qj| nVvr K‡i e„wó bvgj| e„wói †duvUv 10 ms–1 †e‡M Zvi Mv‡q cov ïiæ n‡jv| evqyi cÖevn Lye †ewk wQjbv| ZeyI e„wói †dvUv Zvi Mv‡q 45 †Kv‡Y co‡Q| mvB‡K‡ji †eM KZ? [JU-H, Set-A. 20-21] A. 6 ms–1 B. 8 ms–1 C. 10 ms–1 D. 12 ms–1 S C info Avgiv Rvwb, tan = gvby‡li ev mvB‡K‡ji †eM e„wói †eM mvB‡K‡ji †eM = tan 45 10 = 10 ms–1 Concept 5 ga¨eZ©x †KvY msµvšÍ MvwYwZK cÖ‡qvM 01. = cos1 A. B | A|| B| 02. = tan–1 ‡f±i ¸Yd‡ji gvb ‡¯‥jvi ¸Yd‡ji gvb = tan–1 |A | B A . B Model Example01 `ywU †f±‡ii †¯‥jvi ¸Ydj 18 GKK| G‡`i †f±i ¸Yd‡ji gvb 6 3 n‡j, †f±i؇qi ga¨eZ©x †KvY KZ? General Rules [Written] 3 in 1 Shortcut Tricks & Tips [MCQ] A . B = 18 AB cos = 18 ............................. (1) Avevi, |A B | = 6 3 AB sin = 6 3 ............................. (2) (2) (1) AB sin AB cos = 6 3 18 tan = 1 3 tan = tan 300 = 300 ga¨eZ©x †KvY = tan–1 ‡f±i ¸Yd‡ji gvb ‡¯‥jvi ¸Yd‡ji gvb = tan–1 6 3 18 = 300 NOW START PRACTICE 01. P = ˆ i + 2ˆ j – ˆk Ges Q = – ˆ i + ˆ j – 2 ˆk `yBwU w`K ivwk| G‡`i ga¨eZx© †Kv‡Yi gvb nj02. `yB †f±‡ii gvb h_vµ‡g 8 Ges 6 GKK| Zviv ci¯ú‡ii mv‡_ 30˚ †Kv‡Y wµqv K‡i| G‡`i †f±i ¸Ydj KZ? 03. A = 2i Ges B = 3j – 2k n‡j A Ges B Gi ga¨eZx© †KvY n‡e? 04. `ywU †f±‡ii WU ¸Ydj I µm ¸Yd‡ji gvb mgvb n‡j †f±i ؇qi ga¨eZ©x †KvY KZ? NOW PRACTICE SOLVE : 01. ga¨eZx© †KvY, = cos –1 P. Q PQ = cos –1 –1 +2 + 2 6 6 = 60˚ 02. =AB sin = 8 6 sin30˚ = 24 GKK 03. ga¨eZx© †KvY, = cos–1 A. B AB = cos–1 0 2 13 = 90 04. ABcos = ABsin ev, tan = 1 = 45 3 3 tan REAL TEST ANALYSIS OF PREVIOUS YEAR QUESTIONS FORMULA A B

80 An Exclusive Parallel Text Book of Physics ASPECT PHYSICS ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES 01. `yBwU †f±i A= 3.0 ˆ i – 3.0 ˆ j Ges B = 5.0 ˆ i + 5.0 ˆ k Gi ga¨eZ©x †KvY KZ? [DU. 14-15] A. 60o B. 30o C. 45o D. 90o S A info A= 3.0 ˆ i – 3.0 ˆ j, B = 5.0 ˆ i + 5.0 ˆ k, A. B = AB cos ev, 15= 3 2. 5 2 cos ev, cos = 1 2 = 60 02. hw` p = 2 ˆ i + 4 ˆ j – 5 ˆ k Ges q = ˆ i + 2 ˆ j + 3 ˆ k nq Z‡e ga¨eZ©x †KvY- [DU. 09-10, KU. 14-15] A. 78.51° B. 105.25° C. 11.49° D. 101.49° S D info cos = 2.1 + 4.2 + (–5 3) (2) 2 + (4) 2 + ( 5) 2 (1) 2 + (2) 2 + (3) 2 = 2 + 8 – 15 45 14 = cos-1 –5 630 = –5 25.09 ev, = 101.49° 01. (i – j) Ges (i + j) Gi ga¨eZx© †KvY KZ? [JU-A, Set-D. 19-20] A. 60 B. 30 C. 90 D. 180 S C info = cos–1 0 2 2 = cos–1 0 = 90 STEP 03 ANALYSIS OF CU QUESTION 01. Ges †f±i؇qi cÖ‡Z¨‡Ki gvb 3 Ges n‡j Ges Gi ga¨eZx© †KvY KZ? [CU-A, Set-2. 19-20] A. B. C. D. S D info |A × B | = (–5) 2 + 22 = 29 GLv‡b, |A × B | = ABsin = sin–1 29 9 02. A= 2 ˆ i + 2 ˆ j – ˆ k Ges B = 6 ˆ i – 3 ˆ j + 2 ˆ k n‡j A I B Gi ga¨eZ©x †Kvb n‡e? [CU. 08-09] A. 59° B. 69° C. 79° D. 89° E. 99° S C info cos = A. B | A| | B| = 2.6 + 2(–3) + (–1).2 2 2 + 22 + (–1) 2 (6) 2 + (–3) 2 + (2) 2 = 12 – 6 – 2 9. 49 = 4 3 7 = 79 STEP 04 ANALYSIS OF GST QUESTION 01. hw` †f±i A= 3 ^ i + 3 ^ j + 3 ^ k Ges B = 2 ^ i + ^ j – 3 ^ k nq Zvn‡j A I B Gi ga¨eZx© †KvY wbY©q Ki? [JnU. 2006-07] A. 45 B. 0 C. 30 D. 90 S D info A= 3 ˆ i + 3 ˆ j + 3 ˆ k Ges B = 2 ˆ i + ˆ j – 3 ˆ k A. B = 3 2 + 3 1– 3 3 = 0 = 900 01. P=2^ i + ^ j – 2 ^ k Ges Q= 5^ i – 4 ^ j + ^ k n‡j P I Q Gi ga¨eZ©x †KvY- [IU. 15-16] A. 50.5 B. 65.7 C. 77.9 D. 78.12 S D info P = 2i + j – 2k, Q = 5i – 4j + k , Zv‡`i ga¨eZ©x †KvY = cos = A. B |A||B| = 10 – 4 – 2 (2) 2 + (1) 2 (–2) (5) 2 + (4) 2 + (1) 2= 4 3 42 = 78.12 PART B Analysis of Science & Technology Question 01. `ywU †f±‡ii †¯‥jvi ¸Ydj 20 Ges †f±i ¸Ydj 6 2| †f±i؇qi ga¨eZ©x †KvY n‡eÑ [MBSTU-A, Set-2 19-20] A. 60 B. 90 C. 30 D. 120 S Blank info AB sin AB cos = 6 2 20 tan = 0.42 = 22.59˚ 23˚ 02. ‡Kvb ¯’v‡b evZvm N›Uvq 352km †e‡M `w¶Y c~e© w`‡K 45 †KvY K‡i cÖevwnZ nq| evZv‡mi †e‡Mi c~e©g~Lx Ask wbY©q Ki| [BSMRSTU. 14-15] A. 35km/h B. 30km/h C. 25km/h D. 20km/h S A info c~e©gyLx Dcvsk = 35 2sin45° = 35km/h 01. GKwU KYvi DËi I c~e© w`‡K h_vµ‡g 4km Ges 8km miY n‡j, DËi w`‡K mi‡Yi mv‡_ jwä mi‡Yi ga¨eZ©x †KvY wbY©q Ki? [HSTU. 15-16] A. 50.20 B. 21.80 C. 118.10 D. †KvbwUB bq S D info sin = 8 4 5 ev, = 63.43° `w¶Y c~e© cwðg DËi 4 8 4 5 STEP 05 ANALYSIS OF HSC BOARD QUESTION 01. 4 GKK I 5 GKK gv‡bi `ywU †f±i †Kv‡bv we›`y‡Z 60 †Kv‡Y wµqvkxj n‡j †¯‥jvi ¸Ydj n‡eÑ [Xv.‡ev 2021] A. 0 GKK B. 1 GKK C. 10 GKK D. 100 GKK S C info A . B = AB cos = 4 5 cos60 = 10 02. `ywU †f±‡ii jwäi gvb m‡e©v”P n‡e hLb G‡`i ga¨eZ©x †KvY- [w`.‡ev 2021] A. 0 B. 456 C. 60 D. 180 S A info Rmax = – P + – Q [ = 0] 03. |A + B | = |A – B | n‡j A I B Gi ga¨eZx© †KvY n‡e- [w`. †ev. 2017] A. 0˚ B. 90˚ C. 45˚ D. 180˚ S B info |A + B | = |A – B | |A + B | 2 = |A – B | 2 A 2 + 2A .B + B 2 = A 2 – 2A .B + B 2 4A .B = 0 A .B = 0 A.B cos = 0 cos = 0 = 90˚ REAL TEST ANALYSIS OF PREVIOUS YEAR QUESTIONS STEP 01 ANALYSIS OF DU QUESTION STEP 02 ANALYSIS OF JU QUESTION A B A B 5k 2i ˆ ˆ A B 2 29 cos 1 2 5 tan 1 5 2 sin 1 9 29 sin 1 PART A Analysis of General University Question JnU IU MBSTU HSTU

ASPECT PHYSICS cÖ_g cÎ †f±i 81 ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES 04. A = i , B = 2i + k , A I B †f±‡ii ga¨eZx© †KvY- [w`. †ev. 2016] A. 25.12 B. 26.57 C. 90.67 D. 180.25 S B info = cos–1 A .B |A | .B = cos–1 2 1 × 5 = 26.57˚ 05. |A B | = A .B n‡j G‡`i ga¨eZx© †KvY KZ? [w`. †ev. 2016] A. 4 B. 2 C. D. 2 S A info ABsin = ABcos tan = 1 = 4 06. hw` C = A B Ges D = B A nq Zvn‡j C Ges D ga¨eZx© †KvY KZ? [w`. †ev. 2015] A. 90 B. 0 C. 180 D. 45 Ans C 07. `ywU mgvb †f±i †_‡K k~b¨ †f±i †c‡Z n‡j G‡`i ga¨eZx© †KvY n‡e- [Kz. †ev. 2015] A. 0 B. 45 C. 90 D. 180 Ans D 08. P I Q `ywU mggv‡bi †f±i ci®úi wecixZ w`‡K wµqv Ki‡Q| †f±i `ywUi jw× R I P Gi ga¨eZ©x †KvY †KvbwU? [wm.‡ev 2021] A. 90 B. 60 C. 45 D. 0 Ans A 09. wZbwU mggv‡bi ej GKwU we›`y‡Z wµqv K‡i mvg¨ve¯’vi m„wó Ki‡j Zv‡`i AšÍfz©³ †Kv‡Yi AbycvZ KZ? [g.‡ev 2021] A. 60 : 60 : 240 B. 90 : 90 : 180 C. 120 : 120 : 120 D. 150 : 150 : 60 S C info P = Q = R n‡j = 120 10. cÖwZwU KYvi Dci F = (2 i + 3 j – k)N ej cÖ‡qvM Kivq KYvwUi r = ( i + j + k)m miY N‡U| F I r Gi ga¨eZ©x †KvY KZ? [e.‡ev 2021] A. 48.19 B. 51.88 C. 81.84 D. 84.53 S B info F. r = Fr cos = cos1 F. r | | F . | | r = cos1 2 + 3 1 14 3 = 51.88 11. `ywU mgvb †f±i †_‡K k~b¨ †f±i †c‡Z G‡`i ga¨eZx© †KvY n‡eÑ [e. †ev. 2015] A. 0 B. 45 C. 90 D. 180 S D info R 2 = p2 + p2 + 2p2 cos 2p2 cos = – 2p2 [∵ R = 0] cos = – 1 = 180˚ Concept 6 A‡ÿi mv‡_ †KvY wbY©q msµvšÍ MvwYwZK cÖ‡qvM A = Ax i + Ay j + Az k n‡j, 01. A †f±‡ii x A‡ÿi mv‡_ m„ó †KvY, x = cos–1 Ax | | – A 02. A †f±‡ii y A‡ÿi mv‡_ m„ó †KvY, y = cos–1 Ay | | – A 03. A †f±‡ii z A‡ÿi mv‡_ m„ó †KvY, z = cos–1 Az | | – A 04. cos2 x + cos2 y + cos2 z = 1 CONCEPTUAL MATH MEx 01 n‡j p Gi mv‡_ x, y, z A‡¶i mv‡_ †K․wYK e¨eavb KZ? x = cos–1 3 2 = 30, cosy = ev, y = 120, z = cos–1 0 2 = 90 MEx 02 3 i + 2 j + 2 k, y A‡ÿi mv‡_ KZ †Kv‡Y _v‡K? cosy = 2 9 + 4 + 4 = 2 17 y = cos–1 2 17 NOW START PRACTICE 01. P = 2 j + 5 k, x A‡ÿi mv‡_ KZ †KvY •Zwi Ki‡e? 02. B = 3 i – 2 j + 5 k, x A‡ÿi mv‡_ KZ †KvY •Zwi Ki‡e? 03. A = 2 i – j + 3 k †f±iwUi x A‡ÿi mv‡_ w`K †KvmvBb KZ? NOW PRACTICE SOLVE : 01. cosx = 0 4 + 25 x = cos–1 (0) = 90 02. cosx = 3 9 + 4 + 25 = 3 38 x = cos–1 3 38 03. cosx = 2 14 FORMULA P 3 i j 2 1

82 An Exclusive Parallel Text Book of Physics ASPECT PHYSICS ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES STEP 01 ANALYSIS OF JU QUESTION 01. †f±i A = 6 i 4 k n‡j †f±i A Ges Y A‡¶i ga¨eZ©x †KvY n‡e- [JU. 12-13] A. 30 B. 90 C. 60 D. 0 S B info A = 6 i 4 k, cosy = 0 6 2 + ( 4) 2 ev, y = 90 STEP 02 ANALYSIS OF HSC BOARD QUESTION 01. P = i + 2 j – 3 k †f±iwUi YZ Z‡j gvb KZ? [iv.‡ev 2021] A. 5 B. 10 C. 13 D. 14 S C info | – P| = 2 2 + (– 3) 2 = 13 02. wÎgvwÎK ¯’v‡b P I Q `ywU mgvšÍivj †f±i n‡j- [iv.‡ev 2021] i. P. Q = 0 ii. P Q = 0 iii. Px Qx = Py Qy = Pz Qz wb‡Pi †KvbwU mwVK? A. i I ii B. i I iii C. ii I iii D. i, ii I iii Ans C 03. Y-A‡ÿi mv‡_ r = 4i − 4k †f±‡ii Drcbœ †KvY n‡eÑ [w`. †ev. 2017, wm. †ev. 2017] A. 0 B. 45 C. 90 D. 180 Ans C 04. Ae¯’vb †f±i cÖKv‡ki †ÿ‡Î e¨eüZ nq- [wm.‡ev 2021] i. r = x i + y j ii. r(x2 i + y2 j) – (x1 i + y1 j) iii. r= x i + y j + z k wb‡Pi †KvbwU mwVK? A. i I ii B. i I iii C. ii I iii D. i, ii I iii Ans B Concept 7 `ywU †f±i ci¯úi j¤^ msµvšÍ MvwYwZK cÖ‡qvM FORMULA `ywU †f±i ivwki WU ¸Y‡bi gvb k~b¨ n‡j †f±i ci¯úi j¤^| [A .B = 0] CONCEPTUAL MATH MEx 01 Ges n‡j a- Gi †Kvb gv‡bi Rb¨ †f±i Ges †f±i ci¯ú‡ii Dci j¤^ n‡e? (2 ) ^ i + a ^ j ^ k . (4 ) ^ i + 2 ^ j 2 ^ k = 0 8 2a + 2 = 0 a = 5 MEx 02 a Gi gvb KZ n‡j A = aˆ i – 2 ˆ j + ˆk Ges B = 2aˆ i + aˆ j – 4 ˆk †f±iØq ci¯úi j¤^ n‡e? †f±iØq ci¯úi j¤^ n‡e hw` nq| A. B = 0 AxBx + AyBy + AzBz = 0 a.2a + (–2).a + (1)(–4) = 0 2a2 – 2a – 4 = 0 a = 2 or a = –1 NOW START PRACTICE 01. a Gi gvb KZ n‡j A = 3ˆ i + aˆ j + ˆk Ges B = 4ˆ i + 3ˆ j – 6 ˆk †f±i ivwk `ywU ci¯úi j¤^ n‡e| NOW PRACTICE SOLVE : 01 . A. B = 0 ev, 3.4 + a.3 +1(-6) = 0 ev, 12 + 3a - 6 = 0 ev, 3a + 6 = 0 ev, a = -2 REAL TEST ANALYSIS OF PREVIOUS YEAR QUESTIONS STEP 01 ANALYSIS OF DU QUESTION 01. a Gi gvb KZ n‡j A = 2 i + 2 j k Ges B = a i + j †f±iØq ci¯úi j¤^ n‡e? [DU. 20-21] A. 1 B. 7 3 C. 0 D. 2 S A info A . B = AB coscos A . B = 0 2a + 2 – 0 = 0 2a = – 2 a = –1 02. hw` A = 2ˆ i + ˆ j + ˆk Ges B = – 2 ˆ i + ˆ j – 2 ˆk ci¯úi j¤^ nq Z‡e Gi gvb n‡e- [DU. 16-17] A.4 B.6 C. 6 D.2 S C info j¤^ A B n‡j A. B = 0, A. B = AxBx + AyBy + AzBz = 0 ev,–4+–2=0 ev, = 6 03. hw` A = 2ˆ i + 3ˆ j – 5 ˆk Ges B = mˆ i + 2ˆ j + 10ˆk Z‡e m Gi gvb KZ n‡j †f±iØq ci¯ú‡ii Dci j¤^ n‡e ? [DU. 13-14; 08-09] A. 12 B. 20 C. 22 D. 120 S C info A = 2ˆ i + 3ˆ j – 5 ˆk Ges B = mˆ i + 2ˆ j + 10ˆk ‡f±i Øq ci®úi j¤^| ZvB Zv‡`i WU¸‡bi gvb k~Y¨| 2m + 6 – 50 = 0, ev, 2m = 44, m = 22 04. a Gi gvb KZ n‡j A = 2ˆ i + aˆ j + ˆk Ges B = 4ˆ i – 2 ˆ j – 2 ˆk †f±iØq ci¯úi j¤^ n‡e? [DU. 10-11, 01-02; CU. 15-16; RU. 11-12; CoU. 12-13] A. 1 B. 2 C. 3 D. 4 S C info A = 2ˆ i + aˆ j + ˆk Ges B = 4ˆ i – 2 ˆ j – 2 ˆk Zviv ci¯úi j¤^| ZvB WU¸‡bi gvb = 0 2 4 + a(–2) +1(–2) =0 ev, 8–2a–2=0 ev, 6=2a ev, a=3 STEP 02 ANALYSIS OF JU QUESTION 01. †f±i A = 2 i + 4 j – 5 k Ges B = i + 2 j + 3 k †`Iqv Av‡Q| Zvn‡j | A . B| Gi gvb †KvbwU? [JU-A, Set-C. 20-21] A. 5 B. 9 C. 7 D. 4 S A info | A . B| = |21 + 42 – 53| = |–5| = 5 02. A = 2i + j – k I B = 4j – k †f±i؇qi †¯‥jvi MyYdj KZ? [JU. 18-19] A. 3 B. 7 C. 9 D. 11 S Blank info (2i + j – k ).(4j – k ) = 4 1 + (–1)(–1) = 5 REAL TEST ANALYSIS OF PREVIOUS YEAR QUESTIONS A i aj k ˆ ˆ ˆ 2 B i j k ˆ 4 ˆ 2 ˆ 2 A B

ASPECT PHYSICS cÖ_g cÎ †f±i 83 ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES 03. †f±i P = 2ˆ i + 3ˆ j – 6 ˆk Ges Q = mˆ i + 2ˆ j + 10ˆk. m Gi gvb KZ n‡j P I Q ci®ú‡ii Dci j¤^ n‡e- [JnU. 09-10] A. 8 B. 15 C. 27 D. 32 S C info P I Q ci®úi j¤^| Zv‡`i WU ¸Yb = 0 2m + 32 + (– 6)10 = 0 ev, m + 3 – 30 = 0 ev, m = 27 04. †f±i A = ˆ i – 3 ˆ j + 5ˆk Ges B = a ˆ i + ˆ j – ˆk. a-Gi gvb KZ n‡j †f±i `ywU ci¯ú‡ii Dci j¤^ n‡e? [JnU. 07-08] A. 8 B. 2 C. 10 D. 0 S D info a – 3 – 5 = 0 ev, a = 8 Zv‡`i WU ¸b =0 STEP 03 ANALYSIS OF RU QUESTION 01. A I B †f±iØq ci¯úi j¤^ n‡j wb‡Pi †KvbwU mZ¨ n‡e? [RU-C, Set-1. 19-20] A. | A + B| > A B| B. | A + B| < | A B| C. | A + B| = | A B| D. Dc‡ii me KqwU n‡Z cv‡i S C info |A | + B = |A | – B n‡j A I B Gi ga¨eZx© †KvY 90˚ nq| 02. ej Fˆ = 2 ˆ i – ˆ j – ˆk cÖ‡qvM K‡i e¯‘i miY ej ˆr = 3 ˆ i + 2ˆ j – 5 ˆk n‡j, K…Z Kv‡Ri cwigvY KZ GKK? [RU. 15-16] A. 9 B. 15 C. 17 D. 8 S A info F = 2 ˆ i – ˆ j – ˆk, r = 3 ˆ i + 2ˆ j – 5 ˆk KvR w = F. r = (2)(3) + (–1)(2) + (–1)(–5) = 6 – 2 + 5 = 9 STEP 04 ANALYSIS OF CU QUESTION 01. hw`, P = 2 i + j – 3 k Ges Q = 4 j – k nq, Z‡e Zv‡`i †¯‥jvi ¸Yb wK nq? [CU-A, Set-1. 20-21] A. 7 B. 3 C. 9 D. 11 S A info P. Q = (2 i + j – 3 k) . (4 j – k) = 0 + 4 + 3 = 7 02. Aˆ = 2 ˆ i + 3ˆ j – ˆk Ges Bˆ = mˆ i + 2ˆ j – 4 ˆk Gi gvb KZ n‡j †f±iØq ci®úi j¤^ n‡e? [CU. 13-14] A. m = 1 B. m = 2 C. m = – 1 D. m = 0 E. m = – 21 S C info †f±iØq ci®úi j¤^| Zv‡`i WU ¸b = 0 2m + 6 – 4 = 0 ev, 2m+ 2 = 0 ev, m = -1 03. ˆ j.(2 ˆ i – 3 ˆ j + ˆk) Gi gvb KZ? [CU. 13-14] A. 2 B. – 3 C. 1 D. – 2 E. 3 Ans B 04. †`Iqv Av‡Q A = 2 ˆ i + 2ˆ j + ˆk Ges B = i + 2j +mˆk | m Gi gvb KZ n‡j †f±iØq ci®ú‡ii Dci j¤^ n‡e [CU. 09-10] A. 5 B. – 6 C. 4 D. 1 E. 2 S B info †f±iØq ci®úi j¤^ n‡j, A.B = 0 ev, 21+ 22+1m =0 ev, 6+m = 0 ev, m = – 6 STEP 05 ANALYSIS OF DU-7 Clg QUESTION 01. hw` F = 8 i + 2 j I r = 6 i + 6 k nq Z‡e F. r KZ n‡e?[DU-7Clg.A.19-20] A. 48 B. 36 C. 32 D. 64 S A info F. r = 48 STEP 06 ANALYSIS OF GST QUESTION PART A Analysis of General University Question CoU 01. a Gi gvb KZ n‡j A = 2i – aj + 3k Ges B = 3i + j + 3k †f±iØq ci¯ú‡ii Dci j¤^ n‡e? [CoU. 18-19] A. 15 B. 22 C. 3 D. 9 S A info A . B = 0 6 – a + 9 = 0 a = 15 02. y Gi †Kvb gv‡bi Rb¨ 2 ˆ i + yˆ j + ˆk Ges 2 ˆ i – 2 ˆ j –2 ˆk ci®ú‡ii Dci j¤^ n‡e? [CoU. 12-13, 14-15] A. 1 B. 2 C. 3 D. 4 S A info Zviv ci®úi j¤^ n‡j, 4 – 2y – 2 = 0 ev, y = 1 03. A= 2 ˆ i + aˆ j + ˆk Ges B = 4 ˆ i – 2 ˆ j – ˆk †f±Øq ci®úi j¤^ n‡j, a Gi gvb KZ? [CoU. 12-13] A. 7 2 B. 3 C. 4 D. 1 S A info A = 2 ˆ i + aˆ j + ˆk Ges B = 4 ˆ i – 2 ˆ j – ˆkZviv ci®úi j¤^| 8 – 2a – 1 = 0 ev, a = 7 2 IU 01. p Gi gvb KZ n‡j A = 2i ˆ + 2j ˆ – 2kˆ Ges B = pi ˆ + 3j ˆ + 4kˆ ci¯úi j¤^? [IU-D, 19-20] A. 4 B. 5 C. 2 D. 1 S D info A I B ci¯úi j¤^ n‡j A . B = 0 ev, 2P + 6 – 8 = 0 P = 1 JKKNIU 01. m Gi gvb KZ n‡j P = 4i ˆ + mj ˆ Ges Q = 8i ˆ – 4j ˆ + 9kˆ ci¯úi j¤^ n‡e? [JKKNIU-B, Set-3, 19-20, Xv. †ev. 2016] A. 8 B. 6 C. 4 D. –4 S A info P I Q ci¯úi j¤^ n‡j, P . Q = 0 32 – 4m = 0 m = 8 PART B Analysis of Science & Technology Question MBSTU 01. m Gi gvb KZ n‡j A = 2 i + 2 j 2 k Gi B = m i + 3 j + 4 k ci¯úi j¤^ n‡eÑ [MBSTU-C, Set-2 19-20] A. 1 B. 2 C. 3 D. 4 S A info A. B = 0 2m + 6 – 8 = 0 m = 1 NSTU 01. hw` F = (5i ˆ – j ˆ – kˆ)N ej cÖ‡qv‡M GKwU e¯‘i miY S = (3i ˆ + 5j ˆ)m nq Z‡e e‡ji Øviv m¤úvw`Z Kv‡Ri cwigvY KZ? [NSTU-A, 19-20] A. 10 B. 20 C. 30 D. 40 S A info KvR, W = F .s = (5i ˆ – j ˆ – kˆ).(3i ˆ + 5j ˆ) = 15 – 5 = 10J BSFMSTU 01. GKwU KYvi Dci F = (6i ˆ – 3j ˆ + 2kˆ) N ej cÖ‡qv‡M KYvwUi r = (2i ˆ + 2j ˆ – kˆ) m miY n‡j Kv‡Ri cwigvY n‡e- [BSFMSTU-A, 19-20] A. 40 Joules B. 4.0 Joules C. 0.4 Joules D. 4.0 N S B info W = F . r = 12 – 6 – 2 = 4J.

84 An Exclusive Parallel Text Book of Physics ASPECT PHYSICS ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES 02. hw` A = 2i ˆ + aj ˆ + kˆ Ges B = –2i ˆ + j ˆ – 2kˆ †f±iØq ci¯úi j¤^ n‡j Z‡e a Gi gvb n‡e- [BSFMSTU-A, 19-20] A. –4 B. –6 C. 6 D. 5 S C info ci¯úi j¤^ n‡j, A. B = 0 –4 + a – 2 = 0 a = 6 STEP 07 ANALYSIS OF HSC BOARD QUESTION 01. A= 3^ i – 2 ^ j + ^ k, B = 6^ i – m ^ j + 4^ k, m Gi gvb KZ n‡j †f±iØq j¤^ n‡e? [Xv. †ev. 2015] A. 9 B. –11 C. 12 D. 13 S B info (3 ^ i – 2 ^ j + ^ k) . (6 ^ i – m ^ j + 4^ k) = 0 18 + 2m + 4 = 0 m = – 11 02. A = 2 ^ l + 5 ^ j ^ k, B = P ^ l ^ j + 3 ^ k p Gi gvb KZ n‡j, †f±iØq ci¯úi j¤^ n‡e? [P.‡ev. 2019] A. –4 B. -1 C. 4 D. 5 S C info 2P – 5 – 3 = 0 P = 4 03. P I Q †f±iØq j¤^ nIqvi kZ© †KvbwU? [P. †ev. 2017] A. P . Q = 0 B. P . Q = 1 C. P Q = 0 D. P Q = 1 Ans A 04. †Kvb †f±iwU P = 4i + 2j - Gi Dci j¤^? [P. †ev. 2016] A. 4i + 4j B. 6i C. 5k D. 4j Ans C 05. ‡Kvb †f±iwU P = 4i + 3j Gi Dci j¤^? [P. †ev. 2016] A. 3i + 4j B. 6j C. 5 ^ k D. 4j Ans C 06. GKwU KYvi Dci F = (2i + 2j + k ) N ej cÖ‡qv‡M KYvwUi miY r (6i 3j 2k )m nq| cÖ‡qvMK…Z ej KZ…©K m¤úvw`Z Kv‡Ri cwigvY n‡e- [w`. †ev. 2017] A. 20 Ryj B. 4 Ryj C. (8i j k ) Ryj D. (4i + 5j + 3k ) Ryj S B info W = F .r = (2i + 2j + k ).(6i 3j 2k ) W = (12 – 6 – 2) J = 4 J 07. P=2^ i+ ^ j-3 ^ k Ges Q= 4^ i- ^ k n‡j, G‡`i †¯‥jvi MyYdj KZ? [wm. †ev. 2015] A. 3 B. 7 C. 9 D. 11 S D info P . Q = 8 + 0 + 3 = 11 Concept 8 `ywU †f±i ci¯úi mgvšÍivj msµvšÍ MvwYwZK cÖ‡qvM 01. `ywU †f±‡ii µm¸bb k~b¨ n‡j †f±iØq ci¯úi mgvšÍivj n‡e| 02. `ywU †f±i A i A j A k x y z ˆ ˆ ˆ Ges B i B j B k x y z ˆ ˆ ˆ mgvšÍivj nIqvi kZ©: x x B A = y y B A = z z B A ASPECT SPECIAL: hw` Ax = Ay = Az Ges Bx = By = Bz nq, Zvn‡j Zv‡`i wbY©vq‡Ki gvb k~Y¨ n‡e| Model Example01 A = i – 3 j + 5 k Ges B = m i + 6 j – 10 k| m Gi gvb KZ n‡j †f±iØq ci¯úi mgvšÍivj n‡e? General Rules [Written] 3 in 1 Shortcut Tricks & Tips [MCQ] hw` A B = 0 nq Z‡e A I B ci¯úi mgvšÍivj n‡e| GLv‡b, A B= ( i– 3 j + 5 k) (m i + 6 j – 10 k) = i j k 1 –3 5 m 6 –10 = i(30 – 30) – j(–10 – 5m) + k(6 + 3m) = – j(–10 – 5m) + k (6 + 3m) kZ©vbymv‡i, 10 + 5m = 0 6 + 3m = 0 5m = – 10 3m = – 6 m = – 2 m = – 2 Ax Bx = Ay By 1 m = –3 6 m = – 2 A_ev, 1 m = –10 5 = –2 CONCEPTUAL MATH MEx 01 a Gi †Kvb gv‡bi Rb¨ I mgvšÍivj n‡e †hLv‡b Ges 15 5 = a 2 a = 6 NOW START PRACTICE 01. `ywU †f±i Ges †`qv Av‡Q x Gi †h gv‡bi Rb¨ †f±i Ges †f±i mgvšÍivj n‡e Zv nj02. a Gi †Kvb gv‡bi Rb¨ A I B mgvšÍivj n‡e †hLv‡b A = 5ˆ i + 2ˆ j + 3ˆk Ges B = 15ˆ i + aˆ j + 9ˆk NOW PRACTICE SOLVE : 01. I mgvšÍivj 2 x = 3 6 ev x = 4 02. A = 5ˆ i + 2ˆ j + 3ˆk Ges B = 15ˆ i + aˆ j + 9ˆk So, 5 15 = 2 a a = 3 2 = 6 FORMULA A B A 5 i 2 j 3k B 15i a j 9k A i j k ˆ 2 ˆ 3 ˆ 4 B xi j k ˆ ˆ 6 ˆ 8 A B A B

ASPECT PHYSICS cÖ_g cÎ †f±i 85 ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES 01. †f±i A = ˆ i – 3 ˆ j + 5ˆk Ges B = aˆ i + 6ˆ j – 10ˆk| a- Gi gvb KZ n‡j †f±i `ywU mgvšÍivj n‡e? [DU. 06-07, PSTU. 14-15] A. 0 B. –2 C. –1 D. 1 S B info A = ˆ i – 3 ˆ j + 5ˆk Ges B = aˆ i + 6ˆ j – 10ˆk ‡f±i `yBwU mgvšÍivj 1 a = –3 6 ev, a = –2 02. hw` (If) A = ˆ i + ˆ j + ˆk, B = 2ˆ i + 2ˆ j + 2ˆk, then A B = ? [DU. 03-04] A. 3 ˆ i +3ˆ j +3ˆk B. 2 ˆ i + 2ˆ j + 2ˆk C. 12( ˆ i + ˆ j + ˆk) D. 0 S D info Abyiƒc mn‡Mi AbycvZ mgvb n‡j µm ¸‡Yi gvb = 0 1 2 = 1 2 = 1 2 STEP 02 ANALYSIS OF RU QUESTION 01. hw` 2 i + 3 j + k I –4 i – 6 j – k `ywU †f±i ci¯úi mgvšÍivj nq, Zvn‡j – i gvb KZ n‡e? [RU. Astrazeneca, Set-1. 20-21] A. 2 B. 2 C. 0.5 D. 0.5 S A info †f±i Dcvsk mg~‡ni Abycv‡Zi m~Îvbymv‡i, 2 –4 = 3 –6 = 1 – = 2 02. `yÕwU mgvšÍivj †f±i A = 3i – 2j + 4k Ges B = 12i – mj + 16k n‡j m = ? [RU-C, Set-3. 19-20] A. 4 B. –4 C. 8 D. –8 S C info A = 3i – 2j + 4k Ges B = 12i – mj + 16k ci¯úi mvgšÍivj| 3 12 = –2 –m = 4 16 m = 8 STEP 03 ANALYSIS OF CU QUESTION 01. `ywU †f±‡ii gvb h_vµ‡g 8 Ges 6 GKK| Zviv ci¯ú‡ii mv‡_ 30° †Kv‡b wµqv K‡i| G‡`i †f±i ¸bdj KZ? [CU. 08-09] A. 16 GKK B. 20 GKK C. 24 GKK D. 28 GKK E. 48 GKK S C info †f±i ؇qi †f±i ¸Yb = 86 sin 30° = 24 GKK STEP 04 ANALYSIS OF GST QUESTION 01. A = 5ˆ i + 2ˆ j – 3 ˆk Ges B = 15ˆ i + aˆ j – 9 ˆk, a Gi gvb KZ n‡j †f±iØq ci¯úi mgvšÍivj n‡e? [KU. 07-08, SUST. 07-08; CU. 14-15; BUET. 10-11; CU. 12-13] A. 6 B. 3 C. 7 D. 11 S A info †f±iØq ci®úi mgvšÍivj| 5 15 = 2 a ev a = 6 01. y Gi gvb KZ n‡j A = 2ˆ i – 3 ˆ j + ˆk Ges B = 4ˆ i – 6 ˆ j + yˆk ci®úi mgvšÍivj n‡e- [BRUR. 12-13] A. 2 B. – 2 C. 8 D. – 4 S A info A = 2ˆ i – 3 ˆ j + ˆk Ges B = 4ˆ i – 6 ˆ j + yˆk –3 6 = 1 y ev, y = 2 PART B Analysis of Science & Technology Question 01. hw` A = – B nq, Z‡e A × B Gi gvb KZ? [DU-Tech.19-20] A. A2 B. 1 C. 0 D. –A 2 S C info A × B = –BB sin 180 = 0 [†h‡nZz wecix‡Z] STEP 05 ANALYSIS OF HSC BOARD QUESTION 01. = 2 + − 4 I = + 6 − 8 | x I y Gi gvb KZ n‡j A I B ci¯úi mgvšÍivj n‡e? [Xv.†ev. 2019] A. x = 3, y = 4 B. x = 4, y = 3 C. x = 6, y = 2 D. x = 12, y = 1 S A info A I B mgvšÍivj n‡e hLb, Ax Bx = Ay By = Az Bz 2 y = x 6 = –4 –8 GLb, 2 y = –4 –8 Or, x 6 = –4 –8 y = 4 x = 3 02. A = 5 i – 5 j + 3 k; B = 15 i – m j + 9 k; m Gi gvb KZ n‡j A|| B n‡e? [P.‡ev 2021] A. 15 B. –15 C. 16 D. –16 S A info 5 15 = 5 m m = 15 03. A I B mgvšÍivj n‡j G‡`i ga¨eZ©x †Kv‡Yi gvb KZ? [e.‡ev. 2019] A. 0 B. 90 C. 180 D. 270 Ans A Concept 9 WU ¸Yb, µm ¸Yb I †ÿÎdj msµvšÍ MvwYwZK cÖ‡qvM FORMULA 01. hw` A I B †Kvb mvgšÍwiK mwbœwnZ evû nq Z‡e mvgšÍwiK †¶Îdj = | | A × B 02. hw` A I B †Kvb mvgšÍwiK A_ev i¤^‡mi KY© nq Z‡e mvgšÍwiK ev i¤^‡mi †¶Îdj = 1 2 | | A × B 03. hw` A I B †Kvb wÎfz‡Ri evû nq Z‡e wÎfz‡Ri †¶Îdj = 1 2 | | A × B 04. wZbwU †f±i GKB Z‡j nIqvi kZ©: A.( B C) = 0 /( A B). C = 0 / ( A C). B = 0 A_ev, A B C Gi wbY©q‡Ki gvb 0 n‡e| 05. (i) = r F (ii) v = r (iii) L = r P (iv) W = F. S REAL TEST ANALYSIS OF PREVIOUS YEAR QUESTIONS STEP 01 ANALYSIS OF DU QUESTION PART A Analysis of General University Question KU BRUR DU Technology

86 An Exclusive Parallel Text Book of Physics ASPECT PHYSICS ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES we‡kl †ÿÎmg~n: †¯‥jvi ¸Ydj †f±i ¸Ydj hw` = 0 nq, Z‡e P. Q = PQ cos0 = PQ. hw` = 0 nq, Z‡e R = P Q = PQ sin 0 = 0 hw` = 90 nq, Z‡e P. Q = PQ cos90 = 0. hw` = 90 nq, Z‡e R = P Q = PQ sin 90 = PQ hw` = 180 nq, Z‡e P. Q = PQ cos180 = –PQ. hw` = 180 nq, Z‡e R = P Q = PQ sin 180 = 0 Model Example01 A = ˆ i + ˆ j + ˆk Ges B = 3ˆ i + 3ˆ j + 3ˆk †f±Øi GKwU mvgvšÍwi‡Ki `ywU mwbœwnZ KY© wb‡`©k Ki‡j †¶Îdj KZ n‡e? General Rules [Written] 3 in 1 Shortcut Tricks & Tips [MCQ] hw` A I B †Kvb mvgšÍwiK KY© nq Z‡e mvgšÍwiK †¶Îdj = 1 /2 A B mvgšÍwi‡Ki `ywU KY©, A = ˆ i + ˆ j + ˆk Ges B = 3ˆ i + 3ˆ j + 3ˆk n‡j, A B = ˆ i 1 3 ˆ j 1 3 ˆ k 1 3 = ˆ i (3 3) ˆ j (3 3) + ˆk (3 3) = 0 A_©vr mvgšÍwiK †¶Îdj = 1 /2 A B = 0 ASPECT SPECIAL: hw` Ax = Ay = Az Ges Bx = By = Bz nq Zv‡ni G‡`i wbY©vqK Gi gvb k~Y¨ n‡e| A_©vr mvgšÍwi‡Ki †ÿÎdj 0 n‡e| CONCEPTUAL MATH MEx 01 P = 4 ˆ i – 4 ˆ j + ˆk Ges Q = 2 ˆ i – 2 ˆ j – ˆk †f±Øi GKwU mvgvšÍwi‡Ki `ywU mwbœwnZ evû wb‡`©k Ki‡j Gi †¶Îdj n‡e- P = 4 ˆ i – 4 ˆ j + ˆk; Q = 2 ˆ i – 2 ˆ j – ˆk P Q = ˆ i 4 2 ˆ j –4 –2 ˆ k 1 –1 = ˆ i (4 + 2) ˆ j ( 4 2) + ˆk ( 8 + 8) = 6 ˆ i + 6ˆ j + 0.ˆk = 6ˆ i – 6 ˆ j †¶Îdj =| P Q| = (6) 2 + (–6) 2 = 72 = 36 2 = 6 2 MEx 02 A = 4 i + 3 j + k Ges B = 2 i + j + 5 k; A I B †f±iØq GKwU wÎfz‡Ri `ywU mwbœwnZ evû wb‡`©k Ki‡j wÎfzRwUi †ÿÎdj KZ? Avgiv Rvwb, `ywU ‡f±i †Kv‡bv GKwU wÎfz‡Ri `ywU mwbœwnZ evû wb‡`©k Ki‡j H wÎfz‡Ri †ÿÎdj n‡e, †f±i `ywUi µm ¸Yd‡ji gv‡bi A‡a©K| A_©vr 1 2 | A B| = wÎfz‡Ri †ÿÎdj GLb, A B = i j k Ax Ay Az Bx By Bz = i j k 4 3 1 2 1 5 = i ( 15 1) j(20 2) + k ( 4 6) = 14 i 18 j 2 k 1 2 | A B| = 1 2 (14) 2 + (18) 2 + (2) 2 = 11.45 NOW START PRACTICE 01. a Gi gvb KZ n‡j k ˆ j 4 ˆ i 2 ˆ k,3 ˆ j ˆ i ˆ 2 Ges k ˆ j a ˆ i 3 ˆ †f±iÎq GKB mgZ‡j _vK‡e? 02. 3kg f‡ii GKwU MwZkxj KYvi MwZ‡eM v 2i 2j k ˆ ˆ ˆ | KYvi Ae¯’vb †f±i r i j ˆ ˆ n‡j g~jwe›`y mv‡c‡¶ Gi †K․wYK fi‡eM (L) KZ? 03. hw` A = 3 i – k Ges B = i + 2 j GKwU mvgšÍwi‡Ki `ywU mwbœwnZ evû nq, Z‡e mvgšÍwi‡Ki †ÿÎdj KZ ? NOW PRACTICE SOLVE : 01. A B C GKB mgZ‡j _vK‡j Gi wbY©q‡Ki gvb 0 n‡e A_©vr 0 a 5 1 3 a 3 2 4 2 1 1 02. p = m v = 3 (2 i + 2 j k) = 6 i + 6 j 3 k GLb, L= r p = i j k 1 1 0 6 6 3 = 3 i + 3 j 03. A B = i j k 3 0 –1 1 2 0 k ˆ j 6 ˆ i - ˆ 2 | A B| = (2) 2 + (–1) 2 + (6) 2 = 41

ASPECT PHYSICS cÖ_g cÎ †f±i 87 ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES REAL TEST ANALYSIS OF PREVIOUS YEAR QUESTIONS STEP 01 ANALYSIS OF DU QUESTION 01. `yBwU †f±i Ges Gi ga¨eZx© †KvY KZ? [DU.A 19-20] A. 60 B. 30 C. 45 D. 90 S A info A = 3^ i 3 ^ j ; | A| = 3 2 + (3) 2 = 18 B = 5^ i + 5^ k ; | B| = 5 2 + 52 = 25 + 25 = 50 cos = A. B | A| | B| = _ (3 ) ^ i 3 ^ j . (5 ) ^ i + 5^ k 18 . 50 = 15 3 2 5 2 = 1 2 = 60 02. hw` P = ^ i – ^ j + ^ k Ges Q = ^ i + ^ j – ^ k GKwU mvgvšÍwi‡Ki `yBwU mwbœwnZ evû wb‡`©k K‡i, Zvn‡j Dchy³ GK‡K mvgvšÍwi‡Ki †¶Îdj wbY©q Ki| [DU. 15-16] A. 22 B. 2 C.1 D. 2 S A info P = i – j + k Ges Q = i + j - k P Q = i 1 1 j –1 1 k 1 –1 = i(1–1)–j(–1–1)+k(1+1) = 2j+2k | P Q| = 2 2 + 22 = 2 2 mvgšÍwi‡Ki ‡¶Îdj = 2 2 STEP 02 ANALYSIS OF JU QUESTION 01. hw` A = i + j + k Ges B = 2 i +2 j + 2 k nq Z‡e A × B = ? [JU-A, Set-G. 20-21] A. 3 i +2 j +6 k B. 2 i +3 j –7 k C. i +3 j –2 k D. 0 S D info hw` GKwU †f±i Aci †f±‡ii mij ¸wYZK nq A_©vr Ax = Ay = Az Ges Bx = By = Bz nq, Zvn‡j G‡`i wbY©vqK k~b¨| A_©vr | A × B| = 0 KviY, G‡ÿ‡Î sin = 0| STEP 03 ANALYSIS OF CU QUESTION 01. hw` A = ˆ i, B = ˆ j+ ˆk I C = ˆ i + ˆ j + ˆk nq, Z‡e A .(B C ) = ? [CU. 14-15] A. 0 B. 1 C. 2 D. -1 E. -2 S A info A = ˆ i, B = ˆ j+ ˆk, C = ˆ i + ˆ j + ˆk B C = ^ i ^ j ^ k 0 1 1 1 1 1 = 1(1 – 1) = 0 STEP 04 ANALYSIS OF GST QUESTION PART A Analysis of General University Question KU 01. GKwU mvgvšÍwi‡Ki KY© `yBwU h_vµ‡g A = 3i – j + 2k I B = i – 2j + 4k n‡j, mvgšÍwi‡Ki †ÿÎdjKZ? [KU. 18-19] A. 5.59 B. 6.87 C. 7.83 D. 8.79 S A info A B = i 3 1 j –1 –2 k 2 4 = – 10j – 5k ; Area = 1 2 | A | B = 1 2 102 + 52 = 5.59 Part B Analysis of Science & Technology Question MBSTU 01. `yBwU †f±i ci¯úi KZ wWMÖx †Kv‡Y wµqv Ki‡j G‡`i †¯‥jvi ¸Ydj I †f±i ¸Yd‡ji gvb mgvb n‡e? [MBSTU-B, Set-2 19-20] A. 0 B. 45 C. 90 D. 180 S B info ABsin = ABcos tan = 1 = 45˚ 02. †h mgvšÍwi‡Ki mwbœwnZ `ywU evû h_vµ‡g a = 3 i + j 2 k Ges b = i 3 j + 4 k, Zvi †ÿÎdj KZ? [MBSTU-C, Set-2 19-20] A. 23 GKK B. 310 GKK C. 103 GKK D. 204 GKK S C info mvgšÍwi‡Ki †ÿÎdj = |a b| a b = i j k 3 1 2 1 3 4 = i(4 6) j(12 + 2) + k (9 1) = 2 i 14 j 10 k | a b| = (2) 2 + (14) 2 + (10) 2 = 300 = 10 3 BSMRSTU 01. The three vectors are : A = 3 i + 2 j + k, B = i + 2 j + 3 k Ges C = i + j + 2 k Ges A.( B C). [BSMRMU. 2020-21] A. 8 B. 10 C. 21 D. 54 S Blank info B C = i j k 1 2 3 1 1 2 = i (4 – 3) – j(2 – 3) + k(1 – 2) = i + j – k A.( B C) = (3 i + 2 j + k)( i + j – k = 3 + 2 – 1 = 4 STEP 05 ANALYSIS OF ENGINEERING & BUTex QUESTION KUET 01. GKwU mvgvšÍwi‡Ki mwbœwnZ evû `yBwU h_vµ‡g A = (3i + j – 2k )m Ges B = (2i – 2j – k )m| mvgvšÍwi‡Ki †ÿÎdj KZ? [KUET. 18-19] A. 5.92m2 B. 2.76m2 C. 10.39m2 D. 2.96m2 E. 2.56m2 S A info | A | B = ^ i ^ j ^ k 3 1 2 2 2 1 = 5.92m2 02. hw` P = 4i – 4j + k Ges Q = 2i – 2j – k †f±iØq GKwU mvgvšÍwi‡Ki `yBU mwbœwnZ evû wb‡`©k K‡i Z‡e Dnvi †¶Îdj n‡e- [KUET. 06-07] A. 32 sq.unit B. 81 sq.unit C. 72 sq.unit D. 98 sq.unit E. 50 sq.unit S C info P = 4i – 4j + k Ges Q = 2i – 2j – k mwbœwnZ evû a‡i †¶Îdj = ˆ i 4 2 ˆ j –4 –2 ˆk 1 –1 = i (4 + 2) j ( 4 2) = 6i + 6j †¶Îdj = 6 2 + 62 = 72 03. GKwU mvgvšÍwi‡Ki †¶Îdj wbY©q Ki hvi KY©Øq h_vµ‡g A = 3ˆ i – 2 ˆ j + 5 ˆk Ges B = ˆ i + 6ˆ j – ˆk [KUET. 05-06] A. 10.95units B. 17.6units C. 17.66 units D. 15.74 units E. 18.97 units A 3i 3j ˆ ˆ B 5i 5k ˆ ˆ

88 An Exclusive Parallel Text Book of Physics ASPECT PHYSICS ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES S C info A B = ˆ i 3 1 ˆ j –2 6 ˆk 5 –1 = ˆ i(2-30)– ˆ j(–3–5)+ ˆk(18+2) = –28ˆ i + 8ˆ j + 20ˆk | – A – B | = 4 78 †¶Îdj= 1 2 | – A – B | = 4 78 2 = 2 78 = 17.66 Ans. CUET 01. wb¤œwjwLZ ‡f±i ‡cÖvWv‡±i gvb †ei Ki? [CUET. 11-12] (2i – 3j).[( ˆ i + ˆ j – ˆk) (3ˆ i – ˆk)] A. 4 B. 8 C. – 4 D. None S A info (2i – 3j).[( ˆ i + ˆ j – ˆk) (3ˆ i – ˆk)] = 2 1 3 –3 1 0 0 –1 –1 = 2(-1) + 3(-1+3) = - 2 + 6 = 4 STEP 06 ANALYSIS OF MEDICAL & DENTAL QUESTION MAT 01. `ywU †f±i A I B Gi gvb h_vµ‡g 5 I 6 GKK| Giv †Kvb we›`y‡Z 60 †Kv‡Y wµqvkxj| A B gvb KZ? [MAT. 13-14; HSC B.2018] A. 15 2 B. 10 3 C. 15 3 D.15 5 S C info A B = 5 6 sin60 = 15 3 STEP 07 ANALYSIS OF HSC BOARD QUESTION 01. A I B - †K mwbœwnZ evû a‡i Aw¼Z wÎfz‡Ri †ÿÎdj- [iv.‡ev. 2016] A. A . B B. | A . B | C. 1 2 | A B | D. 1 2 (A . B ) Ans C wb‡Pi wP‡Îi Av‡jv‡K 02 I 03 bs cÖ‡kœi DËi `vI : [h. †ev. 2017] A D C B i ˆ j ˆ wP‡Î KY©Øq n‡”Q AC = i ˆ I BD = j ˆ 02. AB †f±‡ii mwVK i~c †KvbwU? A. (i + j )/4 B. (i − j )/2 C. (i + j )/2 D. (i − j )/2 S B info AB = DC = 1 2 (AC ) + BD = 1 2 (i ˆ – j ˆ ) 03. ABCD mvgvšÍwiKwUi †ÿÎdj KZ? A. 0.5 GKK B. 1.0 GKK C. 1.5 GKK D. 2.0 GKK S A info = 1 2 |i ˆ × j ˆ | = 0.5 04. A = 3i 4j + 2k Ges B = 6i + 2j 3k n‡j A B -Gi Rb¨ wb‡Pi †KvbwU mwVK? [Kz. †ev. 2015] A. 18i + 21j + 30k B. 8i + 21j + 18k C. 8i + 3j + 30k D. 8i + 21j + 30k S D info A B = i ˆ j ˆ k ˆ 3 –4 2 6 2 –3 = i ˆ (12 – 4) j ˆ (– 9 – 12) + k ˆ (6 + 24) = 8i ˆ + 21j ˆ + 30k ˆ 05. hw` A = B nq, Z‡e A B -Gi gvb n‡e- [wm. †ev. 2016] A. A 2 B. 1 C. B 2 D. 0 Ans D 06. wb‡Pi †KvbwU X-A‡ÿi mgvšÍivj? [wm. †ev. 2015] A. (i j ) i B. (i j ) k C. (i j ) j D. (k j ) k Ans C 07. ( ^ j+ ^ k) ^ k = KZ? [e. †ev. 2015] A. 1 B. ^ i C. ^ j D. ^ k Ans B wP‡Îi wb‡`©kbvi Av‡jv‡K 08 I 09 bs cÖ‡kœi DËi `vI : [e. †ev. 2016] 08. O C †f±i †KvbwU? A. i +j B. j + k C. i + k D. i + j + k S A info wPÎvbyhvqx, GUv ¯úó †h, OC †f±iwU XY mgZ‡j Aew¯
Z| myZivs OC Gi Z, Dcvs‡ki gvb k~b¨ n‡e A_©vr k ˆ _vK‡e bv| 09. OABC †ÿ‡Îi †ÿÎdj A. 1 2 B. 2 C. 2 D. 2 2 S B info OB = i ˆ + j ˆ + k ˆ Ges OC = i ˆ + j ˆ ; OB , OC Ges OA Gi jwä A_©vr OA + OC = OB OA = OB – OC OA = (i ˆ + j ˆ + k ˆ ) – (i ˆ + j ˆ ) = k ˆ GLb, OABC †ÿ‡Îi †ÿÎdj = |OA × OC | = 2 Concept 10 Awf‡ÿc I Dcvsk msµvšÍ MvwYwZK cÖ‡qvM 01. A eivei B Gi j¤^ Awf‡ÿc, Bcos = A . B | | A = a B 02. B eivei A Gi j¤^ Awf‡ÿc, Acos = A . B | | B = A b 03. A eivei B Gi Dcvsk = A . B | | A a [ a = A | | A ] 04. B eivei A Gi Dcvsk = A . B | | B b [ b = B | | B ] 05. Uvbvi mgq IRb †Vjv A‡c¶v Kg n‡e = 2F sin [Note:] (i) Awf‡ÿc : †¯‥jvi ivwk (ii) Dcvsk : †f±i ivwk ◈ Awf‡ÿc I Dcvsk welqK m~Îvejx| (D‡jøL¨ Dcvsk‡K AskKI ejv nq|) [hvi Awf‡ÿc Zvi cos, hvi w`‡K/eivei Zvi GKK †f±i g‡b ivL‡e hv j¤^ Awf‡ÿc †m wb‡RB cos] FORMULA

ASPECT PHYSICS cÖ_g cÎ †f±i 89 ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES CONCEPTUAL MATH MEx 01 A = 2 i + j + k, B = –2 i – j + 3 k n‡j B eivei A Gi Dcvsk KZ? A . B | | B b = –4 –1 + 3 14 –2 i – j + 3 k 14 = – 2 14 (2 i – j + 3 k) = – 1 7 (–2 i – j + 3 k) MEx 02 . ˆ , ˆ 4 ˆ 2 ˆ A 3i ˆ ˆ j 3k B i j k A eivei B Gi Awf‡¶c KZ? A eivei B Gi Awf‡¶c, Bcos = A A.B = 3.1 + (–4) (–1) + 3.2 3 2 + (–1) 2 + 32 = 13 19 NOW START PRACTICE 01. A = i + 2 j + k †f±iwUi B = i + j †f±i Awfgy‡L AskK KZ? 02. A = 2 i + 2 j + k Ges B = 6 i – 3 j +2 k n‡j B eivei A Gi Awf‡¶c KZ n‡e? NOW PRACTICE SOLVE : 01. AskK Gi gvb, Acosθ = A.B |B | = 1+ 2 + 0 1 2 + 12 = 3 2 02. A = 2 i + 2 j + k, B = 6 i – 3 j +2 k; B eivei A †f±‡ii Awf‡¶c = A.B |B | = 12 – 6 + 2 (6) 2 + (– 3) 2 + (2) 2 = 8 7 REAL TEST ANALYSIS OF PREVIOUS YEAR QUESTIONS STEP 01 ANALYSIS OF DU QUESTION 01. GKwU Kv‡Vi LÛ‡K Avbyf‚wg‡Ki mv‡_ 60 †Kv‡Y 200N ej Øviv Uvbv n‡”Q| e¯‘wUi Dci Avbyf‚wg‡Ki w`‡K Kvh©Kvix ej KZ? [DU. 13-14, JKKNIU. 19-20] A. 200N B. 100 N C. 174 N D. zero S B info ej GKwU †f±i ivwk| AbyfwzgK w`‡K e†ji Dcvs‡ki gvb, Fx = Fcos = 200 cos600 = 100N STEP 02 ANALYSIS OF JU QUESTION 01. GKwU jb‡ivjvi Uvbv I †Vjvi Rb¨ Avbyf~wgKfv‡e 30 †Kv‡Y 20N ej cÖ‡qvM Kiv n‡jv| Uvbvi mgq IRb †Vjv A‡c¶v Kg n‡e- [JU. 15-16] A. 20N B. 10N C. 15 N D. †KvbwUB bq S A info jb †ivjvi †Vjvi †¶‡Î †gvU IRb = W+F sin jb †ivjvi Uvbvi †¶‡Î †gvU IRb = W– F sin Uvbvi mgq IRb †Vjv A‡c¶v Kg n‡e = W+F sin – (W–F sin) = 2F sin = 2×10×sin30°= 20N STEP 03 ANALYSIS OF GST QUESTION PART A Analysis of General University Question KU 01. †Kvb ¯’v‡b evZvm 20Km/h †e‡M cwðg w`‡Ki mv‡_ 60° †Kv‡b `w¶b w`K †_‡K eB‡Q| evZv‡mi †e‡Mi DËi gyLx Dcvs‡ki gvb KZ? [KU. 12-13] A. 17.32Km/h B. 10Km/h C. 12Km/h D. 8 Km/h S A info VN = Vsin60° = 20 3 2 = 17.32 Km/h CoU 01. GKwU jb †ivjvi Uvbv ev †Vjvi Rb¨ Abyf~wg‡Ki mv‡_ 30 †Kv‡Y 19.6N ej cÖ‡qvM Kiv n‡jv| Uvbvi mgq IRb †Vjv A‡cÿv KZ Kg n‡e? [CoU. 18-19] A. 21.6N B. 18.6N C. 19.6N D. 17.6N S C info Uvbvi †ÿ‡Î AvcvZ IRb = w – Fy †Vjvi †ÿ‡Î AvcvZ IRb = w + Fy AwZwi³ IRb = 2Fy = 2 19.6 sin30 = 19.6 Or, 2Fsin = 2 19.6 1 2 = 19.6 02. B eivei A Gi j¤^ Awf‡¶c ‡KvbwU? [CoU. 15-16] A. Bcos B. Acos C. Bsin D. Asin Ans B PART B Analysis of Science & Technology Question MBSTU 01. j + 2 k †f±iwU X-A‡ÿi mv‡_ KZ wWMÖx †Kv‡Y AvbZ? [MBSTU-C, Set-2 19-20] A. 0 B. 45 C. 90 D. †KvbwUB bq = cos–1 0 5 = 90 STEP 04 ANALYSIS OF HSC BOARD QUESTION 01. A, X A‡ÿi mv‡_ 30 †Kv‡Y wµqvkxj| Y-Aÿ eivei Dcvs‡ki gvb 3 GKK n‡j X-Aÿ eivei Dcvs‡ki gvb- [iv. †ev. 2016] A. 3 2 GKK B. 3 GKK C. 3 3 GKK D. 6 GKK S C info Ay = A sin30˚ A cos60˚ = 3 A = 3 cos60˚ Ax = A cos30˚ = 6 × 3 2 = 3 3 02. wPÎvbyhvqx Gi Dci Gi Awf‡ÿc KZ? [w`.‡ev. 2019] A. . B. × C. . D. × Ans A

90 An Exclusive Parallel Text Book of Physics ASPECT PHYSICS ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES 03. A I B Gi ga¨eZ©x †KvY Ges A Gi w`‡K GKwU GKK †f±i a n‡j A Gi Dci B Gi j¤^ Awf‡ÿc n‡jv- [Kz.‡ev 2021] i. Acos ii. Bcos iii. B. a wb‡Pi †KvbwU mwVK? A. i B. ii C. i I iii D. ii I iii S B info A Gi Dci B Gi j¤^ Awf‡ÿc, Bcos = A . B | A| Or Bcos = B . a a = A | – A| 04. wP‡Î A I B †h Z‡j Av‡Q POQ †mB Z‡ji Dci j¤^| A B Gi w`K- [Kz.‡ev 2021] Q O P A B A. OP Gi w`‡K B. OQ Gi w`‡K C. A Gi mgvšÍivj D. B Gi mgvšÍivj Ans A 05. 10N Gi GKwU ej‡K j¤^ Dcvs‡k wefvwRZ Ki‡j OY Gi gvb KZ?[Kz.‡ev 2021] Y O 4N 10N X A. 4N B. 9N C. 12N D. 14N S B info (OX)2 + (OY)2 = R2 [ = 90] (OY) = R2 – (OX)2 = 102 – 4 2 = 100 – 16 OY = 9.16 9N 06. wPÎvbymv‡i wPÎ Q -Gi Ici P -Gi Awf‡ÿc- [Kz. †ev. 2019; Xv. †ev. 2016] P Q A. Q cos B. P cos C. P sin D. Q sin Ans B 07. I Gi ga¨eZx© †KvY n‡j Gi Dci Gi j¤^ Awf‡ÿcÑ [Kz.‡ev. 2019] A. A sin B. A cos C. B sin D. B cos Ans D 08. 10 GKK gv‡bi GKwU †f±i `ywU j¤^ Dcvs‡k wef³ Kivq GKwUi gvb 8 GKK n‡j AciwUi gvb KZ? [g.‡ev 2021] A. 2 GKK B. 4 GKK C. 6 GKK D. 8 GKK S C info RX 2 + RY 2 = R2 RY 2 = R2 – RX 2 = 102 – 8 2 RY = 36 = 6 09. hw` A = i + j + k Ges B = 2 i + 2 j + 2 k nq n‡e B eivei A Gi j¤^ Awf‡ÿc KZ? [g.‡ev 2021] A. 1 3 B. 3 C. 2 3 D. 2 3 S B info B eivei A Gi j¤^ Awf‡ÿc, Acos = B. A | B| = 2 + 2 + 2 2 2 + 22 + 22 = 3 Concept 11 WvBfvi‡RÝ, †MÖwW‡q›U, Kvj© msµvšÍ MvwYwZK cÖ‡qvM 01. MÖvwW‡q›U : = x i + y j + z k 02. WvBfvi‡RÝ : . v = vx x + vy y + vz z 03. Kvj©: V = i j k x y z Vx Vy Vz CONCEPTUAL MATH MEx 01 (x, y, z) = 3xy2 z 3 4xy nq Z‡e (grad ) †ei Ki| ( we›`y‡Z KZ n‡e? GLv‡b, (x, y, z) = 3xy2 z 3 4xy Avgiv Rvwb, = i x + j y + k z (3xy2 z 3 4xy) = i x (3xy2 z 3 4xy) + j( y (3xy2 z 3 4xy) + k z (3x2 yz 3 4xy); = (3y2 z 3 4y) i + (6xyz3 4x) j + (9xy2 z 2 ) k GLb, (2, 1, 1) we›`y‡Z = {(3 (1)2 1 3 4 (1)} i + {6 2 (–1) 1 3 4 j + (9 2 2 (1)2 1 2 } k = 7 i –20 j – 18 k MEx 02 †`Iqv Av‡Q, r = i cos 5t + j sin 5t| †`LvI †h, r †f±‡ii †ÿÎwU mwjbqWvj| GLv‡b, = i x + j y + k z ; r = icos 5t + j sin 5t †`Lv‡Z n‡e †h, . r = 0 Avgiv Rvwb, †Kv‡bv †f±i †ÿÎ mwjbqWvj n‡e hw` Gi WvBfvi‡RÝ k~b¨ nq A_©vr, . r = 0 n‡j| GLb, r = i x + j y + k z . (rx i + ry j rz k) i x + j y + k z . ( i cos 5t + j sin 5t) x cos 5t + y sin 5t + z 0 = 0 + 0 + 0 = 0 . r = 0 r †f±i †ÿÎwU mwjbqWvj| FORMULA

ASPECT PHYSICS cÖ_g cÎ †f±i 91 ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES MEx 03 Ae¯’vb †f±i r = x i + y j k n‡j Gi WvBfvi‡RÝ wbY©q Ki| GLv‡b, = i x + j y + k z r = x i + y j k ; . r = ? Avgiv Rvwb, Ae¯
vb †f±i Gi WvBfvi‡RÝ n‡”Q . r = i x + j y + k z . (x i + y j k) x x + y y + (2) z = 1 + 1 + 0 = 2 NOW START PRACTICE 01. Ae¯’vb †f±i r = x i + y j z k n‡j †`LvI †h, . r = 3 02. Ae¯’vb †f±i r = 2 i + 3 j 2 k n‡j †`LvI †h, †f±i r mwjbqWvj| NOW PRACTICE SOLVE : 01. GLv‡b, Ae¯
vb †f±i r = x i + y j z k = i x + j y + k z . r = ? Avgiv Rvwb, . r = i x + j y + k z . (x i + y j z k) = x x + y y + (2) z = 1 + 1 + 1 = 3 02. GLv‡b, Ae¯
vb †f±i r = 2 i + 3 j 2 k; = i x + j y + k z †`Lv‡Z n‡e †h, div r = 0 Avgiv Rvwb, †Kv‡bv †f±‡ii WvBfvi‡RÝ k~b¨ n‡j †f±iwU mwjbqWvj| div r = . r = i x + j y + k z (2 i + 3 j 3 k) (2) x + y (3) + z (2) 0 + 0 + 0 = 0 div r = 0 r = mwjbqWvj| REAL TEST ANALYSIS OF PREVIOUS YEAR QUESTIONS STEP 01 ANALYSIS OF RU QUESTION 01. r = 2 i + j + 2 k n‡j . r = KZ? [RU. Moderna, Set-2. 20-21] A. 0 B. 17 C. 7 D. †KvbwUB bq S A info . r = x i + y j + z k . (2 i + j + 2 k) = 0 [ n‡jv †f±i Acv‡iUi] STEP 02 ANALYSIS OF CU QUESTION 01. Ae¯’vb †f±i r = 3xi ˆ + 2yj ˆ + 4zkˆ-Gi WvBfvi‡RÝ KZ? [CU-A, 19-20] A. 9 B. 24 C. 5 D. 9xyz S A info .r = x i + y j + z k . (3xi ) + 2yj + 4zk = 3 + 2 + 4 = 9 02. Ae¯’vb †f±i r = 3xi – 2yj + 2zk = n‡j . r = ? [CU. 18-19] A. 9 B. 5 C. 10 D. 12 S B info x i + y j + z k (3xi – 2yj + 4zk ) = 3 – 2 + 4 = 5 STEP 03 ANALYSIS OF GST QUESTION PART A Analysis of Science & Technology Question NSTU 01. Ae¯’vb †f±i r = x i + y j + z k n‡j, ▽. r = ?[NSTU-A, 19-20; Kz.†ev. 2016] A. 1 B. 9 C. 3 D. 4 S C info . r = x i + y j + z k . (x i + y j + z k) = x x + y y + z z = 1 + 1 + 1 = 3 STEP 04 ANALYSIS OF HSC BOARD QUESTION DÏxcKwU c‡o 01 I 02 bs cÖ‡kœi DËi `vI : [w`. †ev. 2015] †Kv‡bv MwZkxj KYvi †Kv‡bv gyn~‡Z©i Ae¯
vb †f±i r= ^ i cos5t + ^ j sin 5t. 01. KYvi ZvrÿwYK †eM v n‡eÑ A. 5 (^ j cos 5t - ˆi sin 5t) B. ( ^ j cos 5t + ^ i sin 5t) C. 5 (^ i cos 5t + ^ j sin 5t) D. 5 (^ j cos 5t + ^ i sin 5t) S A info v = d dt ( r) = d dt (i ˆcos 5t + j ˆ sin 5t) = – i ˆ sin 5t.5 + j ˆ cos 5t.5 = 5 (j ˆ .cos 5t – i ˆ sin 5t) 02. r†f±‡ii †ÿÎwU n‡jvÑ i. mwjbqWvj ii. AN~Y©bkxj iii. N~Y©bkxj wb‡Pi †KvbwU mwVK? A. i B. i I ii C. i I iii D. i, ii I iii S B info . r = 0 n‡j mwjbqWvj; × r = 0 n‡j AN~Y©bxj| 03. hw` r = xi + yj 2k nq Z‡e . r KZ? [Kz. †ev. 2015] A. 1 B. 2 C. 3 D. 4 S B info . r = x i ˆ + y j ˆ + z k ˆ . (x ^ i + y ^ j – 2 ^ k) = x (x) + y (y) + z (– 2) = 1 + 1 + 0 = 2 04. hw` Q(x, y) = 3x2 y nq, Z‡e (1, 2) we›`y‡Z Q wbY©q Ki| [wm. †ev. 2016] A. 6i 3j B. 12i + 3j C. 3i + 6j D. 6i +12j S B info Q = x i ˆ + y j ˆ + z k ˆ (3x2 y) = 6xy i ˆ + 3x2 j ˆ + 0 = 6xy i ˆ + 3x2 j ˆ (1, – 2) we›`y‡Z Q = 6 × 1 × (–2) × i ˆ + 3 × 12 j ˆ = – 12i ˆ + 3j ˆ

92 An Exclusive Parallel Text Book of Physics ASPECT PHYSICS ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES SAQ Short Answer Questions WRITTEN PART BAQ Broad Answer Questions 01. Ae¯’vb †f±i r = 2ˆ i + 3ˆ j ej‡Z Kx †evSvq? Solve Ae¯
vb †f±i r = 2ˆ i + 3ˆ j ej‡Z †evSvq, wØ-gvwÎK ¯
vbvsK e¨e¯
vq r GKwU Ae¯
vb †f±i| X A‡ÿi w`‡K †f±‡ii Dcvs‡ki gvb 2 GKK Ges Y-A‡ÿi w`‡K †f±‡ii Dcvs‡ki gvb 3 GKK| 02. `ywU mgvb gv‡bi †f±i n‡Z k~b¨ †f±i †c‡Z n‡j †f±i ؇qi ga¨eZ©x †KvY KZ nIqv cÖ‡qvRb? Solve Avgiv Rvwb, = 180 n‡j Rmin = P Q ; P = Q n‡j R = 0 03. wÎfz‡Ri wZbwU evû hw` GKB µ‡g wZbwU †f±i‡K wb‡`©k K‡i Zvn‡j †f±i·qi jwä k~b¨ nq †Kb? e¨vL¨v K‡iv| Solve wÎfz‡Ri wZbwU evû hw` GKB µ‡g wZbwU mgRvZxq †f±i‡K wb‡`©k K‡i Zvn‡j †f±i †hv‡Mi wÎfzR m~Îvbymv‡i †h‡Kv‡bv `ywU †f±‡ii jw× Z…Zxq †f±iwUi mgvb I wecixZ nq| awi, †Kv‡bv wÎfz‡Ri wZbwU evû Øviv GKB µ‡g wZbwU mgRvZxq †f±i A, B, Cwb‡`©wkZ nq| G‡ÿ‡Î A I B ‡f±i؇qi jw× R n‡j, R = A+ B Ges R = – C A + B = – C ev, A + B + C = 0 G Kvi‡YB †f±i·qi jw× k~b¨ nq| 04. i + j †f±‡ii w`‡K A = 2 i + 3 j †f±‡ii Dcvsk wbY©q Ki| Solve awi, A = 2 i + 3 j; B = i + j; b = 1 2 ( i + j) wb‡Y©q Dcvsk = b A.B |B| = 1 2 ( i + j). 1 2 . (2 + 3) = 5 2 ( i + j) 05. ci¯ú‡ii mv‡_ j¤^fv‡e wµqvkxj `yBwU e‡ji jwä 80N| hw` jwä GKwU e‡ji m‡½ 60 ‡Kv‡Y AvbZ _v‡K, Z‡e ej `yBwUi gvb wbY©q Ki| Solve GLb R cos60 = P cos0 + Q cos90 P = 80 cos60 = 40N Avevi, R sin60 = P sin0Q sin90 Q = 80 sin60 = 40 3N 06. GKwU BwÄb PvwjZ †b․Kvi †eM N›Uvq 14 wK‡jvwgUvi| GKwU b`x AvovAvwo cvi n‡Z n‡j †b․KvwU‡K †Kvb w`‡K Pvjv‡Z n‡e? b`xi cÖ¯’ 12.125km n‡j Zv cvwo w`‡Z KZ mgq jvM‡e? †¯ªv‡Zi †eM N›Uvq 7km| Solve P + Q cos = R cos 90 7 + 14 cos = 0 cos = – 1 2 = 120 R = P 2 + Q2 + 2PQ cos = 7 2 + 142 + 2.7.14 cos 120 = 12.124 kmh–1 t = 12.125 12.124 = 1 hour †b․KvwU‡K †¯ªv‡Zi †e‡Mi mv‡_ 120 †Kv‡Y Pvjv‡Z n‡e| 07. j¤^ Awf‡ÿc A = 2 i + 2 j – k Ges B = 2 i + j – 2 k n‡j B eivei A Gi j¤^ Awf‡ÿc wbY©q Ki| Solve B eivei A Gi j¤^ Awf‡ÿc Acos A. B = ABcos Acos = A. B | B| Acos = (2 i + 2 j – k).(2 i + j – 2 k) 2 2 + 12 + (–2) 2 = 4 + 2 + 2 3 = 8 3 08. A = 2 i + 4 j – 5 k I B = i + 2 j + 3 k n‡j A I B ‡f±iØq †h mgZ‡j Aew¯’Z Zvi j¤^ eivei GKK †f±i wbY©q Ki? Solve A I B †h mgZ‡j Aew¯
Z Zvi j¤^ eivei GKK †f±i = A B | A B| A B = i 2 1 j 4 2 k –5 3 = i(12 + 10) – j(5 + 6) + k(4 – 4) = 22 i 11 j | A B| = 222 + (– 11) 2 = 605 j¤^ GKK †f±i, = A B | A B| = 22 605 i 11 605 j 09. aªæeK a Gi gvb KZ n‡j A = 3 i – 4 j + a k, B = 2 i – j + k I C = i + 2 j – 3 k GKB mgZ‡j Aew¯’Z n‡e? Solve A, B I C GKB mgZ‡j Aew¯
Z n‡e hw` A.( B C) = 0 nq, ev, 3 2 1 –4 –1 2 a 1 –3 = 0 3 – 28 + 5a = 0 5a = 25 a = 5 10. `ywU e‡ji e„nËg jwä 7N Ges ÿz`ªZg jwä 1N ej `ywU ci¯ú‡ii mv‡_ 90 †Kv‡Y GKwU KYvi Dci wµhv Ki‡j jwäi gvb KZ n‡e? Solve cÖkœg‡Z, P + Q = 7N ...... (i) Ges P – Q = 1N ....... (ii) (i) + (ii) P + Q + P – Q = 8N 2P = 8N P = 4N (i) – (ii) P + Q – P + Q = 6N 2Q = 6N Q = 3N Avgiv Rvwb, = 90 n‡j, jwäi gvb R = P 2 + Q2 = 4 2 + 32 N = 25N = 5N 11. `ywU †f±i ivwki e„nËg jwä 28 GKK I ÿz`ªZg jwä 4 GKK| ivwk `ywU ci¯ú‡ii mv‡_ wKfv‡e wµqv Ki‡j jwäi gvb ÿz`ªZg jwäi cuvP¸Y n‡e| Solve e„nËg jwä P + Q = 28 ........... (i) ÿz`ªZg jwä P – Q = 4 ............ (ii) (i) + (ii) P + Q + P – Q = 32 2P P = 16 (i) – (ii) P + Q – P + Q = 24 2Q Q = 12 kZ©g‡Z, R = 5 (P – Q) R = 4 5 = 20 R 2 = P2 + Q2 + 2PQ cos (20)2 = (16)2 + (12)2 + 2 16 12 cos = 90 PQ 12. 10 wK‡jvwgUvi/N›Uvq e„wó co‡Q Ges 60 wK‡jvwgUvi/N›Uvi c~e© n‡Z cwð‡g evZvm eB‡Q| c~e© n‡Z cwðg AwfgyLx PjšÍ Mvwoi MwZ‡eM wbY©q Ki hv‡Z (a) Mvoxi mvg‡bi I wcQ‡bi KuvP wf‡R (b) ïaygvÎ wcQ‡bi KuvP wf‡R| Solve (a) e„wói jwä ‡e‡Mi Avbyf~wgK Ask 60 km/h 60 km/h †e‡M Mvwo Pj‡j mvg‡b I wcQ‡bi KuvP wfR‡e| (b) 60 km/h Gi †P‡q Kg †e‡M Pj‡j ïaygvÎ wcQ‡bi KuvP wfR‡e 13. †Kvb we›`y‡Z wµqviZ 1N, 2N, 5 N ejÎq mvg¨e¯’vq _vK‡j, ÿz`ªZg ej؇qi AšÍM©Z †KvY KZ n‡e? Solve GLv‡b, 1N I 2N ej؇qi jwä = 1 2 + 22 = 1 + 4 = 5N R 2 = P2 + Q2 + 2PQ cos ( 5) 2 = 12 + 22 + 2.1.2.cos 5 = 1 + 4 + 4 cos 4 cos = 0 cos = 0 = 90 14. b Gi KZ gv‡bi Rb¨ †f±i v = (x + 3y) i + (by – z) j + k(x – 2z) mwjbqWvj n‡e? Solve . v = i x + j y + k z .{(x + 3y) i + (by – z) j + (x – 2z) k} = 1 + b – 2 = b – 1 . v = b – 1 = 0 b = 1 b = 1 n‡j v ‡Pv½vK…wZ ev mwjbqWvj n‡e|

ASPECT PHYSICS cÖ_g cÎ †f±i 93 ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES 15. cÖgvY Ki †h, (A .B ) 2 + (A B ) 2 = A2B 2 Solve Avgiv Rvwb, A . B = AB cos [GLv‡b, n‡jv †f±i؇qi AšÍfz©³ †KvY] Ges A B = AB sin (A .B ) 2 + (A B ) 2 = (AB cos) 2 + (AB sin) 2 = A 2B 2 cos2 + A2B 2 sin2 = A2B 2 (cos2 + sin2 ) = A2B 2 16. P = 2i + 3j – 4k Ges Q = – 2j + i + 3k †f±iØq †h Z‡j Ae¯’vb K‡i Zvi Djø¤^ †_‡K GKwU GKK †f±i wbY©q Ki| Solve P Q GKwU †f±i hv P Ges Q -Gi Z‡j j¤^| P Q = i 2 1 j 3 –2 k –4 3 = i (9 – 8) j (4 + 6) + k (–4 – 3) = i – 10j – 7k g‡b Kwi, P I Q †h Z‡j Aew¯
Z Zvi j¤^ Awfgy‡L GKK †f±i ivwk = = P Q | P Q | = i – 10j – 7k (1) 2 + (–10) 2 + (–7) 2= i – 10j – 7k 1 + 100 + 49 = i – 10j – 7k 150 17. GKwU N~Y©biZ KYvi e¨vmva© †f±i r = (2i + 2j – k )m Ges cÖhy³ ej F = (6i + 3j – 3k ) N n‡j U‡K©i gvb I w`K wbY©q Ki| Solve Avgiv Rvwb, = r F = i 2 6 j 2 3 k –1 –3 = i (–6 + 3) – j (– 6 + 6) + k (6 – 12) = – 3i – 6k GLv‡b, e¨vmva© †f±i, r = (2 i + 2j – k )m ej, F = (6i + 3j – 3k )N UK©, = ? U‡K©i gvb, = ? = (– 3i 6k ) N-m -Gi gvb = (–3) 2 + (–6) 2 = 9 + 36 = 45 18. GKwU mvgvšÍwi‡Ki †ÿÎdj wbY©q Ki hvi KY© `yBwU h_vµ‡g A = 3i + j – 2k Ges B = i – 3j + 4k Solve Avgiv Rvwb, mvgvšÍwi‡Ki †ÿÎdj = 1 2 |A B | A B = i 3 1 j 1 –3 k –2 4 = i (4 – 6) – j (12 + 2) + k (– 9 – 1) = – 2i – 14j – 10k 1 2 |A B | = 1 2 (–2) 2 + (–14) 2 + (–10) 2 = 1 2 300 = 8.66 19. (1, –1, 1) Ae¯’v‡b A = 3xyz3 i + 2xy2 j – x 3 y 2 zk -Gi WvBfvi‡RÝ wbY©q Ki| Solve Avgiv Rvwb, . A = x i + y j + z k . (3xyz3 i + 2xy2 j – x 3 y 2 zk ) = x (3xyz3 ) + y (2xy2 ) + z (–x 2 y 2 z) = 3yz3 + 4xy – x 3 y 2 (1, –1, 1) Ae¯
v‡b, . A = 3(–1) (1)3 + 4(1) (–1) – (1)3 (–1)2 = – 3 – 4 – 1 = – 8 20. (–1, 1, –1) we›`y‡Z A = 3xz2 i + yzj – xz 3 k Gi Kvj© wbY©q Ki| Solve A = i x 3xz2 j y yz k z –xz 2 y (–xz 3 ) – z (yz) i + z (3xz2 ) – x (–xz 3 ) j + x (yz) – y (3xz2 ) k = (–y)i + (6xz + z3 ) j (–1, 1, –1) we›`y‡Z, A = [ (1)] i + [6(–1) (–1) + (1)3 ] j = i + 5j 21. hw` A = i – j + k Ges B = i + j – k GKwU mvgvšÍwi‡Ki `yBwU mwbœwnZ evû wb‡`©k K‡i, Zvn‡j Dchy³ GK‡K mvgvšÍwi‡Ki †ÿÎdj wbY©q Ki| Solve hw` A B = i Ax Bx j Ay By k Az Bz = i 1 1 j –1 1 k 1 –1 = i (1– 1) – j (–1 – 1) + k (1 + 1) = 2j + 2k mvgvšÍwi‡Ki †ÿÎdj = |A B | = 2 2 + 22 = 2 2 22. GKwU jb †ivjv‡ii IRb 1000 N Ges Gi nvZjwUi IRb †ivjv‡ii IR‡bi Zzjbvq bMY¨| nvZjwU 100 N e‡j (i) Abyf‚wg‡Ki mv‡_ 30 †Kv‡Y †Vj‡j Ges (ii) Abyf‚wg‡Ki mv‡_ 30 Uvb‡j †ivjviwUi IR‡bi Kxiƒc cwieZ©b NU‡e? Solve (i) G‡ÿ‡Î cÖhy³ evwn¨K e‡ji Dj¤^ Dcvsk †ivjv‡ii IR‡bi mv‡_ hy³ n‡e| myZivs, †ivjv‡ii IRb e„w×, W = F sin ev, W = (100 N) sin 30 W = 50 N (ii) G‡ÿ‡Î cÖhy³ evwn¨K e‡ji Dj¤^ Dcvsk †ivjv‡ii IRb n‡Z we‡qvM n‡e| myZivs, †ivjv‡ii IRb n«vm, W = F sin = (100 N) sin 30 = 50 N W = 50N 23. †`LvI †h, F = yz ^ i + zx^ j + xy^ k ejwU msiÿYkxj ej| Solve F ejwU msiÿYkxj n‡j F = 0 n‡e, GLb, F = ^ i ^ j ^ k x y z yz zx xy = ^ i y (xy) z (zx) ^ j x (xy) z (yz) + ^ k x (zx) y (yz) = ^ i (x x) ^ j (y y) + ^ k (z z) = 0 0 + 0 = 0 A_©vr, F = 0; A_©vr F †f±i msiÿYkxj| 24. GKwU evbi Dj¤^ GKwU LywU a‡i 5m/s `ªæwZ‡Z Dc‡i DVwQ‡jv| GKwU KzKzi LywUwUi w`‡K 10m/s `ªæwZ‡Z †`․ovw”Qj| evbi mv‡c‡ÿ KzKz‡ii †eM KZ? m m R d

94 An Exclusive Parallel Text Book of Physics ASPECT PHYSICS ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES ASPECT SERIES Solve awi, evb‡ii †eM Vm , KzKz‡ii †eM Vd Ges evb‡ii mv‡c‡ÿ KzKz‡ii †eM, VR; myZivs VR = Vd + ( ) Vm = Vd Vm VR Gi gvb | | VR = (Vd) 2 + ( Vm) 2 = (10 m/s) 2 + ( 5 m/s) 2 = 125 m2 /s2 = 5 5 m/s Abyf‚wg‡Ki w`‡K VR hw` †KvY Drcbœ K‡i, Zvn‡j tan = Vm Vd = 5 m/s 10 m/s = 1 2 ev, = tan1 1 2 25. `ywU e‡ji e„nËg jwä 7N Ges ÿz`ªZg jwä 1N; ej `ywU ci¯ú‡ii mv‡_ 90 †Kv‡Y GKwU KYvi Dci wµqv Ki‡j jwäi gvb KZ n‡e? [RU-C, Set-3. 19-20] Solve awi, ej `ywU P I Q Ges jwä R GLv‡b, P + Q = 7 (+ K‡i) P – Q = 1 2P = 8 P = 4; Q = 3 jwä, R = 4 2 + 32 + 2.4.3.cos 90˚ R = 5N weKí c×wZ: Avgiv Rvwb, Rmax 2 + Rmin 2 = 2RP 2 7 2 + 12 = 2RP 2 2RP 2 = 50 RP 2 = 25 RP = 5 26. GKwU G‡iv‡cø‡bi cvBjU 288 km/h †e‡M Abyf~wgKfv‡e ågYKv‡j e›`yK †_‡K ¸wj K‡ib| 3 seconds c‡i f~wg †_‡K Zvi cÖwZaŸwb †kvbv hvq| hw` k‡ãi †eM 350 ms–1 nq, Z‡e G‡iv‡cø‡bi D”PZv wbY©q Ki| [RUET: 19-20] Solve cvBjU A we›`y‡Z ¸wj K‡i, B †Z wM‡q cÖwZaŸwb ï‡b| kã f~wgi C we›`y‡Z cÖwZdwjZ nq| G‡ÿ‡Î, AD = BD : AC = BC h A D B C AB = vt = 288 3.6 3 = 240 m AD = BD = 120 m AC = BC = vt = 350 3 2 = 525 m h = AC2 – AD2 = 5252 – 1202 = 511.1 m 27. Ggb GKwU GKK †f±i wbb©q Ki hv xy Z‡ji mgvšÍivj Ges (i – j + k) †f±‡ii mg‡KvY Aew¯’Z? [BUTex. 2020-21] Solve awi, X – Y Z‡j GKwU GKK †f±i, – A = x i + y j cÖkœg‡Z, (x i + y j). ( i – j + k) = 0 x – y = 0 x y GLb, | – A| = 1 x 2 + y2 = 1 x 2 + x2 = 1 x = 1 2 = y †f±i, – A = i + j 2 28. B = ˄ i + ˄ j †f±‡ii w`‡K A = 2˄ i + 3˄ j †f±‡ii Dcvsk wbY©q Ki| [BUET; 19-20] Solve awi, A = 2˄ i + 3˄ j; B = ˄ i + ˄ j; ˄ b = 1 2 ( ˄ i+ ˄ j) B eivei A Gi Dcvsk, Acos = A.B |B| ˄ b = 1 2 . (2 + 3) . 1 2 ( ˄ i+ ˄ j) = 5 2 ( ˄ i+ ˄ j) STEP 3 mKj cvV¨eB‡qi NCTB QUESTIONS ANALYSIS cÖkœ e¨vLvmn mgvavb cÖkœ 01. †Kvb `ywU †f±i ivwk? [Bm&nvK, Avwgi] A. MwZkw³, †eM B. Zwor wefe, Z¡iY C. ‡K›`ªgyLx Z¡iY, ZvcgvÎv D. Zwor †ÿÎ, ej Ans D 02. GKB we›`y‡Z GKB mg‡q wµqviZ wZbwU mgZjxq †f±i ivwk‡K †Kv‡bv wÎfz‡Ri wZbwU evû Øviv GKB µ‡g wb‡`©k Ki‡j G‡`i jwä- [Bm&nvK, Avwgi] A. Kg n‡e B. †ewk n‡e C. k~b¨ n‡e D. †Kv‡bv cwieZ©b n‡e bv Ans C 03. 10 N Gi GKwU ej‡K j¤^ Dcvs‡k wefvwRZ Ki‡j OY Gi gvb KZ? [Bm&nvK, Avwgi] Y O X 10 4N A. 4N B. 9N C. 12N D. 14N S B info R 2 = P2 + Q2 [ ∵ 90°] Q 2 = R2 – P 2 = 102 – 4 2 Q = 9.17 9 N P = 8i ˆ + 10k ˆ , Q = 4j ˆ + 3k ˆ Dc‡ii †f±i `ywU †_‡K wb‡Pi 04 I 05 bs cÖ‡kœi DËi `vI: 04. P †f±iwU †Kvb mgZ‡j Aew¯’Z? [Bm&nvK, Avwgi] A. XY B. XZ C. YZ D. †Kv‡bvwUB bq Ans B 05. Q †f±iwU †Kvb mgZ‡j Aew¯’Z? [Bm&nvK, Avwgi] A. XY B. YZ C. XZ D. †Kv‡bvwUB bq Ans B 06. . = 0 n‡j wb‡Pi †Kvb wPÎwU mwVK? [Bm&nvK, Avwgi] A. B. C. D. Ans C 07. `ywU †f±‡ii †hvM I we‡qvMdj GKB| G‡`i gv‡S †KvY n‡jv- [Bm&nvK, Avwgi] A. 00 B. 900 C. 1200 D. 600 S B info ev, a 2 + b2 + 2ab = a2 + b2 – 2ab 4ab = 0 ev, = 0 ev, abcos = 0 ev, cos = 0 ev, = cos –1 (0) = 90° 08. P I Q †f±i `ywUi- [Bm&nvK, Avwgi] i. †f±i ¸Yb wewbgq m~Î †g‡b P‡j ii. †¯‥jvi ¸Yb wewbgq m~Î †g‡b P‡j iii. †¯‥jvi I †f±i ¸Yb DfqB wewbgq m~Î †g‡b P‡j wb‡Pi †KvbwU mwVK? A. ii B. ii I iii C. i I iii D. i, ii I iii Ans A 09. DÏxc‡Ki D‡jøwLZ F ej Abyf~wg‡Ki mv‡_ †Kv‡Y wµqvkxj| [Bm&nvK, Avwgi] (i) Abyf~wg‡Ki Dcvsk F cos Gi wµqvi †b․Kv mvg‡bi w`‡K MwZkxj nq (ii) Djø¤^ Dcvs‡ki gvb Fsin (iii) Abyf~wgK Dcvsk †b․Kvi nvj Øviv cÖgvwYZ nq wb‡Pi †KvbwU mwVK? A. i I ii B. i I iii C. ii I iii D. i,ii I iii Ans A 10. wP‡Îi = ‡f±i `ywU- [Bm&nvK, Avwgi] (i) WU ¸Yb wewbgq m~Î †g‡b P‡j (ii) µm ¸Yb wewbgq m~Î †g‡b P‡j (iii) WU I µm ¸Yb DfqB wewbgq m~Î †g‡b P‡j wb‡Pi †KvbwU mwVK? A. i B. i I ii C. ii I iii D. i,ii I iii Ans A A B 2 2 a b a b a b . A B