Title SUST Model Test-01 (Set-A) Solution.pdf ✅

1 SUST Standard Model Test-01 [Set-A (Solution)] c~Y©gvb: 80 †b‡MwUf gvK©: 0.25 mgq: 1 NÈv 30 wgwbU MCQ c`v_©weÁvb (Physics) 1. A 27C 40g O2 R = 8.31 JK–1 mol–1 A cv‡Îi M ̈v‡mi †gvUkw3 KZ? 33.65  10 J 42.07  10 J 37.39  102 J 46.74  102 J DËi: 46.74  102 J e ̈vL ̈v: Ek = 3 2 nRT = 3 2  w M  R  T = 3  40  8.31  300 2  32 = 46.74  102 J 2. m1 I m2 f‡ii `ywU e ̄` R `~i‡Z¡ Aew ̄’Z| Z...Zxq m f‡ii GKwU e ̄`‡K m2 fi n‡Z KZ `~i‡Z¡ ̄’vcb Ki‡j e ̄`wUi Dci wbU ej k~b ̈ n‡e? R m1 m2 – 1 m1 m2 + 1 R R    m1  m2 + 1 R m1 m2 + 1 DËi: R m1 m2 + 1 e ̈vL ̈v: m1 R–x x F1 F2 m2 R awi, m2 n‡Z x `~i‡Z¡ ̄’vcb Ki‡Z n‡e| wbU ej k~b ̈ n‡j, F1 = F2  Gmm1 (R – x) 2 = Gmm2 x 2  R – x x = m1 m2  R x = m1 m2 + 1  x = R m1 m2 + 1 3. GKwU Zv‡ii cÖ ̄’‡”Q‡`i †ÿÎdj 2  10–4 m 2 | Zv‡ii ˆ`N© ̈ 10% e„w× Kivi Rb ̈ 4  106 N ej cÖ‡qvM Kiv n‡j, Zv‡ii Dcv`v‡bi Bqs Gi ̧Yv1⁄4 KZ n‡e? 3  1011 Nm–2 2.5  1011 Nm–2 2  1011 Nm–2 †KvbwUB bq DËi: 2  1011 Nm–2 e ̈vL ̈v: Y = F A l L = 4  106 2  10–4 10 100 = 2  1011 Nm–2 4. †KŠwYK fi‡eM 5.26 × 10–34 n‡j, n =? 4 3 6 5 DËi: 5 e ̈vL ̈v: L = nh 2  5.26 × 10–34 = n × 6.63 × 10–34 2 × 3.1416  n = 4.99  5 5. mij †`vj‡Ki MwZkw3i †jLwPÎ †KvbwU? t Kk t Kk t Ek t Ek DËi: t Ek e ̈vL ̈v: Ek = 1 2 mv2 = 1 2 m 2A 2 cos2 (t + ) Ek = 1 2 kA2 cos2 (t + )  Ek ebvg t Gi †jLwPÎ n‡jv cos2 (t + ) Gi †jLwPÎ-  2 3 2 O  2 1 2 kA 2 6. 10 MÖvg fiwewkó Zvgvi wcÛ †_‡K ˆZwi †Kv‡bv Zv‡ii ˆ`N© ̈ l| ˆ`N ̈© KZ n‡j ZviwUi †iva 2 n‡e? †hLv‡b Zvgvi NbZ¡ = 9 g/cm3 , Zvgvi †ivav1⁄4 = 1.8  10–6  cm. 11 cm 11.11 m 11.5 cm 11.2 m
2 DËi: 11.11 m e ̈vL ̈v: awi, ZviwUi ˆ`N© ̈ l Ges †ÿÎdj A  ZviwUi AvqZb, V = Al GLb, Al = 10 9 cc  l = 10 9A cm Zv‡ii fi, m = 10g fi = AvqZb  NbZ¡  Al  9  †iva, R =  l A = 10 9A2  2 = 10 9A2  1.8  10–6  2 = 10 9A2  18 10  10–6  A 2 = 10–6 cm4  A = 10–3 cm2  ˆ`N© ̈, l = 10 9A = 10 9  10–3 cm = 10  10–2 9  10–3 m = 11.11 m 7. wW‡cøkb ̄Íi Kx w`‡q c~Y© _v‡K? B‡jKUab †nvj Avqb †cÖvUb DËi: Avqb e ̈vL ̈v: Wv‡qv‡Wi wbt‡kwlZ ̄Íi ev wW‡cøkb ̄Íi Avqb Øviv c~Y© _v‡K| 8. †iwd«Rv‡iU‡ii Kvh©KvwiZvi mnM n‡jv 2. GwU cÖwZwU P‡μ Kg ZvcgvÎvi Zvc Drm †_‡K 250 J Zvc MÖnY K‡i| cÖwZwU P‡μi Zvc wm‡1⁄4 †iwd«Rv‡iUi KZ cwigvY Zvc †ei K‡i? 450 J 300 J 250 J 375 J DËi: 375 J e ̈vL ̈v: Q1 Q2 – Q1 = 2  250 Q2 – 250 = 2  Q2 = 375 J 9. 40C ZvcgvÎvi 1L cvwbi mv‡_ 120C Gi 3L cvwb †gkv‡bv n‡jv| wgkÖ‡Yi ZvcgvÎv KZ? 160C 60C 100C 80C DËi: 100C e ̈vL ̈v: awi, wgkÖ‡Yi ZvcgvÎv C m1s ( – 40) = m2s (120 – )  1 ( – 40) = 3 (120 – )   – 40 = 360 – 3  4 = 400  = 100C 10. GKwU Rjwe`y ̈r †K‡›`ai euv‡ai MfxiZv 30m cÖwZ †m‡K‡Û KZ †KwR cvwb Aek ̈B UvievBb †eø‡Wi Dci co‡j GwU 0.5 MW we`y ̈r Drcv`b Ki‡e? (g = 10 m/s2 ) 6  10–4 kg 3000 kg 1666.67 kg 4333.33 kg DËi: 1666.67 kg e ̈vL ̈v: P = mgh t  m = Pt gh = 0.5  106  1 10  30 = 5  106 100  30 = 1 6  104 = 104 6 kg = 1666.67 kg 11. k  . (i )  + j  = ? 2 0 4 1 DËi: 0 e ̈vL ̈v: k  . i  = |k|  |i|  cos90 = 0 Ges k  . j  = |k|  |j|  cos90 = 0 k  .i  + k  .j  = 0 + 0 = 0 †h‡nZz i  , j  I k  h_vμ‡g x, y I z Aÿ eivei GKK †f±i Ges x, y I z Aÿ ci ̄ú‡ii mv‡_ j¤^fv‡e Aew ̄’Z| ZvB k  I i  Gi †ÿ‡Î  = 90 Ges k  I j  Gi †ÿ‡Î  = 90| 12. GKRb gwnjv 40 eQi eq‡m Zvi 10 eQ‡ii GKwU Kb ̈v‡K †i‡L 3 2 c †e‡M MwZkxj gnvk~b ̈hv‡b P‡o åg‡Y †M‡jb| c„w_exi wnmv‡e wZwb 40 eQi ci wd‡i G‡jb| †divi ci Zv‡`i eq‡mi mgwó KZ? 100yr 105yr 110yr 115yr DËi: 110yr e ̈vL ̈v: t  40yr; t0  ? t  t0 1 – v 2 c 2  t0  t 1 – v 2 c 2  t0  40  1 –      3  2 c c 2  t0  40  1 – 3 4  t0  40  1 2  t0  20 yr Kb ̈vi eqm  10  40  50 yr Ges gwnjvi eqm  40  20  60 yr  eq‡mi mgwó  50  60  110yr 13. V  = axi  – 4yj  + 8x3 y 2 k  , †f±i †ÿÎwU mwjbqWvj n‡j, a Gi gvb KZ? 3 2 5 4 DËi: 4 e ̈vL ̈v: Avgiv Rvwb, GKwU †f±i †ÿÎ ZLbB mwjbqWvj n‡e hw`, div V  = 0 nq|    b ̈vejv
3   = i   x + j   y + k   z V  = axi  – 4yj  + 8x3 y 2 k  div V  =   . V  = 0      i   x + j   y + k   z . (axi )  – 4yj  + 8x3 y 2 k  = 0  i  .i   x ax – j  .j   y 4y + k  .k   z 8x3 y 2 = 0  a – 4 + 0 = 0 [i  .i  = j  .j  = k  .k  = 1]  a – 4 = 0      x x n = nxn–1  a = 4 14. C v  B 7 m A  †jvnvi ej C Ae ̄’v‡b e‡ji ˆiwLK †eM KZ? [g = 10 ms–2 ] 4 ms–1 9 ms–1 10 ms–1 10.9 ms–1 DËi: 10 ms–1 e ̈vL ̈v: A-†Z †gvU kw3 = c-†Z †gvU kw3 EPA + EKA = EPC + EKC  mghA + 0 = 0 +     1 2 mv2 + 1 2 I 2  mghA = 1 2 mv2 + 1 2     2 5 mr2     v r 2  ghA = 1 2 v 2 + 1 5 v 2  ghA = 7 10 v 2  v = 10 7 ghA = 10 7  10  7 = 100 = 10 Shortcut : AvbZ Zj eivei Mwo‡q cov e ̄`i †ÿ‡Î, v = 10 7 gh = 10 7  10  7 = 10 ms–1 15. K ̈vÝvi †Kvl aŸsm Kivi Kv‡R †Kvb †gŠj e ̈eüZ nq? C Co I K DËi: Co e ̈vL ̈v: †ZRw ̄Œq †Kvevë Co n‡Z wbM©Z  iwk¥ K ̈vÝvi †Kvl aŸsm Kivi Kv‡R e ̈eüZ nq| _vBi‡qW MÖwš’i wPwKrmvq Av‡qvwWb 131 e ̈eüZ nq| 16. GKwU cv¤ú cÖwZ wgwb‡U 200 L cvwb 5 m DuPz‡Z Zzj‡Q Ges H cvwb 2 cm e ̈v‡mi cvBc w`‡q wb‡ÿc Ki‡Q| wbwÿß cvwbi MwZ‡eM KZ? 11.6 ms–1 10.6 ms–1 9.6 ms–1 8.6 ms–1 DËi: 10.6 ms–1 e ̈vL ̈v: r l m t = cÖwZ †m‡K‡Û wbwÿß cvwb m t = 200 60 = 10 3 kg/s  V t = 10 3 kg/s  r 2 l t = 10 3  103  3.14  (1  10–2 ) 2 v = 10 3     v = l t  v = 10.61 m/s 17. GKwU Aš`wiZ Ges Zwor AvwnZ cwievnx †Mvj‡Ki 2cm bx‡P 0.1g fiwewkó – 20 esu Avav‡bi GKwU wc_ej k~‡b ̈ w ̄’i Av‡Q| †MvjKwUi Avavb KZ? – 16.9 esu + 19.6 esu – 19.6 C – 19.6 esu DËi: + 19.6 esu e ̈vL ̈v: F q mg – 20 esu m = 0.1g F = mg  1 K qq2 r 2 = mg      q (– 20) 2 2 = 0.1  980  q = 0.1  980  4 20  q = 392 20 = + 19.6 esu †h‡nZz wc_ejwU FYvZ¥K Pv‡R© PvwR©Z Ges w ̄’i n‡q Av‡Q, Kv‡RB Gi Dci AvKl©Y ej wμqv K‡i| Kv‡RB †MvjKwU abvZ¥K Pv‡R© PvwR©Z n‡e| 18. †Kv‡bv mvaviY f~wg UavbwR÷v‡ii msMÖvnK cÖevn 84 mA| cÖevn weea©b ̧YK 0.84 n‡j, wbtmviK cÖevn KZ? 0.01 mA 100 mA 70.56 mA 94.26 mA DËi: 100 mA e ̈vL ̈v:  = IC IE  IE = IC  = 84 0.84
4 = 84  100 84 = 100 mA 19. 120 kg f‡ii GKwU K...wÎg DcMÖn‡K f‚c„ô n‡Z GKwU wbw`©ó D”PZvq Zz‡j Zvi g‡a ̈ 3.6  109 J MwZkw3 mÂvwiZ Kiv n‡jv| DcMÖnwU f‚c„ô n‡Z KZ D”PZvq i‡q‡Q? [c„w_exi fi I e ̈vmva© h_vμ‡g 6  1024 kg I 6.4  106 m, G = 6.6  10–11 Nm2 kg–2 ] 1  105 m 2  105 m 3  105 m 4  105 m DËi: 2  105 m e ̈vL ̈v: c„w_ex n‡Z K...wÎg DcMÖ‡ni D”PZv, h K...wÎg DcMÖ‡ni †eM v n‡j, Ek = 1 2 mv2  v 2 = 2Ek m  v 2 = 2  3.6  109 120 kg  v 2 = 6  107 m 2 s –2 Avevi, Avgiv Rvwb, v = GM R + h  v 2 = GM R + h  h = GM v 2 – R = 6.6  10–11 Nm2 kg–2  6  1024 kg 6  107 m 2 s –2 – 6.4  106 m  h = 6.6  106m – 6.4  106m = 2  105m 20. GKwU Mvwo 5 ms–1 †e‡M Pjvi mgq ej cÖ‡qvM Kivq 5s G 20 ms–1 †eM jvf K‡i| MvwowUi IRb 700 N n‡j, cÖhy3 ej KZ? [g = 10 ms–2 ] 110 N 720 N 210 N 1010 N DËi: 210 N e ̈vL ̈v: W = mg  m = W g = 700 10 = 70 kg  F = m(v – u) t = 70  (20 – 5) 5 = 70  15 5 = 210 N imvqb (Chemistry) 1. GKwU np AiweUv‡j KZwU †bvW _vK‡Z cv‡i? n msL ̈K n – 1 msL ̈K n – 2 msL ̈K n + 1 msL ̈K DËi: n – 2 msL ̈K 2. †Kvqv›Uvg msL ̈vi gv‡bi †Kvb †mUwU Aev ̄Íe? 3, 2, – 2, + 1 2 4, 0, 0, + 1 2 3, 2, – 3, + 1 2 5, 3, 0, – 1 2 DËi: 3, 2, – 3, + 1 2 e ̈vL ̈v: n = 3 n‡j l = 0, 1, 2 Ges m = – 2, – 1, 0, + 1, + 2 n‡Z cv‡i| myZivs n = 3 n‡jv m = – 3 m¤¢e bq| 3. †KvbwU †bmjvi weKviK? Zn-Hg I Mvp HCl CuSO4 + 2NaOH K2HgI4 I KOH `aeY [Ag(NH3)2]OH DËi: K2HgI4 I KOH `aeY 4. CuSO4.5H2O †hŠ‡M Kq ai‡bi eÜb we` ̈gvb? 2 3 4 5 DËi: 4 e ̈vL ̈v: Cu O H H H H O O O H H H H O H O H O S O O 2 CuSO4. 5H2O GLv‡b 4 cÖKv‡ii eÜb i‡q‡Q (i) mg‡hvRx eÜb msL ̈v = 12wU (ii) mwbœ‡ek eÜb msL ̈v = 6wU (iii) nvB‡Wav‡Rb eÜb = 4wU (iv) AvqwbK eÜb = 1wU 5. CO2 †hŠ‡Mi †K›`axq †gŠ‡ji msKivqb n‡jvÑ sp sp2 sp3 sp3 d DËi: sp e ̈vL ̈v: CO2 Gi msKivqb  1 2 (4  0 – 0  0)  2; (sp) 6. Avq‡bi †cvjvivqb †ewk n‡j mswkøó †hŠ‡MiÑ i. mg‡hvRx ˆewkó ̈ †ewk nq ii. cvwb‡Z `ave ̈Zv Kg nq iii. Av`a© we‡kølY cÖeYZv e„w× cvq wb‡Pi †KvbwU mwVK? i I ii i I iii ii I iii i, ii I iii DËi: i I ii e ̈vL ̈v: dvRv‡bi bxwZ Abymv‡i †cvjvivqb hZ †ewk NU‡e mg‡hvRx ˆewkó ̈ ZZ AwaK nq| †cvjvivq‡bi cwigvY e„w×i mv‡_ mv‡_ AvqwbK †hŠ‡Mi wewfbœ a‡g©i (†hgbÑ Mjbv1⁄4, ýzUbv1⁄4, DØvwqZv, `aeYxqZv cÖf...wZ) μg n«vm I mg‡hvRx †hŠ‡Mi ˆewk‡ó ̈i μg e„w× N‡U|