Tiêu đề mathematics 2018.pdf ✅

18 mKj †evW© 2018 welq †KvW : 1 0 9 mgq : 30 wgwbU MwYZ eûwbe©vPwb Afxÿv c~Y©gvb : 30 [we‡kl `aóe ̈ : mieivnK...Z eûwbe©vPwb Afxÿvi DËic‡Î cÖ‡kœi μwgK b¤^‡ii wecix‡Z cÖ`Ë eY©msewjZ e„Ëmg~n n‡Z mwVK/ m‡e©vrK...ó Dˇii e„ËwU ej c‡q›U Kjg Øviv m¤ú~Y© fivU Ki| cÖwZwU cÖ‡kœi gvb 1| mKj cÖ‡kœi DËi w`‡Z n‡e| cÖkœc‡Î †Kv‡bv cÖKvi `vM/wPý †`Iqv hv‡e bv|] 1. 3784.8 msL ̈vwU‡Z j‡Mi c~Y©K KZ? K 4 L 3 M 2 N 1 2. 4 x+1 = 32 n‡j x Gi gvb KZ? K 1 L 3 2 M 7 2 N 5 3. a  R n‡j i. a = 1 (hLb a  0) ii. a 1 = 1 a iii. a n = 1 a (n) wb‡Pi †KvbwU mwVK? K i I ii L i I iiiM ii I iii N i, ii I iii 4. log2 2 64 Gi gvb wb‡Pi †KvbwU? K 1 4 L 1 M 2 2 N 4 5. wÎfzR AuvK‡Z cÖ‡qvRb i. wZbwU evû ii. `yBwU evû Ges Zv‡`i AšÍfz©3 †KvY iii. `yBwU †KvY I GKwU evû wb‡Pi †KvbwU mwVK? K i I ii L i I iiiM ii I iii N i, ii I iii 6. A D B O C AB = KZ †mwg? K 7 L 2 7 M 7 N 14 7. †Kv‡bv wÎfz‡R KqwU ewne„©Ë AuvKv hvq? K 1 L 2 M 3 N 4  DÏxcKwU c‡o 8 I 9bs cÖ‡kœi DËi `vI : ABC GKwU mgevû wÎfzR| Gi BC †K D ch©šÍ ewa©Z Kiv n‡jv| A B C D 8. BAC Gi m¤ú~iK †Kv‡Yi gvb †KvbwU? K 120 L 90 M 60 N 30 9. ABC + ACD Gi gvb †KvbwU? K 60 L 120 M 150 N 180 10. H AÿiwUi N~Y©b †KvY KZ? K 30 L 60 M 90 N 180 11. ABC Gi C ̄’~j‡KvY; AD, BC Gi Dci j¤^ n‡j, wb‡Pi †KvbwU mwVK? K AB2 = AC2 + BC2 + 2AC.CD L AB2 = AC2 + BC2 + 2BC.CD M AC2 = AB2 + BC2 + 2BC.CD N BC2 = AB2 + AC2 + 2BC.CD 12. †Kv‡bv wÎfz‡Ri `yB evûi ˆ`N© ̈ h_vμ‡g 9 †m.wg. I 10 †m.wg Ges G‡`i AšÍfz©3 †KvY 60| wÎfzRwUi †ÿÎdj KZ eM© †m.wg| K 22.5 L 38.97 M 45 N 77.94 13. GKwU e„‡Ëi e ̈vm 24 †m. wg| Gi cwiwa KZ? K 15.07 L 37.7 M 75.4 N 150.77 14. GKwU Nb‡Ki GK c„‡ôi K‡Y©i ˆ`N© ̈ 8 2 †m. wg| NbKwUi KY© KZ †m. wg.? K 8 3 L 8 2 M 8 3 N 24 15. MYmsL ̈v mviwY cÖ ̄‘Z Ki‡Z n‡j cÖ_‡g †KvbwU cÖ‡qvRb? K †kÖwY msL ̈v L †kÖwY e ̈eavb M cwimi N MYmsL ̈v 16. cwimsL ̈v‡bi †ÿ‡Î i. ga ̈K = L + ( ) n 2  Fc  h m ii. cÖPziK = L + 1 1 + 2  h iii. MvwYwZK Mo = n + 1 2 wb‡Pi †KvbwU mwVK? K i I ii L i I iiiM ii I iii N i, ii I iii 17. †KvbwU ̄^vfvweK msL ̈v? K  1 L 2 M 5 2 N 3 18. wb‡Pi †KvbwU Øviv A  B cÖKvk Kiv hvq? K {x : x  A Ges x  B} L {x : x  B Ges x  A} M {x : x  A Ges x  B} N {x : x  A Ges x  A} 19. wb‡Pi †Kvb Aš^qwU dvskb? K {(1,2), (1,3)} L {(1, 1), (  1, 2)} M {(2, 3), (1, 2)} N {(  3, 5), ( 3,  4)}  DÏxcKwU c‡o 20 I 21bs cÖ‡kœi DËi `vI : a 2  5a  1 = 0 20. a 2 + 1 a 2 Gi gvb KZ? K 23 L 25 M 27 N 29 21. a + 1 a Gi gvb KZ? K 29 L 27 M 23 N 21 22. 3x  5y = 7, 6x  10y = 15 GB mgxKiY †RvUwU i. AmgÄm ii. GKwU gvÎ mgvavb Av‡Q iii. ci ̄úi Awbf©ikxj wb‡Pi †KvbwU mwVK? K i I ii L i I iiiM ii I iii N i, ii I iii 23. 35  2y  y 2 Gi Drcv`K †KvbwU? K 5 + y L y  6 M 7 + y N 7  y 24. tan A = 4 3 n‡j sec AGi gvb KZ? K 3 4 L 4 5 M 5 4 N 5 3 25. w·KvYwgwZi †ÿ‡Î i. sec2  + tan2  = 1 ii. cot2  = 1 + cosec2  iii. cos2  = 1  sin2  wb‡Pi †KvbwU mwVK? K i L iii M ii I iii N i, ii I iii 26. (x + 3) (x  3) = 16, n‡j x Gi gvb KZ? K  5 L  4 M 4 N 5 27. 6m B 60 C A BC Gi ˆ`N© ̈ KZ wgUvi? K 2 3 L 6 2 M 2 3 N 6 28. e„‡Ëi cÖwZmvg ̈ †iLv KZwU? K 1 L 3 M 3 N AmsL ̈ 29. GKwU wÎfz‡Ri wZbwU †Kv‡Yi AbycvZ 3 : 4 : 5 n‡j, ÿz`aZg †Kv‡Yi cwigvY KZ? K 15 L 45 M 60 N 75 30. 8 + 16 + 24 + ......avivi beg c` KZ? K 72 L 88 M 360 N 432 Self test 1 KLMN 2 KLMN 3 KLMN 4 KLMN 5 KLMN 6 KLMN 7 KLMN 8 KLMN 9 KLMN10 KLMN 11 KLMN 12 KLMN13 KLMN14 KLMN 15 KLMN 16 KLMN17 KLMN18 KLMN19 KLMN20 KLMN 21 KLMN22 KLMN23 KLMN24 KLMN25 KLMN 26 KLMN27 KLMN28 KLMN29 KLMN30 KLMN --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1 L 2 L 3 K 4 N 5 K 6 L 7 M 8 K 9 N 10 N 11 L 12 L 13 M 14 M 15 M 16 K 17 N 18 M 19 M 20 M 21 K 22 L 23 M 24 N 25 L 26 K 27 K 28 N 29 L 30 K