Title higher-math 2018.pdf ✅

m„Rbkxj D”PZi MwYZ : beg-`kg †kÖwY  27 M †mU 27 mKj †evW© 2018 welq †KvW : 1 2 6 mgq : 25 wgwbU D”PZi MwYZ eûwbe©vPwb Afxÿv c~Y©gvb : 25 [we. `a. : 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|] 1. cos  = 1 2 ,  <  < 2 n‡j  Gi gvb KZ? K  3 L 4 3 M 5 3 N 11 6 2. a, b, c ci ci wZbwU abvZ¥K ALÐ msL ̈v, †hLv‡b a < b < c n‡j, wb‡Pi †KvbwU mwVK? K 1 + ac = b2 L 1  ac = b2 M a b = b c N 1 + bc = a2 3. (x2  2xy + y2 ) 2 Gi we ̄Í...wZ‡Z c` msL ̈v KqwU? K 2 L 3 M 4 N 5 4. P(x, y) we›`y †_‡K y-A‡ÿi `~iZ¡ KZ? K x GKK L y GKK M x2 + y2 GKK N x GKK 5. A(3, 2), B(6, 5) Ges C( 1, 4) kxl©wewkó ABC wÎfz‡Ri †ÿÎdj KZ? K 6 eM© GKK L 9 eM© GKK M 18 eM© GKK N 29 eM© GKK 6. 3x  2y  1 = 0 †iLvi Xvj KZ? K  1 2 L  1 3 M 2 3 N 3 2 7. B C A ABC-G i.  BC =  BA +  AC ii.  AC +  BA +  CB =  0 iii.  AB +  CA =  BC wb‡Pi †KvbwU mwVK? K i I ii L i I iii M ii I iii N i, ii I iii  wb‡Pi Z‡_ ̈i Av‡jv‡K 8 I 9bs cÖ‡kœi DËi `vI : wP‡Î OA = 4 †m.wg., OC = 3 †m.wg. Ges †KvYKwU †ej‡bi wfZi wVKfv‡e Gu‡U hvq| A B O C 8. †KvY‡Ki †njv‡bv D”PZv KZ? K 5 †m.wg. L 7 †m.wg. M 12 †m.wg. N 25 †m.wg. 9. †ejb Ges †KvY‡Ki AvqZ‡bi cv_©K ̈ KZ? K 75.40 Nb †m.wg. L 100.53 Nb †m.wg. M 134.04 Nb †m.wg. N 301.59 Ni †m.wg.  wb‡Pi Z‡_ ̈i Av‡jv‡K 10 I 11bs cÖ‡kœi DËi `vI : GKwU Szwo‡Z 4wU jvj, 5wU mv`v I 9wU Kv‡jv gv‡e©j Av‡Q| ˆ`efv‡e GKwU gv‡e©j †bIqv n‡jv| 10. gv‡e©jwU njy` nIqvq m¤¢vebv KZ? K 0 L 2 9 M 5 18 N 1 2 11. gv‡e©jwU Kv‡jv A_ev jvj nIqvi m¤¢vebvi †hvMdj KZ? K 1 9 L 1 2 M 7 9 N 13 18 12. GKwU Q°v wb‡ÿ‡c †gŠwjK msL ̈v Avmvi m¤¢vebv KZ? K 1 3 L 1 2 M 2 3 N 1 13. A = {1, 2, 3, 4, 5} n‡j, P(A) Gi Dcv`vb KqwU? K 5 L 16 M 31 N 32 14. S = {(x, y) : x2 + y2  36 = 0} n‡j i. A¤^qwU dvskb bq ii. A¤^qwUi †jLwPÎ GKwU e„Ë iii. A¤^qwUi †jLwPÎ y-Aÿ‡K (6, 0) we›`y‡Z †Q` K‡i wb‡Pi †KvbwU mwVK? K i I ii L i I iii M ii I iii N i, ii I iii 15. 5x2  3x  1 †K (2x + 1) Øviv fvM Ki‡j fvM‡kl KZ? K  5 4 L  4 5 M 4 7 N 7 4  wb‡Pi Z‡_ ̈i Av‡jv‡K 16 I 17bs cÖ‡kœi DËi `vI : B C D A M G N M I N h_vμ‡g AC I CD Gi ga ̈we›`y| 16. ACD-Gb AN : AG = KZ? K 2 : 1 L 1 : 2 M 3 : 2 N 3 : 1 17. AB = AD = 3 †m.wg., BC = 2.5 †m.wg., CD = 3.5 †m.wg. I AM = 2 †m.wg. n‡j, BD = KZ? K 4.0 †m.wg. L 4.5 †m.wg. M 5.5 †m.wg. N 6.5 †m.wg. 18. GKwU mgevû wÎfz‡Ri cÖwZwU ga ̈gvi ˆ`N© ̈ 4 †m.wg. n‡j cÖwZwU evûi ˆ`N© ̈ KZ? K 3.46 †m.wg. L 4.62 †m.wg. M 6.92 †m.wg. N 21.33 †m.wg. 19. GKwU wÎfz‡Ri bewe›`y e„‡Ëi e ̈vmva© 2 †m.wg. n‡j H wÎfz‡Ri cwie„‡Ëi †ÿÎdj KZ? K 2 eM© †m.wg. L 4 eM© †m.wg. M 8 eM© †m.wg. N 16 eM© †m.wg. 20. 4x  4 = 32x  8 n‡j, x Gi gvb KZ? K 4 L 1 4 M  1 4 N  4 21.  x + 1 > 21 AmgZvwUi mgvavb †mU †KvbwU? K S = {xR : x <  20} L S = {xR : x >  20} M S = {xR : x   20} N S = {xR : x < 22} 22. 1 + 1 3 + 1 9 + ..... avivi (AmxgZ‡Ki) mgwó KZ? K 2 3 L 3 4 M 13 9 N 3 2 23. ( 980) †KvYwU †Kvb PZzf©v‡M _vK‡e? K 1g L 2q M 3q N 4_© 24. mKvj 8 : 30 Uvq Nwoi NÈvi KuvUv I wgwb‡Ui KuvUvi AšÍM©Z †KvY KZ wWMÖx? K 105 L 90 M 75 N 60 25. hw` m, n, x > 0 Ges m  1, n  1 nq, Z‡e i. 4log m m + log n n = 10 ii. log m + log n  log x = log mn x iii. mx = 5 m2 , hLb x = 2 5 wb‡Pi †KvbwU mwVK? K i I ii L i I iii M ii I iii N i, ii I iii 1 KLMN 2 KLMN 3 KLMN 4 KLMN 5 KLMN 6 KLMN 7 KLMN 8 KLMN 9 KLMN 10 KLMN 11 KLMN 12 KLMN 13 KLMN 14 KLMN 15 KLMN 16 KLMN 17 KLMN 18 KLMN Self test 19 KLMN 20 KLMN 21 KLMN 22 KLMN 23 KLMN 24 KLMN 25 KLMN --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1 M 2 K 3 N 4 K 5 L 6 N 7 K 8 K 9 K 10 K 11 N 12 L 13 N 14 K 15 N 16 M 17 L 18 L 19 N 20 K 21 K 22 N 23 L 24 M 25 N