Tiêu đề Permutations & Combinations Engg Practice Sheet Solution (HSC 26).pdf ✅

web ̈vm I mgv‡ek  Engineering Practice Sheet Solution (HSC 26) 3  cÖ_‡g 1 wewkó 5 Øviv AwefvR ̈ msL ̈v, = 1  5  4  3  2  1  5 = 600wU A_©vr, msL ̈vwUi cÖ_g A1⁄4 4 wØZxq Ae ̄’v‡b 1 †i‡L web ̈vm: 1 1 4 3 2 1 4  (2, 3, 6, 7)  (4)  (1)  cÖ_‡g 4 I wØZxq Ae ̄’v‡b 1 †i‡L web ̈vm, = 1  1  4  3  2  1  4 = 96wU  cÖ_‡g 4 I wØZxq Ae ̄’v‡b 1 A_ev 2 †i‡L web ̈vm = 96  2 = 192 A_©vr, msL ̈vwUi wØZxq A1⁄4 3 Z...Zxq Ae ̄’v‡b 1 †i‡L web ̈vm: 1 1 1 3 2 1 3  (2, 6, 7)  (4)  (3)  (1)  cÖ_‡g 4, wØZxq 3 Ges Z...Zxq Ae ̄’v‡b 1 †i‡L web ̈vm = 1  1  1  3  2  1  3 = 18wU  431 w`‡q ïiæ Ggb msL ̈v (1800 + 192 + 18)wU = 2010wU  431 w`‡q ïiæ Ggb 8Zg msL ̈vwUB wb‡Y©q 2000 Zg msL ̈v 4312567 4315267 4312576 4315276 4312657 4315627 4312675 4315672  wb‡Y©q e„nËg msL ̈v = 4315672 (Ans.) 16| PERMUTATIONS kãwUi eY© ̧‡jv †_‡K GKwU ̄^ieY© Ges 2wU e ̈ÄbeY© wb‡q KZ ̧‡jv kã MVb Kiv hvq, †hb ̄^ieY©wU memgq gvSLv‡b _v‡K? [RUET 12-13] mgvavb: PERMUTATIONS kãwU‡ZÑ (i) wfbœ e ̈ÄbeY© Av‡Q (7 – 2 + 1) = 6wU (P, R, M, N, S, T) GKB e ̈Äb eY© T Av‡Q 2wU (ii) wfbœ ̄^ieY© Av‡Q 5wU (A, E, I, O, U) 1wU ̄^ieY© I 2wU e ̈ÄbeY© wb‡q MwVZ msL ̈v †hb ̄^ieY© memgq gvSLv‡b _v‡KÑ Case-1: 2wU e ̈ÄbeY©(GKB), 1wU ̄^ieY© 2C2  5C1  2! 2! = 5 Case-2: 2wU e ̈ÄbeY©(wfbœ), 1wU ̄^ieY© 6C2  5C1  2! = 150 †gvU kã msL ̈v = (5 + 150) = 155wU (Ans.) 17| ENGINEERING kãwU n‡Z cÖwZevi 4 wU K‡i Aÿi wb‡q KZ ̧‡jv kã MVb Kiv hv‡e? [RUET 11-12; 10-11] mgvavb: kã MV‡bi Dcvqmg~n wb¤œiƒc: ENGINEERING kãwU‡Z E-3; N-3; G-2; I-2; R-1 evQvB c×wZ web ̈vm msL ̈v Case-1: 3 wU GKB, GKwU wfbœ 2C1  4C1  4! 3! = 32 Case-2: 2 wU GKB, 2 wU GKB 4C2  4! 2! 2! = 36 Case-3: 2 wU GKB, 2 wU wfbœ 4C1  4C2  4! 2! = 288 Case-4: 4 wUB wfbœ 5 P4 = 120  †gvU Dcvq msL ̈v = 32 + 36 + 288 + 120 = 476 (Ans.) 18| „COMPUTER‟ k‡ãi Aÿi ̧‡jv n‡Z 3wU Aÿi wb‡q MwVZ kã msL ̈v wbY©q Ki hvi cÖ‡Z ̈KwU‡Z Kgc‡ÿ GKwU ̄^ieY© _v‡K| [RUET 09-10] mgvavb: ̄^ieY© Av‡Q Av‡Q 3 wU| e ̈ÄbeY© Av‡Q 5 wU|  Dchy3 kZ© †g‡b MwVZ kã msL ̈v 8 P3 – 5 P3 = 276 (Ans.) 19| „ENGINEERING‟ kãwUi meKqwU eY©‡K KZ wewfbœ iK‡g mvRv‡bv hvq Zv wbY©q Ki| Zv‡`i KZ ̧‡jv‡Z e wZbwU GK‡Î ̄’vb `Lj Ki‡e Ges KZ ̧‡jv‡Z Giv cÖ_g ̄’vb `Lj Ki‡e? [RUET 08-09, 03-04; KUET 03-04] mgvavb: mvRv‡bv msL ̈v = 11! 3! 3! 2! 2! (Ans.) E wZbwU‡K GK‡Î ivL‡j, mvRv‡bvi Dcvq = 9! 3! 2! 2! (Ans.) E wZbwU‡K hw` 1g ̄’vb `Lj K‡i Z‡e mvRv‡bv msL ̈v = 8! 3! 2! 2! (Ans.) 20| MATHEMATICS kãwUi meKqwU eY©‡K KZ wewfbœ iK‡g mvRv‡bv hvq Zv wbY©q Ki| ̄^ieY© ̧‡jv‡K GK‡Î †i‡L KZ cÖKv‡i mvRv‡bv hvq Zv wbY©q Ki| [RUET 07-08] mgvavb: ‘MATHEMATICS’ kãwU‡ZÑ (i) †gvU eY© Av‡Q 11wU (GKB eY© 2M, 2A, 2T) (ii) ̄^ieY© Av‡Q 4wU (GKB eY© 2A) Ges e ̈ÄbeY© Av‡Q 7wU (GKB eY© 2M, 2T)  meKqwU eY© wb‡q mvRv‡bvi Dcvq msL ̈v = 11! 2!2!2! (Ans.)  ̄^ieY© ̧‡jv GK‡Î †i‡L mvRv‡bv Dcvq msL ̈v = 8! 2!2!  4! 2! = 120960 (Ans.) 21| cÖgvY Ki †h, „Rajshahi‟ kãwUi Aÿi ̧‡jvi web ̈vm msL ̈v „Barisal‟ kãwUi Aÿi ̧‡jvi web ̈vm msL ̈vi Pvi ̧Y| [RUET 06-07] mgvavb: Rajshahi Gi web ̈vm msL ̈v = 8! 2! 2! = 10,080; Barisal Gi web ̈vm msL ̈v = 7! 2! = 2,520  Rajshahi Gi web ̈vm msL ̈v = 4  Barisal Gi web ̈vm msL ̈v|
4  Higher Math 1st Paper Chapter-5 22| TECHNOLOGY kãwU‡Z ̄^ieY© ̧‡jv‡K cvkvcvwk †i‡L KZ ̧‡jv kã MVb Kiv hvq? [RUET 05-06] mgvavb: TECHNOLOGY kãwU‡ZÑ ̄^ieY© Av‡Q 3 wU (GKB eY© 2O) Ges e ̈ÄbeY© Av‡Q 7wU (me ̧‡jv wfbœ wfbœ)  ̄^ieY© ̧‡jv cvkvcvwk †i‡L kã MVb Kiv hvq = 8!  3! 2! = 3  8! (Ans.) 23| „TEXTILE‟ kãwUi eY© ̧‡jv‡K KZ cÖKv‡i mvRv‡bv hvq Zv †ei Ki| KZ ̧‡jv‡Z ̄^ieY© ̧‡jv GK‡Î _vK‡e? KZ ̧‡jv‡Z ̄^ieY© ̧‡jv †Rvo ̄’vb `Lj Ki‡e? [RUET 05-06; BUTex 02-03] mgvavb: ‘TEXTILE’ kãwU‡ZÑ (i) †gvU eY© Av‡Q 7 wU (GKB eY© 2wU T, 2wU E) (ii) ̄^ieY© Av‡Q 3wU (GKB eY© 2wU E) Ges e ̈ÄbeY© Av‡Q 4wU (GKB eY© 2wU T)  me ̧‡jv eY© wb‡q mvRv‡bvi Dcvq = 7! 2!2! = 1260 (Ans.)  ̄^ieY© ̧‡jv GK‡Î wb‡q mvRv‡bvi Dcvq = 5! 2!  3! 2! = 180 (Ans.) 7wU e‡Y©i g‡a ̈ †Rvo Ae ̄’vb 2 nd, 4th, 6th A_©vr 3wU  wZbwU Ae ̄’v‡b wZb ̄^iYx Ges evwK Ae ̄’vb ̧‡jv‡Z e ̈ÄbeY© mvRv‡bv Dcvq = 3! 2!  4! 2! = 36 (Ans.) 24| „IMMEDIATE‟ kãwUi Aÿi ̧‡jv KZ cÖKv‡i mvRv‡bv hvq? G‡`i g‡a ̈ KZ ̧‡jv‡Z cÖ_‡g T Ges †k‡l A _vK‡e? [RUET 04-05; CUET 13-14] mgvavb: ‘IMMEDIATE’ kãwU‡Z †gvU eY© Av‡Q = 9 wU GLv‡b, I Av‡Q 2 wU, M Av‡Q 2 wU, E Av‡Q 2 wU  †gvU mvRv‡bv msL ̈v = 9! 2! 2! 2! = 45360 (Ans.) cÖ_‡g T Ges †k‡l A †i‡L MwVZ msL ̈v = 7! 2! 2! 2! = 630 weMZ mv‡j CUET-G Avmv cÖkœvejx 25| „IMMEDIATE‟ kãwUi Aÿi ̧‡jv KZ cÖKv‡i mvRv‡bv hvq? G‡`i g‡a ̈ KZ ̧‡jv‡Z cÖ_‡g T Ges †k‡l A _vK‡e? [CUET 13-14; RUET 04-05] mgvavb: ‘IMMEDIATE’ kãwU‡Z †gvU eY© Av‡Q = 9 wU GLv‡b, I Av‡Q 2 wU, M Av‡Q 2 wU, E Av‡Q 2 wU  †gvU mvRv‡bv msL ̈v = 9! 2! 2! 2! = 45360 (Ans.) cÖ_‡g T Ges †k‡l A †i‡L MwVZ msL ̈v = 7! 2! 2! 2! = 630 weMZ mv‡j BUTex-G Avmv cÖkœvejx 26| cÖ‡Z ̈K AsK cÖ‡Z ̈K msL ̈vq †Kej GKevi e ̈envi K‡i 6, 5, 4, 7, 0 Øviv cvuP AsK wewkó KZ ̧wj A_©c~Y© we‡Rvo msL ̈v MVb Kiv hvq? [BUTex 19-20] mgvavb: 3 3 2 1 2  (5, 7)  0 Ges 5 I 7 Gi g‡a ̈ GKwU mn †gvU `yBwU ev`  †gvU Dcvq = 3  3  2  1  2 = 36 (Ans.) 27| „DIRECTOR‟ kãwUi eY© ̧wj‡K web ̈vm Ki hv‡Z e ̈Äb eY© ̧wj GKmv‡_ bv _v‡K| [BUTex 18-19] mgvavb: DIRECTOR kãwU‡Z: (i) †gvU eY© Av‡Q 8wU, (GKB eY© R = 2wU) (ii) e ̈ÄbeY© Av‡Q 5wU (GKB eY© R = 2wU)  wb‡Y©q web ̈vm msL ̈v = kãwUi web ̈vm msL ̈v – e ̈ÄbeY© ̧‡jv‡K GK‡Î †i‡L web ̈vm msL ̈v = 8! 2! – 4!  5! 2! = 18720 (Ans.) 28| KZfv‡e 5 Rb †jvK GKwU jvB‡b `vov‡Z cv‡i? [BUTex 10-11] mgvavb: 5! = 120 fv‡e| 29| GKwU K‡j‡Ri Aa ̈vc‡Ki 3 Lvwj c‡`i Rb ̈ 10 Rb cÖv_©x wbe©vPb Kiv hvq? [BUTex 08-09] mgvavb: wbe©vPb Kivi Dcvq = 10P3 = 720 fv‡e [GKRb GKvwaK c‡` hv‡e bv] 30| 7 Rb †jv‡Ki GKwU `j `yBwU hvbevn‡b ågY Ki‡e hvi GKwU‡Z 7 R‡bi †ewk Ges AciwU‡Z 4 R‡bi †ewk a‡i bv| `jwU KZ cÖKv‡ii ågY Ki‡Z cvi‡e? [BUTex 07-08, 04-05] mgvavb: 1g hvbevn‡b †jvKmsL ̈v 2q hvbevn‡b †jvKmsL ̈v åg‡Yi Dcv‡qi msL ̈v 7 0 7C7 6 1 7C6 5 2 7C5 4 3 7C4 3 4 7C3  †gvU åg‡Yi Dcvq msL ̈v = 7C7 + 7C6 + 7C5 + 7C4 + 7C3 = 99 31| „TEXTILE‟ kãwUi eY© ̧‡jv‡K KZ cÖKv‡i mvRv‡bv hvq Zv †ei Ki| KZ ̧‡jv‡Z ̄^ieY© ̧‡jv GK‡Î _vK‡e? KZ ̧‡jv‡Z ̄^ieY© ̧‡jv †Rvo ̄’vb `Lj Ki‡e? [BUTex 02-03; RUET 05-06] mgvavb: ‘TEXTILE’ kãwU‡ZÑ (i) †gvU eY© Av‡Q 7 wU (GKB eY© 2wU T, 2wU E) (ii) ̄^ieY© Av‡Q 3wU (GKB eY© 2wU E) Ges e ̈ÄbeY© Av‡Q 4wU (GKB eY© 2wU T)  me ̧‡jv eY© wb‡q mvRv‡bvi Dcvq = 7! 2!2! = 1260 (Ans.)  ̄^ieY© ̧‡jv GK‡Î wb‡q mvRv‡bvi Dcvq = 5! 2!  3! 2! = 180 (Ans.) 7wU e‡Y©i g‡a ̈ †Rvo Ae ̄’vb 2 nd, 4th, 6th A_©vr 3wU  wZbwU Ae ̄’v‡b wZb ̄^iYx Ges evwK Ae ̄’vb ̧‡jv‡Z e ̈ÄbeY© mvRv‡bv Dcvq = 3! 2!  4! 2! = 36 (Ans.)