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

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.)