Quiz — Lycée Pilote Bizerte - Arithmétiques 1.pdf

Question 1 sur 10 20:00

[{"id":2095,"question":"Quel est le PGCD de 84 et 126 ?","option_a":"21","option_b":"42","option_c":"63","option_d":"84","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le PGCD de 84 et 126 est 42, car 42 est le plus grand diviseur commun à ces deux nombres.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"21\", \"b\": \"42\", \"c\": \"63\", \"d\": \"84\"}}","_debug_options_count":4},{"id":2096,"question":"Le théorème de Bézout s'applique uniquement aux nombres premiers.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le théorème de Bézout s'applique à tous les entiers, pas seulement aux nombres premiers.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":2097,"question":"Quelle est la solution générale de l'équation 3x + 5y = 1 ?","option_a":"x = 2 + 5k, y = -1 - 3k","option_b":"x = 1 + 5k, y = -2 - 3k","option_c":"x = 3 + 5k, y = -1 - 3k","option_d":"x = 2 + 3k, y = -1 - 5k","option_e":"","option_f":"","bonne_reponse":"a","explication":"La solution générale est x = 2 + 5k et y = -1 - 3k, car 3*2 + 5*(-1) = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"x = 2 + 5k, y = -1 - 3k\", \"b\": \"x = 1 + 5k, y = -2 - 3k\", \"c\": \"x","_debug_options_count":4},{"id":2098,"question":"Si a ≡ b (mod m), alors a et b ont le même reste dans la division par m.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, a ≡ b (mod m) signifie que a et b ont le même reste dans la division par m.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":2099,"question":"Quel est le PPCM de 12 et 18 ?","option_a":"36","option_b":"72","option_c":"24","option_d":"18","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le PPCM de 12 et 18 est 36, car 36 est le plus petit multiple commun à ces deux nombres.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"36\", \"b\": \"72\", \"c\": \"24\", \"d\": \"18\"}}","_debug_options_count":4},{"id":2100,"question":"Le théorème de Gauss permet de simplifier une fraction.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le théorème de Gauss est utilisé pour établir des conditions de divisibilité, mais il ne simplifie pas directement une fraction.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":2101,"question":"Quelle est la décomposition en facteurs premiers de 210 ?","option_a":"2 × 3 × 5 × 7","option_b":"2 × 3 × 7","option_c":"2 × 5 × 7","option_d":"3 × 5 × 7","option_e":"","option_f":"","bonne_reponse":"a","explication":"210 = 2 × 3 × 5 × 7, car 210 est divisible par 2, 3, 5 et 7.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"2 × 3 × 5 × 7\", \"b\": \"2 × 3 × 7\", \"c\": \"2 × 5 × 7\", \"d\": \"","_debug_options_count":4},{"id":2102,"question":"Si a et b sont premiers entre eux, alors PGCD(a, b) = 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, deux nombres sont premiers entre eux si leur PGCD est égal à 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":2103,"question":"Quelle est la solution de l'équation diophantienne 4x + 6y = 2 ?","option_a":"x = 1 + 3k, y = -1 - 2k","option_b":"x = 2 + 3k, y = -1 - 2k","option_c":"x = 1 + 2k, y = -1 - 3k","option_d":"x = 3 + 2k, y = -2 - 3k","option_e":"","option_f":"","bonne_reponse":"c","explication":"La solution générale est x = 1 + 3k et y = -1 - 2k, car 4*1 + 6*(-1) = -2, et on ajuste pour obtenir 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"x = 1 + 3k, y = -1 - 2k\", \"b\": \"x = 2 + 3k, y = -1 - 2k\", \"c\": \"x","_debug_options_count":4},{"id":2104,"question":"Le théorème de Bézout est un cas particulier du théorème de Gauss.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le théorème de Bézout est plus général que celui de Gauss, car il s'applique à tous les entiers, tandis que Gauss nécessite des conditions supplémentaires.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4}]