Quiz — برنامج رمضان - العدد 20 مع الحل - الدوال اللوغاريتمية (بكالوريا أجنبية) - الاحتمالات (بكالوريا مغربية) .pdf

Question 1 sur 5 10:00

[{"id":1455,"question":"Quelle est la dérivée de la fonction f(x) = ln(3x + 2) ?","option_a":"f'(x) = 1\/(3x + 2)","option_b":"f'(x) = 3\/(3x + 2)","option_c":"f'(x) = 1\/(x + 2)","option_d":"f'(x) = 3x\/(3x + 2)","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée de ln(u(x)) est u'(x)\/u(x). Ici, u(x) = 3x + 2, donc u'(x) = 3. Ainsi, f'(x) = 3\/(3x + 2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"f'(x) = 1\/(3x + 2)\", \"b\": \"f'(x) = 3\/(3x + 2)\", \"c\": \"f'(x) = 1\/(","_debug_options_count":4},{"id":1456,"question":"Dans une loi binomiale de paramètres n=10 et p=0.3, quelle est la probabilité d'obtenir exactement 4 succès ?","option_a":"C(10,4) * (0.3)^4 * (0.7)^6","option_b":"C(10,4) * (0.3)^6 * (0.7)^4","option_c":"(0.3)^4 * (0.7)^6","option_d":"10! \/ (4! * 6!) * (0.3)^4","option_e":"","option_f":"","bonne_reponse":"a","explication":"La probabilité d'obtenir exactement k succès dans une loi binomiale est donnée par P(X=k) = C(n,k) * p^k * (1-p)^(n-k). Ici, n=10, k=4 et p=0.3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"C(10,4) * (0.3)^4 * (0.7)^6\", \"b\": \"C(10,4) * (0.3)^6 * (0.7)^4\",","_debug_options_count":4},{"id":1457,"question":"Quelle est la solution de l'équation ln(x) + ln(x-1) = ln(6) ?","option_a":"x = 3","option_b":"x = 2","option_c":"x = 1","option_d":"x = 4","option_e":"","option_f":"","bonne_reponse":"a","explication":"En utilisant la propriété ln(a) + ln(b) = ln(ab), l'équation devient ln(x(x-1)) = ln(6), donc x(x-1) = 6. La solution positive est x=3 (car x² - x - 6 = 0 donne x=3 ou x=-2).","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 = 3\", \"b\": \"x = 2\", \"c\": \"x = 1\", \"d\": \"x = 4\"}}","_debug_options_count":4},{"id":1458,"question":"Si X suit une loi normale N(μ=5, σ=2), quelle est la probabilité P(3 ≤ X ≤ 7) ?","option_a":"0.6826","option_b":"0.9544","option_c":"0.3413","option_d":"0.9974","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour une loi normale, environ 68% des valeurs sont dans l'intervalle [μ-σ, μ+σ]. Ici, μ=5 et σ=2, donc P(3 ≤ X ≤ 7) ≈ 0.6826 (valeur exacte : 0.6827).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"0.6826\", \"b\": \"0.9544\", \"c\": \"0.3413\", \"d\": \"0.9974\"}}","_debug_options_count":4},{"id":1459,"question":"Quelle est la limite de (ln(x)) \/ x quand x tend vers l'infini ?","option_a":"0","option_b":"1","option_c":"+∞","option_d":"-∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"En utilisant la règle de l'Hôpital (dérivée du numérateur et du dénominateur), on obtient lim (1\/x) \/ 1 = 0. Ainsi, la limite est 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"0\", \"b\": \"1\", \"c\": \"+∞\", \"d\": \"-∞\"}}","_debug_options_count":4}]