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[{"id":2255,"question":"Quelle est la valeur de \u003Cem\u003Elog\u003Csub\u003E2\u003C\/sub\u003E(8)\u003C\/em\u003E ?","option_a":"2","option_b":"3","option_c":"4","option_d":"log\u003Csub\u003E2\u003C\/sub\u003E(4)","option_e":"","option_f":"","bonne_reponse":"B","explication":"log\u003Csub\u003E2\u003C\/sub\u003E(8) = log\u003Csub\u003E2\u003C\/sub\u003E(2\u003Csup\u003E3\u003C\/sup\u003E) = 3, car log\u003Csub\u003Ea\u003C\/sub\u003E(a\u003Csup\u003En\u003C\/sup\u003E) = n.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":2256,"question":"Soit X une variable aléatoire suivant une loi binomiale B(10; 0,3). Quelle est l'espérance mathématique E(X) ?","option_a":"3","option_b":"7","option_c":"10","option_d":"0,3","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour une loi binomiale B(n; p), E(X) = n × p = 10 × 0,3 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":2257,"question":"Résoudre l'inéquation \u003Cem\u003Eln(x) \u003E 2\u003C\/em\u003E (avec x \u003E 0).","option_a":"x \u003E e\u003Csup\u003E2\u003C\/sup\u003E","option_b":"x \u003C e\u003Csup\u003E2\u003C\/sup\u003E","option_c":"x \u003E 2","option_d":"x \u003C 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"ln(x) \u003E 2 ⇒ x \u003E e\u003Csup\u003E2\u003C\/sup\u003E, car la fonction ln est croissante sur ]0; +∞[.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":2258,"question":"On lance un dé équilibré à 6 faces. Quelle est la probabilité d'obtenir un nombre pair ?","option_a":"1\/6","option_b":"1\/2","option_c":"1\/3","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"B","explication":"Les nombres pairs sont 2, 4 et 6 : 3 cas favorables sur 6 possibles, soit 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":2259,"question":"Quelle est la dérivée de la fonction \u003Cem\u003Ef(x) = ln(3x + 1)\u003C\/em\u003E ?","option_a":"f'(x) = 3\/(3x + 1)","option_b":"f'(x) = 1\/(3x + 1)","option_c":"f'(x) = 3x\/(3x + 1)","option_d":"f'(x) = 1\/x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de ln(u) est u'\/u, ici u = 3x + 1 ⇒ u' = 3, donc f'(x) = 3\/(3x + 1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]