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Question 1 sur 10 10:00

[{"id":39725,"question":"Quelle est la limite de la fonction f(x) = (3x² + 2x - 1)\/(x² - 4) lorsque x tend vers l'infini ?","option_a":"A. 0","option_b":"B. 3","option_c":"C. -1","option_d":"D. +∞","option_e":"","option_f":"","bonne_reponse":"B","explication":"La limite d'un quotient de polynômes de même degré est égale au rapport des coefficients dominants. Ici, 3x²\/x² = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":39726,"question":"Une suite géométrique de raison q = -2 et de premier terme u₀ = 3 est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une suite géométrique converge si et seulement si |q| \u003C 1. Ici, |q| = 2 \u003E 1, donc la suite diverge.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":39727,"question":"Soit X une variable aléatoire suivant une loi normale N(μ, σ²). Quelle est la valeur de P(μ - σ ≤ X ≤ μ + σ) ?","option_a":"A. 0,68","option_b":"B. 0,95","option_c":"C. 0,997","option_d":"D. 0,5","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour une loi normale, environ 68% des valeurs se situent dans l'intervalle [μ - σ, μ + σ].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":39728,"question":"Quel est le nombre de solutions de l'équation sin(x) = 0,5 dans l'intervalle [0, 2π] ?","option_a":"A. 1","option_b":"B. 2","option_c":"C. 3","option_d":"D. 4","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'équation sin(x) = 0,5 admet deux solutions dans [0, 2π] : x = π\/6 et x = 5π\/6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":39729,"question":"La fonction f(x) = x³ - 3x + 2 est-elle strictement croissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée f'(x) = 3x² - 3 s'annule en x = ±1. La fonction n'est donc pas strictement croissante sur ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":39730,"question":"Quel est le coefficient binomial C(5, 2) ?","option_a":"A. 5","option_b":"B. 10","option_c":"C. 15","option_d":"D. 20","option_e":"","option_f":"","bonne_reponse":"B","explication":"C(5, 2) = 5! \/ (2! * 3!) = (5×4)\/(2×1) = 10.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":39731,"question":"Soit une urne contenant 4 boules rouges et 6 boules bleues. On tire 3 boules sans remise. Quelle est la probabilité d'obtenir exactement 2 boules rouges ?","option_a":"A. 0,3","option_b":"B. 0,4","option_c":"C. 0,5","option_d":"D. 0,6","option_e":"","option_f":"","bonne_reponse":"B","explication":"P = (C(4,2) × C(6,1)) \/ C(10,3) = (6 × 6) \/ 120 = 0,3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":39732,"question":"La fonction exponentielle est-elle égale à sa propre dérivée ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de la fonction exponentielle e^x est bien e^x, donc elle est égale à sa propre dérivée.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":39733,"question":"Quel est le produit scalaire de deux vecteurs u(2, -1, 3) et v(-1, 4, 2) ?","option_a":"A. 0","option_b":"B. 4","option_c":"C. 6","option_d":"D. 8","option_e":"","option_f":"","bonne_reponse":"C","explication":"u·v = (2×-1) + (-1×4) + (3×2) = -2 -4 +6 = 0 ? Non, calculons : -2 -4 +6 = 0. Correction : le produit scalaire est 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":39734,"question":"Soit une suite définie par uₙ₊₁ = 2uₙ - 1 avec u₀ = 3. Quelle est la limite de cette suite ?","option_a":"A. 0","option_b":"B. 1","option_c":"C. +∞","option_d":"D. La suite diverge","option_e":"","option_f":"","bonne_reponse":"B","explication":"La suite converge vers la solution de L = 2L - 1, soit L = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]