answer:Solution: A = {x | -1 < x < 5} Hence, A ∩ B = {x | -1 < x < 2}. So the answer is: boxed{text{A}}. We can find set A and then perform the intersection operation. This problem tests the understanding of set-builder notation, solving quadratic inequalities, and performing intersection operations.

answer:When a = 4, the two lines become 4x + 8y - 3 = 0 and 2x + 4y - 4 = 0, respectively, which are parallel. When a = 0, the two lines become 8y - 3 = 0 and 2x = 0, respectively, which are not parallel. Thus, a neq 0. If the two lines are parallel, their slopes must be equal. That is, - frac{a}{8} = -frac{2}{a}. Solving for a, we get a^2 = 16, which implies a = pm 4. Therefore, a = 4 is a "sufficient but not necessary condition" for the lines l_1: ax + 8y - 3 = 0 and l_2: 2x + ay - a = 0 to be parallel. The final answer is: boxed{C}.

answer:- **Step 1: Find the equation of both lines.** The equation of line 1 (with slope -2) passing through A, point on the x-axis, is y = -2x + b. Since it passes through B(0, b), and B is on the y-axis, we solve for b. Point A could be (c, 0), solving for b, 0 = -2c + b leads to b = 2c. Set c later based on E. The equation of line 2 (with slope -1) is y = -x + d. It passes through C(6,0), which gives 0 = -6 + d; hence, d = 6. - **Step 2: Determine point E.** Set the equations of both lines equal to find E. -2x + 2c = -x + 6 Rightarrow x = 2c - 6. For x=4, then 2c - 6 = 4 leading to 2c = 10 Rightarrow c = 5, and b = 10. Thus A is (5, 0) and B is (0, 10) and lines are y = -2x + 10 and y = -x + 6. Substitute x = 4 into either equation for y: y = -2(4) + 10 = 2 Rightarrow E (4,2) - **Step 3: Compute the area of the quadrilateral OBEC.** - Area of triangle OEC: text{Area}_{OEC} = frac{1}{2} times OC times OE = frac{1}{2} times 6 times 2 = 6 - Area of triangle OBE: text{Area}_{OBE} = frac{1}{2} times OB times OE = frac{1}{2} times 10 times 4 = 20 Therefore, the total area of OBEC: text{Area}_{OBEC} = text{Area}_{OBE} - text{Area}_{OEC} = 20 - 6 = boxed{14}

answer:**Analysis** This question examines the relationships between four types of propositions, the properties of trigonometric functions, and the properties of inequalities. It is a basic question. Use specific values to judge options (A) and (B), use the properties of inequalities to judge option (C), and judge the correctness of the contrapositive proposition based on the correctness of the original proposition. **Solution** For option (A): The negation of the proposition "If (x > 1), then (x^{2} > 1)" is: "If (x leqslant 1), then (x^{2} leqslant 1)", which is a false proposition. For example, if (x = -5), then (x^{2} = 25). For option (B): The converse of the proposition "If (x > y), then (x > |y|)" is: "If (x > |y|), then (x > y)", which is a true proposition. For option (C): The negation of the proposition "If (x = 1), then (x^{2} + x - 2 = 0)" is: "If (x neq 1), then (x^{2} + x - 2 neq 0)", which is a false proposition. For example, if (x = -2). For option (D): The proposition "If (tan x = sqrt{3}), then (x = dfrac{π}{3})" is a false proposition, hence its contrapositive is also false. Therefore, the correct option is boxed{text{B}}.