answer:For ①, there are two 2s, so it does not satisfy the uniqueness property of sets, thus ① is incorrect. For ②, {0} contains only one element "0", so ② is correct. For ③, since the elements in a set are unordered, {1, 2, 3} = {3, 2, 1}, thus ③ is incorrect. For ④, there are infinitely many positive rational numbers less than 1, so ④ is incorrect. Therefore, the correct choice is boxed{text{B}}.

answer:Given the expression: [ x^4 - xy^3 - x^3y - 3x^2y + 3xy^2 + y^4 ] we need to find its value when ( x - y = 1 ). 1. **Rewrite the Original Expression:** [ x^4 - xy^3 - x^3y - 3x^2y + 3xy^2 + y^4 ] 2. **Factor the Expression:** Notice that we can group and factor terms in the expression: [ x^4 - xy^3 - x^3y - 3x^2y + 3xy^2 + y^4 = x(x^3 - y^3) - y(x^3 - y^3) - 3xy(x - y) ] 3. **Combine Terms Using Common Factors:** We observe that both ( x(x^3 - y^3) ) and ( y(x^3 - y^3) ) have common terms. Rewrite: [ = (x^3 - y^3)(x - y) - 3xy(x - y) ] 4. **Use the Given Condition ( x - y = 1 ):** Using the identity ( (x^3 - y^3) = (x-y)(x^2 + xy + y^2) ) and substituting ( x - y = 1 ), the expression becomes: [ left(x^3 - y^3right)(x-y) - 3xy(x-y) ] When ( x - y = 1 ), substitute into the expression: [ (x-y)(x^2 + xy + y^2)(x-y) - 3xy(x-y) = (x^2 + xy + y^2)(x-y)^2 - 3xy(x-y) ] 5. **Simplify the Expression:** Substitute ( x - y = 1 ): [ (x^2 + xy + y^2)(1)^2 - 3xy(1) = x^2 + xy + y^2 - 3xy ] Simplify further: [ x^2 + xy + y^2 - 3xy = x^2 + y^2 - 2xy ] 6. **Use ( (x-y)^2 = 1^2 = 1 ):** Notice that: [ x^2 + y^2 - 2xy = (x-y)^2 ] 7. **Substitute ( (x-y)^2 = 1 ):** Therefore: [ (x-y)^2 = 1 ] Hence the value of the given expression is: [ boxed{1} ] So, the correct choice is (C).

answer:Since a sphere with radius r is inside a cone, and its axial section is an equilateral triangle with the sphere inscribed in it, the height of the cone is: 3r, and the height of the equilateral triangle is also: 3r. Therefore, for the side length a of the triangle, frac { sqrt {3}}{2}a=3r, thus a=2sqrt {3}r, The surface area of the sphere is: 4pi r^2, The surface area of the cone is: ( sqrt {3}r)^{2}pi+ frac {1}{2}times 2 sqrt {3}rpitimes 2 sqrt {3}r = 9pi r^2. The ratio of the total surface area of the cone to the surface area of the sphere is: 9:4. Therefore, the answer is: boxed{9:4}. By considering the axial section as an equilateral triangle with its inscribed circle, we can find the radius of the base of the cone and the height of the cone, and then calculate the surface area of the sphere and the total surface area of the cone to get the ratio. This problem tests the concept of a sphere inscribed in a cone, the calculation of the surface area of the sphere and the cone, computational skills, and spatial imagination ability.

answer:Given the problem, let's analyze each option step by step based on the information provided: **Option A Analysis:** - Original sample median: With 10 data points, the median is the average of the 5^{th} and 6^{th} points, so it's frac{x_5 + x_6}{2}. - Remaining points median: After removing the largest and smallest, we have 8 points left, and their median also falls between the 5^{th} and 6^{th} points, which is again frac{x_5 + x_6}{2}. - Conclusion: Since both medians are frac{x_5 + x_6}{2}, boxed{text{A is correct}}. **Option B Analysis:** - Given overline{x_1} = overline{x_2}, we know overline{x_1} = frac{x_2 + x_3 + ldots + x_9}{8} and overline{x_2} = frac{x_1 + x_{10}}{2}. - The overall mean overline{x} = frac{x_1 + x_2 + ldots + x_{10}}{10}. - Since overline{x_1} = overline{x_2}, substituting the means, we find that overline{x} = overline{x_1}. - Conclusion: Hence, boxed{text{B is correct}}. **Option C Analysis:** - Lower quartile for remaining 8 data points: It's the average of the 2^{nd} and 3^{rd} smallest of these 8, so it's frac{x_3 + x_4}{2}. - Lower quartile for original 10 data points: It's the 2.5^{th} point, which rounds to the third smallest point, x_3. - Since x_4 geq x_3, it follows that frac{x_3 + x_4}{2} geq x_3. - Conclusion: Therefore, boxed{text{C is correct}}. **Option D Analysis:** - We know overline{x} = overline{x_1} = overline{x_2}. - Variance calculations give us {s_1}^2 = frac{1}{8}(sum_{i=2}^{9} x_i^2) - overline{x}^2 and {s_2}^2 = frac{1}{2}(x_1^2 + x_{10}^2) - overline{x}^2. The overall variance S^2 is frac{1}{10}(sum_{i=1}^{10} x_i^2) - overline{x}^2. - Substituting the expressions for {s_1}^2 and {s_2}^2 into S^2 and simplifying, we find S^2 = frac{4}{5}{s_1}^2 + frac{1}{5}{s_2}^2. - Conclusion: Thus, boxed{text{D is correct}}. Therefore, after analyzing each option with the respective steps, all options A, B, C, and D are correct. The final answer is boxed{ABCD}.