answer:Since the symmetric point of the origin O with respect to the line l: 2xtanalpha + y - 1 = 0 is A(1, 1), The midpoint of O and A, which is left( frac {1}{2}, frac {1}{2} right), lies on the line l. Therefore, solving tanalpha + frac {1}{2} - 1 = 0 gives tanalpha = frac {1}{2}. Using the double angle formula for tangent, we get tan2alpha = frac {2tanalpha}{1-tan^2alpha} = frac {2× frac {1}{2}}{1- left( frac {1}{2} right)^2} = frac {4}{3}. Hence, the correct choice is: boxed{text{B}} By symmetry, the midpoint of O and A, left( frac {1}{2}, frac {1}{2} right), lies on the line l, and substituting the point yields tanalpha = frac {1}{2}. The double angle formula for tangent is then used to calculate the result. This problem tests the concept of symmetry of points with respect to a line and involves the double angle formula, making it a basic question.

answer:Since log_{2} frac{1}{5} represents the exponent to which 2 must be raised to get frac{1}{5}, and we know 2^0 = 1 and frac{1}{5} < 1, so log_{2} frac{1}{5} < 0 because powers of 2 greater than 0 yield values larger than 1. Next, consider 2^{0.1}. Since 0.1 > 0 and the function f(x) = 2^x is strictly increasing, 2^{0.1} > 2^0 = 1. Then, for 2^{-1}, remember that negative exponents indicate an inverse, thus 2^{-1} = frac{1}{2^{1}} = frac{1}{2}. Knowing that 0 < frac{1}{2} < 1, we can conclude that 2^{-1} is positive but less than 1. Putting it all together, we can see that: log_{2} frac{1}{5} < 2^{-1} < 2^{0.1} Because log_{2} frac{1}{5} < 2^{-1} and 2^{-1} < 2^{0.1}. So the correct choice is boxed{text{C}}: log_{2} frac{1}{5} < 2^{-1} < 2^{0.1}.

answer:Let's denote the percentage of students who failed in Hindi as H%. We know that 44% failed in English and 22% failed in both Hindi and English. Since the students who failed in both subjects are included in the percentage of students who failed in each subject, we can use the principle of inclusion-exclusion to find the percentage of students who failed in at least one of the two subjects. The percentage of students who failed in at least one subject (either Hindi or English or both) is given by: H% (failed in Hindi) + 44% (failed in English) - 22% (failed in both) Now, we are given that 44% of the students passed in both subjects. This means that 100% - 44% = 56% of the students failed in at least one subject. Using the equation above, we can set up the following equation: H% + 44% - 22% = 56% Solving for H%: H% = 56% + 22% - 44% H% = 78% - 44% H% = 34% Therefore, the percentage of students who failed in Hindi is boxed{34%} .

answer:Let's denote the distance from the center of the moving circle to the line x = -1 as r. Since the center of the circle is on the parabola y^2 = 4x, and the equation of the directrix of the parabola is x = -1, the center of the circle is at an equal distance from the directrix x = -1 and the focus (1,0). By the definition of a parabola, any point (in this case, the center of the circle) equidistant from the directrix and the focus lies on the parabola. Thus, (1,0), the focus of the parabola, must lie on the moving circle. Hence, the moving circle must pass through the fixed point (1,0). Therefore, the correct answer is: [ boxed{B: (1,0)} ] From the equation of the parabola, we obtain that the line x = -1 is the directrix. By the definition of a parabola, we conclude that the moving circle must pass through the focus of the parabola, leading to the answer. This problem examines the relationship between a line and a circle, as well as the definition of a parabola, and is considered to be of moderate difficulty.