The differential equation representing the family of parabolas having vertex at the origin and axis along the positive Y -axis is

$$ \int \frac{\mathrm{d} x}{x^{\frac{1}{2}}+x^{\frac{1}{3}}}=\mathrm{A} x^{\frac{1}{2}}+\mathrm{B} x^{\frac{1}{3}}+\mathrm{C} x^{\frac{1}{6}}+\mathrm{D} \log \left(x^{\frac{1}{6}}+1\right)+\mathrm{k} $$

(where k is the integration constant) then values of $\mathrm{A}, \mathrm{B}, \mathrm{C}$ and D are respectively,

The probability that a non leap year selected at random will contain 52 Saturdays or 53 Sundays is

The population of towns A and B increase at the rate proportional to their population present at that time. At the end of the year 1984, the population of both the towns was 20,000 . At the end of the year 1989, the population of town A was 25,000 and that of town B was 28,000 . The difference of populations of towns A and B at the end of 1994 was