A solution of the differential equation
$${\left( {{{dy} \over {dx}}} \right)^2} - x{{dy} \over {dx}} + y = 0$$ is

The differential equation representing the family of curves
$${y^2} = 2c\left( {x + \sqrt c } \right),$$ where $$c$$ is a positive parameter, is of

If the integers $$m$$ and $$n$$ are chosen at random from $$1$$ to $$100$$, then the probability that a number of the form $${7^m} + {7^n}$$ is divisible by $$5$$ equals

The probabilities that a student passes in Mathematics, Physics and Chemistry are $$m, p$$ and $$c,$$ respectively. Of these subjects, the student has a $$75%$$ chance of passing in at least one, a $$50$$% chance of passing in at least two, and a $$40$$% chance of passing in exactly two. Which of the following relations are true?