The probabilities that a student passes in Mathematics, Physics and Chemistry are $$m, p$$ and $$c$$ respectively. Of these subjects, the student has $$75$$% 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. Following relations are drawn in $$m, p, c:$$
$${\rm I}.$$ $$\,\,\,\,\,\,$$ $$p+m+c=27/20$$
$${\rm I}{\rm I}.$$ $$\,\,\,\,\,\,$$ $$p+m+c=13/20$$
$${\rm I}{\rm I}{\rm I}.$$ $$\,\,\,\,\,\,$$ $$\left( p \right) \times \left( m \right) \times \left( c \right) = 1/10$$

A solution of the ordinary differential equation $$\,\,{{{d^2}y} \over {d{t^2}}} + 5{{dy} \over {dt}} + 6y = 0\,\,$$ is such that $$y(0)=2$$ and $$y(1)=$$ $$ - \left( {{{1 - 3e} \over {{e^3}}}} \right).$$ The value of $${{dy} \over {dt}}\left( 0 \right)$$ is

If a continuous function $$f(x)$$ does not have a root in the interval $$\left[ {a,b} \right],\,\,$$ then which one of the following statements is TRUE?

In the following chopper, the duty ratio of switch $$S$$ is $$0.4.$$ If the inductor and capacitor are sufficiently large to ensure continuous inductor current and ripple free capacitor voltage, the charging current (in Ampere) of the $$5$$ $$V$$ battery, under steady-state, is_____