If $$y(x)$$ satisfies the differential equation $$y' - y\,tan\,x = 2x\,secx$$ and $$y(0)=0,$$ then

A ship is fitted with three engines $${E_1},{E_2}$$ and $${E_3}$$. The engines function independently of each other with respective probabilities $${1 \over 2},{1 \over 4}$$ and $${1 \over 4}$$. For the ship to be operational at least two of its engines must function. Let $$X$$ denote the event that the ship is operational and Let $${X_1},{X_2}$$ and $${X_3}$$ denote respectively the events that the engines $${E_1},{E_2}$$ and $${E_3}$$ are functioning. Which of the following is (are) true?

The point $$P$$ is the intersection of the straight line joining the points $$Q(2, 3, 5)$$ and $$R(1, -1, 4)$$ with the plane $$5x-4y-z=1.$$ If $$S$$ is the foot of the perpendicular drawn from the point $$T(2, 1, 4)$$ to $$QR,$$ then the length of the line segment $$PS$$ is

If $$\overrightarrow a ,\overrightarrow b $$ and $$\overrightarrow c $$ are unit vectors satisfying
$${\left| {\overrightarrow a - \overrightarrow b } \right|^2} + {\left| {\overrightarrow b - \overrightarrow c } \right|^2} + {\left| {\overrightarrow c - \overrightarrow a } \right|^2} = 9,$$ then $$\left| {2\overrightarrow a + 5\overrightarrow b + 5\overrightarrow c } \right|$$ is