A person goes office either by car, scooter, bus or train, proability of which being $$\frac{1}{7}, \frac{3}{2}, \frac{2}{7}$$ and $$\frac{1}{7}$$, respectively. Probability that he reaches office late, if he takes car, scooter, bus or train is $$\frac{2}{9}, \frac{1}{9}, \frac{4}{9}$$ and $$\frac{1}{9}$$, respectively. Given that he reached office in time, then what is the probability that he travelled by a car?

Find the range of value of $$t$$ for which

$$2 \sin t=\frac{1-2 x+5 x^{2}}{3 x^{2}-2 x-1}, t \in\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$$

Circles with radii 3, 4 and 5 touch each other externally if P is the point of intersection of tangents to these circles at their points of contact. Find the distance of P from the point of contact.

Find the equation of the plane containing the line $$2 x-y+z-3=0,3 x+y+z=5$$ and at a distance of $$\frac{1}{\sqrt{6}}$$ from the point $$(2,1,-1)$$.