The Cartesian equation of a line passing through $$(1,2,3)$$ and parallel to $$x-y+2 z=5$$ and $$3 x+y+z=6$$ is

If the lines $$3 x-4 y-7=0$$ and $$2 x-3 y-5=0$$ pass through diameters of a circle of area $$49 \pi$$ square units, then the equation of the circle is

A spherical iron ball of $$10 \mathrm{~cm}$$ radius is coated with a layer of ice of uniform thickness that melts at the rate of $$50 \mathrm{~cm}^3 / \mathrm{min}$$. If the thickness of ice is $$5 \mathrm{~cm}$$, then the rate at which the thickness of ice decreases is

$$\int \frac{\sin \frac{5 x}{2}}{\sin \frac{x}{2}} d x=$$

(where $$C$$ is a constant of integration.)