The equation of the plane passing through the point (1, 2, -3) and perpendicular to the planes

3x + y - 2z = 5 and 2x - 5y - z = 7, is :

If f : R $$ \to $$ R is a function defined by f(x)= [x - 1] $$\cos \left( {{{2x - 1} \over 2}} \right)\pi $$, where [.] denotes the greatest integer function, then f is :

The distance of the point (1, 1, 9) from the point of intersection of the line $${{x - 3} \over 1} = {{y - 4} \over 2} = {{z - 5} \over 2}$$ and the plane x + y + z = 17 is :

The population P = P(t) at time 't' of a certain species follows the differential equation

$${{dP} \over {dt}}$$ = 0.5P – 450. If P(0) = 850, then the time at which population becomes zero is :