If any two columns of a determinant $$P = \left| {\matrix{ 4 & 7 & 8 \cr 3 & 1 & 5 \cr 9 & 6 & 2 \cr } } \right|$$ are interchanged, which one of the following statements regarding the value of the determinant is CORRECT?

Consider a spatial curve in three -dimensional space given in parametric form by $$\,\,x\left( t \right)\,\, = \,\,\cos t,\,\,\,y\left( t \right)\,\, = \,\,\sin t,\,\,\,z\left( t \right)\,\, = \,\,{2 \over \pi }t,\,\,\,0 \le t \le {\pi \over 2}.$$ The length of the curve is ________.

The value of $$\mathop {Lim}\limits_{x \to 0} \,{{1 - \cos \left( {{x^2}} \right)} \over {2{x^4}}}$$ is

Consider an ant crawling along the curve $$\,{\left( {x - 2} \right)^2} + {y^2} = 4,$$ where $$x$$ and $$y$$ are in meters. The ant starts at the point $$(4, 0)$$ and moves counter $$-$$clockwise with a speed of $$1.57$$ meters per second. The time taken by the ant to reach the point $$(2, 2)$$ is _________ (in seconds).