The coordinates of a particle moving in $XY$-plane vary with time as $x=4 t ^2 ; y=2 t$. The locus of the particle is a :-
The slope of the tangent to the curve $y = ln\, (cos\,x)$ a $x = \frac{3\pi}{4}$ is
The area $'A'$ of a blot of ink is growing such that after $t$ second its area is given by $A = (3t^2 + 7)\,cm^2$. Calculate the rate of increase of area at $t = 2\, sec$. .......... $cm^2/s$