Questions in differentiation

Select	Question
	A particle is moving along the curve $x=a{{t}^{2}}+bt+c.$ If $ac={{b}^{2}},$ then the particle would be moving with uniform
	The sides of an equilateral triangle are increasing at the rate of 2 cm/sec. The rate at which the area increases, when the side is 10 cm is
	The rate of change of the surface area of a sphere of radius r when the radius is increasing at the rate of 2 cm/sec is proportional to
	Moving along the x-axis are two points with $x=10+6t;x=3+{{t}^{2}}.$ The speed with which they are reaching from each other at the time of encounter is (x is in cm and t is in seconds)
	The position of a point in time ‘t’ is given by $x=a+bt-c{{t}^{2}}$ , $y=at+b{{t}^{2}}$ . Its acceleration at time ‘t’ is
	Gas is being pumped into a spherical balloon at the rate of $30 ft^3/min$. Then the rate at which the radius increases when it reaches the value 15 ft is
	If the distance ‘s’ metre traversed by a particle in t seconds is given by $s={{t}^{3}}-3{{t}^{2}}$ , then the velocity of the particle when the acceleration is zero, in metre/sec is
	A particle moves in a straight line so that $s=\sqrt{t}$ , then its acceleration is proportional to
	A point on the parabola ${{y}^{2}}=18x$ at which the ordinate increases at twice the rate of the abscissa is
	A spherical iron ball 10 cm in radius is coated with a layer of ice of uniform thickness that melts at a rate of 50 $cm^3/min$. When the thickness of ice is 5 cm, then the rate at which the thickness of ice decreases, is