Questions in differentiation

Select	Question
	A spherical balloon is being inflated at the rate of 35 cc/min. The rate of increase of the surface area of the balloon when its diameter is 14 cm is
	A population p(t) of 1000 bacteria introduced into nutrient medium grows according to the relation $p(t)=1000+\frac{1000t}{100+{{t}^{2}}}$ . The maximum size of this bacterial population is
	If a particle moves such that the displacement is proportional to the square of the velocity acquired, then its acceleration is
	The radius of a cylinder is increasing at the rate of 3 m/sec and its altitude is decreasing at the rate of 4m/sec. The rate of change of volume when radius is 4 metres and altitude is 6 metres is
	A ladder 10 m long rests against a vertical wall with the lower end on the horizontal ground. The lower end of the ladder is pulled along the ground away from the wall at the rate of 3 cm/sec. The height of the upper end while it is descending at the rate of 4 cm/sec is
	The points on the curve $y=12x-{{x}^{3}}$ at which the gradient is zero are
	The area of the triangle formed by the coordinate axes and a tangent to the curve $xy={{a}^{2}}$ at the point $({{x}_{1}},{{y}_{1}})$ on it is
	The slope of tangent to the curve $x={{t}^{2}}+3t-8$ , $y=2{{t}^{2}}-2t-5$ at the point (2, –1) is
	The point of the curve ${{y}^{2}}=2(x-3)$ at which the normal is parallel to the line$y-2x+1=0$ is
	The line $x+y=2$ is tangent to the curve ${{x}^{2}}=3-2y$ at its point