The point on the curve x²+y²-2x-3=0 at which the tangent is parallel to x-axis is

The equation of the tangent to the curve 2x²-xy+3y2=18 at (3, 1) is

If there is an error of 0.02 cm in the measurement of the side 10 cm of a cube, then error in the surface area is

The side of an equilateral triangle increases at the uniform rate 0.05 cm/sec. the rate of increase in the area of the triangle when the side is 20 cm is

The equation of the normal to the curve 2x²-xy+3y²=18 at (3, 1) is

The length of the normal of the curve y²=x³/2a-x at (a, a) is

If h is the height of the maximum cone inscribed in a sphere of radius r then h:r=

The radius and height of a cylinder are measured as 5 cm and 10 cm respectively and there is an error of 0.02 cm in both the measurements. The approximate error in the volume of the cone is

The point of intersection of straight lines represented by 6x² + xy - 40y² – 35x - 83y + 11 = 0 is:

The radius of the base and depth of a conical funnel are 20 cm and 40 cm respectively. Water flows from the funnel at the rate 2.25 cc/sec. the rate at which the water level decreases when altitude is 30 cm is