Through the point (2, 3) a straight line is drawn making positive intercept on the coordinate axes. The area of the triangle thus formed is least, when the ratio of the intercepts on the x and y axes is

In measuring the vertical angle  of the sector of acircle of radius  30cms, an error of  1⁰ is made. The error in the area of the sector is

The radius of a sphere is 3 cm. if an error of 0.03 cm is made in measuring the radius of the sphere, then the error in surface area is

The function f(x)= x³-9x²+15x+25 is decreasing in

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

Water flows into a conical  vessel is at the rate of 5 cubic cm per sec. if the semi vertical angle of the vessel is 30⁰, then the rate of increase of water level when the water level in the vessel is 6 cm is

The volume of a metal hollow sphere is constant. If the outer radius is increasing at the rate of ¼ cm per sec. the rate at which the inner radius is increasing when the radii are 8 cm and 4 cm respectively is

f(x)=(sin^-1x)²+(cos^-1x)² is stationary at

On the interval [0, 1] the function x²⁵(1-x)⁷⁵ takes its maximum value at the point

The diameter x of a circle is found by measurements to be 5 cm with maximum error of 0.05 cm. the relevant error in the area is