PUC Science 2nd PUC Class 12 - Karnataka Board PUC Question Bank Solutions for Mathematics

If a particle moves in a straight line such that the distance travelled in time t is given by s = t³ − 6t²+ 9t + 8. Find the initial velocity of the particle ?

The volume of a sphere is increasing at 3 cubic centimeter per second. Find the rate of increase of the radius, when the radius is 2 cms ?

The sides of an equilateral triangle are increasing at the rate of 2 cm/sec. How far is the area increasing when the side is 10 cms?

The side of a square is increasing at the rate of 0.1 cm/sec. Find the rate of increase of its perimeter ?

The radius of a circle is increasing at the rate of 0.5 cm/sec. Find the rate of increase of its circumference ?

The side of an equilateral triangle is increasing at the rate of \[\frac{1}{3}\] cm/sec. Find the rate of increase of its perimeter ?

If the rate of change of volume of a sphere is equal to the rate of change of its radius, find the radius of the sphere ?

The amount of pollution content added in air in a city due to x diesel vehicles is given by P(x) = 0.005x³ + 0.02x² + 30x. Find the marginal increase in pollution content when 3 diesel vehicles are added and write which value is indicated in the above questions ?

If \[V = \frac{4}{3}\pi r^3\] ,  at what rate in cubic units is V increasing when r = 10 and \[\frac{dr}{dt} = 0 . 01\] ?  _________________

Side of an equilateral triangle expands at the rate of 2 cm/sec. The rate of increase of its area when each side is 10 cm is

The radius of a sphere is changing at the rate of 0.1 cm/sec. The rate of change of its surface area when the radius is 200 cm is

A cone whose height is always equal to its diameter is increasing in volume at the rate of 40 cm³/sec. At what rate is the radius increasing when its circular base area is 1 m²?

A cylindrical vessel of radius 0.5 m is filled with oil at the rate of 0.25 π m³/minute. The rate at which the surface of the oil is rising, is

The distance moved by the particle in time t is given by x = t³ − 12t² + 6t + 8. At the instant when its acceleration is zero, the velocity is

The altitude of a cone is 20 cm and its semi-vertical angle is 30°. If the semi-vertical angle is increasing at the rate of 2° per second, then the radius of the base is increasing at the rate of

For what values of x is the rate of increase of x³ − 5x² + 5x + 8 is twice the rate of increase of x ?

The coordinates of the point on the ellipse 16x² + 9y² = 400 where the ordinate decreases at the same rate at which the abscissa increases, are