Arts (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

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

The radius of the base of a cone is increasing at the rate of 3 cm/minute and the altitude is decreasing at the rate of 4 cm/minute. The rate of change of lateral surface when the radius = 7 cm and altitude 24 cm is

The radius of a sphere is increasing at the rate of 0.2 cm/sec. The rate at which the volume of the sphere increase when radius is 15 cm, is

The volume of a sphere is increasing at 3 cm³/sec. The rate at which the radius increases when radius is 2 cm, is

The distance moved by a particle travelling in straight line in t seconds is given by s = 45t + 11t² − t³. The time taken by the particle to come to rest is

The volume of a sphere is increasing at the rate of 4π cm³/sec. The rate of increase of the radius when the volume is 288 π cm³, is

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

If the rate of change of area of a circle is equal to the rate of change of its diameter, then its radius is equal to

Each side of an equilateral triangle is increasing at the rate of 8 cm/hr. The rate of increase of its area when side is 2 cm, is

If s = t³ − 4t² + 5 describes the motion of a particle, then its velocity when the acceleration vanishes, is

The equation of motion of a particle is s = 2t² + sin 2t, where s is in metres and t is in seconds. The velocity of the particle when its acceleration is 2 m/sec², is

The radius of a circular plate is increasing at the rate of 0.01 cm/sec. The rate of increase of its area when the radius is 12 cm, is