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

If \[f\left( x \right) = \begin{cases}\frac{1 - \cos x}{x \sin x}, & x \neq 0 \\ \frac{1}{2} , & x = 0\end{cases}\] 

then at x = 0, f (x) is

If A is a matrix of order 3 and |A| = 8, then |adj A| = __________ .

Find the rate of change of the total surface area of a cylinder of radius r and height h, when the radius varies?

Find the rate of change of the area of a circular disc with respect to its circumference when the radius is 3 cm ?

Find the rate of change of the volume of a ball with respect to its radius r. How fast is the volume changing with respect to the radius when the radius is 2 cm?

The total cost C (x) associated with the production of x units of an item is given by C (x) = 0.007x³ − 0.003x² + 15x + 4000. Find the marginal cost when 17 units are produced ?

The total revenue received from the sale of x units of a product is given by R (x) = 13x² + 26x + 15. Find the marginal revenue when x = 7 ?

The money to be spent for the welfare of the employees of a firm is proportional to the rate of change of its total revenue (Marginal revenue). If the total revenue (in rupees) recieved from the sale of x units of a product is given by R(x) = 3x² + 36x + 5, find the marginal revenue, when x = 5, and write which value does the question indicate ?

The side of a square sheet is increasing at the rate of 4 cm per minute. At what rate is the area increasing when the side is 8 cm long?

An edge of a variable cube is increasing at the rate of 3 cm per second. How fast is the volume of the cube increasing when the edge is 10 cm long?

The side of a square is increasing at the rate of 0.2 cm/sec. Find the rate of increase of the perimeter of the square.

The radius of a circle is increasing at the rate of 0.7 cm/sec. What is the rate of increase of its circumference?

The radius of a spherical soap bubble is increasing at the rate of 0.2 cm/sec. Find the rate of increase of its surface area, when the radius is 7 cm.

A balloon which always remains spherical, is being inflated by pumping in 900 cubic centimetres of gas per second. Find the rate at which the radius of the balloon is increasing when the radius is 15 cm.

The radius of an air bubble is increasing at the rate of 0.5 cm/sec. At what rate is the volume of the bubble increasing when the radius is 1 cm?

A man 2 metres high walks at a uniform speed of 5 km/hr away from a lamp-post 6 metres high. Find the rate at which the length of his shadow increases.