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

Let f (x) = |cos x|. Then,

The function f (x) = 1 + |cos x| is

The function \[f\left( x \right) = \frac{\sin \left( \pi\left[ x - \pi \right] \right)}{4 + \left[ x \right]^2}\] , where [⋅] denotes the greatest integer function, is

Let f (x) = a + b |x| + c |x|⁴, where a, b, and c are real constants. Then, f (x) is differentiable at x = 0, if

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| = __________ .

The area enclosed between the curves y = log_e (x + e), x = log_e \[\left( \frac{1}{y} \right)\] and the x-axis is _______ .

The area between x-axis and curve y = cos x when 0 ≤ x ≤ 2 π is ___________ .

Area enclosed between the curve y² (2a − x) = x³ and the line x = 2a above x-axis is ___________ .

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 ?