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

If f is defined by  \[f\left( x \right) = x^2 - 4x + 7\] , show that \[f'\left( 5 \right) = 2f'\left( \frac{7}{2} \right)\] 

If  \[f \left( x \right) = \sqrt{x^2 + 9}\] , write the value of

If \[f\left( x \right) = \begin{cases}\frac{\left| x + 2 \right|}{\tan^{- 1} \left( x + 2 \right)} & , x \neq - 2 \\ 2 & , x = - 2\end{cases}\]  then f (x) is

The function f (x) = |cos x| is

If \[f\left( x \right) = a\left| \sin x \right| + b e^\left| x \right| + c \left| x \right|^3\] 

The function f (x) = x − [x], where [⋅] denotes the greatest integer function is

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 ?