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

The total area of a page is 150 cm². The combined width of the margin at the top and bottom is 3 cm and the side 2 cm. What must be the dimensions of the page in order that the area of the printed matter may be maximum?

The space s described in time t by a particle moving in a straight line is given by S = \[t5 - 40 t^3 + 30 t^2 + 80t - 250 .\] Find the minimum value of acceleration.

A particle is moving in a straight line such that its distance at any time t is given by  S = \[\frac{t^4}{4} - 2 t^3 + 4 t^2 - 7 .\]  Find when its velocity is maximum and acceleration minimum.

If f(x) attains a local minimum at x = c, then write the values of `f' (c)` and `f'' (c)`.

Write the minimum value of f(x) = \[x + \frac{1}{x}, x > 0 .\]

Write the maximum value of f(x) = \[x + \frac{1}{x}, x > 0 .\] 

Find the least value of f(x) = \[ax + \frac{b}{x}\], where a > 0, b > 0 and x > 0 .

Write the maximum value of f(x) = \[\frac{\log x}{x}\], if it exists .

The maximum value of x^1/x, x > 0 is __________ .

If \[ax + \frac{b}{x} \frac{>}{} c\] for all positive x where a,b,>0, then _______________ .

The minimum value of \[\frac{x}{\log_e x}\] is _____________ .

For the function f(x) = \[x + \frac{1}{x}\]

Let f(x) = x³+3x² \[-\] 9x+2. Then, f(x) has _________________ .

The minimum value of f(x) = \[x4 - x2 - 2x + 6\] is _____________ .

The number which exceeds its square by the greatest possible quantity is _________________ .