Black Jack is an ore of

$A$ poster is to be printed on a rectangular sheet of paper of area $18 \ m^2$. The margins at the top and bottom of $75 \ cm$ each and at the sides $50 \ cm$ each are to be left. Then the dimensions i.e. height and breadth of the sheet so that the space available for printing is maximum,are . . . . . . respectively.

The ratio of angular speeds of the minute hand and the hour hand of a watch is:

The pulleys in the diagram are all smooth and light. The acceleration of $A$ is $a$ upwards and the acceleration of $C$ is $f$ downwards. The acceleration of $B$ is

One thousand small water drops of equal radii combine to form a big drop. The ratio of final surface energy to the total initial surface energy is

Evaluate $\int_{-2}^1 f(x) dx$,where $f(x)= \begin{cases} 1-2x, & x \leq 0 \\ 1+2x, & x > 0 \end{cases}$