The resistance across $M$ and $N$ in the given figure is

An organ pipe $P_1$ closed at one end is vibrating in its first overtone. Another pipe $P_2$ open at both ends is vibrating in its third overtone. They are in resonance with a given tuning fork. The ratio of the length of $P_1$ to that of $P_2$ is

$A$ straight line passing through the origin $O$ meets the parallel lines $4x + 2y = 9$ and $2x + y + 6 = 0$ at points $P$ and $Q$ respectively. In what ratio does the point $O$ divide the line segment $PQ$?

$A$ container of mass $m$ is pulled by a constant force $F$. Inside the container,a second block of the same mass $m$ is placed,connected to the wall by a massless spring of constant $k$. Initially,the spring is at its natural length. Find the velocity of the container at the instant when the compression in the spring is maximum for the first time.

Plants which are attached to the rocks are called

$A$ 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.