With what acceleration should the table be moved so that the 10 kg block remains at rest relative to the table?

Two wooden blocks are moving on a smooth horizontal surface such that the block having mass $m$ remains stationary with respect to block of mass $M$ as shown in the figure below. The magnitude of the applied force $P$ is, 

Two blocks $A$ and $B$ are placed one over the other on a smooth horizontal surface. The maximum horizontal force that can be applied on lower block $A$, so that $A$ and $B$ move without separation is $49 \mathrm{N}$. The coefficient of friction between $A$ and $B$ is

A $90 \mathrm{N}$ mass is hung on a rope tied between two poles as shown in the figure. The tension $T_1$ and $T_2$ in the two parts of the rope are (in $\mathrm{N}$)

A maximum of $3 \mathrm{N}$ force can be applied on a block, down the incline, that would still not move the block which is placed on a rough inclined plane as shown in the figure. The maximum external force up the inclined plane that does not move the block is $12 \mathrm{N}$. The coefficient of static friction between the block and the plane is $\left[\mathrm{Take} g=10 \mathrm{m} {\mathrm{s}}^{-2}\right]$