Two blocks of mass $M$ and $m$ are used to compress two different massless springs, as shown. The left spring is compressed by, $3 \mathrm{cm}$ while the right spring is compressed by an unknown amount. The system is at rest and all surfaces are fixed and smooth. Which of the following statements are true?

In the figure shown, all the surfaces are smooth. All the blocks $A$, $B$ and $C$ are movable, $x$-axis is horizontal and $y$-axis is vertical, as shown. Just after the system is released from the position as shown,

A block $A (5 \mathrm{kg})$ rests over another block $B\mathit{ }(3 \mathrm{kg})$ placed over a smooth horizontal surface. There is friction between $A$ and $B$. A horizontal force $F_1$, gradually increasing from zero to a maximum, is applied to $A$, so that the blocks move together without relative motion. Instead of this, another horizontal force $F_2$, gradually increasing from zero to a maximum, is applied to $B$, so that the blocks move together without relative motion. Then,

${\mathrm{M}}_{\mathrm{A}}=3 \mathrm{kg}, {\mathrm{M}}_{\mathrm{B}}=4 \mathrm{kg}$ and ${\mathrm{M}}_{\mathrm{C}}=8 \mathrm{kg}$. The coefficient of friction between any two surface is $0.25$. The pulley is frictionless and the string is massless. $A$ is connected to a wall by a massless rigid rod. 

The acceleration of the block $B$ in the figure, assuming the surfaces and the pulleys $P_1$ and $P_2$ are all smooth and pulleys and string are light is $\frac{3F}{xm}$ then value of $x$ is.

In the arrangement shown in figure, the mass of the body $A$ is $n=4$ times that of body $B$. The height $h=20 \mathrm{cm}$. At a certain instant, the body $B$ is released and the system is set in motion. What is the maximum height (in $\mathrm{cm}$) the body $B$ will go up? Assume enough space above $B$ and $A$ sticks to ground. ($A$ and $B$ are of small size) $(g=10 \mathrm{m} {\mathrm{s}}^{-2})$