If the mean of a Poisson distribution is $\frac{1}{2}$,then the ratio of $P(X=3)$ to $P(X=2)$ is

$A$ lead bullet of mass $10 \ g$ travelling at $300 \ m/s$ strikes against a block of wood and comes to rest. Assuming $50\%$ of heat is absorbed by the bullet,the increase in its temperature is (Specific heat of lead $= 150 \ J/kg \cdot ^{\circ}C$) (in $^{\circ}C$)

The coefficient of static friction,$\mu_s$ between block $A$ of mass $2\,kg$ and the table as shown in the figure is $0.2$. What would be the maximum mass value of block $B$ so that the two blocks do not move (in $,kg$)? The string and the pulley are assumed to be smooth and massless. $(g = 10\,m/s^2)$

For skywave propagation of a $10\, MHz$ signal,what should be the minimum electron density in the ionosphere?

The maximum value of $\left(\frac{1}{x}\right)^{x}$ is

If $f:[-6,6] \rightarrow R$ is defined by $f(x)=x^2-3$ for $x \in R$,then $(f \circ f \circ f)(-1)+(f \circ f \circ f)(0)+(f \circ f \circ f)(1)$ is equal to