$A$ bullet fired into a fixed target loses half of its velocity after penetrating $3 \ cm$. How much further will it penetrate before coming to rest,assuming that it faces constant resistance to motion? (in $cm$)

If $f: R \rightarrow R$ and $g: R \rightarrow R$ are defined by $f(x)=x-[x]$ and $g(x)=[x]$ for $x \in R$,where $[x]$ is the greatest integer not exceeding $x$,then for every $x \in R, f(g(x))$ is equal to

The particles emitted during the sequential radioactive decay of ${}^{238}U_{92}$ to ${}^{206}Pb_{82}$ are

In a compound microscope,the focal length of the objective lens is $f_o = 1.2 \ cm$ and the focal length of the eyepiece is $f_e = 3.0 \ cm$. When the object is kept at $u_o = -1.25 \ cm$ in front of the objective,the final image is formed at infinity. The magnifying power of the compound microscope is:

The binding energy per nucleon versus mass number curve for nuclei is shown in the figure. $W, X, Y$ and $Z$ are four nuclei indicated on the curve. The process that would release energy is

Identify the product in the following reaction:
$Phenol + CHCl_3 + NaOH \rightarrow \text{Product}$