The most abundant prokaryotes helpful to humans in making curd from milk and in production of antibiotics are categorised as

$A$ thin hollow sphere of mass $m$ is completely filled with a liquid of mass $m$. When the sphere rolls with a velocity $v$,the kinetic energy of the system is (neglect friction).

If $b+c=3a$,then $\cot \frac{B}{2} \cot \frac{C}{2}$ is equal to :

For $k=1, 2, 3$,the box $B_k$ contains $k$ red balls and $(k+1)$ white balls. Let $P(B_1)=\frac{1}{2}$,$P(B_2)=\frac{1}{3}$,and $P(B_3)=\frac{1}{6}$. $A$ box is selected at random and a ball is drawn from it. If a red ball is drawn,then the probability that it has come from box $B_2$ is:

Stokes' law states that the viscous drag force $F$ experienced by a sphere of radius $a$,moving with a speed $v$ through a fluid with coefficient of viscosity $\eta$,is given by $F=6 \pi \eta a v$. If this fluid is flowing through a cylindrical pipe of radius $r$,length $l$ and a pressure difference of $p$ across its two ends,then the volume of water $V$ which flows through the pipe in time $t$ can be written as $\frac{V}{t}=k\left(\frac{p}{l}\right)^a \eta^b r^c$,where $k$ is a dimensionless constant. The correct values of $a, b$ and $c$ are

In the given figure,what does the part labeled '$a$' represent?