To get maximum current through a resistance of 2.5 $\Omega ,$one can use m rows of cells, each row having n cells. The internal resistance of each cell is 0.5  $\Omega$ What are the values of n and m, if the total number of cells is 45. 

Sine total number of cell is 45,

$mn=\mathrm{45...................}\left(i\right)$

Now n cells are in series, then resistance is $n\times 0.5\Omega$

Now there are m rows with such series, then

$\frac{1}{R_{eq}}=\frac{1}{n\times 0.5}+\frac{1}{n\times 0.5}+\mathrm{.....}\left(mtimes\right)$

$R_{eq}=\frac{n\times 0.5}{m}=2.5\Omega$

$[\because I=\frac{nE}{R+r_{eq}}]$

$n=5m$

Using eqs (i) and (ii), m= 3 and n= 15