The minimum number of cells in mixed grouping required to produce a maximum current of 1.5 A through an external resistance of $30\mathrm{\Omega }$, given the emf of each cell is 1.5 V and internal resistance is $1\mathrm{\Omega }$ is

For a mixed grouping of a cells in series and b rows :

Emf of the grouping is 

$E_{eff} = aE$

and 

$r_{eff} = \frac{ar}{b}$

Given E = 1.5 v and r = $1\mathrm{\Omega }$ and R = $30\mathrm{\Omega }$

For this circuit, 

For a maximum current :

$R = r_{eff} \Rightarrow 30= \frac{ar}{b}$

$a = 30b$

Current through R is 

$i = \frac{E_{eff}}{R+r_{eff}}=\frac{aE}{R+ar/b}$

Maximum value of i is given as 1.5 A

$\frac{aE}{R+ar/b}=1.5A$

$\frac{a\times 1.5}{30+\left(a\times 1\right)/b}=1.5A$

$a=30+a/b$

$\Rightarrow 30b = 30+30\Rightarrow b =2$

$a = 30b =60$

Total number of cells is

$n = ab = 120$