1. Half-deflection setup relation

For a galvanometer of resistance $G$, cell emf $E$, series resistance $R$, and figure of merit $k$:

$I_g = \frac{E}{R+G}$

If the galvanometer shows deflection $\theta$, then

$I_g = k\theta$

So,

$k\theta = \frac{E}{R+G}$

Rearranging,

$\frac{1}{\theta} = \frac{k}{E}(R+G) = \frac{k}{E}R + \frac{kG}{E}$

Thus, the graph of $\dfrac{1}{\theta}$ vs $R$ is a straight line with slope

$m = \frac{k}{E}$

Hence,

$k = mE$

2. Read slope from the graph

From the given straight-line plot, the slope is

$m = 0.25\; \text{division}^{-1}\,\Omega^{-1}$

(Equivalently, if two convenient points are read, the rise/run gives $0.25$.)

3. Calculate figure of merit

Given

$E = 2\,\text{V}$

Therefore,

$k = mE = 0.25 \times 2 = 0.50\;\text{A/division}$

Since the answer is to be written in the form

$\underline{\hspace{1cm}} \times 10^{-1}\;\text{A/division}$

we write

$0.50 = 5 \times 10^{-1}$

So the figure of merit is

$\boxed{5 \times 10^{-1}\;\text{A/division}}$

Hence, the required integer is:

$\boxed{5}$