In Binomial distribution, Mean $= np$,
Variance $= npq$ and the mode is $r$
if for $x = r$, the probability function $p(x)$ is maximum.
Given $np = 4$ and $ npq = 3 $
$\therefore q = \frac{3}{4} p = 1 -q = 1 - \frac{3}{4} = \frac{1}{4} $
Also, $ n = \frac{4}{p} = \frac{4}{1/4} = 16 $
Now , $ \left(n+1\right)p = \left(16 +1\right) \frac{1}{4} = \frac{17}{4} = 4 + \frac{1}{4} $
$\Rightarrow $ The distribution will have unique mode (unimodal) & the mode $= 4$