Given : $a=3$
$b=5$
$c=4$
$\Rightarrow a^2+b^2=c^2$[By pythogorus theorem]
$\Rightarrow 3^2+4^2=5^2$
$\Rightarrow 9+16=25$
$25=25$
Angle is $90^{\large\circ}$.Hence it is right angled $\Delta$le.$\angle B=90^{\large\circ}$
$\sin\large\frac{B}{2}$$+\cos\large\frac{B}{2}$$=\sqrt 2$
Hence (d) is the correct option.