A particle of mass m moves in the  XY-plane with a constant velocity ‘V’ along the straight line $X\text{'}Y\text{'}$. If the angular momentum of the particle with respect to origin O is $L_A$ when it is at A, and  $L_B$ when it is at B, then 

Since the particle is moving on a straight line with a constant speed, the velocity will remain constant
As we know  $\overrightarrow{L}=\overrightarrow{r}\times m\overrightarrow{v}$
$\Rightarrow \left|\overrightarrow{L}\right|=mvr$ 
r= Perpendicular distance
v= Speed
m= Mass
We can see at point  A and  B the product  mvr is constant.
Hence  $\left|{\overrightarrow{L}}_A\right|=\left|{\overrightarrow{L}}_B\right|$
$\Rightarrow L_A=L_B$ 
Therefore, the correct answer is (B).