The correct option is C mva√2
Step-1: Draw a rough diagram of path of particle.
Given: path equation y=x+a
Comparing with equation y=mx+c
We get m=1,c=a
So, angle with x axis is 45∘ and it intersects y axis at y=a
Step-2 : Find angular momentum of particle about origin
Formula used: L=mvr
r is perpendicular distance between line of motion and origin
From figure r=acos45∘=a√2
L=mva√2
Final answer (c)