An electric field $3\hat{j}+4\hat{k}$ N/C is present at a place. What will be the electric flux passing through a square plate of area $2m^2$ if the plate is placed in the y-z plane?

The electric field is present in the y-z plane. So, if we place a square surface in the y-z plane, the area vector of the plane will be perpendicular to the electric field and hence cos⁡θ becomes 0 as θ is 90 degrees. So, EA cosθ becomes zero i.e. no flux through the surface.