Step 1: Land levelling (land grading) design is normally taught with three named methods: the profile method, the contour adjustment method, and the plane method. Check each statement against what these three methods actually involve.
Step 2: Statement (A) invents a "plan inspection method" and claims it suits moderate to flat slopes. This is not one of the standard named methods of land levelling design, so the statement does not correspond to real practice and is treated as incorrect.
Step 3: Statement (B) describes the profile method exactly as taught: you plot the ground profile along each grid line first, then lay the desired final grade line on top of that profile to compute cut and fill at each grid point. This is the textbook description, so (B) is correct.
Step 4: Statement (C) describes the contour adjustment method: existing contour lines on the plan are shifted by trial and error until a smooth, workable set of new contours is reached with cut balancing fill. This matches the standard definition, so (C) is correct.
Step 5: Statement (D) says the contour adjustment method suits smoothing of flat land meant for irrigation. Because this method works directly with the contour pattern rather than a single design plane, it is naturally suited to gently sloping or flat fields being prepared for surface irrigation such as border or basin methods, matching the standard description, so (D) is correct.
Step 6: Statement (E) claims the plane method is rarely used. In fact the plane method (fitting one or more planes to the field elevations) is a commonly applied technique for reasonably regular fields, not a rare one, so (E) is incorrect.
Step 7: The statements that hold up are (B), (C) and (D), matching option 2.