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In addition to the options in the Render Settings, which are global for the scene, you can set different render settings on a per-object basis. Some of those properties (primary and secondary visibility, visibility to camera, etc.) are accessible through the V-Ray Object Properties rollout of the Object tab. 

If you wish to learn how to create a Shadow Catcher object using V-Ray Object Properties, see How to Turn an Object Into a Shadow Catcher.

UI Path: (while selecting an object) ||Object tab|| > V-Ray Object Properties

Object ID – Specifies an ID for the object. This is used by V-Ray for the Multi Matte render channel. Note that when used with a Cloner - the object ID of the original geometry is always considered over the Cloner Object ID.

Matte Surface – Enabling this option turns the object into a matte object. This means that the object is not directly visible in the scene; instead, the background color is shown in its place. However, the object appears normally in reflections/refractions and generates indirect illumination based on its actual material.

Alpha contribution – Controls how the object appears in the alpha channel. Note that an object doesn't have to be a matte object for this setting to work - the alpha contribution can be changed regardless of whether the object is matte or not. A value of 1.0 means that the object appears normally in the alpha channel. E.g. if the object is opaque, the alpha is white; if the object is fully transparent, it does not influence the alpha channel at all. A value of 0.0 means that the object, regardless of its actual opacity, is not present in the alpha channel, although it is present, as usual, in the RGB channel. A value of -1.0 means that the object's alpha is cut out from the alpha of the objects behind it. E.g., if the object is fully opaque, its alpha is black, and it blocks the alpha of the objects behind it, whereas if the object is fully transparent, it does not influence the alpha of the other objects at all. Note that turning an object into a matte object does not change its appearance in the alpha channel. You need to explicitly change its alpha contribution. This option can also be mapped by a texture.

Shadows – When enabled, the matte object receives shadows.

Affect alpha – When enabled, makes the shadows affect the alpha contribution of the matte surface. Areas in perfect shadow produce white alpha, while completely unoccluded areas produce black alpha. Note that GI shadows (from skylight) are also computed. However, GI shadows on matte objects are not supported by the Light Cache GI engine, when used as the primary engine. You can safely use Light Cache with matte surfaces as a secondary engine.

Shadow Tint Color – Specifies the color of the shadows.

Shadow Brightness – An optional brightness parameter for the shadows on the matte surface. A value of 0.0 makes the shadows completely invisible, while a value of 1.0 shows the full shadows.

Reflection Amount – If the material of the object is a reflective V-Ray material, this controls how much of the reflection is visible on the matte object.

Refraction Amount – If the material of the object is a refractive V-Ray material, this controls how much of the refraction is visible on the matte object.

GI Amount – Controls how much of the indirect illumination received by the object is visible on the matte.

No GI on Other Mattes – When enabled, the object appears as a matte object in reflections, refractions, GI, etc., for other matte objects. Note that if this is enabled, refractions for the matte object might not be calculated. (The object appears as a matte object to itself and is not able to "see" the refractions on the other side.)

Matte for Secondary Rays – Normally, the base material is used when an object with a V-Ray Override Material is seen through reflections/refractions. Enable this option, if you want the Override Material to show the environment when seen through reflections/refractions. V-Ray can also do projection mapping to increase the realism.

Surface Properties – Enable to edit the surface properties on a per-object basis.

Generate GI –  Controls whether the object generates indirect illumination. A Multiplier can be specified for the generated indirect illumination. The Multiplier has a soft limit of 1 and a hard limit of 1000.

Receive GI – Controls whether the object receives indirect illumination. A Multiplier can be specified for the received indirect illumination. The Multiplier has a soft limit of 1 and a hard limit of 1000.

Subdivs Multiplier – Specifies a multiplier for the subdivisions of all secondary ray tracing done for the particular surface. The Multiplier has a soft limit of 2 and a hard limit of 1000.

Generate Caustics – When enabled, the selected object refracts the light coming from light sources that are caustics generators, so that caustics are produced. Note that in order to generate caustics, an object must have a reflective or refractive material.

Receive Caustics – When enabled, the object becomes a caustic receiver. When light is refracted by objects that generate caustics, the resulting caustics are only visible when they are projected on caustics receivers.

Caustics Multiplier – Specifies a multiplier for the caustics generated by the selected object. Note that this value has no effect unless Generate caustics is enabled. The Multiplier has a soft limit of 1 and a hard limit of 1000. 

GI Surface ID – This number can be used to prevent the blending of Light Cache samples across different surfaces. If two objects have different GI surface IDs, the light cache samples of the two objects are not blended. This can be useful for preventing light leaks between objects of vastly different illumination.

Generate Render Elements – This option can include or exclude the selected objects from certain render channels on a per-object basis. When disabled, the selected objects' information is excluded from the following render channels, when they are added to the scene from the View Layer tab:

Visibility options can be animated.

Visibility – Determines the opacity of the entire object.

Camera Visibility – When disabled, the object appears perfectly transparent to camera rays.

Visible to GI – When disabled, the object is considered perfectly transparent to GI rays.

Visible in Reflections – When disabled, the object appears perfectly transparent to reflection rays.

Visible in Refractions – When disabled, the object appears perfectly transparent to refraction rays.

Cast Shadows – When disabled, the object appears perfectly transparent to shadow rays.

Receive Shadows – When disabled, the object does not receive shadows.

Include / Exclude

Mode – Specifies how the list items are considered. You can include or exclude an object from the reflection and refraction visibility lists.

Reflection Objects – Specifies a list of objects with reflective properties that are excluded/included from the render.

Refraction Objects – Specifies a list of objects with refractive properties that are excluded/included from the render.

Round Edges is an effect that uses bump mapping to smooth out edges during render time. This rollout is only available when any V-Ray Material node is applied to the selected geometry.

Round Edges – Enables the Round Edges effect.

Radius – Specify a radius (in world units) for the Round Edges effect. Since the actual geometry is not being changed and only the normals of the faces are affected, large values may produce undesirable effects.

Consider Same Object Only – When enabled, the rounded corners are produced only along edges that belong to the object, which has the attribute applied. When disabled, rounded corners are also produced along edges formed when the object with the attribute intersects other objects in the scene. 

Corners – Choose which edges are considered in the calculation. Possible options are:

Convex and Concave – Considers all edges. 
Convex Only – Only applies Round Edges effect to edges with convex angles. 
Concave Only – Only applies Round Edges effect to edges with concave angles.