MongoDB shell version: 1.8.1
connecting to: test
> show dbs
admin   (empty)
blog_testing    (empty)
local   (empty)
mydb    0.078125GB
ondot   0.203125GB
payment 0.203125GB
test    0.203125GB
things  0.203125GB
> use places
switched to db places
> db.places.insert({name:"AB",loc:[22.82,84.32]})
> db.places.insert({name:"CD",loc:[21.34,83.10]))
Fri May 20 12:01:10 SyntaxError: missing } after property list (shell):1
>  db.places.insert({name:"CD",loc:[21.34,83.10]})
> db.places.ensureIndex({loc:"2d"})
> db.places.find({loc:{$near:[22.82,84.32]}})
error: { "$err" : "invalid operator: $near" }
>  db.places.find({loc:{near:[22.82,84.32]}})
>  db.places.find({loc:{geoNear:[22.82,84.32]}})
> db.places.find()
{ "_id" : ObjectId("4dd60a7b5492efa8a8326476"), "name" : "AB", "loc" : [ 22.82, 84.32 ] }
{ "_id" : ObjectId("4dd60abd5492efa8a8326477"), "name" : "CD", "loc" : [ 21.34, 83.1 ] }
> db.places.find({geoNear : "places" , near : [22.82,84.32] })
> db.places.find({loc:{near:[22,84]}})
> db.places.find({loc:{$near:[22,84]}})
error: { "$err" : "invalid operator: $near" }
> polygonA = [ [ 10, 20 ], [ 10, 40 ], [ 30, 40 ], [ 30, 20 ] ]
[ [ 10, 20 ], [ 10, 40 ], [ 30, 40 ], [ 30, 20 ] ]
> polygonB = { a : { x : 10, y : 20 }, b : { x : 15, y : 25 }, c : { x : 20, y : 20 } }                                                                                 
{
        "a" : {
                "x" : 10,
                "y" : 20
        },
        "b" : {
                "x" : 15,
                "y" : 25
        },
        "c" : {
                "x" : 20,
                "y" : 20
        }
}
> db.places.find({ "loc" : { "$within" : { "$polygon" : polygonA } } })
error: { "$err" : "invalid operator: $within" }