for(i=0;i<1000;i++){db.doc.insert({"doc":{"k1":"v_"+i,"k2":i},"scal":i})}

var d1 = db.doc.findOne()
{
    "_id" : ObjectId("5ce25f8920b0be2428648e38"),
    "doc" : {
        "k1" : "v_0",
        "k2" : 0
    },
    "scal" : 0
}

db.doc.createIndex({"doc":1})
db.doc.createIndex({"scal":1})

db.doc.explain(true).find({doc:{$gt:d1.doc}},{_id:0,doc:1})
{
    ...
    "executionStats" : {
        "executionSuccess" : true,
        "nReturned" : 999,
        "executionTimeMillis" : 1,
        "totalKeysExamined" : 999,
        "totalDocsExamined" : 999,
        ...
}

db.doc.explain(true).find({scal:{$gt:d1.scal}},{_id:0,scal:1})
{
    ...
    "executionStats" : {
        "executionSuccess" : true,
        "nReturned" : 999,
        "executionTimeMillis" : 0,
        "totalKeysExamined" : 999,
        "totalDocsExamined" : 0,
        ...
}

db.doc.explain(true).find({doc:d1.doc},{_id:0,doc:1})
{
    ...
    "executionStats" : {
        "executionSuccess" : true,
        "nReturned" : 1,
        "executionTimeMillis" : 0,
        "totalKeysExamined" : 1,
        "totalDocsExamined" : 0,
        ...
}

var dis = db.doc.distinct("doc")
db.doc.explain(true).find({doc:{$in:dis}},{_id:0,doc:1})
{
...
"executionStats" : {
        "executionSuccess" : true,
        "nReturned" : 1000,
        "executionTimeMillis" : 8,
        "totalKeysExamined" : 1000,
        "totalDocsExamined" : 0,
        ...
}