How we get selected element from array using node js query for mongoDB

Question

I am fetching array result by applying query stored inside MONGODB. I am trying to fetch score:1's questionId only I am trying {'quiz.score':1} or {quiz:{$eq:{score:1}}}, but it return all questionId which score is 0 and 1

This is node js code

function(){

               childQuizInfo.find({quiz:{$eq:{score:1}}},function(err,question){
               if(err) return next(err);
               res.send(question);
                });
               }

This is question id schema

quiz: {type: Array,
    questionId: {
            type: mongoose.Schema.Types.ObjectId,
            ref: 'Question',
            index: true
             },
    score: { type: Number },
    time: { type: String }
    }

This is stored result inside mongodb

"quiz" : [
    {
        "time" : "2016-09-07T08:04:30.316Z",
        "score" : 1,
        "questionId" : "57ce608e2a0d6cad8c48ef8f"
    },
    {
        "time" : "2016-09-07T08:06:35.399Z",
        "score" : 0,
        "questionId" : "57ce608e2a0d6cad8c48ef90"
    },
    {
        "time" : "2016-09-07T08:06:49.296Z",
        "score" : 1,
        "questionId" : "57ce608e2a0d6cad8c48ef91"
    },
    {
        "time" : "2016-09-07T08:06:56.699Z",
        "score" : 0,
        "questionId" : "57ce608e2a0d6cad8c48ef92"
    },
    {
        "time" : "2016-09-07T08:07:00.660Z",
        "score" : 1,
        "questionId" : "57ce608e2a0d6cad8c48ef93"
    }

I need a query so that it return only questionId which score is 1 in response.

The output I get

   {
   "message": "unknown top level operator: $eq"
    }