If you want A to stay 'private', you need to update the public length property on every operation which modifies A's length so that you don't need a method which checks when asked. I would do so via 'private' method.

Code:

var a = function(){
    var instance, A, updateLength;

    instance = this;
    A = [];
    this.length = 0;

    updateLength = function()
    {
      instance.length = A.length;
    }

    this.add = function(x){
        A.push(x);
        updateLength();
    };

    this.remove = function(){
        var popped = A.pop();
        updateLength();

        return popped;
    };
};

Demo: http://jsfiddle.net/JAAulde/VT4bb/

For now, here's the best solution I could think of.

makeFunc = function (length, fn) {
    switch (length) {
    case 0 : return function () { return fn.apply(this, arguments); };
    case 1 : return function (a) { return fn.apply(this, arguments); };
    case 2 : return function (a,b) { return fn.apply(this, arguments); };
    case 3 : return function (a,b,c) { return fn.apply(this, arguments); };
    case 4 : return function (a,b,c,d) { return fn.apply(this, arguments); };
    case 5 : return function (a,b,c,d,e) { return fn.apply(this, arguments); };
    case 6 : return function (a,b,c,d,e,f) { return fn.apply(this, arguments); };
    case 7 : return function (a,b,c,d,e,f,g) { return fn.apply(this, arguments); };
    case 8 : return function (a,b,c,d,e,f,g,h) { return fn.apply(this, arguments); };
    case 9 : return function (a,b,c,d,e,f,g,h,i) { return fn.apply(this, arguments); };
    default : return function (a,b,c,d,e,f,g,h,i,j) { return fn.apply(this, arguments); };
    }
};

Example usage:

var realFn = function () {
    return "blah";
};

lengthSix = makeFunc(6, realFn);

lengthSix.length; // 6
lengthSix(); // "blah"

Personally, I always cringe whenever I use copy and paste when programming, so I'd be very happy to hear of any better options.

Update

I thought of a method which could work for any arbitrary size, unlike the example above which is limited by how many times you want to copy-and-paste. Essentially, it dynamically creates a function (using new Function) which will return a function of the right size which then just proxies through to whatever function you pass to it. Yeah that does hurt your head. Anyway, I thought I'd benchmark it against the above...

http://jsperf.com/functions-with-custom-length (you can see the 'evil' code there too).

The evil method is many hundreds of times slower than the hacky copypasta method, so there you go.