how to display two custom object (input)fields in single visual page.

Hi Abhishek,

You need a controller or extension do this (controller is shown here):

public with sharing class controller {
    public ObjectA__c objectA { get; set; }
    public Task       task    { get; set; }
    public controller() {
        objectA = ...; // do query from page parameter, etc);
        task = new schema.task();
    }
    public pagereference save() {
        try {
            update objecta;
            task.whatid = objecta.id;
            insert task;
            return new apexpages.standardcontroller(objecta).view();
        } catch(exception e) {
            apexpages.addmessages(e);
            return null;
        }
    }
}

Refer to your ObjectA fields as {!objecta.provider__c}, and task fields as {!task.category__c}. You can populate other data as well, change the logic around, etc. If you're using the standard controller, you can refer to {!ObjectA__c.Provider__c} instead; you'll want to save the standard controller so you can save the data correctly (calling controller.save()).