Hi Goutam , 
Thanks once again to share your views . 
I did  some change in code and it started working .
EntityCollection results = crmService.RetrieveMultiple(qe);
if(results != null)  // I added this condition and then put for  loop inside it
then placed results.more condition  outside of above if condition.
Any views.. 
public static void UpdateField
{
try
{
var crmService = CRMHelperClass.GetCRMService();
QueryExpression qe = new QueryExpression();
qe.EntityName = "opportunity";
qe.ColumnSet = new ColumnSet();
qe.ColumnSet = new ColumnSet(new string[] { "new_xx1", "new_xx2", "new_xx3", "statuscode" }); //"description",
//Condition where task attribute equals account id. 
ConditionExpression condition = new ConditionExpression();
condition.AttributeName = "statecode";
condition.Operator = ConditionOperator.Equal;
condition.Values.Add(0);
qe.Criteria.AddCondition(condition);
// The number of records per page to retrieve.
int queryCount = 3;
// Initialize the page number.
int pageNumber = 1;
// Initialize the number of records.
// Assign the pageinfo properties to the query expression.
qe.PageInfo = new PagingInfo();
qe.PageInfo.Count = queryCount;
qe.PageInfo.PageNumber = pageNumber;
// The current paging cookie. When retrieving the first page, 
// pagingCookie should be null.
qe.PageInfo.PagingCookie = null;
//Code if Opportunity have more than 5000 records
qe.PageInfo = new PagingInfo();
qe.PageInfo.Count = 5000;
qe.PageInfo.PageNumber = 1;
qe.PageInfo.ReturnTotalRecordCount = true;
while (true)
{
EntityCollection results = crmService.RetrieveMultiple(qe);
if(results != null)  // I added this condition and then put for  loop inside it
{
  foreach (Entity r in results.Entities)
{
statusCode = ((OptionSetValue)r.Attributes["statuscode"]).Value;
if (statusCode == 1) // if Opp in INprogress
{
try
{
  // some logic
crmService.Update(_opportunities);
}
}
catch (Exception ex)
{
}
}
if (results.MoreRecords)    // placed outside of for loop
{
// Increment the page number to retrieve the next page.
qe.PageInfo.PageNumber++;
// Set the paging cookie to the paging cookie returned from current results.
qe.PageInfo.PagingCookie = results.PagingCookie;
}
else
{
// If no more records are in the result nodes, exit the loop.
break;
}
}
}
catch (System.ServiceModel.FaultException ex)   // I am getting error here.
{
}
catch (Exception ex)
{
}