Companies which prepare master budget . Is it important to prepare flexible budget also ?

The master budget is the consolidated budgets of the different departments/units in the organization which includes the operating budgets and the financial budgets. Either a flexible budget or a static budget can be prepared. The difference is that the flexible budget is computed based on the actual activity level for the budget period, whereas the static budget is based on a budgeted activity level. 

Preparation of flexible budget is significant in variance analysis because it shows if they have incurred more expenses or earned more revenue given a certain level of activity.  This budget gives the management an idea if there have been inefficiencies and overspending in the operation

Yes, cause to know the exact picture of the organisation it is very necessary to compute variances between what was actual with the expectations and helps in more understanding of Sales and Productions.

Yes. Although, the flexible budget is part or all of a master budget that is prepared for the actual levels (or any level ) of sales and other cost driver activities.

Not necessarily. But may be important depending on the industry type and seriousness of variances. Flexible budget is a tool to aid the master budget in answering some questions and giving explanations as explained by Ms. Lesley. 

Well explained by @ Lesley Lanag, So  I agree with you.......

Master budget is itself has a consolidation of flexible budgets of different department. so without a flexible budget preparation of a mater budget will not give a accurate master budget. So while preparing a master budget, a flexible budget should be there.