What is the Limit of no of callouts in Apex class and Apex Batch?

These are the governor Limits you need to keep in mind when dealing with Batch Apex

1.Up to five queued or active batch jobs are allowed for Apex.
2.Using Database.QueryLocator batch apex returns 50 million records if more than 50 million records are returned.
3.The batch apex Database.execute method can have batches of a maximum number of 2,000, minimum 1 and by default 200 batches.
4.Salesforce chunks the records returned by the start method and then passes each batch to the execute method where governor limits are reset for each execution of execute.
5.The batch apex can implement up to 10 callouts per each batch methods.
6.250,000 is the maximum number of batch executions per 24 hours.
7.Only one batch Apex job's start method can run at a time in an organization. The batch jobs which haven’t started yet remain in the queue until they are started.