A Custom Object named “Training__c” has field “Trainer__c”. You have set some default value in that field. Will that default value apply to new record created by Salesforce apex code ?

After API 20, it should automatically populate However there is known issue for same here, click here if it impacts you.
Workaround :
If Default value of field is not getting populated by Apex then we have to use “Dynamic Apex”.  Create instance of object from sObjectType like shown below:

view source
print?
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Training__c tr= (Training__c) Training__c.sObjectType.newSObject(null, true);
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//Check if Value in field "Trainer__c" is default value
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System.assertEquals('Jitendra', tr.Trainer__c);