There are no particular banking course after class 10 but you can start building the base of your career.There is no compulsion in selecting stream for banking exam,But selecting commerce that involves subjects like accountancy will be beneficial as commerce students have a better understanding of banking and able to gain skills and knowledge at the school level.After Passing class 12 with high grades join BCom in college preferably institutions of national importance in Government Sector.Then write exams of IBPS(Institute of Banking Personnel Selection) for probationary officer.
Here are Some of the top Bank exams:
State Bank of India: Exam-SBI PO,SBI SO,SBI Clerk.
Reserve Bank of India:Exam-RBI Grade B Exam,RBI Assistant Exam.
Institute of Banking Personnel Selection: Exam-IBPS PO,IBPS SO,IBPS Clerk,IBPS RRB.
National Bank for Agriculture and Rural Development:Exam-NABARD.
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