Hello,
Yes, you can pursue Computer Science in Bachelor's Degree level after passing in Diploma in Computer Science. You can get admission in Bachelor's Degree level through lateral entry after passing in Diploma. Depending on the college in which you want to seek admission you need to fulfill the eligibility criteria that is specified such as age criteria, minimum percentage requirement and other essential requirments. So you need to check the eligibility criteria thoroughly before applying for any college or entrance examination.
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