Let us look at V 4.2 of the Immigration Rules for Visitors in detail:
Genuine intention to visit
V 4.2 The applicant must satisfy the decision maker that they are a genuine visitor. This means that the applicant:
(a) will leave the UK at the end of their visit; and
(b) will not live in the UK for extended periods through frequent or successive visits, or make the UK their main home; and
(c) is genuinely seeking entry for a purpose that is permitted by the visitor routes (these are listed in Appendices 3, 4 and 5); and
(d) will not undertake any prohibited activities set out in V 4.5 – V 4.10; and
(e) must have sufficient funds to cover all reasonable costs in relation to their visit without working or accessing public funds. This includes the cost of the return or onward journey, any costs relating to dependants, and the cost of planned activities such as private medical treatment.
Note that 4.2(a) states: "will leave the UK at the end of their visit". This is in connection with a lack of evidence of your studies.
The entry clearance officer is looking for evidence that you "will leave the UK at the end of your visit". Evidence that you are enrolled at university and will return to your studies would make a strong indication that you are likely to leave the UK and return to India. To resolve this, then, you need only obtain documentation from your university that you are currently enrolled, that you will be enrolled next semester, what you are studying and the expected date of completion of your program. You then include this documentation with your visa application.
While sub paragraph (a) was mentioned in the details, your refusal notice explains that you failed to meet the requirements of Paragraph V 4.2 in its entirety...
"...I am not satisfied that you meet the requirements of paragraph(s)
V 4.2..."
This a grave refusal and indicates that there were severe deficiencies in your application.
Because of this, you will want to review everything else in the rules and ensure that you have included all of the other necessary documentation. Some notes for each of these reasons:
(b): You will not attempt to build up a case for settlement in the UK. If you have travelled to the UK before, and spent significant amounts of time there (e.g. as a student), then they will be aware that you know people in the UK and may have something of a life there. It is even more important in this scenario that you can demonstrate stronger ties to your home country than to the UK.
(c): Your activities in the UK will be restricted to those listed in Appendix 3 of the visitor rules.
(d): Ensure that you include nothing in your visa application, nor bring with you to the UK, that might tend to indicate that you will seek employment, academic studies, using the NHS, getting married, etc. Review these sections of the rules to learn what is not allowed on a standard visitor visa.
(e): That you will not rely upon public funds (i.e., welfare). Pay special attention to your bank statements and your sponsor's financial information as problems with financial documentation are a very common reason for refusals. In addition, your sponsor should not transfer money to your account until after your visa is approved.
You also should not omit any necessary evidence from your future application that you submitted previously. Such documents need to be resubmitted each time.
Finally, if you do opt to make a fresh application, you are emphatically recommended to study the guidance beforehand.
