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Consider the following functional dependencies in a database.

$$\begin{array}{|l|l|}\hline \text{Date_of_Birth \to Age} & \text{Age \to Eligibility} \\\hline \text{Name \to Roll_number} & \text{Roll_number \to Name} \\\hline \text{Course_number \to Course_name} & \text{Course_number \to Instructor} \\\hline \text{(Roll_number, Course_number) \to Grade} & \text{} \\\hline \end{array}$$

The relation (Roll_number, Name, Date_of_birth, Age) is

1. in second normal form but not in third normal form
2. in third normal form but not in BCNF
3. in BCNF
4. in none of the above
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There are three FDs that are valid from the above set of FDs for the given relation :

1. Date_of_Birth $\to$ Age
2. Name $\to$ Roll_number
3. Roll_number $\to$ Name

Candidate keys for the above are : (Date_of_Birth, Name) and (Date_of_Birth, Roll_number)

Clearly there is partial dependency here (Date_of_Birth $\to$ Age) and Age is not a prime attribute. So, it is in 1NF only.

Option (D).

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There are also given two other fds  i.e course no ,course name and instructor.for the ck all fds should be derived from it
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@Neha Singh we need to find dependency btw given relation only which is The relation (Roll_number, Name, Date_of_birth, Age) so all extra dependency other than relation no use
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Prateek kumar but there may be other fd that can be indirectly derived from the attribute not present in the table thus it is always advisable to find all the possible fd's by using the closure method and see which are applicable to the given relation .

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Why bcnf is not
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@Jony Bhatt  When it is not in 2NF then how it can be in bcnf
there is partial dependency hence it is 1st normal form

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