UGC NET CS Practice Set 3

Explanation: Rotation about the Z-axis leaves the Z coordinate unchanged while rotating the X and Y coordinates. The matrix is: [cosθ, −sinθ, 0; sinθ, cosθ, 0; 0, 0, 1]. This is analogous to 2D rotation in the XY plane.

Explanation: A polygon is a back face if N · V < 0, where N is the outward surface normal and V is the view direction vector (from the surface toward the viewer). If this dot product is negative, the surface faces away from the viewer and can be culled.

Explanation: Most modern languages (C, Java, Python, Haskell, etc.) use static (lexical) scoping, where the scope of a variable is determined by its position in the source code. Dynamic scoping (used by some Lisp dialects, Bash) resolves names based on the runtime call chain.

Explanation: The scan-line fill algorithm processes each horizontal scan line, finds the intersection points with polygon edges, sorts them, and fills pixels between pairs of intersections (odd-even rule or winding number rule).

Explanation: A superkey is any set of one or more attributes that, taken collectively, uniquely identifies a tuple in a relation. A candidate key is a minimal superkey (no proper subset is a superkey). Every candidate key is a superkey, but not vice versa.

Explanation: 2NF eliminates partial dependencies — where a non-prime attribute depends on only part of a candidate key. A relation is in 2NF if it is in 1NF and every non-prime attribute is fully functionally dependent on every candidate key.

Explanation: In relational algebra, the innermost operation is evaluated first. Here, π_{name,salary}(EMPLOYEE) projects name and salary first, then σ_{salary>50000} selects tuples with salary > 50000 from the projection result.

Explanation: From A→B→C→D→E, the closure of {A} is {A, B, C, D, E}, which is all attributes. So A is a superkey. Since A is a single attribute, it is trivially minimal and hence a candidate key.

Explanation: UNION combines the results of two SELECT statements and removes duplicate rows by default. UNION ALL keeps all rows including duplicates. INTERSECT returns only common rows. JOIN combines columns from related tables.

Explanation: In a B-tree of order m, each internal node (except root) must have at least ⌈m/2⌉ children and at most m children. This ensures the tree remains balanced after insertions and deletions.

Explanation: Two-phase locking (2PL) guarantees conflict-serializability. In the growing phase, locks are acquired but not released; in the shrinking phase, locks are released but not acquired. However, basic 2PL does NOT prevent deadlocks or cascading rollbacks.

Explanation: ACID stands for Atomicity (all or nothing), Consistency (database moves between consistent states), Isolation (concurrent transactions appear to execute serially), and Durability (committed changes survive system failures).

Explanation: h(31) = 31 mod 11 = 9, placed at index 9. h(42) = 42 mod 11 = 9, collision at 9, linear probe to 10. h(53) = 53 mod 11 = 9, collision at 9, probe to 10 (occupied), probe to 0. Wait: 31→9, 42→10, 53 probes 9(full), 10(full), goes to 0. But let me recheck: h(53) = 53 mod 11 = 9, index 9 is taken by 31, index 10 is taken by 42, so index 0 is tried next (wrap around) and is empty. So 53 goes to index 0. Actually let me reconsider the options. The answer should be 0.

Explanation: The query returns all tuples in R whose A value appears in the A values of S. This is a semi-join: it keeps tuples from R that have a matching A value in S but does not add columns from S.

Explanation: 3NF allows a non-trivial FD X→A if A is a prime attribute (part of some candidate key), even if X is not a superkey. BCNF requires X to be a superkey for every non-trivial FD. The gap between 3NF and BCNF exists when a non-superkey determines a prime attribute.

Explanation: In a B+ tree, all data pointers (pointers to actual records) reside in the leaf nodes. Internal nodes contain only keys and child pointers used for navigation. Leaf nodes are linked together for efficient sequential access.

Explanation: Immediate update allows changes to be written to the database before a transaction commits, requiring both undo (for uncommitted transactions at crash time) and redo (for committed transactions whose changes may not have been flushed to disk) during recovery.

Explanation: A many-to-many (M:N) cardinality means each entity in A can participate in the relationship with multiple entities in B, and each entity in B can participate with multiple entities in A. This typically requires a junction/association table in the relational schema.

Explanation: In timestamp ordering, each transaction receives a unique timestamp when it enters the system. Each data item maintains read and write timestamps. Conflicting operations are ordered by their transaction timestamps; a violation causes the younger transaction to abort and restart.

Explanation: SQL supports INNER JOIN, LEFT/RIGHT/FULL OUTER JOIN, CROSS JOIN, and NATURAL JOIN. There is no such thing as a DIAGONAL JOIN in standard SQL.

Explanation: The WAL protocol mandates that the log record for a modification must be written to stable storage before the modified data page is flushed to disk. This ensures that the system can always undo or redo any operation during recovery.

Explanation: With separate chaining, each bucket is a linked list that can hold multiple elements, so the load factor (n/m where n is elements and m is table size) can exceed 1. In open addressing, the load factor must be ≤ 1 since each slot holds at most one element.

Explanation: A schedule is conflict-serializable if and only if its precedence (serialization) graph is acyclic. The precedence graph has transactions as nodes and edges representing conflicting operations between different transactions. A topological sort of this acyclic graph gives an equivalent serial order.

Explanation: A process moves from Ready to Running when the CPU scheduler selects it for execution (dispatch). Ready→Running is the only way a process begins executing on the CPU.

Explanation: SJF order: P4(3), P1(6), P3(7), P2(8). Waiting times: P4=0, P1=3, P3=3+6=9, P2=3+6+7=16. Average = (0+3+9+16+19)/4. Wait: P4=0, P1=3, P3=9, P2=16. Average = (0+3+9+16)/4 = 28/4 = 7.0. Hmm, let me recalculate. Actually: P4 waits 0, runs 3→finishes at 3. P1 waits 3, runs 6→finishes at 9. P3 waits 9, runs 7→finishes at 16. P2 waits 16, runs 8→finishes at 24. Average waiting = (0+3+9+16)/4 = 28/4 = 7.0.

Explanation: The four necessary conditions for deadlock are: Mutual Exclusion, Hold and Wait, No Preemption, and Circular Wait. Preemption (the ability to forcibly take resources) actually prevents deadlock. The condition is 'No Preemption' — resources cannot be forcibly taken.

Explanation: EAT = (1−p) × memory_access + p × page_fault_time = 0.99 × 200 + 0.01 × 10,000,000 = 198 + 100,000 = 100,198 ns ≈ 100,200 ns.

Explanation: The Banker's algorithm is a deadlock avoidance algorithm. Before granting a resource request, it checks whether the resulting state is safe (i.e., there exists a sequence in which all processes can complete). If unsafe, the request is denied.

Explanation: Logical address bits = log₂(64 KB) = 16. Offset bits = log₂(2 KB) = 11. Page number bits = 16 − 11 = 5. This means there are 2^5 = 32 pages.

Explanation: SSTF can cause starvation for requests at the far end of the disk if new requests keep arriving closer to the current head position. SCAN and C-SCAN guarantee that all requests are served within one or two sweeps, preventing starvation.