Haryana Govt Professor CS Paper 5269 - 2025

Q1. 1. What is the significance of mathematical induction in proving properties of recursive structures?
Use mathematical induction to prove the following: For all integers n ≥ 1, the sum of the first n odd numbers is n².
That is, 1 + 3 + 5 + … + (2n − 1) = n²

Q2.

• (a) That is, 1 + 3 + 5 + \dots + (2n - 1) = n² Consider two cache organizations: The first one is 32KB 2-way set-associative with 10 2. 32B block size. The second one is of the same size but direct mapped. The size of an address is 32 bits in both cases. A 2 × 1 multiplexer has latency of 0.6 ns while a k-bit comparator has a latency of k/10 ns. Find out the hit latency of the set-associative and direct-mapped memory organizations. Consider another setting of the 2-way set-associative cache having 128 lines, each with 86 I 16 words. Suppose the main memory has 16-bit address. Both cache and memory are word addressable. Now suppose we want to read and write a word at memory address 357A. Under this, another set associative mapping technique, what will be the "tag" value in decimal? (Pleuse cead the following instructions excelully before at Using the decision parameter of Bresenham line drawing algorithm for line with slope 10 3. ≤1, find the coordinates of the points that lie on line with end points (1, 1) and (7, 5). Differentiate between Immediate and Deferred Log-based recovery methods. Generate the log file of below given (Figure 1) transaction using both Immediate and Deferred 4. recovery methods. Also state, if the failure happens in T1 before commit, what will happen in both Immediate and Deferred recovery methods? In Figure 2, which one of the two Log-based recovery methods (Immediate or Deferred) is used to generate the file? If crash happens now (after T3 is written to file), and system tries to recover both undo and redo operations also, which transaction will go to each of undo and redo list? File Transaction T1 tol novig ad live R sait basistib you A = A - 100 \langle \textT1, \textStart \rangle per a trop up W(A) [T, Z, 5, 7 апсивело II. Checkpoint R
• (b) 16 FIRE FOR B = B + 200 \langleT2, X, 1, 9> acites Ouestion W(B) IBILIOIREG IENI TOI तक का साथ को पर Commit 50 Freiling (@ 182 pp.) Firming liked for Figure 2 Figure 1 acta ODM \mathbf 2 MOC 2025

Q3. 3. Consider another setting of the 2-way set-associative cache having 128 lines, each with 16 words. Suppose the main memory has 16-bit address. Both cache and memory are word addressable. Now suppose we want to read and write a word at memory address 357A. Under this, another set associative mapping technique, what will be the 'tag' value in decimal?

Q4. 4. Differentiate between Immediate and Deferred Log-based recovery methods. Generate the log file of the below given (Figure 1) transaction using both Immediate and Deferred recovery methods. Also state, if the failure happens in T1 before commit, what will happen in both Immediate and Deferred recovery methods? In Figure 2, which one of the two Log-based recovery methods (Immediate or Deferred) is used to generate the file? If crash happens now (after T3 is written to file), and system tries to recover both undo and redo operations also, which transaction will go to each of undo and redo list?