GATE CSE 2024 previous year paper · official paper and PYQ-pattern practice

GATE CSE 2024 PYQ-pattern questions

Showing 10 of the 12 PYQ-pattern questions in this set — freshly worded in that year's pattern, not the original questions. Answers and solutions open under each question.

1. Q1 · Theory of Computation

   Let L be a regular language over the alphabet {0, 1}. Which of the following languages is guaranteed to be regular?

   • A. L² = {xy | x ∈ L and y ∈ L}
   • B. {ww | w ∈ L}
   • C. {w | w has equal number of 0s and 1s and w ∈ L}
   • D. {0ⁿ1ⁿ | n ≥ 0 and 0ⁿ ∈ L}
   Answer and solution

   Answer: A

   Regular languages are closed under concatenation. L² is the concatenation of L with itself, hence it is regular. Options B, C, and D are not guaranteed to produce regular languages.

2. Q2 · Operating System

   Three processes P1, P2, and P3 require resources R1, R2, and R3. The allocation matrix is [[1,0,1], [1,1,0], [0,0,1]] and the maximum need matrix is [[2,1,2], [3,2,1], [1,1,2]]. Available resources are [1,1,0]. Which of the following sequences is a safe sequence?

   • A. P1, P2, P3
   • B. P3, P1, P2
   • C. P2, P3, P1
   • D. No safe sequence exists
   Answer and solution

   Answer: D

   Need = Max - Allocation: P1[1,1,1], P2[2,1,1], P3[1,1,1]. Available=[1,1,0]. Each process needs 1 unit of R3, but R3 available is 0, and no process can complete to release R3 (P1 and P3 hold 1 R3 each but can't finish without acquiring R3). Thus none can proceed; no safe sequence exists.

3. Q3 · Databases

   Consider a relation Student(ID, Name, Dept) with 500 tuples and Department(Dept, Building) with 20 tuples. If a natural join is performed on Dept attribute and every student belongs to exactly one department that exists in Department relation, what is the minimum possible number of tuples in the result?

   • A. 20
   • B. 100
   • C. 500
   • D. 10000
   Answer and solution

   Answer: C

   Since every student belongs to exactly one department that exists in the Department relation, the natural join will preserve all 500 student tuples. Each student tuple will be joined with exactly one matching department tuple, resulting in exactly 500 tuples in the output.

4. Q4 · Digital Logic

   A combinational circuit is designed using four 2-to-1 multiplexers. What is the maximum number of input variables (excluding control/select inputs of the multiplexers) that such a circuit can have?

   • A. 4
   • B. 6
   • C. 8
   • D. 12
   Answer and solution

   Answer: C

   Each 2-to-1 multiplexer has 2 data inputs and 1 select input. Four such multiplexers can have at most 4×2 = 8 distinct input variables.

5. Q5 · Compiler Design

   In a compiler, which phase is responsible for eliminating common sub-expressions from the intermediate code?

   • A. Lexical Analysis
   • B. Syntax Analysis
   • C. Code Optimization
   • D. Code Generation
   Answer and solution

   Answer: C

   Code Optimization phase eliminates redundant computations including common sub-expressions to improve efficiency of generated code.

6. Q6 · Computer Networks

   In a Go-Back-N ARQ protocol with a window size of 7, if frame 4 is lost during transmission, which frames will the sender retransmit after detecting the loss?

   • A. Only frame 4
   • B. Frames 4, 5, 6, 7
   • C. Frames 4 through 10
   • D. All frames from 4 onward sent so far
   Answer and solution

   Answer: D

   In Go-Back-N, when a frame is lost, the sender retransmits that frame and all subsequent frames that were sent within the window, ensuring sequential delivery.

7. Q7 · Programming and Data Structures

   What is the output of the following C code snippet? int arr[5] = {10, 20, 30, 40, 50}; int *ptr = arr + 2; printf("%d", *(ptr + 1));

   • A. 20
   • B. 30
   • C. 40
   • D. 50
   Answer and solution

   Answer: C

   ptr points to arr[2] (which is 30). *(ptr+1) accesses the element one position ahead, which is arr[3] = 40.

8. Q8 · Databases

   Consider a relation R(A, B, C, D) with functional dependencies: {A → B, B → C, C → D}. What is the highest normal form that R satisfies?

   • A. 1NF
   • B. 2NF
   • C. 3NF
   • D. BCNF
   Answer and solution

   Answer: B

   The only candidate key is A (since A→B→C→D determines all). All determinants (A, B, C) are not superkeys except A, so BCNF fails (B→C and C→D violate BCNF). For 3NF: transitive dependencies B→C and C→D have non-prime attributes on RHS (C, D are non-prime), violating 3NF. However, 2NF is satisfied because there are no partial dependencies (key A is single attribute, so no partial dependency possible). Thus highest normal form is 2NF.

9. Q9 · Quantitative Aptitude

   A shopkeeper marks an article 40% above its cost price. He then offers a discount of 25% on the marked price. If the cost price is ₹500, what is the percentage profit or loss?

   • A. 5% profit
   • B. 5% loss
   • C. 10% profit
   • D. 15% profit
   Answer and solution

   Answer: A

   Marked price = 500 + 40% of 500 = ₹700. Selling price after 25% discount = 700 - 25% of 700 = ₹525. Profit = 525 - 500 = ₹25, which is 5% of cost price.

10. Q10 · Computer Organization and Architecture

    A CPU has a 5-stage pipeline with stages: Fetch (F), Decode (D), Execute (E), Memory (M), and Write-back (W). Each stage takes 2 ns. If there are no hazards and 100 instructions are executed, what is the total execution time in nanoseconds?

    • A. 200
    • B. 208
    • C. 210
    • D. 1000
    Answer and solution

    Answer: B

    For a 5-stage pipeline, the first instruction takes 5×2 = 10 ns. Each subsequent instruction takes 2 ns. Total = 10 + (99×2) = 208 ns.