GATE CSE 2025 previous year paper · official paper and PYQ-pattern practice

GATE CSE 2025 PYQ-pattern questions

Showing 10 of the 15 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 · Verbal Aptitude

   Choose the word most similar in meaning to 'METICULOUS':

   • A. Careless
   • B. Precise
   • C. Lazy
   • D. Hasty
   Answer and solution

   Answer: B

   Meticulous means showing great attention to detail or being very careful and precise, so 'Precise' is the closest synonym.

2. Q2 · Digital Logic

   What is the minimum number of 2-to-1 multiplexers required to implement a 4-to-1 multiplexer?

   • A. 2
   • B. 3
   • C. 4
   • D. 5
   Answer and solution

   Answer: B

   A 4-to-1 multiplexer can be constructed using three 2-to-1 multiplexers: two at the first level to select from pairs of inputs, and one at the second level to select between the outputs of the first two.

3. Q3 · Computer Networks

   A network uses CSMA/CD with a transmission rate of 100 Mbps and a cable length of 2 km. If the propagation speed is 2 × 10⁸ m/s, what is the minimum frame size in bits to ensure collision detection?

   • A. 1000 bits
   • B. 2000 bits
   • C. 500 bits
   • D. 4000 bits
   Answer and solution

   Answer: B

   Round-trip time = (2 × 2000) / (2 × 10⁸) = 20 μs. Minimum frame transmission time = 20 μs. Frame size = 100 × 10⁶ × 20 × 10⁻⁶ = 2000 bits.

4. Q4 · Digital Logic

   The minimal sum-of-products expression for the Boolean function F(A, B, C) = Σm(1, 3, 5, 7) is:

   • A. A
   • B. B
   • C. C
   • D. A + C
   Answer and solution

   Answer: C

   The minterms 1, 3, 5, 7 correspond to all combinations where C = 1. Using a K-map or inspection, the minimal expression simplifies to F = C.

5. Q5 · Engineering Mathematics

   Let A be a 3×3 matrix with eigenvalues 2, 3, and 5. What is the determinant of the matrix (A - I), where I is the 3×3 identity matrix?

   • A. 6
   • B. 8
   • C. 10
   • D. 12
   Answer and solution

   Answer: B

   The eigenvalues of (A - I) are (2-1), (3-1), (5-1) = 1, 2, 4. The determinant equals the product of eigenvalues: 1×2×4 = 8.

6. Q6 · Theory of Computation

   Which of the following languages is NOT context-free?

   • A. L = {a^n b^n c^m | n, m ≥ 0}
   • B. L = {a^n b^m c^n | n, m ≥ 0}
   • C. L = {a^n b^n c^n | n ≥ 0}
   • D. L = {w w^R | w ∈ {a, b}*}
   Answer and solution

   Answer: C

   L = {a^n b^n c^n | n ≥ 0} requires matching three counts simultaneously, which cannot be done by a single stack (PDA). It is context-sensitive but not context-free.

7. Q7 · Databases

   Consider a relational schema R(A, B, C, D, E) with functional dependencies F = {A → B, BC → E, D → A}. Which of the following is a candidate key for R?

   • A. AD
   • B. CD
   • C. BD
   • D. AE
   Answer and solution

   Answer: B

   Starting with CD: C→(none directly), D→A (from D→A), then A→B, then BC→E. So CD→{A,B,C,D,E}, covering all attributes. Hence CD is a candidate key.

8. Q8 · Computer Networks

   A network uses a subnet mask of 255.255.255.224. How many usable host addresses does each subnet support?

   • A. 30
   • B. 32
   • C. 62
   • D. 64
   Answer and solution

   Answer: A

   Subnet mask 255.255.255.224 is /27, giving 2^5=32 addresses per subnet. Usable host addresses = 32 - 2 = 30 (excluding network and broadcast addresses).

9. Q9 · Computer Organization and Architecture

   A processor uses a 5-stage instruction pipeline with stages: Fetch (F), Decode (D), Execute (E), Memory (M), and Write-back (W). Each stage takes exactly one clock cycle. Consider executing 8 independent instructions. If the pipeline operates without any hazards or stalls, how many clock cycles are required to complete the execution of all 8 instructions?

   • A. 8
   • B. 12
   • C. 40
   • D. 13
   Answer and solution

   Answer: B

   In a 5-stage pipeline, the first instruction takes 5 cycles to complete. After that, one instruction completes every cycle. Total cycles = 5 + (8-1) = 12 cycles.

10. Q10 · Verbal Aptitude

    The manager declared that the project was completed _______ schedule, which pleased the stakeholders. Choose the option that correctly fills in the blank.

    • A. ahead of
    • B. ahead to
    • C. ahead from
    • D. ahead off
    Answer and solution

    Answer: A

    'Ahead of' is the correct idiomatic expression used when comparing time or position with respect to a deadline or standard.