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GATE CS - Previous Year Questions

Previous-year GATE CS prompts for practice — options only until official keys are verified

142 questions15 pages~213 min

Practice with previous-year prompts and options. Official answer keys are not shown here yet — mark your choice, then verify against the IIT key PDF.

Use this track for exam reading speed and elimination practice until verified keys are linked.

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Page 4 of 15 • Questions 31-40 of 142

Practice mode: questions and options only. Official IIT answer keys are not linked here yet — mark your choice, then cross-check the official key yourself.

Q31medium

[GATE CS 2025 Set-1 Q48] Which of the following predicate logic formulae/formula is/are CORRECT representation(s) of the statement: “Everyone has exactly one mother”? The meanings of the predicates used are: • 𝑚𝑜𝑡ℎ𝑒𝑟(𝑦,𝑥): 𝑦 is the mother of 𝑥 • 𝑛𝑜𝑡𝑒𝑞(𝑥,𝑦): 𝑥 and 𝑦 are not equal

A)∀𝑥∃𝑦∃𝑧(𝑚𝑜𝑡ℎ𝑒𝑟(𝑦,𝑥)∧¬𝑚𝑜𝑡ℎ𝑒𝑟(𝑧,𝑥))

B)∀𝑥∃𝑦[𝑚𝑜𝑡ℎ𝑒𝑟(𝑦,𝑥)∧∀𝑧(𝑛𝑜𝑡𝑒𝑞(𝑧,𝑦) → ¬𝑚𝑜𝑡ℎ𝑒𝑟(𝑧,𝑥))]

C)∀𝑥∀𝑦[𝑚𝑜𝑡ℎ𝑒𝑟(𝑦,𝑥) → ∃𝑧(𝑚𝑜𝑡ℎ𝑒𝑟(𝑧,𝑥)∧¬𝑛𝑜𝑡𝑒𝑞(𝑧,𝑦))]

D)∀𝑥∃𝑦[𝑚𝑜𝑡ℎ𝑒𝑟(𝑦,𝑥)∧¬∃𝑧(𝑛𝑜𝑡𝑒𝑞(𝑧,𝑦) ∧𝑚𝑜𝑡ℎ𝑒𝑟(𝑧,𝑥))]

Q32medium

[GATE CS 2025 Set-1 Q49] 𝐴 = {0,1,2,3,…} is the set of non-negative integers. Let Ϝ be the set of functions from 𝐴 to itself. For any two functions, 𝑓 ,𝑓 ∈ Ϝ, we define 1 2 (𝑓 ⨀𝑓 )(𝑛) = 𝑓 (𝑛)+𝑓 (𝑛) 1 2 1 2 for every number 𝑛 in 𝐴. Which of the following is/are CORRECT about the mathematical structure (Ϝ,⨀)?

A)(Ϝ,⨀) is an Abelian group.

B)(Ϝ,⨀) is an Abelian monoid.

C)(Ϝ,⨀) is a non-Abelian group.

D)(Ϝ,⨀) is a non-Abelian monoid.

Q33medium

[GATE CS 2025 Set-1 Q50] Consider the following deterministic finite automaton (DFA) defined over the alphabet, Σ = {𝑎,𝑏}. Identify which of the following language(s) is/are accepted by the given DFA.

A)The set of all strings containing an even number of 𝑏’s.

B)The set of all strings containing the pattern 𝑏𝑎𝑏.

C)The set of all strings ending with the pattern 𝑏𝑎𝑏.

D)The set of all strings not containing the pattern 𝑎𝑏𝑎.

Q34medium

[GATE CS 2025 Set-2 Q11] 1 2 If 𝐴 = ( ), then which ONE of the following is 𝐴8 ? 2 −1

A)25 0 ( ) 0 25

B)125 0 ( ) 0 125

C)625 0 ( ) 0 625

D)3125 0 ( ) 0 3125

Q35medium

[GATE CS 2025 Set-2 Q12] The value of 𝑥 such that 𝑥 > 1, satisfying the equation ∫ 𝑥 𝑡 ln 𝑡 𝑑𝑡 = 1 is 1 4

A)√𝑒

B)𝑒

C)𝑒2

D)𝑒−1

Q36medium

[GATE CS 2025 Set-2 Q13] Consider a binary tree 𝑇 in which every node has either zero or two children. Let 𝑛 > 0 be the number of nodes in 𝑇. Which ONE of the following is the number of nodes in 𝑇 that have exactly two children?

A)𝑛−2 2

B)𝑛−1 2 𝑛

C)2

D)𝑛+1 2

Q37medium

[GATE CS 2025 Set-2 Q14] Let 𝐿,𝑀, and 𝑁 be non-singular matrices of order 3 satisfying the equations 𝐿2 = 𝐿−1 , 𝑀 = 𝐿8 and 𝑁 = 𝐿2. Which ONE of the following is the value of the determinant of (𝑀−𝑁)?

A)0

B)1

C)2

D)3

Q38medium

[GATE CS 2025 Set-2 Q15] Let 𝑃(𝑥) be an arbitrary predicate over the domain of natural numbers. Which ONE of the following statements is TRUE?

A)(𝑃(0)∧(∀𝑥 [𝑃(𝑥) ⇒ 𝑃(𝑥+1)])) ⇒ (∀𝑥 𝑃(𝑥))

B)(𝑃(0)∧(∀𝑥 [𝑃(𝑥) ⇒ 𝑃(𝑥−1)])) ⇒ (∀𝑥 𝑃(𝑥))

C)(𝑃(1000)∧(∀𝑥 [𝑃(𝑥) ⇒ 𝑃(𝑥−1)])) ⇒ (∀𝑥 𝑃(𝑥))

D)(𝑃(1000)∧(∀𝑥 [𝑃(𝑥) ⇒ 𝑃(𝑥+1)])) ⇒ (∀𝑥 𝑃(𝑥))

Q39medium

[GATE CS 2025 Set-2 Q16] Consider the following statements: (i) Address Resolution Protocol (ARP) provides a mapping from an IP address to the corresponding hardware (link-layer) address. (ii) A single TCP segment from a sender S to a receiver R cannot carry both data from S to R and acknowledgement for a segment from R to S. Which ONE of the following is CORRECT?

A)Both (i) and (ii) are TRUE

B)(i) is TRUE and (ii) is FALSE

C)(i) is FALSE and (ii) is TRUE

D)Both (i) and (ii) are FALSE

Q40medium

[GATE CS 2025 Set-2 Q17] Consider the routing protocols given in List I and the names given in List II: List I List II (i) Distance vector routing (a) Bellman-Ford (ii) Link state routing (b) Dijkstra For matching of items in List I with those in List II, which ONE of the following options is CORRECT?

A)(i) – (a) and (ii) – (b)

B)(i) – (a) and (ii) – (a)

C)(i) – (b) and (ii) – (a)

D)(i) – (b) and (ii) – (b)

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