GATE 2025 Computer Science

Q1. General Aptitude

The sum of ages of A and B is 45 years. 5 years from now, the ratio of their ages will be 4:5. Find the current age of A.

A. 15 years

B. 20 years

C. 25 years

D. 30 years

Correct Answer: A
Let A's age = x, B's age = 45-x. After 5 years: (x+5)/(50-x) = 4/5. 5x+25 = 200-4x. 9x = 175. x = 15.

Q2. General Aptitude

If LOGIC is coded as 15-15-7-9-3, then what is the code for MATH?

A. 1-13-20-8

B. 13-1-20-8

C. 14-1-21-9

D. 12-1-19-7

Correct Answer: C
Each letter is coded as its position + 1. L(12)+3=15, O(15)+0=15, G(7)+0=7, I(9)+0=9, C(3)+0=3. For MATH: M(13)+1=14, A(1)+0=1, T(20)+1=21, H(8)+1=9 → 14-1-21-9.

Q3. Data Structures & Algorithms

What is the time complexity of binary search on a sorted array of n elements?

A. O(n)

B. O(log n)

C. O(n²)

D. O(n log n)

Correct Answer: B
Binary search divides the search space in half each iteration, giving O(log n) time complexity.

Q4. Data Structures & Algorithms

A stack is implemented using an array. If the top pointer is at index 5, what is the current size of the stack?

A. 6

B. 5

C. 4

D. 7

Correct Answer: A
If top = 5 (0-indexed), there are 6 elements at indices 0 through 5.

Q5. Data Structures & Algorithms

Which data structure is used for implementing recursion?

A. Queue

B. Array

C. Stack

D. Linked List

Correct Answer: C
Recursion uses the call stack (LIFO) to store function call frames and return addresses.

Q6. Computer Organization & OS

Which memory has the fastest access time?

A. RAM

B. Cache

C. Hard Disk

D. SSD

Correct Answer: B
Cache memory is closest to the CPU and has the fastest access time (nanoseconds), followed by RAM, then SSD, then HDD.

Q7. Computer Organization & OS

Which scheduling algorithm is non-preemptive?

A. Round Robin

B. FCFS

C. Shortest Remaining Time First

D. Priority (Preemptive)

Correct Answer: B
First Come First Serve (FCFS) is non-preemptive — once a process gets the CPU, it runs until completion or I/O.

Q8. Computer Organization & OS

The main function of an operating system is:

A. Compiling programs

B. Providing internet access

C. Managing hardware resources

D. Running applications

Correct Answer: C
The OS manages CPU, memory, I/O devices, and provides resource allocation and protection.

Q9. Theory of Computation

A language accepted by a Finite Automaton is called:

A. Regular language

B. Context-free language

C. Context-sensitive language

D. Recursively enumerable language

Correct Answer: A
Finite automata accept exactly the class of regular languages (Type 3 in Chomsky hierarchy).

Q10. Theory of Computation

Which of the following is NOT a valid Boolean algebra property?

A. A · 0 = 0

B. A + 1 = 1

C. A · A = A

D. A + A = 0

Correct Answer: D
A + A = A (idempotent law), not 0. A + A̅ = 1 and A · A̅ = 0.

Q11. Data Structures & Algorithms

What does the following C expression evaluate to? (Assume i = 5) i++ + ++i

A. 10

B. 11

C. 12

D. Undefined

Correct Answer: C
i++ uses current value (5) then increments to 6. ++i increments to 7 then uses 7. So 5 + 7 = 12.

Q12. Computer Organization & OS

In virtual memory, which technique is used for address translation?

A. Segmentation

B. Compaction

C. Paging

D. Swapping

Correct Answer: C
Paging maps virtual addresses to physical addresses using page tables, enabling virtual memory.

Q13. General Aptitude

A train 150 m long passes a pole in 15 seconds. Find the speed of the train in km/h.

A. 12 km/h

B. 24 km/h

C. 36 km/h

D. 48 km/h

Correct Answer: C
Speed = distance/time = 150/15 = 10 m/s. In km/h: 10 × (18/5) = 36 km/h.

Q14. Theory of Computation

Which of the following problems is undecidable?

A. Checking if a DFA accepts a given string

B. Checking if a CFL is empty

C. The Halting Problem for Turing Machines

D. Checking if an NFA accepts a given string

Correct Answer: C
The Halting Problem is undecidable (proved by Alan Turing). All other options are decidable.

Q15. DS & Algorithms

The worst-case time complexity of quicksort is:

A. O(log n)

B. O(n log n)

C. O(n²)

D. O(n)

Correct Answer: C
Quicksort worst-case O(n²) when pivot is smallest/largest element (e.g., sorted array with naive pivot).

Q16. General Aptitude

If 5 men can build a wall in 12 days, how many days will 10 men take?

A. 24

B. 12

C. 6

D. 3

Correct Answer: C
M₁D₁ = M₂D₂ → 5×12 = 10×D₂ → D₂ = 6 days.

Q17. General Aptitude

Find the missing number: 2, 6, 12, 20, ?

A. 28

B. 24

C. 30

D. 36

Correct Answer: C
Pattern: 1×2=2, 2×3=6, 3×4=12, 4×5=20, 5×6=30.

Q18. DS & Algorithms

Which of the following is a linear data structure?

A. Tree

B. Queue

C. Graph

D. Binary Tree

Correct Answer: B
Queue is linear (elements in sequence). Tree and Graph are non-linear data structures.

Q19. DS & Algorithms

The height of a complete binary tree with n nodes is:

A. n

B. n/2

C. ⌊log₂n⌋

D. √n

Correct Answer: C
Height of a complete binary tree with n nodes is ⌊log₂n⌋.

Q20. DS & Algorithms

In a min-heap, the smallest element is at:

A. Root

B. Leftmost leaf

C. Rightmost leaf

D. Last node

Correct Answer: A
Min-heap property: parent ≤ children, so root is always the minimum element.

Q21. CO & OS

Which of the following is a volatile memory?

A. ROM

B. Hard disk

C. RAM

D. Flash drive

Correct Answer: C
RAM (Random Access Memory) is volatile — data is lost when power is turned off.

Q22. CO & OS

The number of bits in a nibble is:

A. 2

B. 4

C. 8

D. 16

Correct Answer: B
1 nibble = 4 bits. 1 byte = 2 nibbles = 8 bits.

Q23. CO & OS

Which of the following is NOT an operating system?

A. Windows

B. Linux

C. Python

D. macOS

Correct Answer: C
Python is a programming language, not an operating system.

Q24. CO & OS

The full form of FIFO is:

A. First In First Out

B. First In First Out

C. Fast Input Fast Output

D. First In Final Out

Correct Answer: B
FIFO = First In First Out — used in queue scheduling and page replacement.

Q25. Theory of Computation

Which language is accepted by Pushdown Automata?

A. Regular

B. Context-Free

C. Context-Sensitive

D. Recursively Enumerable

Correct Answer: B
PDA accepts exactly the class of Context-Free Languages (CFL).

Q26. Theory of Computation

If L and ¬L are both recursively enumerable, then L is:

A. Regular

B. Context-Free

C. Recursive

D. Not recursively enumerable

Correct Answer: C
If L and its complement are both RE, then L is recursive (decidable).

Q27. DS & Algorithms

Which traversal gives sorted order in a BST?

A. Preorder

B. Postorder

C. Inorder

D. Level order

Correct Answer: C
Inorder traversal of BST visits nodes in ascending order (left → root → right).

Q28. General Aptitude

Find the odd one out: 2, 4, 8, 16, 24, 32

A. 4

B. 8

C. 24

D. 32

Correct Answer: C
All others are powers of 2 (2¹, 2², 2³, 2⁴, 2⁵). 24 is not a power of 2.

Q29. CO & OS

A semaphore that is used as a binary lock is called:

A. Counting semaphore

B. Mutex

C. Spinlock

D. Monitor

Correct Answer: B
Mutex (mutual exclusion) is a binary semaphore used for locking in concurrent programming.

Q30. Theory of Computation

Which of the following is a universal gate?

A. AND

B. OR

C. NOT

D. NAND

Correct Answer: D
NAND and NOR are universal gates — any Boolean function can be implemented using only NAND (or only NOR) gates.

GATE 2025 — Computer Science (CS)