List of top Questions asked in GATE CS- 2026

Consider a system consisting of 𝑘 instances of a resource 𝑅, being shared by
5 processes. Assume that each process requires a maximum of two instances of
resource 𝑅 and a process can request or release only one instance at a time. Further,
a process can request the second instance of the resource only after acquiring the
first instance.
The minimum value of 𝑘 for the system to be deadlock-free is ________. (answer
in integer)

Consider the following program in C:
#include <stdio.h>
void func(int i, int j) {
if(i < j) {
int i = 0;
while (i < 10) {
j += 2;
i++;
}
}
printf("%d", i);
}
int main() {
int i = 9, j = 10;
func(i, j);
return 0;
}
The output of the program is _________. (answer in integer)
Note: Assume that the program compiles and runs successfully.

With respect to deadlocks in an operating system, which of the following
statements is/are FALSE?

In the context of relational database normalization, which of the following
statements is/are true?

Let 𝑃, 𝑄, 𝑅 and 𝑆 be the attributes of a relation in a relational schema. Let 𝑋 ⟶𝑌
indicate functional dependency in the context of a relational database, where
𝑋, 𝑌 ⊆{𝑃, 𝑄, 𝑅, 𝑆}.
Which of the following options is/are always true?

Consider the function 𝑓: ℝ→ℝ defined as follows:
𝑓(𝑥) = {𝑐1𝑒𝑥−𝑐2 loge (1
𝑥) , if 𝑥> 0
3 otherwise
where 𝑐1 , 𝑐2 ∈ℝ.
If 𝑓 is continuous at 𝑥 = 0, then 𝑐1 + 𝑐2 = _________. (answer in integer)

The height of a binary tree is the number of edges in the longest path from the root
to a leaf in the tree. The maximum possible height of a full binary tree with
23 nodes is _________. (answer in integer)

Which of the following statements is/are true?

Consider the following C statements:
char *str1 = "Hello; /* Statement S1 */
char *str2 = "Hello;"; /* Statement S2 */
int *str3 = "Hello"; /* Statement S3 */
Which of the following options is/are correct?

Let M be a nondeterministic finite automaton (NFA) with 6 states over a finite
alphabet.
Which of the following options CANNOT be the number of states in the minimal
deterministic finite automaton (DFA) that is equivalent to 𝑀 ?

Consider the following grammar where 𝑆 is the start symbol, and 𝑎 and 𝑏 are
terminal symbols.
𝑆 →𝑎𝑆𝑏𝑆 ∣ 𝑏𝑆 ∣ ϵ
Which of the following statements is/are true?

Consider the 8-bit signed integers 𝑋, 𝑌 and 𝑍 represented using the sign-magnitude
form. The binary representations of 𝑋 and 𝑌 are as follows:
𝑋: 10110100 𝑌: 01001100
Which of the following operations to compute 𝑍 result(s) in an arithmetic
overflow?

Consider a hash table 𝑃[0, 1, … , 10] that is initially empty. The hash table is
maintained using open addressing with linear probing. The hash function used is
ℎ(𝑥) = (𝑥+ 7) mod 11.
Consider the following sequence of insertions performed on 𝑃:
1, 13, 22, 15, 11, 24
Which of the following positions in the hash table is/are empty after these insertions
are performed?

Let 𝑛 be an odd number greater than 100. Consider a binary minheap with
𝑛 elements stored in an array 𝑃 whose index starts from 1.
Which of the following indices of 𝑃 do/does NOT correspond to any leaf node of
the minheap?

Consider the following recurrence relations:
For all 𝑛> 1,
𝑇1(𝑛) = 4𝑇1 (𝑛
2) + 𝑇2(𝑛)
𝑇2(𝑛) = 5𝑇2 (𝑛
4) + Θ(log2 𝑛)
Assume that for all 𝑛≤1, 𝑇1(𝑛) = 1 and 𝑇2(𝑛) = 1.
Which one of the following options is correct?

Consider the following Boolean expression of a function F :
𝐹(𝑃, 𝑄) = (𝑃̅ + 𝑄) ⊕(𝑃̅𝑄)
Which of the following expressions is/are equivalent to F ?

Which of the following statements is/are true with respect to the interaction of a
web browser with a web server using HTTP 1.1?

With respect to a TCP connection between a client and a server, which one of the
following statements is true?

Let 𝑛 > 1. Consider an 𝑛× 𝑛 matrix 𝑀 with its elements from ℝ. Let the vector
(0, 1, 0, 0, … , 0) ∈ℝ𝑛 be in the null space of 𝑀.
Which of the following options is/are always correct?

Which one of the following dependencies among the register operands of different
instructions can cause a data hazard in a pipelined processor?

Consider a processor P whose instruction set architecture is the load-store
architecture. The instruction format is such that the first operand of any instruction
is the destination operand.
Which one of the following sequences of instructions corresponds to the high-level
language statement Z = X + Y ?
Note: X, Y, and Z are memory operands. R0, R1, and R2 are registers.

Match each addressing mode in List I with a data element or an element of a data
structure (in a high-level language) in List II:
List I
List II
P. Immediate
1. Element of an array
Q. Indirect
2. Pointer
R. Base with index
3. Element of a record
S. Base with offset/displacement 4. Constant

For 𝑛 > 1, the maximum multiplicity of any eigenvalue of an 𝑛× 𝑛 matrix with
elements from ℝ is

Consider 4 × 4 matrices with their elements from {𝟎, 𝟏}. The number of such
matrices with even number of 𝟏s in every row and every column is

An urn contains one red ball and one blue ball. At each step, a ball is picked
uniformly at random from the urn, and this ball together with another ball of the
same color is put back in the urn. The probability that there are equal number of red
and blue balls after two steps is