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General Aptitude(10)Engineering Mathematics(8)CS Core(40)

General Aptitude

10 Questions

GATE→2026→General Aptitude→Verbal Ability

Q1

MCQ[1 Mark]

The antonym of the word protagonist is

(A)

agnostic

(B)

antagonist

(C)

arsonist

(D)

anarchist

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q2

MCQ[1 Mark]

The figure shows two 4-tile patterns. Either one or both of the patterns can be used any number of times and in any orientation to construct a new pattern. Which one of the options below cannot be constructed by using only these two 4-tile patterns assuming there are no overlaps among them?

(A)

(B)

(C)

(D)

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q3

MCQ[1 Mark]

Consider a knock-out women's badminton singles tournament where there are no ties. The loser in each game is eliminated from the tournament. Every player plays until she is defeated or remains the last undefeated player. The last undefeated player is declared the winner of the tournament. If there are 64 players in the beginning of the tournament, how many games should be played in total to declare the winner of the tournament?

(A)

127

(B)

64

(C)

63

(D)

32

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q4

MCQ[1 Mark]

A student needs to enroll for a minimum of 60 credits. A student cannot enroll for more than 70 credits. The credits are divided amongst project and three distinct sets of courses namely, core courses, specialization courses, and elective courses. It is compulsory for a student to enroll for exactly 15 credits of core courses and exactly 20 credits of project. In addition, a student has to enroll for a minimum of 10 credits of specialization courses. The maximum credits of elective courses that a student can enroll for is

(A)

10

(B)

15

(C)

20

(D)

25

Explanation

GATE→2026→General Aptitude→Verbal Ability

Q5

MCQ[1 Mark]

'When the teacher is in the room, all students stand silently.' If the above statement is true, which one of the following statements is not necessarily true?

(A)

If any student is not standing silently, then the teacher is not in the room.

(B)

When the teacher is in the room, all students are silent.

(C)

If all students are standing, then the teacher is in the room.

(D)

When the teacher is in the room, all students are standing.

Explanation

GATE→2026→General Aptitude→Data Interpretation

Q6

MCQ[2 Marks]

Combinatorics deals with problems involving counting... Consider the following statements: P: Combinatorics is always invoked in the modeling of physical phenomena. Q: Modeling some physical phenomena involves assigning probabilities to combinatorial possibilities in order to compute average values of physical quantities. Based on the passage above, what can be inferred about statements P and Q?

(A)

P is False and Q is False

(B)

P is False and Q is True

(C)

P is True and Q is False

(D)

P is True and Q is True

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q7

MCQ[2 Marks]

In Panel I of the figure below, the front view and top view of a structure are shown. Which one of the 3D structures shown in Panel II possesses the views shown in Panel I?

(A)

(i)

(B)

(ii)

(C)

(iii)

(D)

(iv)

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q8

MCQ[2 Marks]

For positive real numbers S and K, the function H_K(S) is defined as: H_K(S) = max(S-K, 0)... The graph below shows the plot of a function N(S) versus S. N(S) can be expressed as

(A)

H_10(S) - H_20(S)

(B)

H_10(S) - 2H_20(S)

(C)

-H_10(S) + H_20(S)

(D)

H_15(S) - H_20(S)

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q9

MCQ[2 Marks]

In the 2020 summer Olympics' Javelin throw finals... In which round did Vitezlav Vesely have his best throw?

(A)

Third

(B)

Fourth

(C)

Fifth

(D)

Sixth

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q10

MCQ[2 Marks]

An unbiased six-faced dice... rolled twice in succession... The probability that the number appearing in the second roll is an integer multiple of the number appearing in the first roll is

(A)

1/6

(B)

5/18

(C)

7/18

(D)

5/6

Explanation

Engineering Mathematics

8 Questions

GATE→2026→Engineering Mathematics→Probability and Statistics

Q11

MCQ[1 Mark]

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

(A)

1/4

(B)

1/3

(C)

1/2

(D)

2/3

Explanation

GATE→2026→Engineering Mathematics→Discrete Mathematics

Q12

MCQ[1 Mark]

Consider 4x4 matrices with their elements from {0,1}. The number of such matrices with even number of 1s in every row and every column is

(A)

512

(B)

1025

(C)

1023

(D)

255

Explanation

GATE→2026→Engineering Mathematics→Linear Algebra

Q13

MCQ[1 Mark]

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

(A)

n

(B)

n - 1

(C)

1

(D)

n + 1

Explanation

GATE→2026→Engineering Mathematics→Linear Algebra

Q14

MSQ[1 Mark]

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

(A)

Determinant of M is 1

(B)

Determinant of M is 0

(C)

Rank of M is 1

(D)

There are at least two non-zero vectors in the null space of M

Explanation

GATE→2026→Engineering Mathematics→Calculus

Q15

NAT[1 Mark]

Consider the function f: R -> R defined as f(x) = c1 e^x - c2 log_e(1/x) if x > 0, 6 otherwise. If f is continuous at x = 0, then c1 + c2 =

Explanation

GATE→2026→Engineering Mathematics→Calculus

Q16

MSQ[2 Marks]

Let f: R -> R be defined as f(x) = (|x|/2 - x)(x - |x|/2). Which of the following statements is/are true?

(A)

f has a local maximum

(B)

f has a local minimum

(C)

f' is continuous over R

(D)

f' is not differentiable over R

Explanation

GATE→2026→Engineering Mathematics→Discrete Mathematics

Q17

NAT[2 Marks]

Let G be an undirected graph which is a path on 8 vertices. The number of matchings in G is

Explanation

GATE→2026→Engineering Mathematics→Probability and Statistics

Q18

NAT[2 Marks]

Let X be a random variable taking values in {1, 2, 3, 4, 5, 6, 7, 8} with Pr(X=1)=Pr(X=2)=Pr(X=5)=Pr(X=7)=1/6 and Pr(X=3)=Pr(X=4)=Pr(X=6)=Pr(X=8)=1/12. The expected value E[X] is

Explanation

CS Core

40 Questions

GATE→2026→CS Core→Computer Organization and Architecture

Q19

MCQ[1 Mark]

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

(A)

P-4, Q-3, R-1, S-2

(B)

P-4, Q-2, R-1, S-3

(C)

P-1, Q-4, R-3, S-2

(D)

P-2, Q-3, R-1, S-4

Explanation

GATE→2026→CS Core→Computer Organization and Architecture

Q20

MCQ[1 Mark]

Consider a processor P whose instruction set architecture is the load-store architecture... Which one of the following sequences of instructions corresponds to the high-level language statement Z = X + Y?

(A)

ADD Z, X, Y

(B)

LOAD R0, X; ADD Z, R0, Y

(C)

ADD R0, X, Y; STORE Z, R0

(D)

LOAD R0, X; LOAD R1, Y; ADD R2, R0, R1; STORE Z, R2

Explanation

GATE→2026→CS Core→Computer Organization and Architecture

Q21

MCQ[1 Mark]

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

(A)

Read-after-read

(B)

Read-after-write

(C)

Write-after-read

(D)

Write-after-write

Explanation

GATE→2026→CS Core→Algorithms

Q22

MCQ[1 Mark]

Consider the following recurrence relations: T1(n) = 4 T1(n/2) + T2(n), T2(n) = 5 T2(n/4) + Theta(log2 n)... Which one of the following options is correct?

(A)

T1(n) = Theta(n^2)

(B)

T1(n) = Theta(n^2 log2 n)

(C)

T1(n) = Theta(n^(log_4 5))

(D)

T1(n) = Theta(n^(log_4 5) log2 n)

Explanation

GATE→2026→CS Core→Computer Networks

Q23

MCQ[1 Mark]

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

(A)

The client and server use a two-way handshake mechanism before the start of data transmission

(B)

The server cannot initiate closing of the connection before the client initiates closing of the connection

(C)

The TCP connection is half-duplex

(D)

The client and server can initiate closing of the connection at the same time

Explanation

GATE→2026→CS Core→Computer Networks

Q24

MSQ[1 Mark]

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?

(A)

HTTP 1.1 facilitates downloading multiple objects of the same webpage over the same TCP connection, if the objects are stored in the same server

(B)

HTTP 1.1 facilitates downloading multiple objects of the same webpage over the same TCP connection, even if they are stored in different servers

(C)

HTTP 1.1 facilitates sending a request for downloading one object without waiting for a previously requested object to be downloaded completely

(D)

HTTP 1.1 facilitates downloading multiple webpages on the same server to be downloaded over a single TCP connection

Explanation

GATE→2026→CS Core→Digital Logic

Q25

MSQ[1 Mark]

Consider the following Boolean expression of a function F: F(P,Q) = (not P + Q) (+) (not P * Q). Which of the following expressions is/are equivalent to F?

(A)

P (+) 0

(B)

P (+) Q

(C)

not P (+) Q

(D)

not P (+) not Q

Explanation

GATE→2026→CS Core→Digital Logic

Q26

MSQ[1 Mark]

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

(A)

Z = X + Y

(B)

Z = X - Y

(C)

Z = -X + Y

(D)

Z = -X - Y

Explanation

GATE→2026→CS Core→Algorithms

Q27

MSQ[1 Mark]

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?

(A)

(n + 1) / 2

(B)

(n - 1) / 2

(C)

(n - 3) / 2

(D)

n

Explanation

GATE→2026→CS Core→Programming and Data Structures

Q28

MSQ[1 Mark]

Consider a hash table P[0, 1, ..., 10] initially empty, using linear probing with h(x) = (x + 7) mod 11. Insertions: 1, 13, 22, 15, 11, 24. Which of the following positions is/are empty after these insertions?

(A)

0

(B)

10

(C)

2

(D)

1

Explanation

GATE→2026→CS Core→Theory of Computation

Q29

MSQ[1 Mark]

Consider grammar S -> aSbS | bS | epsilon. Which of the following statements is/are true?

(A)

The grammar is ambiguous

(B)

The string abb has two distinct derivations in this grammar

(C)

The string abab has only one rightmost derivation

(D)

The language generated by the grammar is undecidable

Explanation

GATE→2026→CS Core→Theory of Computation

Q30

MSQ[1 Mark]

Let M be an NFA with 6 states over a finite alphabet. Which of the following options CANNOT be the number of states in the minimal DFA equivalent to M?

(A)

32

(B)

65

(C)

1

(D)

128

Explanation

GATE→2026→CS Core→Compiler Design

Q31

MSQ[1 Mark]

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

(A)

S1 and S2 have syntactic errors

(B)

S2 has a lexical error and S3 has a syntactic error

(C)

S1 has a lexical error and S3 has a semantic error

(D)

S1 has a syntactic error and S3 has a semantic error

Explanation

GATE→2026→CS Core→Compiler Design

Q32

MSQ[1 Mark]

Which of the following statements is/are true?

(A)

LL(1) parser uses backtracking

(B)

For a grammar to be LL(1), it must be left-recursive

(C)

For a grammar to be LL(1) it must be left-factored

(D)

The LL(1) parsers are more powerful than the SLR parsers

Explanation

GATE→2026→CS Core→Operating System

Q33

MSQ[1 Mark]

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

(A)

Banker's algorithm is used to prevent deadlocks

(B)

Deadlock formation can be prevented by ensuring that the hold and wait condition is not allowed

(C)

An assignment edge in a resource allocation graph is marked from a process to a resource

(D)

A safe state guarantees that all processes can finish without formation of a deadlock

Explanation

GATE→2026→CS Core→Databases

Q34

MSQ[1 Mark]

Let P, Q, R and S be attributes. Which of the following functional dependency options is/are always true?

(A)

If ({P,Q} -> {R} and {P} -> {R}), then {Q} -> {R}

(B)

If {P,Q} -> {R} then ({P} -> {R} or {Q} -> {R})

(C)

If ({P} -> {R} and {Q} -> {S}), then {P,Q} -> {R,S}

(D)

If {P} -> {R} then {P,Q} -> {R}

Explanation

GATE→2026→CS Core→Databases

Q35

MSQ[1 Mark]

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

(A)

It is always possible to obtain a dependency-preserving 3NF decomposition

(B)

It is always possible to obtain a dependency-preserving 1NF decomposition

(C)

It is not always possible to obtain a dependency-preserving BCNF decomposition

(D)

It is not always possible to obtain a dependency-preserving 2NF decomposition

Explanation

GATE→2026→CS Core→Programming and Data Structures

Q36

NAT[1 Mark]

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

Explanation

GATE→2026→CS Core→Programming and Data Structures

Q37

NAT[1 Mark]

Consider the following program in C... The output of the program is

Explanation

GATE→2026→CS Core→Operating System

Q38

NAT[1 Mark]

Consider a system consisting of k instances of a resource R, shared by 5 processes... The minimum value of k for the system to be deadlock-free is

Explanation

GATE→2026→CS Core→Computer Organization and Architecture

Q39

MCQ[2 Marks]

Consider IEEE 754 single-precision floating-point variables X (35C00000) and Y (34A00000). Let Z = X + Y. The hexadecimal representation of Z is

(A)

35C80000

(B)

35CC0000

(C)

35E80000

(D)

35EC0000

Explanation

GATE→2026→CS Core→Digital Logic

Q40

MCQ[2 Marks]

Consider a 2-bit saturating up/down counter... Which one of the following options corresponds to the expressions for the inputs of the D flip-flops, D1 and D0?

(A)

(B)

(C)

(D)

Explanation

GATE→2026→CS Core→Computer Organization and Architecture

Q41

MCQ[2 Marks]

Physical address space size 2^32 bytes, cache capacity 2^23 bytes, block size 128 bytes. Tag length M for direct mapped and N for K-way set-associative (K = 2^L). Which option is true?

(A)

N = M + L

(B)

N = M - L

(C)

N = M + K

(D)

N = M - K

Explanation

GATE→2026→CS Core→Programming and Data Structures

Q42

MCQ[2 Marks]

Consider C code computing node count in a linked list... Which option gives correct replacements for E1 and E2?

(A)

E1: head == NULL; E2: 1 + getListSize(head)

(B)

E1: head->next == NULL; E2: 1 + getListSize(head->next)

(C)

E1: head == NULL; E2: 1 + getListSize(head->next)

(D)

E1: head->next == NULL; E2: 1 + getListSize(head)

Explanation

GATE→2026→CS Core→Programming and Data Structures

Q43

MCQ[2 Marks]

Let P be integers 1 to 15. Insertion into BST creating a complete binary tree. Which element can NEVER be the third element inserted?

(A)

4

(B)

2

(C)

10

(D)

5

Explanation

GATE→2026→CS Core→Algorithms

Q44

MCQ[2 Marks]

Let G(V,E) be an undirected edge-weighted graph... Consider statements S1 and S2 regarding shortest paths. Which option is correct?

(A)

Only S1 is true

(B)

Only S2 is true

(C)

Both S1 and S2 are true

(D)

Neither S1 nor S2 is true

Explanation

GATE→2026→CS Core→Compiler Design

Q45

MCQ[2 Marks]

Consider the control flow graph shown in the figure. Which option correctly lists redundant expressions in basic blocks B4 and B5?

(A)

B4: {b+i}, B5: {c+m}

(B)

B4: {g*k}, B5: {c+m}

(C)

B4: {g*k, b+i}, B5: {}

(D)

B4: {g*k}, B5: {}

Explanation

GATE→2026→CS Core→Databases

Q46

MCQ[2 Marks]

Consider relations R(P,Q) and S(X,Y). Let tuple relational calculus expression E = {(u) | exists v ((u,v) in R and (v,u) in S)}. Which relational algebraic expression is equivalent to E?

(A)

Pi_P(R join_{R.P=S.X} S)

(B)

Pi_P(S join_{S.X=R.Q} R)

(C)

Pi_P(R join_{R.P=S.Y} S)

(D)

Pi_P(S join_{S.Y=R.Q} R)

Explanation

GATE→2026→CS Core→Computer Networks

Q47

MCQ[2 Marks]

A TCP sender establishes connection... slow-start threshold 10000 segments, RTT 1 ms. Time t (ms) at which transmission of segment 2000 starts is

(A)

9 <= t < 10

(B)

10 <= t < 11

(C)

11 <= t < 12

(D)

12 <= t < 13

Explanation

GATE→2026→CS Core→Computer Networks

Q48

MCQ[2 Marks]

Sliding window protocol over lossless link, window size W frames, frame size 1000 bits, bandwidth 100 kbps, propagation delay 100 ms. Minimum W for 100% link utilization is

(A)

10

(B)

21

(C)

20

(D)

11

Explanation

GATE→2026→CS Core→Algorithms

Q49

MSQ[2 Marks]

Let G(V,E) be a simple undirected graph, smallest vertex cover size k. For vertex v in V, which constraints ensure v in S?

(A)

Degree of v is at least k + 1

(B)

Vertex v is on a path of length k + 1

(C)

Vertex v is on a cycle of length k + 1

(D)

Vertex v is part of a clique of size k

Explanation

GATE→2026→CS Core→Digital Logic

Q50

MSQ[2 Marks]

Consider Boolean function F(P,Q,R,S) = sum m(1,2,3,4,5,7,10,12,13,14). Which of the following are minimal sum-of-products expressions?

(A)

not(P)not(S) + Q not(R) + not(P)not(Q)R + not(Q)R not(S)

(B)

not(P)not(S) + Q not(R) + not(P)not(Q)R + P R not(S)

(C)

not(P)not(S) + Q not(R) + P Q not(S) + P R not(S)

(D)

not(P)not(S) + Q not(R) + P Q not(S) + not(Q)R not(S)

Explanation

GATE→2026→CS Core→Algorithms

Q51

MSQ[2 Marks]

Let G(V,E) be a simple undirected graph with unique edge weights. Which statements about Minimum Spanning Trees (MST) are true?

(A)

In every cycle C of G, the edge with the largest weight in C is not in any MST

(B)

In every cycle C of G, the edge with the smallest weight in C is in every MST

(C)

For every vertex v, the largest weight edge incident on v is not in any MST

(D)

For every vertex v, the smallest weight edge incident on v is in every MST

Explanation

GATE→2026→CS Core→Algorithms

Q52

MSQ[2 Marks]

Consider DFS pseudocode on a DAG G(V,E). For an edge (u,v) in E, which option will NEVER be correct?

(A)

d[u] < d[v] < f[v] < f[u]

(B)

d[v] < d[u] < f[u] < f[v]

(C)

d[v] < f[v] < d[u] < f[u]

(D)

d[u] < d[v] < f[u] < f[v]

Explanation

GATE→2026→CS Core→Theory of Computation

Q53

MSQ[2 Marks]

Let L1 and L2 be languages such that L1 subset L2 and L2 is regular. Which of the following statements is/are always true?

(A)

L1 is regular

(B)

L1 union L2 is regular

(C)

L2 is context-free

(D)

L1 is context-free

Explanation

GATE→2026→CS Core→Theory of Computation

Q54

MSQ[2 Marks]

Consider context-free grammar G. Let n1(s) be the number of a's and n2(s) be the number of b's in s in L(G). Which statements are true?

(A)

There is a string s in L(G) such that n1(s) < n2(s)

(B)

For every string s in L(G), n1(s) >= n2(s)

(C)

There is a string s in L(G) such that n1(s) > 2 n2(s)

(D)

For every string s in L(G), n1(s) <= 2 n2(s)

Explanation

GATE→2026→CS Core→Compiler Design

Q55

MSQ[2 Marks]

Consider syntax-directed definitions SDD1 and SDD2. Which of the following statements is/are true?

(A)

The languages P and Q specified by G1 and G2 are the same

(B)

SDD2 is S-attributed and contains only synthesized attributes

(C)

SDD1 is L-attributed and contains only inherited attributes

(D)

The specifications of SDD1 and SDD2 are such that the same entries get added to the symbol table

Explanation

GATE→2026→CS Core→Operating System

Q56

MSQ[2 Marks]

Consider a system with cache and MMU with TLB. Evicted pages invalidate corresponding cache blocks. Which sequence of events can NEVER happen?

(A)

TLB miss, Page table hit, Cache hit

(B)

TLB hit, Page table miss, Cache hit

(C)

TLB miss, Page table miss, Cache hit

(D)

TLB miss, Page table miss, Cache miss

Explanation

GATE→2026→CS Core→Algorithms

Q57

MSQ[2 Marks]

An undirected unweighted graph G(V,E) is 2-colorable if there exists c: V -> {0,1} with c(u) != c(v) for all (u,v) in E. Which statements about 2-colorable graphs are true?

(A)

If G is 2-colorable, G may contain cycles of odd length

(B)

If G is 2-colorable, G may contain cycles of even length

(C)

Optimal algorithm for testing 2-colorability runs in Theta(|V|+|E|) with adjacency list

(D)

Optimal algorithm for testing 2-colorability runs in Theta(|E| log |V|) with adjacency list

Explanation

GATE→2026→CS Core→Computer Networks

Q58

MSQ[2 Marks]

An ISP having address block 202.16.0.0/15 assigns a block of 6000 IP addresses to a client using CIDR. Which address blocks can be assigned?

(A)

202.16.0.0/19

(B)

202.17.64.0/19

(C)

202.16.32.0/19

(D)

202.17.24.0/19

Explanation