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General Aptitude(10)Engineering Mathematics(9)CS Core(46)

General Aptitude

10 Questions

GATE→2025→General Aptitude→Verbal Ability

Q1

MCQ[1 Mark]

Ravi had ___ younger brother who taught at ___ university. He was widely regarded as ___ honorable man. Select the option with the correct sequence of articles to fill in the blanks.

(A)

a; a; an

(B)

the; an; a

(C)

a; an; a

(D)

an; an; a

Explanation

GATE→2025→General Aptitude→Verbal Ability

Q2

MCQ[1 Mark]

The CEO's decision to downsize the workforce was considered myopic because it sacrificed long-term stability to accommodate short-term gains. Select the most appropriate option that can replace the word "myopic" without changing the meaning of the sentence.

(A)

visionary

(B)

shortsighted

(C)

progressive

(D)

innovative

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q3

MCQ[1 Mark]

The average marks obtained by a class in an examination were calculated as 30.8. However, while checking the marks entered, the teacher found that the marks of one student were entered incorrectly as 24 instead of 42. After correcting the marks, the average becomes 31.4. How many students does the class have?

(A)

25

(B)

28

(C)

30

(D)

32

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q4

MCQ[1 Mark]

Consider the relationships among P, Q, R, S, and T: P is the brother of Q. S is the daughter of Q. T is the sister of S. R is the mother of Q. The following statements are made based on the relationships given above. (1) R is the grandmother of S. (2) P is the uncle of S and T. (3) R has only one son. (4) Q has only one daughter. Which one of the following options is correct?

(A)

Both (1) and (2) are true.

(B)

Both (1) and (3) are true.

(C)

Only (3) is true.

(D)

Only (4) is true.

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q5

MCQ[1 Mark]

According to the map shown in the figure, which one of the following statements is correct?

(A)

The library is located to the northwest of the canteen.

(B)

The hospital is located to the east of the chemistry lab.

(C)

The chemistry lab is to the southeast of physics lab.

(D)

The classrooms and canteen are next to each other.

Explanation

GATE→2025→General Aptitude→Data Interpretation

Q6

MCQ[2 Marks]

Based only on the information provided in the passage, which one of the following statements is true?

(A)

The author of the passage carries a mirror in his pocket to reflect upon things.

(B)

The author of the passage had decided to write a poem on epics.

(C)

The pocket-knife is described as the infant of the sword.

(D)

Epics are described as too inconvenient to write.

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q7

MCQ[2 Marks]

In the diagram, the lines QR and ST are parallel to each other. The shortest distance between these two lines is half the shortest distance between the point P and line QR. What is the ratio of the area of the triangle PST to the area of the trapezium SQRT?

(A)

1/3

(B)

1/4

(C)

2/5

(D)

1/2

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q8

MCQ[2 Marks]

A fair six-faced dice, with the faces labelled '1', '2', '3', '4', '5', and '6', is rolled thrice. What is the probability of rolling '6' exactly once?

(A)

75/216

(B)

1/6

(C)

1/18

(D)

25/216

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q9

MCQ[2 Marks]

A square paper, shown in figure (I), is folded along dotted lines and cut as shown in figure (IV). Which pattern will be obtained when unfolded?

(A)

(B)

(C)

(D)

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q10

MCQ[2 Marks]

A shop has 4 distinct flavors of ice-cream. One can purchase any number of scoops of any flavor. The order in which the scoops are purchased is inconsequential. If one wants to purchase 3 scoops of ice-cream, in how many ways can one make that purchase?

(A)

4

(B)

20

(C)

24

(D)

48

Explanation

Engineering Mathematics

9 Questions

GATE→2025→Engineering Mathematics→Discrete Mathematics

Q11

MCQ[1 Mark]

g: A->B, f: B->C, fog: A->C. If f and fog are onto, what is TRUE about g?

(A)

g(.) must be an onto (surjective) function.

(B)

g(.) must be a one-to-one (injective) function.

(C)

g(.) must be a bijective function, that is, both one-to-one and onto.

(D)

g(.) is not required to be a one-to-one or onto function.

Explanation

GATE→2025→Engineering Mathematics→Linear Algebra

Q12

MSQ[1 Mark]

System: x + ky = 1, kx + y = -1. Which are CORRECT?

(A)

There is exactly one value of k for which the above system of equations has no solution.

(B)

There exist an infinite number of values of k for which the system of equations has no solution.

(C)

There exists exactly one value of k for which the system of equations has exactly one solution.

(D)

There exists exactly one value of k for which the system of equations has an infinite number of solutions.

Explanation

GATE→2025→Engineering Mathematics→Discrete Mathematics

Q13

NAT[1 Mark]

Number of ternary strings of length 5 containing at least one occurrence of two consecutive identical symbols ("aa", "bb" or "cc").

Explanation

GATE→2025→Engineering Mathematics→Calculus

Q14

NAT[1 Mark]

If f(x) = ax + b for x < 1, x^2 + x + 1 for x >= 1 is differentiable everywhere, value of b?

Explanation

GATE→2025→Engineering Mathematics→Probability and Statistics

Q15

NAT[1 Mark]

Box with 4 regular coins and 1 fake coin. Toss twice, get two heads. Probability coin is fake?

Explanation

GATE→2025→Engineering Mathematics→Linear Algebra

Q16

MCQ[2 Marks]

Matrix A = [[1, 1], [1, -1]]. Eigenvalues of A^13?

(A)

1, -1

(B)

$2\sqrt{2}, -2\sqrt{2}$

(C)

$4\sqrt{2}, -4\sqrt{2}$

(D)

$64\sqrt{2}, -64\sqrt{2}$

Explanation

GATE→2025→Engineering Mathematics→Discrete Mathematics

Q17

MSQ[2 Marks]

Predicate logic representations for "Everyone has exactly one mother".

(A)

$\forall x\exists y\exists z(mother(y,x)\wedge\neg mother(z,x))$

(B)

$\forall x\exists y[mother(y,x)\wedge\forall z(noteq(z,y)\rightarrow\neg mother(z,x))]$

(C)

$\forall x\forall y[mother(y,x)\rightarrow\exists z(mother(z,x)\wedge\neg noteq(z,y))]$

(D)

$\forall x\exists y[mother(y,x)\wedge\neg\exists z(noteq(z,y)\wedge mother(z,x))]$

Explanation

GATE→2025→Engineering Mathematics→Discrete Mathematics

Q18

MSQ[2 Marks]

A = {0, 1, 2, ...}, F = functions A->A. (f1 @ f2)(n) = f1(n) + f2(n). Structure (F, @)?

(A)

(F,O) is an Abelian group.

(B)

(F, ) is an Abelian monoid.

(C)

(F,O) is a non-Abelian group.

(D)

(F, ) is a non-Abelian monoid.

Explanation

GATE→2025→Engineering Mathematics→Probability and Statistics

Q19

NAT[2 Marks]

Probability density function P(x) = C x^2 for 1 <= x <= 4, 0 otherwise. Probability P(2 <= x <= 3)?

Explanation

CS Core

46 Questions

GATE→2025→CS Core→Computer Organization and Architecture

Q20

MCQ[1 Mark]

Suppose a program is running on a non-pipelined single processor computer system. Steps: (i) saves program counter, (ii) loads PC with ISR start address, (iii) finishes present instruction. Correct sequence?

(A)

(iii), (i), (ii)

(B)

(i), (iii), (ii)

(C)

(i), (ii), (iii)

(D)

(iii), (ii), (i)

Explanation

GATE→2025→CS Core→Compiler Design

Q21

MCQ[1 Mark]

Which ONE of the following statements is FALSE regarding the symbol table?

(A)

Symbol table is responsible for keeping track of the scope of variables.

(B)

Symbol table can be implemented using a binary search tree.

(C)

Symbol table is not required after the parsing phase.

(D)

Symbol table is created during the lexical analysis phase.

Explanation

GATE→2025→CS Core→Compiler Design

Q22

MCQ[1 Mark]

Which ONE of the following techniques used in compiler code optimization uses live variable analysis?

(A)

Run-time function call management

(B)

Register assignment to variables

(C)

Strength reduction

(D)

Constant folding

Explanation

GATE→2025→CS Core→Operating System

Q23

MCQ[1 Mark]

Consider a demand paging memory management system with 32-bit logical address, 20-bit physical address, and page size of 2048 bytes. Maximum number of entries in page table?

(A)

$2^{21}$

(B)

$2^{20}$

(C)

$2^{22}$

(D)

$2^{24}$

Explanation

GATE→2025→CS Core→Databases

Q24

MCQ[1 Mark]

Schedule: R1(X) W1(Y) R2(X) R2(Y) R3(Y) ABORT(T1). T1 aborts. Which other transactions rolled back?

(A)

Only T2

(B)

Only T3

(C)

Both T2 and T3

(D)

Neither T2 nor T3

Explanation

GATE→2025→CS Core→Computer Networks

Q25

MCQ[1 Mark]

Identify correct matching between OSI layers and functionalities.

(A)

(a)-(I), (b)-(II), (c)-(III)

(B)

(a)-(I), (b)-(III), (c)-(II)

(C)

(a)-(II), (b)-(I), (c)-(III)

(D)

(a)-(III), (b)-(II), (c)-(I)

Explanation

GATE→2025→CS Core→Algorithms

Q26

MCQ[1 Mark]

Let G be undirected graph with positive weights, T be MST. d1(u,v) and d2(u,v) are shortest distances in G and T respectively. Which is CORRECT?

(A)

d1(u,v) = d2(u,v)

(B)

d1(u,v) <= d2(u,v)

(C)

d1(u,v) >= d2(u,v)

(D)

d1(u,v) != d2(u,v)

Explanation

GATE→2025→CS Core→Theory of Computation

Q27

MCQ[1 Mark]

CFG G: S -> aaB | Abb, A -> a | aA, B -> b | bB. Language L(G)?

(A)

L(G) = {a^2 b^n | n >= 1} union {a^n b^2 | n >= 1}

(B)

L(G) = {a^n b^(2n) | n >= 1} union {a^(2n) b^n | n >= 1}

(C)

L(G) = {a^n b^n | n >= 1}

(D)

L(G) = {a^(2n) b^(2n) | n >= 1}

Explanation

GATE→2025→CS Core→Algorithms

Q28

MCQ[1 Mark]

Recurrence relation: T(n) = 2 T(n-1) + n 2^n for n > 0, T(0) = 1. Solution?

(A)

T(n) = Theta(n^2 2^n)

(B)

T(n) = Theta(n 2^n)

(C)

T(n) = Theta((log n)^2 2^n)

(D)

T(n) = Theta(4^n)

Explanation

GATE→2025→CS Core→Databases

Q29

MSQ[1 Mark]

Inserting 23 into B+ tree with max 3 keys per node. Which are CORRECT?

(A)

None of the nodes will split.

(B)

At least one node will split and redistribute.

(C)

Total number of nodes will remain same.

(D)

The height of the tree will increase.

Explanation

GATE→2025→CS Core→Computer Networks

Q30

MSQ[1 Mark]

TCP 3-way handshake P1, P2, P3 flags. Which are TRUE?

(A)

P3: SYN=1, ACK=1

(B)

P2: SYN=1, ACK=1

(C)

P2: SYN=0, ACK=1

(D)

P1: SYN=1

Explanation

GATE→2025→CS Core→Digital Logic

Q31

MSQ[1 Mark]

Let X be 3-variable majority function. Which statements are CORRECT?

(A)

X(a,b,X(c,d,e))=X(X(a,b,c),d,e)

(B)

X(a,b,X(a,b,c))=X(a,b,c)

(C)

X(a,b,X(a,c,d))=(X(a,b,a) AND X(c,d,c))

(D)

X(a,b,X(a,b,c))=X(a,b,c)

Explanation

GATE→2025→CS Core→Digital Logic

Q32

MSQ[1 Mark]

-6 in 4-bit 2's comp is 1010. Correct 2's complement representations?

(A)

1000 1010 in 8-bits

(B)

1111 1010 in 8-bits

(C)

1000 0000 0000 1010 in 16-bits

(D)

1111 1111 1111 1010 in 16-bits

Explanation

GATE→2025→CS Core→Programming and Data Structures

Q33

MSQ[1 Mark]

Which statements are TRUE for any BST with n distinct integers?

(A)

The maximum length of a path from the root node to any other node is (n-1)

(B)

An inorder traversal will always produce a sorted sequence of elements.

(C)

Finding an element takes O(log2 n) time in the worst case.

(D)

Every BST is also a Min-Heap.

Explanation

GATE→2025→CS Core→Computer Organization and Architecture

Q34

MSQ[1 Mark]

Partial data path of processor. Which are CORRECT related to arithmetic operations?

(A)

The data path can implement arithmetic operations involving two registers.

(B)

The data path can implement arithmetic operations involving one register and one immediate value.

(C)

The data path can implement arithmetic operations involving two immediate values.

(D)

The data path can only implement arithmetic operations involving one register and one immediate value.

Explanation

GATE→2025→CS Core→Theory of Computation

Q35

MSQ[1 Mark]

Regular language L accepted by NFA with n states. Which are FALSE?

(A)

L may have an accepting NFA with < n states.

(B)

L may have an accepting DFA with < n states.

(C)

There exists a DFA with <= 2^n states that accepts L.

(D)

Every DFA that accepts L has > 2^n states.

Explanation

GATE→2025→CS Core→Operating System

Q36

NAT[1 Mark]

Number of times process enters ready queue during lifetime (excluding initial entry) for given program segment.

Explanation

GATE→2025→CS Core→Programming and Data Structures

Q37

NAT[1 Mark]

Array of 30 distinct integers in descending order. Number of swaps performed by bubble sort function fun().

Explanation

GATE→2025→CS Core→Programming and Data Structures

Q38

NAT[1 Mark]

Output of C program with foo(int *p, int x) { *p = x; } and main.

Explanation

GATE→2025→CS Core→Algorithms

Q39

NAT[1 Mark]

Min-Heap stores 32 keys. Height of T (max edges from root to leaf)?

Explanation

GATE→2025→CS Core→Computer Organization and Architecture

Q40

MCQ[2 Marks]

Memory system 1MB main memory, 16KB cache, 20-bit address, 16-byte block size. Direct mapped cache. Bits required to store all tag values?

(A)

$6\times2^{10}$

(B)

$8\times2^{10}$

(C)

$2^{12}$

(D)

$2^{14}$

Explanation

GATE→2025→CS Core→Computer Organization and Architecture

Q41

MCQ[2 Marks]

Processor has 64 general-purpose registers and 50 distinct instruction types. 32-bit instruction format. Maximum bits for immediate operand?

(A)

16

(B)

20

(C)

22

(D)

24

Explanation

GATE→2025→CS Core→Operating System

Q42

MCQ[2 Marks]

Two processors M1 and M2, 4 processes P1, P2, P3, P4 bursts 20, 16, 25, 10. Non-preemptive priority scheduling... Average waiting time?

(A)

9.00

(B)

8.75

(C)

6.50

(D)

7.50

Explanation

GATE→2025→CS Core→Databases

Q43

MCQ[2 Marks]

Tuple relational calculus query for players playing for team 'MI'.

(A)

(B)

(C)

(D)

Explanation

GATE→2025→CS Core→Computer Networks

Q44

MCQ[2 Marks]

Destination IP 145.36.109.70 arrives at router with given routing table. Which interface?

(A)

E3

(B)

E1

(C)

E2

(D)

E5

Explanation

GATE→2025→CS Core→Digital Logic

Q45

MCQ[2 Marks]

Boolean function F(b3, b2, b1, b0) = sum m(0, 2, 4, 8, 10, 11, 12). Minimized SOP expression?

(A)

$\overline{b}_{1}\overline{b}_{0}+\overline{b}_{2}\overline{b}_{0}+b_{1}\overline{b}_{2}b_{3}$

(B)

$\overline{b}_{1}\overline{b}_{0}+\overline{b}_{2}\overline{b}_{0}$

(C)

$\overline{b}_{2}\overline{b}_{0}+b_{1}b_{2}b_{3}$

(D)

$\overline{b}_{0}\overline{b}_{2}+\overline{b}_{3}$

Explanation

GATE→2025→CS Core→Algorithms

Q46

MCQ[2 Marks]

Undirected unweighted graph with 100 vertices, max shortest path distance (diameter) be 30. T is any BFS tree. Height of T?

(A)

The height of T is exactly 15.

(B)

The height of T is exactly 30.

(C)

The height of T is at least 15.

(D)

The height of T is at least 30.

Explanation

GATE→2025→CS Core→Theory of Computation

Q47

MCQ[2 Marks]

Languages L1 and L2 over {a,b}. Which is CORRECT?

(A)

Both L1 and L2 are regular languages.

(B)

L1 is a regular language but L2 is not a regular language.

(C)

L1 is not a regular language but L2 is a regular language.

(D)

Neither L1 nor L2 is a regular language.

Explanation

GATE→2025→CS Core→Theory of Computation

Q48

MCQ[2 Marks]

Languages L1 and L2 over {a,b,c}. Which is CORRECT?

(A)

Both L1 and L2 are context-free languages.

(B)

L1 is a context-free language but L2 is not a context-free language.

(C)

L1 is not a context-free language but L2 is a context-free language.

(D)

Neither L1 nor L2 are context-free languages.

Explanation

GATE→2025→CS Core→Compiler Design

Q49

MSQ[2 Marks]

Which statements are TRUE while computing First and Follow during top-down parsing?

(A)

For a production A -> epsilon, epsilon will be added to First(A).

(B)

If there is any input right end marker, it will be added to First(S).

(C)

For a production A -> epsilon, epsilon will be added to Follow(A).

(D)

If there is any input right end marker, it will be added to Follow(S).

Explanation

GATE→2025→CS Core→Databases

Q50

MSQ[2 Marks]

Relational schema team(name, city, owner) with FDs {name->city, name->owner} decomposed into t1(name, city) and t2(name, owner). Which are TRUE?

(A)

The relation team is NOT in BCNF.

(B)

The relations t1 and t2 are in BCNF.

(C)

The decomposition constitutes a lossless join.

(D)

The relation team is NOT in 3NF.

Explanation

GATE→2025→CS Core→Theory of Computation

Q51

MSQ[2 Marks]

DFA over {a,b}. Which language(s) accepted?

(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.

Explanation

GATE→2025→CS Core→Operating System

Q52

NAT[2 Marks]

Disk 512MB, block size 64KB. Linked allocation, 4 bytes pointer per block. File size 1MB. Internal fragmentation in bytes?

Explanation

GATE→2025→CS Core→Compiler Design

Q53

NAT[2 Marks]

Number of basic blocks in given 3-address code sequence.

Explanation

GATE→2025→CS Core→Computer Organization and Architecture

Q54

NAT[2 Marks]

Memory hierarchy L1 cache (hit rate 95%, access time 10ns), L2 cache (hit rate 85%, access time 20ns), Main memory (200ns). Average memory access time in ns?

Explanation

GATE→2025→CS Core→Operating System

Q55

NAT[2 Marks]

Modified optimal page replacement predicting up to next 4 references. Reference string: 1, 3, 2, 4, 2, 3, 1, 2, 4, 3, 1, 4. 3 frames initially empty. Number of page faults?

Explanation

GATE→2025→CS Core→Databases

Q56

NAT[2 Marks]

Value returned by given SQL query on sports league tables.

Explanation

GATE→2025→CS Core→Computer Networks

Q57

NAT[2 Marks]

5-bit message transmitted, bit flip probability 0.01 independently. Probability message delivered error-free?

Explanation

GATE→2025→CS Core→Computer Networks

Q58

NAT[2 Marks]

Message size 15000 bytes transmitted via IPv4 through two routers with MTU 5000 and 3000 bytes. Number of fragments delivered to destination?

Explanation

GATE→2025→CS Core→Digital Logic

Q59

NAT[2 Marks]

Minimum number of states required to realize FSM given by state transition table.

Explanation

GATE→2025→CS Core→Digital Logic

Q60

NAT[2 Marks]

Sequential circuit with D flip-flops. Number of distinct states before returning to initial state.

Explanation

GATE→2025→CS Core→Programming and Data Structures

Q61

NAT[2 Marks]

Value printed by given C program with foo on array A = {0, 1, 2, 2, 2, 0, 0, 1, 1}.

Explanation

GATE→2025→CS Core→Programming and Data Structures

Q62

NAT[2 Marks]

Linked lists L1 (9 nodes) and L2 (7 nodes). C program modifies L1. Number of nodes in L1 after execution?

Explanation

GATE→2025→CS Core→Programming and Data Structures

Q63

NAT[2 Marks]

Value printed by given C program gate(14362).

Explanation

GATE→2025→CS Core→Algorithms

Q64

NAT[2 Marks]

Maximum value of x such that edge between nodes B and C is included in every minimum spanning tree of given graph.

Explanation

GATE→2025→CS Core→Programming and Data Structures

Q65

NAT[2 Marks]

Double hashing scheme, h1(k) = k mod 11, h2(k) = 1 + (k mod 7), m = 11. Keys inserted in order: 63, 50, 25, 79, 67, 24. Slot at which key 24 gets stored?

Explanation