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General Aptitude(10)Engineering Mathematics(7)CS Core(48)

General Aptitude

10 Questions

GATE→2022→General Aptitude→Verbal Ability

Q1

MCQ[1 Mark]

The ___ is too high for it to be considered ___

(A)

fair/fare

(B)

faer/fair

(C)

fare/fare

(D)

fare/fair

Explanation

GATE→2022→General Aptitude→Quantitative Aptitude

Q2

MCQ[1 Mark]

A function y(x) is defined in the interval [0, 1] on the x-axis... Which one of the following is the area under the curve for the interval [0, 1] on the x-axis?

(A)

5/6

(B)

6/5

(C)

13/6

(D)

6/13

Explanation

GATE→2022→General Aptitude→Quantitative Aptitude

Q3

MCQ[1 Mark]

Let r be a root of the equation x^2 + 2x + 6 = 0. Then the value of the expression (r+2)(r+3)(r+4)(r+5) is

(A)

51

(B)

-51

(C)

126

(D)

-126

Explanation

GATE→2022→General Aptitude→Data Interpretation

Q4

MCQ[1 Mark]

From the given four statements, find the two statements that CANNOT BE TRUE simultaneously, assuming that there is at least one student in the class.

(A)

Statement 1 and Statement 3

(B)

Statement 1 and Statement 2

(C)

Statement 2 and Statement 4

(D)

Statement 3 and Statement 4

Explanation

GATE→2022→General Aptitude→Quantitative Aptitude

Q5

MCQ[1 Mark]

From the additional plates given in the options, which one of the combinations of additional plates would allow the player to construct a five-letter palindrome?

(A)

(B)

(C)

(D)

Explanation

GATE→2022→General Aptitude→Data Interpretation

Q6

MCQ[2 Marks]

Which one of the following is the CORRECT logical inference based on the information in the above passage?

(A)

Metrics are useful in organizations with poor work culture

(B)

Metrics are useful in organizations with good work culture

(C)

Metrics are always counterproductive in organizations with good work culture

(D)

Metrics are never useful in organizations with good work culture

Explanation

GATE→2022→General Aptitude→Quantitative Aptitude

Q7

MCQ[2 Marks]

Which one of the following is the correct logical inference based on the information provided in the above passage?

(A)

Equal number of boys and girls qualified

(B)

Equal number of boys and girls appeared for the test

(C)

The number of boys who appeared for the test is less than the number of girls who appeared

(D)

The number of boys who qualified the test is less than the number of girls who qualified

Explanation

GATE→2022→General Aptitude→Quantitative Aptitude

Q8

MCQ[2 Marks]

First ball is drawn. What is the probability of getting an orange ball in the next draw?

(A)

1/2

(B)

8/25

(C)

19/50

(D)

23/50

Explanation

GATE→2022→General Aptitude→Quantitative Aptitude

Q9

MCQ[2 Marks]

Which one of the following statements is correct based on the above information?

(A)

P cannot be placed at a corner

(B)

S cannot be placed at a corner

(C)

U cannot be placed at a mid-point

(D)

R cannot be placed at a corner

Explanation

GATE→2022→General Aptitude→Quantitative Aptitude

Q10

MCQ[2 Marks]

What is the least number of additional straight ropes needed to create the desired plots? A single rope can pass through three poles that are aligned in a straight line.

(A)

2

(B)

4

(C)

5

(D)

3

Explanation

Engineering Mathematics

7 Questions

GATE→2022→Engineering Mathematics→Linear Algebra

Q11

MCQ[1 Mark]

Consider the following two statements with respect to the matrices A_{m x n}, B_{n x m}, C_{n x n} and D_{n x n}... Which one of the following holds?

(A)

Statement 1 is correct and Statement 2 is wrong.

(B)

Statement 1 is wrong and Statement 2 is correct.

(C)

Both Statement 1 and Statement 2 are correct.

(D)

Both Statement 1 and Statement 2 are wrong.

Explanation

GATE→2022→Engineering Mathematics→Discrete Mathematics

Q12

MSQ[1 Mark]

Which of the following statements is/are TRUE for a group G?

(A)

If for all x, y \in G, (xy)^2 = x^2 y^2, then G is commutative.

(B)

If for all x \in G, x^2 = 1 then G is commutative. Here, 1 is the identity element.

(C)

If the order of G is 2, then G is commutative.

(D)

If G is commutative, then a subgroup of G need not be commutative.

Explanation

GATE→2022→Engineering Mathematics→Discrete Mathematics

Q13

NAT[1 Mark]

The number of arrangements of six identical balls in three identical bins is

Explanation

GATE→2022→Engineering Mathematics→Calculus

Q14

NAT[1 Mark]

The value of the following limit is lim_{x -> 0+} sqrt(x) / (1 - e^(2 sqrt(x)))

Explanation

GATE→2022→Engineering Mathematics→Discrete Mathematics

Q15

MCQ[2 Marks]

Which one of the following is the closed form for the generating function of the sequence {a_n}_{n>=0} defined below?

(A)

\frac{x(1+x^2)}{(1-x^2)^2} + \frac{1}{1-x}

(B)

\frac{x(3-x^2)}{(1-x^2)^2} + \frac{1}{1-x}

(C)

\frac{2x}{(1-x^2)^2} + \frac{1}{1-x}

(D)

\frac{x}{(1-x^2)^2} + \frac{1}{1-x}

Explanation

GATE→2022→Engineering Mathematics→Linear Algebra

Q16

MCQ[2 Marks]

Which one of the following is the correct combination of values for L32, U33, and x1?

(A)

L32 = 2, U33 = -1/2, x1 = -1

(B)

L32 = 2, U33 = 2, x1 = -1

(C)

L32 = -1/2, U33 = 2, x1 = 0

(D)

L32 = -1/2, U33 = -1/2, x1 = 0

Explanation

GATE→2022→Engineering Mathematics→Linear Algebra

Q17

MSQ[2 Marks]

Which of the following is/are the eigenvector(s) for the matrix given below?

(A)

(B)

(C)

(D)

Explanation

CS Core

48 Questions

GATE→2022→CS Core→Algorithms

Q18

MCQ[1 Mark]

Which one of the following statements is TRUE for all positive functions f(n)?

(A)

$f(n^{2})=\theta(f(n)^{2})$, when $f(n)$ is a polynomial

(B)

$f(n^{2})=o(f(n)^{2})$

(C)

$f(n^{2})=O(f(n)^{2})$ when $f(n)$ is an exponential function

(D)

$f(n^{2})=\Omega(f(n)^{2})$

Explanation

GATE→2022→CS Core→Theory of Computation

Q19

MCQ[1 Mark]

Which one of the following regular expressions correctly represents the language of the finite automaton given below?

(A)

ab*bab* + ba*aba*

(B)

(ab*b)*ab* + (ba*a)*ba*

(C)

(ab*b + ba*a)*(a* + b*)

(D)

(ba*a + ab*b)*(ab* + ba*)

Explanation

GATE→2022→CS Core→Compiler Design

Q20

MCQ[1 Mark]

Which one of the following statements is TRUE?

(A)

The LALR(1) parser for a grammar G cannot have reduce-reduce conflict if the LR(1) parser for G does not have reduce-reduce conflict.

(B)

Symbol table is accessed only during the lexical analysis phase.

(C)

Data flow analysis is necessary for run-time memory management.

(D)

LR(1) parsing is sufficient for deterministic context-free languages.

Explanation

GATE→2022→CS Core→Databases

Q21

MCQ[1 Mark]

In a relational data model, which one of the following statements is TRUE?

(A)

A relation with only two attributes is always in BCNF.

(B)

If all attributes of a relation are prime attributes, then the relation is in BCNF.

(C)

Every relation has at least one non-prime attribute.

(D)

BCNF decompositions preserve functional dependencies.

Explanation

GATE→2022→CS Core→Programming and Data Structures

Q22

MCQ[1 Mark]

Which one of the following statements is TRUE about the time complexity of algorithms that solve the above problem in O(1) space?

(A)

The best algorithm for the problem takes \theta(n) time in the worst case.

(B)

The best algorithm for the problem takes \theta(n \log n) time in the worst case.

(C)

The best algorithm for the problem takes \theta(n^2) time in the worst case.

(D)

It is not possible to reverse a singly linked list in O(1) space.

Explanation

GATE→2022→CS Core→Algorithms

Q23

MCQ[1 Mark]

Suppose we are given n keys, m hash table slots, and two simple uniform hash functions h1 and h2. Further suppose our hashing scheme uses h1 for the odd keys and h2 for the even keys. What is the expected number of keys in a slot?

(A)

m/n

(B)

n/m

(C)

2n/m

(D)

n/(2m)

Explanation

GATE→2022→CS Core→Computer Organization and Architecture

Q24

MCQ[1 Mark]

Which one of the following facilitates transfer of bulk data from hard disk to main memory with the highest throughput?

(A)

DMA based I/O transfer

(B)

Interrupt driven I/O transfer

(C)

Polling based I/O transfer

(D)

Programmed I/O transfer

Explanation

GATE→2022→CS Core→Computer Organization and Architecture

Q25

MCQ[1 Mark]

Let R1 and R2 be two 4-bit registers that store numbers in 2's complement form. For the operation R1+R2, which one of the following values of R1 and R2 gives an arithmetic overflow?

(A)

R1=1011 and R2=1110

(B)

R1=1100 and R2=1010

(C)

R1=0011 and R2=0100

(D)

R1=1001 and R2=1111

Explanation

GATE→2022→CS Core→Operating System

Q26

MCQ[1 Mark]

Which initialization of the semaphores would print the sequence BCABCABCA....?

(A)

S1=1, S2=1, S3=1

(B)

S1=1, S2=1, S3=0

(C)

S1=1, S2=0, S3=0

(D)

S1=0, S2=1, S3=1

Explanation

GATE→2022→CS Core→Programming and Data Structures

Q27

MCQ[1 Mark]

What is printed by the following ANSI C program?

(A)

1, 10, 11

(B)

1, 10, 14

(C)

10, 14, 11

(D)

10, 10, 14

Explanation

GATE→2022→CS Core→Computer Networks

Q28

MCQ[1 Mark]

What is the number of subnets inside the enterprise network?

(A)

3

(B)

12

(C)

6

(D)

8

Explanation

GATE→2022→CS Core→Theory of Computation

Q29

MSQ[1 Mark]

Which of the following statements is/are TRUE?

(A)

Every subset of a recursively enumerable language is recursive.

(B)

If a language L and its complement \bar{L} are both recursively enumerable, then L must be recursive.

(C)

Complement of a context-free language must be recursive.

(D)

If L1 and L2 are regular, then L1 \cap L2 must be deterministic context-free.

Explanation

GATE→2022→CS Core→Computer Organization and Architecture

Q30

MSQ[1 Mark]

WB is a write back cache and WT is a write through cache. Which of the following statements is/are FALSE?

(A)

Each cache block in WB and WT has a dirty bit.

(B)

Every write hit in WB leads to a data transfer from cache to main memory.

(C)

Eviction of a block from WT will not lead to data transfer from cache to main memory.

(D)

A read miss in WB will never lead to eviction of a dirty block from WB.

Explanation

GATE→2022→CS Core→Databases

Q31

MSQ[1 Mark]

Which of the following relational algebra expressions return the set of eIds who own all the brands?

(A)

\Pi_{eld}(\Pi_{eld,bld}(Own)/\Pi_{bld}(Brand))

(B)

\Pi_{eld}(Own)-\Pi_{cld}((\Pi_{eld}(Own)\times\Pi_{bld}(Brand))-\Pi_{eld,bld}(Own))

(C)

\Pi_{eld}(\Pi_{eld,bld}(Own)/\Pi_{bld}(Own))

(D)

\Pi_{eld}((\Pi_{eld}(Own)\times\Pi_{bld}(Own))/\Pi_{bld}(Brand))

Explanation

GATE→2022→CS Core→Operating System

Q32

MSQ[1 Mark]

Which of the following statements is/are TRUE with respect to deadlocks?

(A)

Circular wait is a necessary condition for the formation of deadlock.

(B)

In a system where each resource has more than one instance, a cycle in its wait-for graph indicates the presence of a deadlock.

(C)

If the current allocation of resources to processes leads the system to unsafe state, then deadlock will necessarily occur.

(D)

In the resource-allocation graph of a system, if every edge is an assignment edge, then the system is not in deadlock state.

Explanation

GATE→2022→CS Core→Programming and Data Structures

Q33

NAT[1 Mark]

Suppose a binary search tree with 1000 distinct elements is also a complete binary tree. The tree is stored using array representation starting with 0. The 3rd largest element is stored at index

Explanation

GATE→2022→CS Core→Compiler Design

Q34

NAT[1 Mark]

If I_0 is the set of two LR(0) items {[S' -> S.], [S -> S. + R]}, then goto(closure(I_0), +) contains exactly ___ items.

Explanation

GATE→2022→CS Core→Algorithms

Q35

NAT[1 Mark]

Consider a simple undirected graph of 10 vertices. If the graph is disconnected, then the maximum number of edges it can have is

Explanation

GATE→2022→CS Core→Databases

Q36

NAT[1 Mark]

Consider a relation R(A,B,C,D,E) with the following three functional dependencies: AB->C, BC->D, C->E. The number of superkeys in the relation R is

Explanation

GATE→2022→CS Core→Computer Organization and Architecture

Q37

NAT[1 Mark]

The minimum hit rate (rounded off to two decimal places) needed after the optimization such that it should not increase the average memory access time is

Explanation

GATE→2022→CS Core→Computer Networks

Q38

NAT[1 Mark]

Consider the resolution of the domain name www.gate.org.in by a DNS resolver... The number of DNS query-response pairs involved in completely resolving the domain name is

Explanation

GATE→2022→CS Core→Algorithms

Q39

MCQ[2 Marks]

Consider a simple undirected unweighted graph with at least three vertices. If A is the adjacency matrix of the graph, then the number of 3-cycles in the graph is given by the trace of

(A)

A^3

(B)

A^3 divided by 2

(C)

A^3 divided by 3

(D)

A^3 divided by 6

Explanation

GATE→2022→CS Core→Operating System

Q40

MCQ[2 Marks]

Which one of the following statements is FALSE?

(A)

The TLB performs an associative search in parallel on all its valid entries using page number of incoming virtual address.

(B)

If the virtual address of a word given by CPU has a TLB hit, but the subsequent search for the word results in a cache miss, then the word will always be present in the main memory.

(C)

The memory access time using a given inverted page table is always same for all incoming virtual addresses.

(D)

In a system that uses hashed page tables, if two distinct virtual addresses V1 and V2 map to the same value while hashing, then the memory access time of these addresses will not be the same.

Explanation

GATE→2022→CS Core→Databases

Q41

MCQ[2 Marks]

Which one of the following serial schedules is conflict equivalent to S?

(A)

T1 -> T3 -> T4 -> T2

(B)

T1 -> T4 -> T3 -> T2

(C)

T4 -> T1 -> T3 -> T2

(D)

T3 -> T1 -> T4 -> T2

Explanation

GATE→2022→CS Core→Computer Organization and Architecture

Q42

MCQ[2 Marks]

Which one of the following represents the functionality of P, Q, and T?

(A)

Q is 5:1 multiplexer; T is 2:1 multiplexer; P is 10:1 multiplexer

(B)

P is 10:2^10 decoder; Q is 5:2^5 decoder; T is 2:1 encoder

(C)

P is 10:2^10 decoder; Q is 5:2^5 decoder; T is 2:1 multiplexer

(D)

P is 1:10 de-multiplexer; Q is 1:5 de-multiplexer; T is 2:1 multiplexer

Explanation

GATE→2022→CS Core→Computer Organization and Architecture

Q43

MCQ[2 Marks]

Which one of the following is FALSE?

(A)

A + C = 0

(B)

C = A + B

(C)

B = 3C

(D)

(B - C) > 0

Explanation

GATE→2022→CS Core→Operating System

Q44

MCQ[2 Marks]

Which one of the following is NOT possible as CPU burst time (in time units) of these processes?

(A)

P=4, Q=10, R=6, S=2

(B)

P=2, Q=9, R=5, S=1

(C)

P=4, Q=12, R=5, S=4

(D)

P=3, Q=7, R=7, S=3

Explanation

GATE→2022→CS Core→Programming and Data Structures

Q45

MCQ[2 Marks]

What is printed by the following ANSI C program?

(A)

(B)

(C)

(D)

Explanation

GATE→2022→CS Core→Programming and Data Structures

Q46

MCQ[2 Marks]

What is printed by the following ANSI C program?

(A)

ZKS

(B)

75 122 83

(C)

* - +

(D)

P x +

Explanation

GATE→2022→CS Core→Theory of Computation

Q47

MSQ[2 Marks]

Which of the following is/are undecidable?

(A)

Given two Turing machines M1 and M2, decide if L(M1) = L(M2).

(B)

Given a Turing machine M, decide if L(M) is regular.

(C)

Given a Turing machine M, decide if M accepts all strings.

(D)

Given a Turing machine M, decide if M takes more than 10^73 steps on every string.

Explanation

GATE→2022→CS Core→Theory of Computation

Q48

MSQ[2 Marks]

Consider the following languages... Which of the following is/are TRUE?

(A)

L1 and L2 are regular.

(B)

L1 and L2 are context-free.

(C)

L1 is regular and L2 is context-free.

(D)

L1 and L2 are context-free but not regular.

Explanation

GATE→2022→CS Core→Theory of Computation

Q49

MSQ[2 Marks]

Consider the following languages... Which of the following statements is/are FALSE?

(A)

L1 is not context-free but L2 and L3 are deterministic context-free.

(B)

Neither L1 nor L2 is context-free.

(C)

L2, L3 and L2 \cap L3 all are context-free.

(D)

Neither L1 nor its complement is context-free.

Explanation

GATE→2022→CS Core→Algorithms

Q50

MSQ[2 Marks]

Consider a simple undirected weighted graph G, all of whose edge weights are distinct. Which of the following statements about the minimum spanning trees of G is/are TRUE?

(A)

The edge with the second smallest weight is always part of any minimum spanning tree of G.

(B)

One or both of the edges with the third smallest and the fourth smallest weights are part of any minimum spanning tree of G.

(C)

Suppose S subset V... Consider edge with minimum weight across cut... always part of MST.

(D)

G can have multiple minimum spanning trees.

Explanation

GATE→2022→CS Core→Algorithms

Q51

MSQ[2 Marks]

The following simple undirected graph is referred to as the Peterson graph. Which of the following statements is/are TRUE?

(A)

The chromatic number of the graph is 3.

(B)

The graph has a Hamiltonian path.

(C)

The following graph is isomorphic to the Peterson graph.

(D)

The size of the largest independent set of the given graph is 3.

Explanation

GATE→2022→CS Core→Algorithms

Q52

MSQ[2 Marks]

Consider the following recurrence... Which of the following statements is/are TRUE?

(A)

f(2^n - 1) = 2^n - 1

(B)

f(2^n) = 1

(C)

f(5 * 2^n) = 2^(n+1) + 1

(D)

f(2^n + 1) = 2^n + 1

Explanation

GATE→2022→CS Core→Algorithms

Q53

MSQ[2 Marks]

Which of the properties hold for the adjacency matrix A of a simple undirected unweighted graph having n vertices?

(A)

The diagonal entries of A^2 are the degrees of the vertices of the graph.

(B)

If the graph is connected, then none of the entries of A^(n-1) + I_n can be zero.

(C)

If the sum of all the elements of A is at most 2(n-1) then the graph must be acyclic.

(D)

If there is at least a 1 in each of A's rows and columns, then the graph must be connected.

Explanation

GATE→2022→CS Core→Computer Organization and Architecture

Q54

MSQ[2 Marks]

Consider a system with 2 KB direct mapped data cache... Which of the following statements is/are TRUE with respect to the data cache?

(A)

Every access to S is a hit.

(B)

Once P is brought to the cache it is never evicted.

(C)

At the end of the execution only R and S reside in the cache.

(D)

Every access to R evicts Q from the cache.

Explanation

GATE→2022→CS Core→Computer Networks

Q55

MSQ[2 Marks]

Which of the following prefixes in CIDR notation can be collectively used to correctly aggregate all of the subnets in the routing table?

(A)

12.20.164.0/20

(B)

12.20.164.0/22

(C)

12.20.164.0/21

(D)

12.20.168.0/22

Explanation

GATE→2022→CS Core→Databases

Q56

NAT[2 Marks]

The number of rows returned by the above SQL query is

Explanation

GATE→2022→CS Core→Computer Networks

Q57

NAT[2 Marks]

The probability of a routing loop formation (rounded off to one decimal place) between P and Q, leading to count-to-infinity problem, is

Explanation

GATE→2022→CS Core→Algorithms

Q58

NAT[2 Marks]

The number of such directed spanning trees rooted at vertex 5 is

Explanation

GATE→2022→CS Core→Computer Networks

Q59

NAT[2 Marks]

The time taken (in milliseconds, rounded off to two decimal places) for the receiver to completely receive a packet of 1000 bytes transmitted by the sender is

Explanation

GATE→2022→CS Core→Computer Networks

Q60

NAT[2 Marks]

The minimum number of bits required for the sequence number field of the TCP header, to prevent the sequence number space from wrapping around during the MSL is

Explanation

GATE→2022→CS Core→Computer Organization and Architecture

Q61

NAT[2 Marks]

The speed up (rounded off to two decimal places) obtained by X2 over X1 in executing P is

Explanation

GATE→2022→CS Core→Programming and Data Structures

Q62

NAT[2 Marks]

The minimum number of Enqueue operations on Q1 required to place the elements of Q1 in Q2 in reverse order without using any additional storage is

Explanation

GATE→2022→CS Core→Operating System

Q63

NAT[2 Marks]

Let the number of disk accesses required to insert a block in the middle of the file in A and B be nA and nB, respectively, then the value of nA + nB is

Explanation

GATE→2022→CS Core→Operating System

Q64

NAT[2 Marks]

the page fault rate, defined as the ratio of number of page faults to the number of memory accesses (rounded off to one decimal place) is

Explanation

GATE→2022→CS Core→Compiler Design

Q65

NAT[2 Marks]

Using this translation scheme, the computed value of S.val for root of the parse tree for the expression 20#10%5#8%2%2 is

Explanation