## GATE 2023

Question 1 |

We reached the station late, and _____ missed the train.

near | |

nearly | |

utterly | |

mostly |

Question 2 |

Kind : _______ : : Often : Frequently (By word meaning)

Mean | |

Type | |

Cruel | |

Kindly |

Question 3 |

A series of natural numbers F1, F2, F3, F4, F5, F6, F7, … obeys F

_{n+1}= F_{n}+ F_{n-1}for all integers n >= 2 . If F6 = 37, and F7 = 60, then what is F1 ?4 | |

5 | |

8 | |

9 |

Question 3 Explanation:

Given series is Fibonacci series

F(n+1)=F(n)+F(n-1)

Given values are F(6) is 37 and F(7) is 60

F(7)=F(6)+F(5) → 60=37+F(5) → F(5) =60-37=23

F(6)=F(5)+F(4) → 37=23+F(4) → F(4) =37-23=14

F(5)=F(4)+F(3) → 23=14+F(3) → F(3) =23-14=9

F(4)=F(3)+F(2) → 14=9+F(2) → F(2) =14-9=5

F(3)=F(2)+F(1) → 9=5+F(1) → F(1) =9-5=4

F(n+1)=F(n)+F(n-1)

Given values are F(6) is 37 and F(7) is 60

F(7)=F(6)+F(5) → 60=37+F(5) → F(5) =60-37=23

F(6)=F(5)+F(4) → 37=23+F(4) → F(4) =37-23=14

F(5)=F(4)+F(3) → 23=14+F(3) → F(3) =23-14=9

F(4)=F(3)+F(2) → 14=9+F(2) → F(2) =14-9=5

F(3)=F(2)+F(1) → 9=5+F(1) → F(1) =9-5=4

Question 4 |

A survey for a certain year found that 90% of pregnant women received medical care at least once before giving birth. Of these women, 60% received medical care from doctors, while 40% received medical care from other healthcare providers. Given this information, which one of the following statements can be inferred with certainty?

More than half of the pregnant women received medical care at least once from a doctor. | |

Less than half of the pregnant women received medical care at least once from a doctor. | |

More than half of the pregnant women received medical care at most once from a doctor. | |

Less than half of the pregnant women received medical care at most once from a doctor. |

Question 5 |

Looking at the surface of a smooth 3-dimensional object from the outside, which one of the following options is TRUE?

The surface of the object must be concave everywhere. | |

The surface of the object must be convex everywhere. | |

The surface of the object may be concave in some places and convex in other places. | |

The object can have edges, but no corners. |

Question 6 |

The country of Zombieland is in distress since more than 75% of its working population is suffering from serious health issues. Studies conducted by competent health experts concluded that a complete lack of physical exercise among its working population was one of the leading causes of their health issues. As one of the measures to address the problem, the Government of Zombieland has decided to provide monetary incentives to those who ride bicycles to work. Based only on the information provided above, which one of the following statements can be logically inferred with certainty?

All the working population of Zombieland will henceforth ride bicycles to work. | |

Riding bicycles will ensure that all of the working population of Zombieland is free of health issues. | |

The health experts suggested to the Government of Zombieland to declare riding bicycles as mandatory. | |

The Government of Zombieland believes that riding bicycles is a form of physical exercise. |

Question 7 |

Consider two functions of time (t),

f(t) = 0.01 t

g(t) = 4t where 0 < t < ∞ .

Now consider the following two statements:

(i) For some t>0, g(t)>f(t).

(ii) There exists a T, such that f(t)>g(t) for all t>T.

Which one of the following options is TRUE?

f(t) = 0.01 t

^{2}g(t) = 4t where 0 < t < ∞ .

Now consider the following two statements:

(i) For some t>0, g(t)>f(t).

(ii) There exists a T, such that f(t)>g(t) for all t>T.

Which one of the following options is TRUE?

only (i) is correct | |

only (ii) is correct | |

both (i) and (ii) are correct | |

neither (i) nor (ii) is correct |

Question 8 |

Which one of the following sentence sequences creates a coherent narrative?

(i) Once on the terrace, on her way to her small room in the corner, she notices the man right away.

(ii) She begins to pant by the time she has climbed all the stairs.

(iii) Mina has bought vegetables and rice at the market, so her bags are heavy.

(iv) He was leaning against the parapet, watching the traffic below.

(i) Once on the terrace, on her way to her small room in the corner, she notices the man right away.

(ii) She begins to pant by the time she has climbed all the stairs.

(iii) Mina has bought vegetables and rice at the market, so her bags are heavy.

(iv) He was leaning against the parapet, watching the traffic below.

(i), (ii), (iv), (iii) | |

(ii), (iii), (i), (iv) | |

(iv), (ii), (i), (iii) | |

(iii), (ii), (i), (iv) |

Question 9 |

f(x) and g(y) are functions of x and y, respectively, and f(x) = g(y) for all real values of x and y. Which one of the following options is necessarily TRUE for all x and y?

f(x)=0 and g(y ) = 0 | |

f(x)=g(y )=constant | |

f(x)≠constant and g(y)≠ constant | |

f(x)+g(y)-f(x)-g(y) |

Question 10 |

Which one of the options best describes the transformation of the 2-dimensional figure

**P**to**Q**, and then to**R**, as shown?Operation 1: A clockwise rotation by 90º about an axis perpendicular to the plane of the figure Operation 2: A reflection along a horizontal line | |

Operation 1: A counter clockwise rotation by 90º about an axis perpendicular to the plane of the figure Operation 2: A reflection along a horizontal line | |

Operation 1: A clockwise rotation by 90º about an axis perpendicular to the plane of the figure Operation 2: A reflection along a vertical line | |

Operation 1: A counter clockwise rotation by 180º about an axis perpendicular to the plane of the figure Operation 2: A reflection along a vertical line |

Question 11 |

Consider the following statements regarding the front-end and back-end of a compiler

S1: The front-end includes phases that are independent of the target hardware

S2: The back-end includes phases that are specific to the target hardware

S3: The back-end includes phases that are specific to the programming language used in the source code. Identify the CORRECT option

S1: The front-end includes phases that are independent of the target hardware

S2: The back-end includes phases that are specific to the target hardware

S3: The back-end includes phases that are specific to the programming language used in the source code. Identify the CORRECT option

Only S1 is TRUE | |

Only S1 and S2 are TRUE | |

S1, S2, and S3 are all TRUE | |

Only S1 and S3 are TRUE |

Question 12 |

Which one of the following sequences when stored in an array at locations A[1],...,A[10] forms a max-heap?

23, 17, 10, 6, 13, 14, 1, 5, 7, 12 | |

23, 17, 14, 7, 13, 10, 1, 5, 6, 12 | |

23, 17, 14, 6, 13, 10, 1, 5, 7, 15 | |

23, 14, 17, 1, 10, 13, 16, 12, 7, 5 |

Question 13 |

Let SLLdel be a function that deletes a node in a singly-linked list given a pointer to the node and a pointer to the head of the list. Similarly, let DLLdel be another function that deletes a node in a doubly-linked list given a pointer to the node and a pointer to the head of the list. Let n denote the number of nodes in each of the linked lists. Which one of the following choices is TRUE about the worst-case time complexity of SLLdel and DLLdel?

SLLdel is O(1) and DLLdel is O(n) | |

Both SLLdel and DLLdel are O(log(n)) | |

Both SLLdel and DLLdel are O(1) | |

SLLdel is O(n) and DLLdel is O(1) |

Question 14 |

Consider the Deterministic Finite-state Automaton (DFA) A shown below. The DFA runs on the alphabet {0, 1}, and has the set of states {s, p, q, r}, with s being the start state and p being the only final state.

Which one of the following regular expressions correctly describes the language accepted by A?

Which one of the following regular expressions correctly describes the language accepted by A?

1(0*11)* | |

0(0 + 1)* | |

1(0 + 11)* | |

1(110*)* |

Question 14 Explanation:

From the given DFA diagram, it clearly shows that there is no outgoing edge from node “r” so Regular expression won’t start with “0” , Option -B eliminated.

Starting state is "s" and Final state is "p".

There are two outgoing edges from the state "p".

one edge from state "p" to itself with alphabet “0” and another from State "p" to "q” and "q" to "p" with alphabet “1”

So most suitable answer is option C

Starting state is "s" and Final state is "p".

There are two outgoing edges from the state "p".

one edge from state "p" to itself with alphabet “0” and another from State "p" to "q” and "q" to "p" with alphabet “1”

So most suitable answer is option C

Question 15 |

The Lucas sequence L

L

with L

Which one of the options given is TRUE?

_{n}is defined by the recurrence relation:L

_{n}= L_{n-1}+ L_{n-2}, for n >= 3,with L

_{1}= 1 and L_{2}= 3.Which one of the options given is TRUE?

A | |

B | |

C | |

D |

Question 16 |

Which one of the options given below refers to the degree (or arity) of a relation in relational database systems?

Number of attributes of its relation schema. | |

Number of tuples stored in the relation. | |

Number of entries in the relation. | |

Number of distinct domains of its relation schema. |