GATE CS 2022

Question 41

A function y(x) is defined in the interval [0, 1] on the 

• [Tex]\frac {5}{6}[/Tex]

• [Tex]\frac {6}{5}[/Tex]

• [Tex]\frac {13}{6}[/Tex]

• [Tex]\frac {6}{13}[/Tex]

Question 42

Let r be a root of the equation x² + 2x + 6 = 0. Then the value of the expression (r+2) (r+3)(r+4)(r+5) is 

• 51

•  -51

• 126

• -126

Question 43

Given below are four statements.

Statement 1: All students are inquisitive.

Statement 2: Some students are inquisitive.

Statement 3: No student is inquisitive.

Statement 4: Some students are not inquisitive.

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.

• Statement 1 and Statement 3 

• Statement 1 and Statement 2

• Statement 2 and Statement 4 

• Statement 3 and Statement 4

Question 44

A palindrome is a word that reads the same forwards and backward. In a game of words, a player has the following two plates painted with letters. 

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. The player should use all the five plates exactly once. The plates can be rotated

• 
• 
• 
• 

Question 45

Some people believe that “what gets measured, improves”. Some others believe that “what gets measured, gets gamed”. One possible reason for the difference in beliefs is the work culture in organizations. In organizations with good work culture, metrics help improve outcomes. However, the same metrics are counterproductive in organizations with the poor work cultures.

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

• Metrics are useful in organizations with poor work culture

• Metrics are useful in organizations with good work culture

• Metrics are always counterproductive in organizations with good work culture

• Metrics are never useful in organizations with good work culture

Question 46

In a recently conducted national entrance test, boys constituted 65% of those who appeared for the test. Girls constituted the remaining candidates and they accounted for 60% of the qualified candidates.

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

• Equal number of boys and girls qualified

• Equal number of boys and girls appeared for the test

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

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

Question 47

A box contains five balls of same size and shape. Three of them are green coloured balls and two of them are orange coloured balls. Balls are drawn from the box one at a time. If a green ball is drawn, it is not replaced. If an orange ball is drawn, it is replaced with another orange ball.

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

• [Tex]\frac{1}{2}[/Tex]

• [Tex]\frac{8}{25}[/Tex]

• [Tex]\frac{19}{50}[/Tex]

• [Tex]\frac{23}{50}[/Tex]

Question 48

The corners and mid-points of the sides of a triangle are named using the distinct letters P, Q, R, S, T, and U, but not necessarily in the same order. Consider the following statements:

• The line joining P and R is parallel to the line joining Q and S.
• P is placed on the side opposite to corner T.
• S and U cannot be placed on the same side.

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

• P cannot be placed at a corner

• S cannot be placed at a corner

• U cannot be placed at a mid-point

• R cannot be placed at a corner

Question 49

A plot of land must be divided between four families. They want their individual plots to be similar in shape, not necessarily equal in area. The land has equally spaced poles, marked as dots in the below figure. Two ropes, R1 and R2, are already present and cannot be moved.

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.

• 2

• 4

• 5

• 3

Question 50

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

• ab*bab* + ba*aba*

• (ab*b)*ab* + (ba*a)*ba*

• (ab*b+ba*a)*(a*+b*)

• (ba*a+ ab*b)* (ab* + ba*)