Computer Science Gate 2021 Questions

We have 2 rectangular sheets of paper, M and N, of dimensions 6 cm × 1 cm each. Sheet M is rolled to form an open cylinder by bringing the short edges of the sheet together. Sheet N is cut into equal square patches and assembled to form the largest possible closed cube. Assuming the ends of the cylinder are closed, the ratio of the volume of the cylinder to that of the cube is _________.

a) ^π/₂
b) ³/_π
c) ⁹/_π
d) 3π

___________ is to surgery as writer is to ___________ Which one of the following options maintains a similar logical relation in the above sentence ?

a) Plan, outline
b) Hospital, library
c) Doctor, book
d) Medicine, grammar

Consider the following sentences:

(i) Everybody in the class is prepared for the exam.
(ii) Babu invited Danish to his home because he enjoys playing chess.

Which of the following is the CORRECT observation about the above two sentences?

a) (i) is grammatically correct and (ii) is unambiguous.
b) (i) is grammatically incorrect and (ii) is unambiguous.
c) (i) is grammatically correct and (ii) is ambiguous.
d) (i) is grammatically incorrect and (ii) is ambiguous.

The ratio of boys to girls in a class is 7 to 3. Among the options below, an acceptable value for the total number of students in the class is

a) 21
b) 27
c) 50
d) 73

Suppose that L1 is a regular language and L2 is a context-free language. Which one of the following languages is NOT necessarily context-free?

a) L1∩L2
b) L1⋅L2
c) L1−L2
d) L1∪L2

Consider the following statements.

• S1: The sequence of procedure calls corresponds to a preorder traversal of the activation tree.
• S2: The sequence of procedure returns corresponds to a postorder traversal of the activation tree.

a) S1 is true and S2 is false
b) S1 is false and S2 is true
c) S1 is true and S2 is true
d) S1 is false and S2 is false

Let P be an array containing n integers. Let t be the lowest upper bound on the number of comparisons of the array elements, required to find the minimum and maximum values in an arbitrary array of n elements. Which one of the following choices is correct?

a) t>2n−2
b) t>3⌈n/2⌉ and t≤2n−2
c) t>n and t≤3⌈n/2⌉
d) t>⌈log2(n)⌉ and t≤n

Consider the following three functions.
f1 = 10ⁿ
f2 = n^logn
f3 = n^√n
Which one of the following options arranges the functions in the increasing order of asymptotic growth rate?

a) f3,f2,f1
b) f2,f1,f3
c) f1,f2,f3
d) f2,f3,f1

Let the representation of a number in base 3 be 210. What is the hexadecimal representation of the number?

a) 15
b) 588
c) D2
d) 528

There are five bags each containing identical sets of ten distinct chocolates. One chocolate is picked from each bag. The probability that at least two chocolates are identical is __________ .

a) 0.3024
b) 0.4235
c) 0.6976
d) 0.8125

Some people suggest anti-obesity measures (AOM) such as displaying calorie information in restaurant menus. Such measures sidestep addressing the core problems that cause obesity: poverty and income inequality. Which one of the following statements summarizes the passage?

a) A The proposed AOM addresses the core problems that cause obesity B C D
b) If obesity reduces, poverty will naturally reduce, since obesity causes poverty
c) AOM are addressing the core problems and are likely to succeed
d) AOM are addressing the problem superficially