CS and IT GATE 2020 Questions with Answer

Ques 40 DBMS

Consider a relational table R that is in 3NF, but not in BCNF. Which one of the following statements is TRUE ?

R has a nontrivial functional dependency X→A, where X is not a superkey and A is a prime attribute.

R has a nontrivial functional dependency X→A, where X is not a superkey and A is a non-prime attribute and X is not a proper subset of any key.

R has a nontrivial functional dependency X→A, where X is not a superkey and A is a non-prime attribute and X is a proper subset of some key.

A cell in R holds a set instead of an atomic value.

Ques 41 DBMS

Which one of the following is used to represent the supporting many-one relationships of a weak entity set in an entity-relationship diagram ?

Diamonds with double/bold border

Rectangles with double/bold border

Ovals with double/bold border

Ovals that contain underlined identifiers

Ques 42 Design Algorithm Analysis

What is the worst case time complexity of inserting n elements into an empty linked list, if the linked list needs to be maintained in sorted order ?

Θ(n)

Θ(nlogn)

Θ(n²)

Θ(1)

Ques 43 Design Algorithm Analysis

What is the worst case time complexity of inserting n² elements into an AVL-tree with n elements initially ?

Θ(n⁴)

Θ(n²)

Θ(n²log(n))

Θ(n³)

Ques 44 Design Algorithm Analysis

For parameters a and b, both of which are ω(1), T(n)=T(n^1/a)+1, and T(b)=1. Then T(n) is

Θ(log_alog_bn)

Θ(log_abn)

Θ(log_blog_an)

Θ(log₂log₂n)

Ques 45 Design Algorithm Analysis

The number of permutations of the characters in LILAC so that no character appears in its original position, if the two L’s are indistinguishable, is ________ .

12 is the correct answer.

Ques 46 Digital Logic Design

If there are m input lines n output lines for a decoder that is used to uniquely address a byte addressable 1 KB RAM, then the minimum value of m+n is ________ .

1024 is the correct answer.

Ques 47 Discrete Mathematics

Which one of the following predicate formulae is NOT logically valid ? Note that W is a predicate formula without any free occurrence of x.

∀x(p(x) ∨ W) ≡ ∀x(px) ∨ W

∃x(p(x) ∧ W) ≡ ∃xp(x) ∧ W

∀x(p(x) → W) ≡ ∀xp(x) → W

∃x(p(x) → W) ≡ ∀xp(x) → W

Ques 48 Discrete Mathematics

Let G be a group of 35 elements. Then the largest possible size of a subgroup of G other than G itself is ________ .

7 is the correct answer.

Ques 49 Discrete Mathematics

Let R be the set of all binary relations on the set {1, 2, 3}. Suppose a relation is chosen from R at random. The probability that the chosen relation is reflexive (round off to 3 decimal places) is ________ .

0.125 is the correct answer.

Ques 50 Mathematics

Let A and B be two n×n matrices over real numbers. Let rank(M) and det(M) denote the rank and determinant of a matrix M, respectively. Consider the following statements.

I. rank(AB) = rank(A)*rank (B)
II. det(AB) = det(A)*det(B)
III. rank(A+B) ≤ rank(A) + rank(B)
IV. det(A+B) ≤ det(A) + det(B)

Which of the above statements are TRUE ?

I and II only

I and IV only

II and III only

III and IV only

Ques 51 Mathematics

Consider the functions

I. e^-x
II. x² - sin x
III. √x^3+1

Which of the above functions is/are increasing everywhere in [0, 1] ?

Ⅲ only

Ⅱ only

Ⅱ and Ⅲ only

Ⅰ and Ⅲ only

Ques 52 Mathematics

For n>2, let a∈{0, 1}ⁿ be a non-zero vector. Suppose that x is chosen uniformly at random from {0,1}ⁿ. Then, the probability that Σⁱ⁼¹_i=n a_ix_i is an odd number is _________

0.50 is the correct answer.

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CS and IT GATE 2020 Questions with Answer