CS and IT GATE 2021 Set-1 Questions with Answer

Ques 14 Databases

The following relation records the age of 500 employees of a company, where empNo (indicating the employee number) is the key:
empAge(empNo, age)
Consider the following relational algebra expression:
ΠempNo(empAge ⋈(age>age1) ρempNo1,age1(empAge))
What does the above expression generate?

Ques 15 Databases

Let ri(z) and wi(z) denote read and write operations respectively on a data item z by a transaction Ti. Consider the following two schedules.
S1: r1(x) r1(y) r2(x) r2(y) w2(y) w1(x)
S2: r1(x) r2(x) r2(y) w2(y) r1(y) w1(x)
Which one of the following options is correct?

Ques 16 Databases

Consider the relation R(P, Q, S, T, X, Y, Z, W) with the following functional dependencies.
PQ -> X, P -> YX, Q -> Y, Y -> ZW
Consider the decomposition of the relation R into the constituent relations according to the following two decomposition schemes.
D1: R = [(P, Q, S, T); (P, T, X); (Q, Y); (Y, Z, W)]
D2: R = [(P, Q, S); (T, X); (Q, Y); (Y, Z, W)]
Which one of the following options is correct?

Ques 17 Databases

A relation r(A, B) in a relational database has 1200 tuples. The attribute A has integer values ranging from 6 to 20, and the attribute B has integer values ranging from 1 to 20. Assume that the attributes A and B are independently distributed. The estimated number of tuples in the output of σ(A>10)∨(B=18)(r) is _______.

Ques 18 Design Algorithm Analysis

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?

Ques 19 Design Algorithm Analysis

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?

Ques 20 Digital Logic Design

Consider a 3-bit counter, designed using T flip-flops, as shown below:

Ques 21 Digital Logic Design

Consider the following Boolean expression.
F = (X + Y + Z)(X̅ + Y)(Y̅ + Z)
Which of the following Boolean expressions is/are equivalent to F̅ (complement of F)?

Ques 22 Digital Logic Design

Consider the following Boolean expression.
F = (X + Y + Z)(X̅ + Y)(Y̅ + Z)
Which of the following Boolean expressions is/are equivalent to F̅ (complement of F)?

Ques 23 Digital Logic Design

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

Ques 24 Discrete Mathematics

Let G be a group of order 6, and H be a subgroup of G such that 1 < |H| < 6. Which one of the following options is correct?

Ques 25 Discrete Mathematics

Consider the two statements.
S1: There exist random variables X and Y such that (E[(X − E(X))(Y − E(Y))])2 > Var[X]Var[Y]
S2: For all random variables X and Y, Cov[X, Y] = E[|X − E[X]||Y − E[Y]|]
Which one of the following choices is correct?

Ques 26 Discrete Mathematics

Let G = (V, E) be an undirected unweighted connected graph. The diameter of G is defined as:
diam(G) = maxu,v∈V {the length of shortest path between u and v}
Let M be the adjacency matrix of G. Define graph G2 on the same set of vertices with adjacency matrix N, where