GATE CSE 2019
Q41.
Consider three machines M, N and P with IP addresses 100.10.5.2, 100.10.5.5 and 100.10.5.6 respectively. The subnet mask is set to 255.255.255.252 for all the three machines. Which one of the following is true?Q42.
Consider the following relation P(X, Y, Z), Q(X, Y, T) and R(Y, V): How many tuples will be returned by the following relational algebra query? Answer:______Q43.
For \Sigma =\{a,b\}, let us consider the regular language L=\{x|x=a^{2+3k} \; or \; x=b^{10+12k}, k\geq 0\}. Which one of the following can be a pumping length (the constant guaranteed by the pumping lemma) for L?Q44.
If L is a regular language over \Sigma =\{a,b\}, which one of the following languages is NOT regular ?Q45.
Let G be an arbitrary group. Consider the following relations on G: R1: \forall a,b \in G, aR_1b if and only if \exists g \in G such that a=g^{-1}bg R2: \forall a,b \in G, aR_2b if and only if a=b^{-1} Which of the above is/are equivalence relation/relations?Q46.
Let U=\{1,2,,...n\}. Let A=\{(x,X)|x\in X,X\subseteq U\}. Consider the following two statements on |A|. I. |A|=n2^{n-1}II. |A|=\sum_{k=1}^{n}k\binom{n}{k}Which of the above statements is/are TRUE?Q47.
Consider the first order predicate formula: \forall x[\forall z\; z|x\Rightarrow ((z=x)\vee (z=1))\Rightarrow \exists w(w> x)\wedge (\forall z \; z|w\Rightarrow ((w=z)\vee (z=1)))] Here 'a|b' denotes that 'a divides b', where a and b are integers. Consider the following sets: S1: {1, 2, 3, ..., 100} S2: Set of all positive integers S3: Set of all integers Which of the above sets satisfy \varphi ?Q48.
An array of 25 distinct elements is to be sorted using quicksort. Assume that the pivot element is chosen uniformly at random. The probability that the pivot element gets placed in the worst possible location in the first round of partitioning (rounded off to 2 decimal places) is _________.Q49.
Consider the following grammar and the semantic actions to support the inherited type declaration attributes. Let X_1,X_2,X_3,X_4,X_5 \; and \; X_6 be the placeholders for the non-terminals D, T, L or L_1 in the following table: Which one of the following are the appropriate choices for X_1,X_2,X_3 \; and \; X_4?Q50.
A relational database contains two tables Student and Performance as shown below: The primary key of the Student table is Roll_no. For the Performance table, the columns Roll_no. and Subject_code together from the primary key. Consider the SQL query given below: SELECT S.Student_name, sum(P.Marks) FROM Student S, Performance P WHERE P.Marks > 84 GROUP BY S.Student_name;The number of rows returned by the above SQL query is _________ .