GATE CSE 2021 SET-1
Q31.
In an undirected connected planar graph G, there are eight vertices and five faces. The number of edges in G is _________.Q32.
The lifetime of a component of a certain type is a random variable whose probability density function is exponentially distributed with parameter 2. For a randomly picked component of this type, the probability that its lifetime exceeds the expected lifetime (rounded to 2 decimal places) is _________Q33.
A sender (S) transmits a signal, which can be one of the two kinds: H and L with probabilities 0.1 and 0.9 respectively, to a receiver (R) In the graph below, the weight of edge (u,v) is the probability of receiving v when u is transmitted, where u,v\in\{H,L\}. For example, the probability that the received signal is L given the transmitted signal was H, is 0.7. If the received signal is H, the probability that the transmitted signal was H (rounded to 2 decimal places) is __________.Q34.
Consider the following pseudocode, where Sis a semaphore initialized to 5 in line #2 and counter is a shared variable initialized to 0 in line #1. Assume that the increment operation in line #7 is not atomic.1. int counter =0; 2. Semaphore S= init(5); 3. void parop(void) 4. { 5. wait(S); 6. wait(S); 7. counter++; 8. signal(S); 9. signal(S); 10. } If five threads execute the function parop concurrently, which of the following program behavior(s) is/are possible?[MSQ]Q35.
In a pushdown automaton P=(Q, \Sigma, \Gamma, \delta, q_0, F), a transition of the form, where p,q \in Q \; a \in \sigma \cup \{ \epsilon \} ,\;X,Y, \in \Gamma \cup \{ \epsilon \}, represents(q,Y) \in \delta(p,a,X) Consider the following pushdown automaton over the input alphabet \Sigma = \{a,b\} and stack alphabet \Gamma = \{ \#, A\}. The number of strings of length 100 accepted by the above pushdown automaton is ___________Q36.
Consider the two statements. S1: There exist random variables X and Y such that \left(\mathbb E[(X-\mathbb E(X))(Y-\mathbb E(Y))]\right)^2 > \textsf{Var}[X]\textsf{Var}[Y] S2: For all random variables X and Y, \textsf{Cov}[X,Y]=\mathbb E \left[|X-\mathbb E[X]||Y-\mathbb E[Y]|\right ] Which one of the following choices is correct?Q37.
Let p and q be two propositions. Consider the following two formulae in propositional logic. S1: (\neg p\wedge(p\vee q))\rightarrow qS2: q\rightarrow(\neg p\wedge(p\vee q))Which one of the following choices is correct?Q38.
Consider the following recurrence relation. T\left ( n \right )=\left\{\begin{array} {lcl} T(n/2)+T(2n/5)+7n & \text{if} \; n > 0\\1 & \text{if}\; n=0 \end{array}\right. Which one of the following options is correct?Q39.
Let < M > denote an encoding of an automaton M. Suppose that \Sigma =\{0,1\}. Which of the following languages is/are NOT recursive?Q40.
The following relation records the age of 500 employees of a company, where empNo ( indicating the employee number) is the key: empAge(\underline{empNo},age) Consider the following relational algebra expression: \Pi_{empNo}(empAge \Join_{(age > age1)} \rho_{empNo1,age1}(empAge)) What does the above expression generate?