# Recent activity by SomeEarth

1
Two straight lines are drawn perpendicular to each other in $X-Y$ plane. If $\alpha$ and $\beta$ are the acute angles the straight lines make with the $\text{X-}$ axis, then $\alpha + \beta$ is_______. $60^{\circ}$ $90^{\circ}$ $120^{\circ}$ $180^{\circ}$
2
Which one of the following regular expressions represents the set of all binary strings with an odd number of $1’$s? $((0+1)^*1(0+1)^*1)^*10^*$ $(0^*10^*10^*)^*0^*1$ $10^*(0^*10^*10^*)^*$ $(0^*10^*10^*)^*10^*$
3
The figure below shows an annular ring with outer and inner as $b$ and $a$, respectively. The annular space has been painted in the form of blue colour circles touching the outer and inner periphery of annular space. If maximum $n$ ... $\pi [(b^{2}-a^{2})+n(b-a)^{2}]$
4
Consider the following propositional statements: $P_1: ((A ∧ B) → C)) ≡ ((A → C) ∧ (B → C))$ $P_2: ((A ∨ B) → C)) ≡ ((A → C) ∨ (B → C))$ Which one of the following is true? $P_1$ is a tautology, but not $P_2$ $P_2$ is a tautology, but not $P_1$ $P_1$ and $P_2$ are both tautologies Both $P_1$ and $P_2$ are not tautologies
5
Choose the correct alternatives (more than one may be correct) and write the corresponding letters only: Which of the following is/are a tautology? $a \vee b \to b \wedge c$ $a \wedge b \to b \vee c$ $a \vee b \to \left(b \to c \right)$ $a \to b \to \left(b \to c \right)$
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The action for this problem takes place in an island of Knights and Knaves, where Knights always make true statements and Knaves always make false statements and everybody is either a Knight or a Knave. Two friends A and B lives in a house. The census taker (an outsider) knocks on ... and B is a Knave. A is a Knave and B is a Knight. Both are Knaves. Both are Knights. No conclusion can be drawn.
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In a room there are only two types of people, namely $\text{Type 1}$ and $\text{Type 2}$. $\text{Type 1}$ people always tell the truth and $\text{Type 2}$ people always lie. You give a fair coin to a person in that room, without knowing which type he is from and tell ... tail If the person is of $\text{Type 2}$, then the result is tail If the person is of $\text{Type 1}$, then the result is tail
8
Consider the following first order logic formula in which $R$ is a binary relation symbol. $∀x∀y (R(x, y) \implies R(y, x))$ The formula is satisfiable and valid satisfiable and so is its negation unsatisfiable but its negation is valid satisfiable but its negation is unsatisfiable
9
Find the inverse function of $f(x) = x^3 +1.$
10
Consider the following statements: The smallest element in a max-heap is always at a leaf node The second largest element in a max-heap is always a child of a root node A max-heap can be constructed from a binary search tree in $\theta(n)$ time A binary search tree can be constructed ... time Which of te above statements are TRUE? I, II and III I, II and IV I, III and IV II, III and IV
11
Two cars at the same time from the same location and go in the same direction. The speed of the first car is $50$ km/h and the speed of the second car is $60$ km/h. The number of hours it takes for the distance between the two cars to be $20$ km is _____. $1$ $2$ $3$ $6$
12
Consider the grammar given below: $S \rightarrow Aa$ $A \rightarrow BD$ $B \rightarrow b \mid \epsilon$ $D \rightarrow d \mid \epsilon$ Let $a,b,d$ and $\$ be indexed as follows:$\begin{array}{|l|l|l|l|} \hline a & b & d & \$ \\ \hline 3 & 2 & 1 & ... $)$ , then the answer should be $3210$)
13
The value of $3^{51} \text{ mod } 5$ is _____
14
Compute $\displaystyle \lim_{x \rightarrow 3} \frac{x^4-81}{2x^2-5x-3}$ $1$ $53/12$ $108/7$ Limit does not exist
15
For the set $N$ of natural numbers and a binary operation $f : N \times N \to N,$ an element $z \in N$ is called an identity for $f,$ if $f (a, z) = a = f(z, a),$ for all $a \in N.$ Which of the following binary operations have an identity? $f (x, y) = x + y - 3$ $f (x, y) = \max(x, y)$ $f (x, y) = x^y$ I and II only II and III only I and III only None of these
16
Consider the set $\{a, b, c\}$ with binary operators $+$ and $*$ defined as follows: ... $(b * x) + (c * y) = c$ The number of solution(s) (i.e., pair(s) $(x, y)$ that satisfy the equations) is $0$ $1$ $2$ $3$
17
Suppose that a robot is placed on the Cartesian plane. At each step it is allowed to move either one unit up or one unit right, i.e., if it is at $(i,j)$ then it can move to either $(i + 1, j)$ or $(i,j + 1)$. How many distinct paths are there for the robot to reach the point $(10,10)$ starting from the initial position $(0,0)$? $^{20}\mathrm{C}_{10}$ $2^{20}$ $2^{10}$ None of the above
18
The following program consists of $3$ concurrent processes and $3$ binary semaphores. The semaphores are initialized as $S0=1, S1=0$ and $S2=0.$ ... $P0$ print '$0$'? At least twice Exactly twice Exactly thrice Exactly once
19
Consider the set of process with arrival time (in milliseonds), CPU burst time (in millisecods) and priority ($0$ ... The average waiting time (in milli seconds) of all the process using premtive priority scheduling algorithm is ______
20
Consider three data items $D1, D2,$ and $D3,$ and the following execution schedule of transactions $T1, T2,$ and $T3.$ In the diagram, $R(D)$ and $W(D)$ denote the actions reading and writing the data item $D$ ... $T2; T3; T1$ The schedule is serializable as $T2; T1; T3$ The schedule is serializable as $T3; T2; T1$ The schedule is not serializable
21
Consider the relation employee(name, sex, supervisorName) with name as the key, supervisorName gives the name of the supervisor of the employee under consideration. What does the following Tuple Relational Calculus query produce? ... with no immediate male subordinates. Names of employees with no immediate female subordinates. Names of employees with a female supervisor.
22
Consider the set of relations EMP (Employee-no. Dept-no, Employee-name, Salary) DEPT (Dept-no. Dept-name, Location) Write an SQL query to: a)Find all employees names who work in departments located at ‘Calcutta’ and whose salary is greater than Rs.50,000. b)Calculate, for each department number, the number of employees with a salary greater than Rs. 1,00,000.
23
The arrival time, priority, and duration of the CPU and I/O bursts for each of three processes $P_1, P_2$ and $P_3$ ... $P_3$? $\text{11, 15, 9}$ $\text{10, 15, 9}$ $\text{11, 16, 10}$ $\text{12, 17, 11}$
24
Given the relations employee (name, salary, dept-no), and department (dept-no, dept-name,address), Which of the following queries cannot be expressed using the basic relational algebra operations $\left(\sigma, \pi,\times ,\Join, \cup, \cap,-\right)$? ... every employee Employees whose name is the same as their department name The sum of all employees' salaries All employees of a given department
25
$R(A,B,C,D)$ is a relation. Which of the following does not have a lossless join, dependency preserving $BCNF$ decomposition? $A \rightarrow B, B \rightarrow CD$ $A \rightarrow B, B \rightarrow C, C \rightarrow D$ $AB \rightarrow C, C \rightarrow AD$ $A \rightarrow BCD$
26
Consider the schema $R=(S,T, U, V)$ and the dependencies $S \rightarrow T, T \rightarrow U, U \rightarrow V$ and $V \rightarrow S$. Let $R = (R1\text{ and } R2)$ be a decomposition such that $R1 \cap R2 \neq \phi$. The decomposition is not in $2NF$ in $2NF$ but not $3NF$ in $3NF$ but not in $2NF$ in both $2NF$ and $3NF$
Let $P$ be quicksort program to sort numbers in ascending order using the first element as the pivot. Let $t_1$ and $t_2$ be the number of comparisons made by P for the inputs $[1 \ 2 \ 3 \ 4 \ 5]$ and $[4 \ 1 \ 5 \ 3 \ 2]$ respectively. Which one of the following holds? $t_1 = 5$ $t_1 < t_2$ $t_1>t_2$ $t_1 = t_2$
The unusual $\Theta(n^2)$ implementation of Insertion Sort to sort an array uses linear search to identify the position where an element is to be inserted into the already sorted part of the array. If, instead, we use binary search to identify the position, the worst case running time will remain $\Theta(n^2)$ become $\Theta(n (\log n)^2)$ become $\Theta(n \log n)$ become $\Theta(n)$
The following table has two attributes $A$ and $C$ where $A$ is the primary key and $C$ is the foreign key referencing $A$ ... $(5, 2)$ and $(7, 2)$ $(5, 2), (7, 2)$ and $(9, 5)$ $(3, 4), (4, 3)$ and $(6, 4)$
Let $E_1$ and $E_2$ be two entities in an $E/R$ diagram with simple-valued attributes. $R_1$ and $R_2$ are two relationships between $E_1$ and $E_2$, where $R_1$ is one-to-many and $R_2$ is many-to-many. $R_1$ and $R_2$ do not have any attributes of their own. What is the minimum number of tables required to represent this situation in the relational model? $2$ $3$ $4$ $5$