# Recent activity by Arjun

1
Consider the following statements: $S_1:$ There exists infinite sets $A$, $B$, $C$ such that $A \cap (B \cup C)$ is finite. $S_2:$ There exists two irrational numbers $x$ and y such that $(x+y)$ is rational. Which of the following is true about $S_1$ and $S_2$? Only $S_1$ is correct Only $S_2$ is correct Both $S_1$ and $S_2$ are correct None of $S_1$ and $S_2$ is correct
2
Five of India's leading models are posing for a photograph promoting World Peace and Understanding . But then, Sachin Malhotra the photographer is having a tough time getting them to stand in a straight line, because Natasha refuses to stand in a straight line, ... line, promoting world peace. If Natasha stands at the extreme left, who is standing second from left? Cannot say Jessica Rachel Ria
3
Suppose $X_{1a}, X_{1b},X_{2a},X_{2b},\dots , X_{5a},X_{5b}$ are ten Boolean variables each of which can take the value TRUE or FLASE. Recall the Boolean XOR $X\oplus Y:=(X\wedge \neg Y)\vee (\neg X \wedge Y)$ ... $H$ have? $20$ $30$ $32$ $160$ $1024$
4
Show that if $G$ is a group such that $(a. b)^2 = a^2.b^2$ for all $a, b$ belonging to $G$, then $G$ is an abelian.
5
Let $f:\mathbb{R} \rightarrow \mathbb{R}$ be a continuous function such that $\lim _{n\rightarrow \infty} f^n(x)$ exists for every $x \in \mathbb{R}$, where $f^n(x) = f \circ f^{n-1}(x)$ for $n \geq 2$ ... $S \subset T$ $T \subset S$ $S = T$ None of the above
6
How many solutions are there to the equation x1 + x2 + x3 + x4 + x5 = 21, where xi , i = 1, 2, 3, 4, 5, is a nonnegative integer such that: 0$\leq$ x1$\leq$10 ?
7
Consider the following language: $L= \{ w \in \{0,1\}^* \mid w \text{ ends with the substring } 011 \}$ Which one of the following deterministic finite automata accepts $L?$
8
Show that the formula $\left[(\sim p \vee q) \Rightarrow (q \Rightarrow p)\right]$ is not a tautology. Let $A$ be a tautology and $B$ any other formula. Prove that $(A \vee B)$ is a tautology.
9
Consider the following relations $A, B$ and $C:$ ... of $A\cup B$ is the same as that of $A$. $(A\cup B)\bowtie _{A.Id > 40 \vee C.Id < 15} C$ $7$ $4$ $5$ $9$
10
The output $Y$ of the given circuit $1$ $0$ $X$ $X'$
11
In the context of operating systems, which of the following statements is/are correct with respect to paging? Paging helps solve the issue of external fragmentation Page size has no impact on internal fragmentation Paging incurs memory overheads Multi-level paging is necessary to support pages of different sizes
12
Which of the following statement(s) is/are correct in the context of $\text{CPU}$ scheduling? Turnaround time includes waiting time The goal is to only maximize $\text{CPU}$ utilization and minimize throughput Round-robin policy can be used even when the $\text{CPU}$ time required by each of the processes is not known apriori Implementing preemptive scheduling needs hardware support
13
Assume a two-level inclusive cache hierarchy, $L1$ and $L2$, where $L2$ is the larger of the two. Consider the following statements. $S_1$: Read misses in a write through $L1$ cache do not result in writebacks of dirty lines to the $L2$ $S_2$: Write allocate policy must be ... $S_2$ is false $S_1$ is false and $S_2$ is true $S_1$ is true and $S_2$ is true $S_1$ is false and $S_2$ is false
14
A single bus CPU consists of four general purpose register, namely, $R0, \ldots, R3, \text{ALU}, \text{MAR}, \text{MDR}, \text{PC}, \text{SP}$ and $\text{IR}$ (Instruction Register). Assuming suitable microinstructions, write a microroutine for the instruction, $\text{ADD }R0, R1$.
15
Consider a computer system with multiple shared resource types, with one instance per resource type. Each instance can be owned by only one process at a time. Owning and freeing of resources are done by holding a global lock $(L)$. The following scheme ... deadlocks will not occur The scheme may lead to live-lock The scheme may lead to starvation The scheme violates the mutual exclusion property
16
Consider the following statements. $S_1:$ Every $\text{SLR(1)}$ grammar is unambiguous but there are certain unambiguous grammars that are not $\text{SLR(1)}$. $S_2:$ For any context-free grammar, there is a parser that takes at most $O(n^3)$ time to parse a string of length $n$. ... $S_2$ is false $S_1$ is false and $S_2$ is true $S_1$ is true and $S_2$ is true $S_1$ is false and $S_2$ is false
17
The below figure shows a $B^+$ tree where only key values are indicated in the records. Each block can hold upto three records. A record with a key value $34$ is inserted into the $B^+$ tree. Obtain the modified $B^+$ tree after insertion.
18
The given diagram shows the flowchart for a recursive function $A(n)$. Assume that all statements, except for the recursive calls, have $O(1)$ time complexity. If the worst case time complexity of this function is $O(n^{\alpha})$, then the least possible value (accurate up to two decimal positions) of $\alpha$ is ________. Flow chart for Recursive Function $A(n)$.
19
Which one of the following statements about normal forms is $\text{FALSE}?$ $\text{BCNF}$ is stricter than $\text{3NF}$ Lossless, dependency-preserving decomposition into $\text{3NF}$ is always possible Lossless, dependency-preserving decomposition into $\text{BCNF}$ is always possible Any relation with two attributes is in $\text{BCNF}$
20
Consider an excess -$50$ representation for floating point numbers with $4$ BCD digit mantissa and $2$ BCD digit exponent in normalised form. The minimum and maximum positive numbers that can be represented are __________ and _____________ respectively.
21
In the following $C$ program fragment, $j$, $k$, $n$ and TwoLog_n are integer variables, and $A$ is an array of integers. The variable $n$ is initialized to an integer $\geqslant 3$, and TwoLog_n is initialized to the value of $2^*\lceil \log_2(n) \rceil$ for (k = 3; k <= n; k++) A[k] ... $\left\{m \mid m \leq n, \text{m is prime} \right\}$ { }
22
In the following Pascal program segment, what is the value of X after the execution of the program segment? X := -10; Y := 20; If X > Y then if X < 0 then X := abs(X) else X := 2*X; $10$ $-20$ $-10$ None
23
The following postfix expression with single digit operands is evaluated using a stack: $8 \ 2 \ 3 \ {}^\hat{} ∕ \ 2 \ 3 * + 5 \ 1 * -$ Note that $^\hat{}$ is the exponentiation operator. The top two elements of the stack after the first $*$ is evaluated are $6, 1$ $5, 7$ $3, 2$ $1, 5$
24
Delayed branching can help in the handling of control hazards The following code is to run on a pipelined processor with one branch delay slot: I1: ADD $R2 \leftarrow R7 + R8$ I2: Sub $R4 \leftarrow R5 &ndash; R6$ I3: ADD $R1 \leftarrow R2 + R3$ I4: STORE ... Which of the instructions I1, I2, I3 or I4 can legitimately occupy the delay slot without any program modification? I1 I2 I3 I4
25
For a Turing machine $M$, $\langle M \rangle$ denotes an encoding of $M$ ... and $L_2$ are decidable $L_1$ is decidable and $L_2$ is undecidable $L_1$ is undecidable and $L_2$ is decidable Both $L_1$ and $L_2$ are undecidable
26
Which of the following languages are undecidable? Note that $\left \langle M \right \rangle$ indicates encoding of the Turing machine M. $L_1 = \{\left \langle M \right \rangle \mid L(M) = \varnothing \}$ ... $members}\}$ $L_1$, $L_3$, and $L_4$ only $L_1$ and $L_3$ only $L_2$ and $L_3$ only $L_2$, $L_3$, and $L_4$ only
For a statement $S$ in a program, in the context of liveness analysis, the following sets are defined: $\text{USE}(S)$ : the set of variables used in $S$ $\text{IN}(S)$ : the set of variables that are live at the entry of $S$ $\text{OUT}(S)$ : the set of variables that are live at the ... $) }\cup \text{ OUT ($S_2$)}$ $\text{OUT ($S_1$)} = \text{USE ($S_1$)} \cup \text{IN ($S_2$)}$
Consider the following $\text{ANSI C}$ program: #include <stdio.h> #include <stdlib.h> struct Node{ int value; struct Node *next;}; int main( ) { struct Node *boxE, *head, *boxN; int index=0; boxE=head= (struct Node *) malloc(sizeof(struct Node)) ... $\textsf{return}$ which will be reported as an error by the compiler It dereferences an uninitialized pointer that may result in a run-time error
A queue is implemented using an array such that ENQUEUE and DEQUEUE operations are performed efficiently. Which one of the following statements is CORRECT ($n$ refers to the number of items in the queue) ? Both operations can be performed in $O(1)$ time. At most one ... complexity for both operations will be $\Omega (n)$. Worst case time complexity for both operations will be $\Omega (\log n)$