# Recent activity by Sankha Narayan Bose

1
The rank of the matrix $\begin{bmatrix} 0 &1 &t \\ 2& t & -1\\ 2& 2 & 0 \end{bmatrix}$ equals $3$ for any real number $t$ $2$ for any real number $t$ $2$ or $3$ depending on the value of $t$ $1,2$ or $3$ depending on the value of $t$
2
Which of the following concurrency control protocols ensure both conflict serializability and freedom from deadlock? 2-phase locking Time-stamp ordering I only II only Both I and II Neither I nor II
3
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 ________
4
Let $G$ be an arbitrary group. Consider the following relations on $G$: $R_1: \forall a , b \in G, \: a R_1 b \text{ if and only if } \exists g \in G \text{ such that } a = g^{-1}bg$ $R_2: \forall a , b \in G, \: a R_2 b \text{ if and only if } a= b^{-1}$ Which of the above is/are equivalence relation/relations? $R_1$ and $R_2$ $R_1$ only $R_2$ only Neither $R_1$ nor $R_2$
5
Let $G$ be any connected, weighted, undirected graph. $G$ has a unique minimum spanning tree, if no two edges of $G$ have the same weight. $G$ has a unique minimum spanning tree, if, for every cut of $G$, there is a unique minimum-weight edge crossing the cut. Which of the following statements is/are TRUE? I only II only Both I and II Neither I nor II
6
Consider the first order predicate formula $\varphi$: $\forall x [ ( \forall z \: z \mid x \Rightarrow (( z=x) \vee (z=1))) \rightarrow \exists w ( w > x) \wedge (\forall z \: z \mid w \Rightarrow ((w=z) \vee (z=1)))]$ Here $a \mid b$ ... $S3:$ Set of all integers Which of the above sets satisfy $\varphi$? S1 and S2 S1 and S3 S2 and S3 S1, S2 and S3
7
Two numbers are chosen independently and uniformly at random from the set $\{1,2,\ldots,13\}.$ The probability (rounded off to 3 decimal places) that their $4-bit$ (unsigned) binary representations have the same most significant bit is _______________.
8
Consider the language: L = {a^(2+3k) or b^(10+12k) } for k ≥ 0. Which of the following is correct for the length of string L to satisfy Pumping Lemma? (A) 5 (B) 24 (C) 9 (D) 3 Answer?
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If $f(x)$ is defined as follows, what is the minimum value of $f(x)$ for $x \in (0, 2]$ ? $f(x) = \begin{cases} \frac{25}{8x} \text{ when } x \leq \frac{3}{2} \\ x+ \frac{1}{x} \text { otherwise}\end{cases}$ $2$ $2 \frac{1}{12}$ $2\frac{1}{6}$ $2\frac{1}{2}$
11
Suppose three coins are lying on a table, two of them with heads facing up and one with tails facing up. One coin is chosen at random and flipped. What is the probability that after the flip the majority of the coins(i.e., at least two of them) will have heads facing up? ... $\left(\frac{1}{4}\right)$ $\left(\frac{1}{4}+\frac{1}{8}\right)$ $\left(\frac{2}{3}\right)$
12
There are two elements $x,\:y$ in a group $(G,*)$ such that every element in the group can be written as a product of some number of $x$'s and $y$'s in some order. It is known that $x*x=y*y=x*y*x*y=y*x*y*x=e$ where $e$ is the identity element. The maximum number of elements in such a group is ____.
13
Let $X$ and $Y$ be finite sets and $f:X \to Y$ be a function. Which one of the following statements is TRUE? For any subsets $A$ and $B$ of $X, |fA \cup B| = |f(A)| + |f(B)|$ For any subsets $A$ and $B$ of $X, f(A \cap B) = f(A) \cap f(B)$ For any subsets $A$ and $B$ of $X, |f(A \cap B)| = \min \{|f(A)|, |f(B)|\}$ For any subsets $S$ and $T$ of $Y, f^{-1}(S \cap T) = f^{-1}(S) \cap f^{-1}(T)$
14
Show that the conclusion $(r \to q)$ follows from the premises: $p, (p \to q) \vee (p \wedge (r \to q))$
15
Suppose a fair six-sided die is rolled once. If the value on the die is $1, 2,$ or $3,$ the die is rolled a second time. What is the probability that the sum total of values that turn up is at least $6$ ? $\dfrac{10}{21}$ $\dfrac{5}{12}$ $\dfrac{2}{3}$ $\dfrac{1}{6}$
16
The ALU, the bus and all the registers in the data path are of identical size. All operations including incrementation of the PC and the GPRs are to be carried out in the ALU. Two clock cycles are needed for memory read operation - the first one for loading address in the MAR ... $2$ $3$ $4$ $5$
17
Consider the following data path of a CPU. The ALU, the bus and all the registers in the data path are of identical size. All operations including incrementation of the PC and the GPRs are to be carried out in the ALU. Two clock cycles are needed for memory read operation - the ... <= R0 + R1. The minimum number of clock cycles needed for execution cycle of this instruction is: $2$ $3$ $4$ $5$
18
Consider the following program segment. Here $\text{R1, R2}$ and $\text{R3}$ ... Assume that the memory is word addressable. After the execution of this program, the content of memory location $2010$ is: $100$ $101$ $102$ $110$
19
Consider the following program segment. Here $\text{R1, R2}$ and $\text{R3}$ ... that the memory is word addressable. The number of memory references for accessing the data in executing the program completely is $10$ $11$ $20$ $21$
20
A processor takes $12$ cycles to complete an instruction I. The corresponding pipelined processor uses $6$ stages with the execution times of $3, 2, 5, 4, 6$ and $2$ cycles respectively. What is the asymptotic speedup assuming that a very large number of instructions are to be executed? $1.83$ $2$ $3$ $6$
21
A pipelined processor uses a 4-stage instruction pipeline with the following stages: Instruction fetch (IF), Instruction decode (ID), Execute (EX) and Writeback (WB). The arithmetic operations as well as the load and store operations are carried out in the EX stage. The ... ID stage is used. The number of clock cycles required to complete the sequence of instructions is $10$ $12$ $14$ $16$
22
The size of the data count register of a $\text{DMA}$ controller is $16 \text{bits}$. The processor needs to transfer a file of $29,154$ kilobytes from disk to main memory. The memory is byte addressable. The minimum number of times the $\text{DMA}$ controller needs to get the control of the system bus from the processor to transfer the file from the disk to main memory is _________-.
23
Consider a typical disk that rotates at $15000$ rotations per minute (RPM) and has a transfer rate of $50 \times 10^6$ bytes/sec. If the average seek time of the disk is twice the average rotational delay and the controller's transfer time is $10$ times the disk transfer time, the average time (in milliseconds) to read or write a $512$-byte sector of the disk is _____
24
Consider a disk pack with a seek time of $4$ milliseconds and rotational speed of $10000$ rotations per minute (RPM). It has $600$ sectors per track and each sector can store $512$ bytes of data. Consider a file stored in the disk. The file ... accessing each sector is half of the time for one complete rotation. The total time (in milliseconds) needed to read the entire file is__________________
25
Consider a hard disk with $16$ recording surfaces $(0-15)$ having 16384 cylinders $(0-16383)$ and each cylinder contains $64$ sectors $(0-63)$. Data storage capacity in each sector is $512$ bytes. Data are organized cylinder-wise and the addressing format is <cylinder no., ... is the cylinder number of the last sector of the file, if it is stored in a contiguous manner? $1281$ $1282$ $1283$ $1284$
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A hard disk with a transfer rate of $10$ Mbytes/second is constantly transferring data to memory using DMA. The processor runs at $600$ MHz, and takes $300$ and $900$ clock cycles to initiate and complete DMA transfer respectively. If the size of the transfer is $20$ Kbytes, what is the percentage of processor time consumed for the transfer operation? $5.0 \%$ $1.0\%$ $0.5\%$ $0.1\%$
Consider the main memory system that consists of $8$ memory modules attached to the system bus, which is one word wide. When a write request is made, the bus is occupied for $100$ nanoseconds (ns) by the data, address, and control signals. During the same $100$ ns, ... be on the bus at any time. The maximum number of stores (of one word each) that can be initiated in $1$ millisecond is ________
Consider a hypothetical processor with an instruction of type $\text{LW R1, 20(R2)}$, which during execution reads a $32-bit$ word from memory and stores it in a $32-bit$ register $\text{R1}$. The effective address of ... addressing mode implemented by this instruction for the operand in memory? Immediate addressing Register addressing Register Indirect Scaled Addressing Base Indexed Addressing
Frames of $1000\text{ bits}$ are sent over a $10^6$ bps duplex link between two hosts. The propagation time is $25ms$. Frames are to be transmitted into this link to maximally pack them in transit (within the link). Let $I$ be the minimum number of ... wait before starting transmission of the next frame? (Identify the closest choice ignoring the frame processing time) $16ms$ $18ms$ $20ms$ $22ms$