In the worst case, the number of comparisons needed to search a singly linked list of length n for a given element is

Consider the following algorithm for searching for a given number x in an unsorted array A[1..n] having n distinct values:
1. Choose an i uniformly at random fro 1..n;
2. If A[i]=x then stop else Goto 1;
Assuming that x is present A, what is the expected number of comparisons made by the algorithm before it terminates?

The running time of the following algorithm Procedure A(n)
If n<=2 return (1) else return (A([$$\sqrt n $$])); is best described by

The solution to the recurrence equation
T(2^k) = 3 T(2^k-1) + 1, T (1) = 1, is:

In absolute addressing mode

Sign extension is the step in

Which of the following is not a form of memory?

In $$2’s$$ complement addition, the overflow

The performance of a pipelined processor suffers if

Horizontal micro programming

In serial data transmission, every byte of data is padded with a $$‘0’$$ in the beginning and one or two $$‘1’s$$ at the end of byte because

The number of leaf nodes in a rooted tree of n nodes, with each node having 0 or 3 children is:

In the worst case, the number of comparisons needed to search a singly linked list of length n for a given element is

Relation $$R$$ is decomposed using a set of functional dependencies, $$F,$$ and relation $$S$$ is decomposed using another set of functional dependencies, $$G.$$ One decomposition is definitely $$BCNF,$$ the other is definitely. $$3NF,$$ but it is not known which is which. To make a guaranteed identification, which one of the following tests should be used on the decompositions? (Assume that the closures of $$F$$ and $$G$$ are available).

From the following instance of a relation schema $$R(A, B, C),$$ we can conclude that:

Relation $$R$$ with an associated set of functional dependencies, $$F,$$ is decomposed into $$BCNF.$$ The redundancy (arising out of functional dependencies) in the resulting set of relations is

With regard to the expressive power of the formal relational query languages, which of the following statements is true?

A B⁺ - tree index is to be built on the Name attribute of the relation STUDENT. Assume that all student names are of length 8 bytes, disk blocks are of size 512 bytes, and index pointers are of size 4 bytes. Given this scenario, what would be the best choice of the degree (i.e. the number of pointers per node) of the B⁺ - tree?

Consider the following multiplexer where $$10, 11, 12, 13$$ are four data input lines selected by two address line combinations $${A_1}\,{A_0} = 00,01,10,11$$ respectively and $$f$$ is the output of the multiplex (or). $$EN$$ is the Enable input.

The function $$f(x,y,z)$$ implemented by the above circuit is

The $$2's$$ compliment representation of the decimal value $$-15$$ is

Transform the following logic circuit (without expressing its switching function) into an equivalent logic circuit that employs only $$6$$ $$NAND$$ gates each with $$2$$-inputs.

The decimal value $$0.25$$

Minimum $$SOP$$ for $$f(w, x, y, z)$$ shown in karnaugh $$-$$ map below is

Sign extension is the step in

$$f\left( {A,B} \right) = A' + B$$ Simplified expression for function $$f((x+y,y),z)$$ is

Express the function $$f( x, y, z)= xy'+ yz'$$ with only one complement operation and one or more $$AND/OR$$ operations. Draw the logic circuit implementing the expression obtained, using a single NOT gate and one or more $$AND/OR$$ gates.

Consider the following logic circuit whose inputs are functions $${f_1},$$ $${f_2},$$ $${f_3},$$ and output is $$f.$$

The binary relation $$S = \phi $$ (emply set) on set A = {1, 2, 3} is

Determine whether each of the following is a tautology, a contradiction, or neither ("$$ \vee $$" is disjunction, "$$ \wedge $$" is conjuction, "$$ \to $$" is implication, "$$\neg $$" is negation, and "$$ \leftrightarrow $$" is biconditional (if and only if).

(i)$$\,\,\,\,\,\,A \leftrightarrow \left( {A \vee A} \right)$$
(ii)$$\,\,\,\,\,\,\left( {A \vee B} \right) \to B$$
(iii)$$\,\,\,\,\,\,A \vee \left( {\neg \left( {A \vee B} \right)} \right)$$

The minimum number of colors required to color the vertices of a cycle with $$n$$ nodes in such a way that no two adjacent nodes have the same colour is:

The rank of the matrix$$\left[ {\matrix{ 1 & 1 \cr 0 & 0 \cr } } \right]\,\,is$$

Four fair coins are tossed simultaneously. The probability that at least one head and one tail turn up is

(a) $$S = \left\{ { < 1,2 > ,\, < 2,1 > } \right\}$$ is binary relation on set $$A = \left\{ {1,2,3} \right\}$$. Is it irreflexive?
Add the minimumnumber of ordered pairs to $$S$$ to make it an $$\,\,\,\,\,$$equivalence relation. Give the modified $$S$$.

(b) Let $$S = \left\{ {a,\,\,b} \right\}\,\,\,\,$$ and let ▢ $$S$$ be the power set of $$S$$. Consider the binary relation $$'\underline \subset $$ (set inclusion)' on ▢ $$S$$. Draw the Hasse diagram corresponding to the lattice (▢$$(S)$$, $$\underline \subset $$)

Let $$A$$ be a set of $$n\left( { > 0} \right)$$ elements. Let $${N_r}$$ be the number of binary relations on $$A$$ and Let $${N_r}$$ be the number of functions from $$A$$ to $$A$$.
(a) Give the expression for $${N_r}$$ in terms of $$n$$.
(b) Give the expression for $${N_f}$$ in terms of $$n$$.
(c) Which is larger for all possible $$n, $$ $${N_r}$$ or $${N_f}$$?

Maximum number of edges in a n - node undirected graph without self loops is

Obtain the eigen values of the matrix $$$A = \left[ {\matrix{ 1 & 2 & {34} & {49} \cr 0 & 2 & {43} & {94} \cr 0 & 0 & { - 2} & {104} \cr 0 & 0 & 0 & { - 1} \cr } } \right]$$$

The function $$f\left( {x,y} \right) = 2{x^2} + 2xy - {y^3}$$ has

"If X then Y unless Z" is represented by which of the following formulas in propositional logic? (" $$\neg $$ " is negation, " $$ \wedge $$ " is conjunction, and " $$ \to $$ " is implication)

Which of the following scheduling algorithms is non-preemptive?

Which of the following is not a form of memory?

A computer system uses $$32$$-bit virtual address, and $$32$$-bit physical address. The physical memory is byte addressable, and the page size is $$4$$ kbytes. It is decided to use two level page tables to translate from virtual address to physical address. Equal number of bits should be used for indexing first level and second level page table, and the size of each page table entry is $$4$$ bytes.

(a) Give a diagram showing how a virtual address would be translated to a physical address.

(b) What is the number of page table entries that can be contained in each page?

(c) How many bits are available for storing protection and other information in each page table entry?

Dynamic linking can cause security concerns because

The optimal page replacement algorithm will select the page that.

In the index allocation scheme of blocks to a file, the maximum possible size of the file depends on

Which of the following scheduling algorithms is non-preemptive?

Draw the process state transition diagram of an $$OS$$ in which
(i) each process is in one of the five states: created, ready, running, blocked (i.e. sleep or wait), or terminated, and
(ii) only non-preemptive scheduling is used by the $$OS.$$ Label the transitions appropriately.

Which combination of the following features will suffice to characterize an $$OS$$ as a multi-programmed $$OS?$$
$$(a).$$ More than one program may be loaded into main memory at the same time for execution.
$$(b).$$ If a program waits for certain events such as $$I/O$$, another program is immediately scheduled for execution.
$$(c).$$ If the execution of a program terminates, another program is immediately scheduled for execution.

Consider the following declaration of a two-dimensional array in C:

char a[100][100];

Assuming that the main memory is byte-addressable and that the array is stored starting from memory address 0, the address of a[40][50] is

In the C language

The results returned by function under value-result and reference parameter passing conventions

Which of the following is true?

The $$C$$ language is:

The language accepted by a pushdown Automation in which the stack is limited to $$10$$ items is best described as

The smallest finite automaton which accepts the language
$$L = \left. {\left\{ x \right.} \right|$$ length of $$x$$ is divisible by $$\left. 3 \right\}$$ has

The Finite state machine described by the following state diagram with $$A$$ as starting state, where an arc label is $$x/y$$ and $$x$$ stands for $$1-bit$$ input and $$y$$ stands for $$2$$-bit output