Handshaking theorem states that the sum of degrees of the vertices of a graph is twice the number of edges.

If G=(V,E) be a graph with E edges,then-

Σ deg_G(V) = 2E

This theorem applies even if multiple edges and loops are present.

Since the given graph is undirected, every edge contributes as twice in sum of degrees. So the sum of degrees is 2e.

Unshielded twisted pair (UTP) is a ubiquitous type of copper cabling used in telephone wiring and local area networks (LANs).
There are five types of UTP cables -- identified with the prefix CAT, as in category -- each supporting a different amount of bandwidth.g a different amount of bandwidth.

The Address Resolution Protocol (ARP) is a communication protocol used for discovering the link layer address, such as a MAC address, associated with a given internet layer address, typically an IPv4 address.

A media access control address (MAC address) of a device is a unique identifier assigned to a network interface controller (NIC).
MAC addresses are recognizable as six groups of two hexadecimal digits, separated by hyphens, colons, or no separator.
Option (A) is example for IP address
Option (B) and (C ) are not examples for any address representation in computer
01:A5:BB:A7:FF:60 is the MAC address which consists of six groups of two hexadecimal digits, separated by hyphens, colons, or no separator.

1. A virtual local area network (VLAN) is a logical group of workstations, servers and network devices that appear to be on the same LAN despite their geographical distribution. A VLAN allows a network of computers and users to communicate in a simulated environment as if they exist in a single LAN and are sharing a single broadcast and multicast domain.
2. Higher-end switches allow the functionality and implementation of VLANs.
3. VLANs address issues such as scalability, security, and network management. Network architects set up VLANs to provide network segmentation

SHA-1 produces a 160-bit hash value or message digests from the inputted data (data that requires encryption), which resembles the hash value of the MD5 algorithm.

The Advanced Encryption Standard, or AES, is a symmetric block cipher chosen by the U.S. government to protect classified information.
AES is Symmetric key algorithm

Explanation: An operating system has three main functions:
(1) manage the computer’s resources, such as the central processing unit, memory, and other input – output sources
(2) establish a user interface, and
(3) execute and provide services for applications software.
OS provides an interface between the user and the hardware and thus making the computer easy to use for the user but the primary function of OS is to manage the hardware in the most efficient way.

From the below process state diagram, we can easily that the option (B) is correct.

Scan is disk scheduling algorithm
In the round robin algorithm, each process will execute for particular time quantum,So it is the example for time sharing,
Stack is last in first out(LIFO)
In the batching processing, whatever process arrives first, it execute that process. So it First in First out(FIFO)

A page fault is a type of exception raised by computer hardware when a running program accesses a memory page that is not currently mapped by the memory management unit (MMU) into the virtual address space of a process

Given Expression = A + (B – C)* D

Prefix Notation:

A + (- B C) * D

A + (* - B C D)

+ A * - B C D

Given the function f(x) = (e^-22^x)/x!

Poisson Formula. Suppose we conduct a Poisson experiment, in which the average number of successes within a given region is μ.

Then, the Poisson probability is: P(x; μ) = (e^-μ) (μ^x) / x!

where x is the actual number of successes that result from the experiment, and e is approximately equal to 2.71828.

From the given function the “μ” value is 2 which is the mean.

Number of min resources required = (3-1) + (4-1) + (6-1) + 1 = 11

Following is the Gantt diagram:



Average Waiting Time = (30 + 3 + 3 + 18)/ 5 = 10.8

The range of integers that can be represented by n bit 2’s complement number system is -2^n-1 to (2^n-1 – 1).

After determining the effective address, the value in the base register is incremented by the size of the data item that is to be accessed.
For example, (A7)+ would access the content of the address register A7, then increase the address pointer of A7 by 1 (usually 1 word). Within a loop, this addressing mode can be used to step through all the elements of an array or vector.

1. An absolute address is represented by the contents of a register. This addressing mode is absolute in the sense that it is not specified relative to the current instruction address.

2. Indirect addressing is a scheme in which the address specifies which memory word or register contains not the operand but the address of the operand.

Immediate Operand:

The simplest way for an instruction to specify an operand is for the address part of the instruction actually to contain the operand itself rather than an address or other information describing where the operand is. Such an operand is called an immediate operand because it is automatically fetched from memory at the same time the instruction itself is fetched. It is immediately available for use.

Index mode:

The address of the operand is obtained by adding to the contents of the general register (called index register) a constant value. The number of the index register and the constant value are included in the instruction code

Consider case-1: I3 is executed without other interrupts:

Time interval = Interrupt processing time(I3) + Execution time(I3) = 4.5 + 20 microseconds = 24.5 microseconds

Consider case-2: I3 is executed simultaneously with other interrupts:

Time interval =( Interrupt processing time + Execution time) for I1, I2, I3 = 4.5 + 25 + 4.5 + 35 + 4.5 + 20 = 93.5 microseconds

Interleaved memory is a design made to compensate for the relatively slow speed of dynamic random-access memory (DRAM) or core memory, by spreading memory addresses evenly across memory banks.
Contiguous memory reads and writes are using each memory bank in turn, resulting in higher memory throughputs due to reduced waiting for memory banks to become ready for desired operations.
Two-Way Interleaved : Two memory blocks are accessed at same time for writing and reading operations

Binary search trees (BST), sometimes called ordered or sorted binary trees, are a particular type of container: data structures that store "items" (such as numbers, names etc.) in memory.

The in-order traversal of BST will gives the elements in the sorted order( ascending order)

Heap is a balanced binary tree (or almost complete binary tree), insertion complexity for heap is O(logn). We can get smallest element from the min heap in O(logn) time. But we can’t insert an element if it is not already present in O(logn) time .

A self-balancing binary search tree containing n items allows the lookup, insertion, and removal of an item in O(log n) worst-case time. Since it’s a self balancing BST, we can easily find out minimum element in O(logn) time which is always the leftmost element.

So, height of the tree is defined maximum distance of a leaf node from the root.The root node is “10” and lead node is “5”.The maximum distance is 3

The operators in the expression are +,x,- ^



First we will convert e^f ad ef^ (as highest precedence and right associativity) and later

d ^( e f ^ ) to def^^ and so on , you can find the same thing from the below steps.

The postfix expression:

a + b × c − ( d ^( e ^ f))

a + b × c − ( d ^( e f ^ ))

a + b × c − ( d e f ^ ^)

(a + (b × c)) − d e f ^ ^

(a + (b c x)) − d e f ^ ^

(a (b c x) +) − d e f ^ ^

(a b c x +) - (d e f ^ ^)

(a b c x +) - (d e f ^ ^)

a b c x + d e f ^ ^ -

Given data is each string takes up three memory words which is nothing but size is 3.
Base or starting address of the array is 1120.
The address of the 49^th element = base address of array + number of elements before current element * size of element
= 1120 + 48 * 3 = 1264

A Binary Tree is full if every node has 0 or 2 children. So, in such case, the binary tree with n leaves contains a total of 2*n-1 nodes.

The expression consists of the following operators *, ^
Between * and ^ , operator ‘^’ is highest precedence so it will execute first.
The expression consists of more than one ‘^’ operator is presented then it will follow right to left associativity.
Multiplication operator associativity is left to right.
1 * 2 ^ 3 * 4 ^ 5 * 6 = 1 * (2 ^ 3)* (4 ^ 5) * 6
= 1 * 8 * 1024 * 6
= 49152

In object-oriented programming, inheritance is the mechanism of basing an object or class upon another object (prototype-based inheritance) or class (class-based inheritance), retaining similar implementation.

In any object-oriented programming language,Overriding is a feature that allows a subclass or child class to provide a specific implementation of a method that is already provided by one of its superclasses or parent classes

Polymorphism is the provision of a single interface to entities of different types or the use of a single symbol to represent multiple different types

The number of bits in Control memory =26.
From the given data each instruction divided into op field (13)+X(next address field)+Y(MUX)
8(2³) status bits in the inputs of the MUX then three bits in the MUX select field.
No. of bits in control memory next address field=26-13-3 =10
size of the control memory in number of words is 2¹⁰=1024 words

C.P.U will use 24- bit instructions and instructions size(bytes) is 24/8 = 3 bytes

Program execution will start from address at 300 and from there on words every operation will takes 3- bytes and so on , So the address should be multiple of “3”. From the given options only 600 address value is valid.

Number of surfaces =16
Tracks per surface=128
Sectors per track=256
Data which will store per sector=512 bytes
Capacity of the disk = 16 surfaces X 128 tracks X 256 sectors X 512 bytes = 256 Mbytes.
The number of bits required to access a sector =Total number of sectors.
= 16 surfaces X 128 tracks X 256 sectors
=2⁴x2⁷x2⁸=2¹⁹

Number one is 0100 (4-Decimal value)
Another number is 1101(-3 is decimal value)
Adding of -3 and 4, the result is 1 and there is no overflow

Relative address means an address specified by indicating its distance from another address, called the base address.
In absolute addressing, you specify the actual address (called the absolute address) of a memory location.

Expressions with constant operands can be evaluated at compile time, thus improving run-time performance and reducing code size by avoiding evaluation at compile-time.
Example:
In the code fragment below, the expression (3 + 5) can be evaluated at compile time and replaced with the constant 8.

int f (void)
{
return 3 + 5;
}

Below is the code fragment after constant folding.

int f (void)
{
return 8;
}

Substitute the values of x (0,1,2 and 3) in the options and check which option gives the corresponding y(x) values. The function x³ – 2 x² + 1 gives the required values.
x = 0: y(x) = 1
x = 1: y(x) = 0
x = 2: y(x) = 8 - 8 + 1 = 1
x = 3: y(x) = 27 - 18 + 1 = 10

An ellipse can be defined as the locus of all points that satisfy the equations
x = a cos t
y = b sin t
where:
x,y are the coordinates of any point on the ellipse,
a, b are the radius on the x and y axes respectively,
t is the parameter, which ranges from 0 to 2π radians

Given function is y = x² – 3x + 1
To find the minimum value, calculate the derivative until at what point given function is minimum value.
Applying First order derivative to the function y is y’ = 2x – 3
Again applying derivative of y ’is y” = 2 (Since y” > 0, it has a minimum value)
So the minima value at that point is (2x – 3) = 0 and x = 3/2

A graph is a tree if and only if there is exactly one path between every pair of its vertices.

Let G be a graph and let there be exactly one path between every pair of vertices in G. So G is connected. Now G has no cycles, because if G contains a cycle, say between vertices u and v, then there are two distinct paths between u and v, which is a contradiction. Thus G is connected and is without cycles, therefore it is a tree.

A tree is a minimally connected graph i.e. removing a single edge will disconnect the graph. A tree with n vertices has n−1 edges and only one path exists between every pair of vertices.

Let G be a graph with k components. Let ni be the number of vertices in the i^th component, where 1 ≤ i ≤ k. Then, the number of edges in G is equal to sum of the edges in each of its components.

So, G has maximum number of edges if each component is a complete graph.

Hence, the maximum possible number of edges in the graph G is:

And in every case, (n − k)(n − k + 1)/2 will be greater than or equal to the above expression.

So, at maximum, there can be (n − k)(n − k + 1)/2 edges in a simple graph with n vertices and k components.

P(X)=a₀+a₁+a₂X²+a₃X³
=a₀+X(a₁+X(a₂+a₃X))
↓ ↓ ↓
③ ② ①
Here, minimum 3 multiplication needed

An orthogonal matrix is a square matrix whose columns and rows are orthogonal unit vectors (i.e., orthonormal vectors), i.e. AA^T=A^TA =I (Identity matrix)
This leads to the equivalent characterization: a matrix Q is orthogonal if its transpose is equal to its inverse: A^T=A^-1

If any two rows (or columns) of a determinant are interchanged, then sign of determinant changes.
The value of the determinant remains unchanged if both rows and columns are interchanged.

Verification is the process of evaluating products of a development phase to find out whether they meet the specified requirements.
Validation is the process of evaluating software at the end of the development process to determine whether software meets the customer expectations and requirements.

System testing is the type of testing to check the behaviour of a complete and fully where to buy generic modafinil integrated software product based on the software requirements specification (SRS) document. The main focus of this testing is to evaluate Business / Functional / End-user requirements.
Regression testing is type of testing carried out to ensure that changes made in the fixes or any enhancement changes are not impacting the previously working functionality. It is executed after enhancement or defect fixes in the software or its environment.
A Unit testing is a Level of Testing where smallest part of individual unit / component (called unit) is tested to determine if they are fit for use

1. The REPLACE() function replaces all occurrences of a substring within a string, with a new substring.

2. The UPDATE statement is used to modify the existing records in a table.

3.An SQL join clause - corresponding to a join operation in relational algebra - combines columns from one or more tables in a relational database. It creates a set that can be saved as a table or used as it is. A JOIN is a means for combining columns from one (self-join) or more tables by using values common to each. ANSI-standard SQL specifies five types of JOIN: INNER, LEFT OUTER, RIGHT OUTER, FULL OUTER and CROSS. As a special case, a table (base table, view, or joined table) can JOIN to itself in a self-join.

4.There is no change command in SQL

File locking is a data management feature that restricts other users from changing a specific file.
This allows only one user or process access to this file at any given time.
This is to prevent the problem of interceding updates on the same files.

The transaction log is an integral part of database.
Every database has a transaction log that is stored within the log file that is separate from the data file.
A transaction log basically records all database modifications. When a user issues an INSERT, for example, it is logged in the transaction log.
This enables the database to roll back or restore the transaction if a failure were to occur and prevents data corruption.

A foreign key is a field (or collection of fields) in one table that uniquely identifies a row of another table or the same table.
In simpler words, the foreign key is defined in a second table, but it refers to the primary key or a unique key in the first table.
For example, a table called Employees has a primary key called employee_id.
Another table called Employee Details has a foreign key which references employee_id in order to uniquely identify the relationship between the two tables.

Irrecoverable error occurs when a transaction reads a data item after it is written by uncommitted transaction.
An irrecoverable error is an error that remains an error, no matter how many times you try to perform the same action. In the integration space, that could mean trying to access a database table that does not exist, which would cause the JDBC driver to throw back a SQLException

IPSec can be used to create VPN Tunnels to end-to-end IP Traffic (also called as IPSec Transport mode) or site-to-site IPSec Tunnels (between two VPN Gateways, also known as IPSec Tunnel mode).
IPSec Tunnel mode: In IPSec Tunnel mode, the original IP packet (IP header and the Data payload) is encapsulated within another packet.
In IPSec tunnel mode the original IP Datagram from is encapsulated with an AH (provides no confidentiality by encryption) or ESP (provides encryption) header and an additional IP header. The IP addresses of the newly added outer IP header are that of the VPN Gateways.
The traffic between the two VPN Gateways appears to be from the two gateways (in a new IP datagram), with the original IP datagram is encrypted (in case of ESP) inside IPSec packet.

Spooling is a specialized form of multi-programming for the purpose of copying data between different devices.
A dedicated program, the spooler, maintains an orderly sequence of jobs for the peripheral and feeds it data at its own rate
Conversely, for slow input peripherals, such as a card reader, a spooler can maintain a sequence of computational jobs waiting for data, starting each job when all of the relevant input is available

A process is the instance of a computer program that is being executed by one or many threads. It contains the program code and its activity.
Depending on the operating system (OS), a process may be made up of multiple threads of execution that execute instructions concurrently

1. The CPU then performs a state save, and transfers control to the interrupt handler routine at a fixed address in memory. ( The CPU catches the interrupt and dispatches the interrupt handler)
2. The interrupt handler determines the cause of the interrupt, performs the necessary processing, performs a state restore, and executes a return from interrupt instruction to return control to the CPU. ( The interrupt handler clears the interrupt by servicing the device. )

A reduced instruction set computer, or RISC , is one whose instruction set architecture (ISA) allows it to have fewer cycles per instruction (CPI) than a complex instruction set computer (CISC).
In RISC architecture, the instruction set of the computer is simplified to reduce the execution time. It uses small and highly optimized set of instructions which are generally register to register operations

The K-Map for the boolean function of four variables can be drawn as:

The above formula is for trapezoidal rule.

The above formula is NEWTON’S GREGORY BACKWARD INTERPOLATION FORMULA

From the given data is determinant = 3
The determinant of 2x2 matrix is (ad-bc), If the elements are a,b,c and d.
From the given matrix, a=3,b=3,c=x and d=5 then ad-bc =15-3x
15-3x=3 ⇒ 3x=12 ⇒ x=4

Determinant of any symmetric matrix is zero

A non-discrete random variable X is said to be absolutely continuous, or simply continuous, if its distribution function may be represented as

To find whether hosts belong to same network or not , we have to find their net id, if net id is same then hosts belong to same network and net id can be find by ANDing subnet mask and IP address.
128.8.129.43 (Bitwise AND) 255.255.31.0 = 128.8.1.0
128.8.161.55 (Bitwise AND) 255.255.31.0 = 128.8.1.0

→ While using a larger block size means that contains less number of blocks then that results better throughput.
→ This can be implemented in a fixed block size then the space utilization is not upto the mark. So the statement results better disk throughput but poorer disk space utilization

→ Synchronous I/O mean that some flow of execution (such as a process or thread) is waiting for the operation to complete.
Asynchronous I/O means that nothing is waiting for the operation to complete and the completion of the operation itself causes something to happen.
→ Synchronous I/O -- some execution vehicle (like a process or thread) that initiates the I/O also waits for the I/O to complete (and perhaps completes it). When the I/O completes, that same execution vehicle goes on to do something else, perhaps using the results of the I/O.
→ Asynchronous I/O -- no execution vehicle waits for the I/O to complete. When the I/O completes, whatever execution vehicle happens to complete the I/O may arrange for later things to happen.
Option B is not true, because both synchronous and asynchronous I/O, an ISR (Interrupt Service Routine) is not invoked after completion of the I/O.

→ While a vertex is removed from a graph then that can be itself be forms a new component. The minimum number of components is k-1.
→ If a vertex is removed then it results that all the components are also be disconnected. So removal can create (n-1) components

Swap operation perform between the ia and temporary nameless cell, therefore the value of ib is remains unchanged.
Swap (8, 13)
⇒ ia will returns value with 13.
⇒ ib is unchanged, because here we using pass by reference value.
➝ Temporary nameless is initialized to 13.
➝ There is No runtime error.

→ When a process is rolled back as a result of deadlock the difficulty which arises is starvation.
→ Resource starvation is a problem encountered in concurrent computing where a process is perpetually denied necessary resources to process its work.
→ Starvation may be caused by errors in a scheduling or mutual exclusion algorithm, but can also be caused by resource leaks, and can be intentionally caused via a denial-of-service attack such as a fork bomb

Since operand forwarding is there, by default we consider the operand forwarding from EX stage to EX stage.

→ I is true because when we make a function call there are some input registers and some output registers. If function F() is calling function G(), we can make the caller function F()'s output registers the same as the called procedure G()'s input registers this is done using overlapping register windows.This will reduce the memory accesses so that F()'s output need not be put into memory for G() to access again from memory.
→ II is false as register saves and restores would still be required for each and every variable.
→ III is also false as instruction fetch is not affected by memory access using multiple register windows.

w and y are not needed to represent the function f. So f is independent of two variables.