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OR gate implements logical addition

AND gate implements logical multiplication

Inverter(NOT gate) implements complementation

• The decision which results into either YES (TRUE) or NO (FALSE) is called a Binary Decision.
• Variables which can store truth values TRUE or FALSE are called logical variables or binary valued variables. 

A Gate is simply an electronic circuit which operates on one or more signals to produce an output signal. 

Three basic logic gates are as following

1.  Inverter (NOT Gate) 

2.  OR Gate

3.  AND Gate

If result of any logical statement or expression is always TRUE or 1, it is called Tautology and if the result is always FALSE or 0 it is called Fallacy.

If result of any logical statement or expression is always TRUE or 1, it is called Tautology and if the result is always FALSE or 0 it is called Fallacy.

We will prove 1 + Y is a tautology with the help of truth table which is given below :

From truth table it is prove that 1 + Y is a tautology.

Logic statements or truth functions are combined with the help of Logical Operators like AND, OR and NOT to form a Logical function. Its alternative name is Compound statement. Examples for logical functions are as Following : 

• He prefers tea not coffee.
• He plays guitar and she plays sitar.
• I watch TV on Sundays or I go for swimming.

(b)  (y + x)(z’ + x)

The other name of Karnaugh map is Veitch diagrams. Maurice Karnaugh was invented Karnaugh maps. 

NAND and NOR gates are called Universal gates because NAND and NOR gates are less expensive and easier to design. Also other functions (NOT, AND, OR) can easily be implemented using NAND/NOR gates.

Dispose () used for hide and dispose of the frame when the user close it. This removes the frame from the screen and frees up any resources used by it.

Circuits using NAND and NOR are popular as they are easier to design and therefore cheaper. Functions of other gates can easily be implemented using NAND and NOR gates. For this reason they are called universal gates.

\(y = tan(x \,sin\,x)\)

\(\frac{dy}{dx} = sec^2(x\,sin\,x)\, \frac{d}{dx}(x \,sin\,x)\)

\(= sec^2(x\,sin\,x)(x\,cos\,x + sin\,x)\)

\(v = (1 - 4 \,cos\,5y)^{\frac{-1}{2}}\)

\(\frac{dv}{dy} = \frac{-1}{2}(1 - 4\,cos\,5y)^{\frac{-3}2} \,\frac d{dy}(1 - 4\,cos \,5y)\)

\(= \frac{-1}{2}(1 -4\, cos \,5y)^{\frac{-3}2} \,x -4x - 5 sin\,5y\)

\(= - 10 \,sin\,5y(1 -4 \,cos\,5y)^{\frac{-3}{2}}\)

sin²θ - cos²θ = -(cos²θ - sin²θ) = -cos 2θ

Correct option is (D) 2π - x

cos^-1(cos x) = 2x

But π < x 2π and principal range of cos^-1x is (0, π)

Now, cos^-1(cos x) = cos^-1(-(-cos x))

 = π - cos^-1(-cos x)

 = π - cos^-1(cos(π - x)) (cos(π - θ) = - cos θ)

But π - (π - x) = x \(\notin\) [0, π]

= π - cos^-1(cos(-(x - π)))

 = π - cos^-1(cos(x - π)) ( ∵ cos^-1(cos θ) = θ)

 = π - x + π

 = 2π - x and 2π - 2π \(\leq\) 2π - x \(\leq\) 2π - π

⇒ 0 \(\leq\) 2π - x \(\leq\)π

Correct option is (B)  x + \(\frac{\pi}4\)

sin^-1(\(\frac{sin x+cos x}{\sqrt2}\)) ; \(\frac{\pi}4<x<\frac{\pi}4\)

 = sin^-1(sin x cos\(\frac{\pi}4\) + cos x sin \(\frac{\pi}4\))

 = sin^-1(sin (x + \(\frac{\pi}4\))); 0 < x + \(\frac{\pi}4\) < \(\frac{\pi}2\)

 = x + \(\frac{\pi}4\)

\(r = 2(tan^3\, 2y-1 )^{\frac12}\)

\(\frac{dr}{dy}= 2\times\frac12(tan^32y-1)^\frac{-1}2 \,\frac{d}{dy}(tan^32y-1)\)

\(= (tan^32y - 1)^\frac{-1}{2} (3\times2\,tan^22y \,sec^22y)\)

\(=6\, tan^22y\,sec^22y(tan^32y - 1)^{\frac{-1}{2}}\)

Given A sin θ = 3, A cos θ = 4

⇒ A²sin²θ = 9, A²cos²θ = 16

⇒ A²sin²θ + A²cos²θ = 9 + 16 = 25

⇒ A²(cos²θ + sin²θ) = 25

⇒ A² = 25 = 5²

⇒ A = \(\pm5\)

(A sin θ) (A cos θ) = 3 x 4  = 12

⇒ A² sin θ cos θ = 12

⇒ \(\frac{A^2}2\times\) 2 sin θ cos θ = 12

⇒ sin 2θ = \(\frac{24}{A^2}=\frac{24}{25}\) 

⇒ 2θ = sin^-1\((\frac{24}{25})\)

⇒ θ = \(\frac12\) sin^-1\((\frac{24}{25})\)

Given that

\(Asinθ = 3\)

⇒  \(sinθ = 3/A\) ... (1)

Also, 

\(Acosθ = 4\)

⇒ \(cosθ = 4/A\) ... (2)

Squaring (1) and (2), and adding them both we get

\(sin^2θ + cos^2θ = \frac{9}{A^2} + \frac{16}{A^2} = \frac{25}{A^2}\)

⇒ \(1 = \frac{25}{A^2}\)

⇒ \(A = 5\) 

Putting Value of \(A\) in (1), we get

\(sinθ = \frac{3}{5} \)

⇒ \(θ = 37°\)

NAND and NOR gates are more popular as these are less expensive and easier to design. Also other functions (NOT, AND, OR) can easily be implemented using NAND/NOR gates. Thus NAND, NOR gates are also referred to as Universal Gates.

(i) is Editable() -Returns the setting (true/false) whether the user can edit the text in the text area. 

(ii) set Editable() -Sets whether the user can edit the text in the text area. 

(iii) get Echo Char() -Returns the echo character.

NAPCC stands for National action plan on climate change. Its aim is to create awareness among the public, agencies of government and community as a whole and focuses on India's development simultaneously keeping climate change related objectives.

NAPCC- National Action Plan on Climate Change.

National Action Plan on Climate Change (NAPCC)

A) Select Name from EXAM where division =” FIRST”; 

B) Select Name, Subject from Exam where Stipend between 400 and 800; 

C) Alter table Exam drop Division; 

D) Create Database SCHOOL;

Referential Integrity is used to maintain accuracy and consistency of data in a relationship. In Base, data can be linked between two or more tables with the help of primary key and foreign key constraints. 

Referential integrity helps to avoid: 

1. Records can be added to a related table, if there is no associated record available in the primary key table. 

2. The values can be modified in a primary if any dependent records are present in the associated table(s). 

3. Deleting records from a primary key table if there are any matching related records available in associated table(s)

Entry Required – if set to yes then it will be necessary for the user to insert the value in the field which means that field cannot be left blank. 

Default Value – A default value can be set for a field if user don’t provide any value while entering the values in the table.

A wired setup uses physical cables to transfer data between different devices and computer systems. Wireless network does not use wires for data or voice. Examples Wired: Dial-up, DSL or Cable Internet Access etc 

Wireless .3G or WiMAX or Wi-Fi 

An Internet service provider (ISP) is an organization which provides you with access to the Internet via a dial-up (using modem) or direct (hard wired) or wireless connection. DSL, cable modem, dial-up, broadband wireless, WiMAX etc

3) Radio waves

The correct answer is Hacker.

• A person who breaks into the computer system to get access to the information stored there for unauthorised use is called Hacker.
• An example of computer hacking can be: using a password cracking algorithm to gain access to a computer system.
• Computers have become mandatory to run successful businesses. 
• It is not enough to have isolated computer systems; they need to be networked to facilitate communication with external businesses.
• This exposes them to the outside world and hacking. System hacking means using computers to commit fraudulent acts such as fraud, privacy invasion, stealing corporate/personal data, etc. 
• Cybercrimes cost many organizations millions of dollars every year.

BSNL is an ISP.

Answer: Network within a School

Geometrical arrangement of computers in a network is called Topology.

Answer: Firewall

SMTP (Simple Mail Transfer Protocol) is a TCP/IP protocol used in sending and receiving e-mail.

VOIP (Voice Over Internet Protocol)

Client-side scripting:

HTML, CSS and javascript are used.

Server-side scripting

PHP, Python, Java, Ruby are used.

No. Internet and intranet are not same. They are different. 

1. Internet: 

It is a network of networks. It means that international network. We can transfer information between computers within nations very cheaply and speedily. 

2. Intranet: 

A private network inside a company or organisation is called intranet.

Domain Name System