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The given sequence is 5, 20, 80, 320, ………., 81920

We can see that, the given series is is a geometric progression with common ratio 4.

n^th term of a geometric progression is given as: ar^{n – 1}

Where, a = first term, r = common ratio

∴ 5 × 4^{n – 1} = 81920

⇒ 4^{n – 1} = 81920/5 = 16384

⇒ n – 1 = 7

⇒ n = 8

As we can see, the given series is an arithmetic progression, with first term 20 and common difference 5.

n^th term of an arithmetic progression is given as: a + (n – 1)d

150 = 20 + (n – 1) × 5

⇒ n – 1 = 130/5 = 26

⇒ n = 27

A has 62% spirit.

Amount of spirit in 2 liters of A = 0.62 × 2 = 1.24 liters

B has 84% spirit.

Amount of spirit in 4 liters of B = 0.84 × 4 = 3.36 liters

Total amount of mixture = 2 + 4 = 6 liters

Amount of spirit in the final mixture = 1.24 + 3.36 = 4.6 liters

Amount of water in the final mixture = 6 – 4.6 = 1.4

Required ratio = 4.6 : 1.4 = 23 : 7

Let’s assume that the original price of eggs is $x per dozen.

Now, the reduced price = x – 40% of x = $ 0.6x per dozen

As per given condition, reduced price enabled a woman to buy 64 more eggs for $50

\(\begin{array}{l} \therefore \frac{{50}}{{0.6x}} - \frac{{50}}{x} = \frac{{64}}{{12}}\ \Rightarrow \frac{{50}}{{0.6x}} - \frac{{30}}{{0.6x}} = \frac{{20}}{{0.6x}} = \frac{{64}}{{12}} \end{array}\)

⇒ 0.6x = 20 × 12/64 = 3.75

∴ Reduced price = $ 3.75 per dozen

We know that, \(A = P{\left( {1 + \frac{R}{{100}}} \right)^T}\)

Where, A = total amount, P = Principal, R = % interest rate; T = time period

Here, the interest rate is 20% per annum, and interest is compounded quarterly.

∴ interest rate per interest period is 20/4 = 5%.

Also, the interest is calculated after six months, number of periods = 6/3 = 2

∴ Amount \(= 4000 \times {\left( {1 + \frac{5}{{100}}} \right)^2} = 4000 \times \frac{{21}}{{20}} \times \frac{{21}}{{20}} = 4410\)

L = {ab, c}

L² = {ab, c} × {ab, c}

= {abab, abc, cab, c²}

L³ = {abab, abc, cab, c²} × {ab, c}

= {ababab, ababc, abcab, abc², cabab, cabc, c²ab, c³}

File transfer protocol (FTP) is the mechanism provided by TCP/IP for copying a file from one host to another. It is built on the client- server architecture and uses separate control and data connections between the client and the server.

Explanation:

FTP is different from other client/ server applications as it uses two connections to transfer the file. One is control connection and other is data connection. In this only a line of command or a line of response is transferred at a time. Here is the basic model of FTP.

Communication in FTP is achieved through commands and responses. Using control connection, only one command is sent at a time.  Purpose of data connection is different from control connection. File transfer occurs over the data connection under the control connection. FTP can transfer a file across the data connection by using one of the three modes: stream mode, block mode and compressed mode.

Telnet:

Telnet stands for terminal network. It is a standard TCP/IP protocol for virtual terminal service. It enables the establishment of a connection to a remote system in such a way that the local terminal appears to be a terminal at the remote system.

SMTP:

SMTP stands for simple mail transfer protocol. SMTP simply defines how commands and responses must be sent back and forth between client and server.

POP:

POST office protocol is a protocol that extracts and retrieves email from a remote mail server for access by the host machine. It provides end user the ability to fetch and receive mail.

Concept:   

A primary key is a field in a table which uniquely identifies each row/record in a database table.

Explanation:

Primary key must contain unique values and cannot contain NULL values. A table can have only one primary key. It can consist of single or multiple fields.

Entity integrity constraint enforces that the value of the primary key cannot be NULL because it is used to identify the rows in a relation and if it contains NULL value, then it cannot identify the rows. Allowing a primary key as NULL will cause a potential conflict with uniqueness constraint.

Candidate key column can have null value.

Option 4: int (*pf) (int, int);

It means that pf is a pointer to a function which takes two integer arguments and returns an integer.

Option 1: (int *) pf(int, int);

It means that pf is a function with two integer arguments and returns an integer as pointer.

Option 2: int *pf(int, int);

It means that pf is a function with two integer arguments and returns a pointer to an integer.

Option 3: int (int *pf(int, int));

It is incorrect.  It is a pointer which takes two integer arguments and returns a pointer to an integer to integer.

Concept:

Multiplexer is also known as data selector that selects between several analogy or digital input signals and forwards it to a single output line.

Explanation:

Multiplexer with n select line contains 2ⁿ inputs and a single output. A multiplexer is also known as parallel to serial converter or many to one circuit. A multiplexer can be used to implement if-else statements. So, here selection line is used to select the inputs for the output.

Y = S̅ B + SA

if S = 1

then Y = A

else Y = B

Hence option 1 is correct here.