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Answer: [A] = [A] ₀e ^− kt.

Correct option is B) heyday

Correct option is E) extolled

Correct option is E) make

Absorption law states that 

A + A . B = A and A . (A + B) = A 

Proof: 

The Truth table of the expression A + A . 

B = A is as follows.

Here both columns A and A + A . B are identical. Hence proved. 

For A . (A + B) = A, the truth table is as follows:

Both columns A & A . (A + B) are identical. Hence proved

Idempotent law states that

1. A + A = A and 

2. A . A = A 

Proof

1. A + A = A 

Truth table is as follows: 

ie. A + A = A as it is true for both values of A. 

Hence proved. 

2. A . A = A 

Truth table is as follows: 

ie. A . A = A itself. It is true for both values of A. 

Hence proved.

Given, perimeter of a square park = 320 m 

We know that, perimeter of square = 4 x side 

⇒ 4 × s i d e = 320 

⇒ side = 320/4 = 80 m 

Also, area of a square = side × side

 ∴ Area of square park = 80 x 80 = 6400 m² 

Thus, the area of square park is 6400 m² .

1. A + A = A

 A = A = A

2. (A¹)¹ = A

Demorgan’s first theorem states that (A + B)’ = A’ . B’ 

ie. the complement of sum of two variables equals product of their complements, 

The second theorem states that (A . B)’ = A’ + B’ 

ie. The complement of the product of two variables equals the sum of the complement of that variables. 

Proof: 

Truth table of first one is as follows:

From the truth table the columns of both (A + B)’ and A’ . B’ are identical. Hence proved.

According to De Morgan's first law, the complement of the union of two sets A and B is equal to the intersection of the complement of the sets A and B. 

proof:

DeMorgan's 1st law states X+Y¯¯¯¯¯¯¯¯¯¯¯¯¯¯=X¯¯¯¯⋅Y¯¯¯¯

It is sufficient to prove that (X+Y)+X¯¯¯¯⋅Y¯¯¯¯=1

LHS=Y+(X+X¯¯¯¯⋅Y¯¯¯¯)=Y+X+Y¯¯¯¯=(Y+Y¯¯¯¯)+X=1+X=1=RHS

Second Law:: DeMorgan's 2nd Law states that X⋅Y¯¯¯¯¯¯¯¯¯¯¯¯=X¯¯¯¯+Y¯¯¯¯

It is sufficient to prove that X⋅Y+(X¯¯¯¯+Y¯¯¯¯)=1

LHS=Y¯¯¯¯+(X¯¯¯¯+X¯¯¯¯¯¯¯¯¯⋅Y)=Y¯¯¯¯+(X¯¯¯¯+Y)=(Y+Y¯¯¯¯)+X¯¯¯¯=1+X¯¯¯¯=1=RHS

x.y + x.\(\bar y\) .z = x(y + \(\bar y\) .z)

= x. (y + z) = x.y +x.z

Hence proved.

De Morgan’s law

Software is available free of cost to use and distribute, but not for modification and without source code.

A computer is an electronic device used to perform operations at very high speed and accuracy. 

Following are the characteristics of the computer.

1. Speed: 

It can perform operations at a high speed.

2. Accuracy: 

It produces result at a high degree of accuracy. 

3. Diligence: 

Unlike human beings, a computer is free from monotony, tiredness, lack of concentration etc. We know that it is an electronic ma chine. Hence it can work four hours without making any errors. 

4. Versatility: 

It is capable of performing many tasks. It is useful in many fields. 

5. Power of Remembering: 

A computer consists of huge amount of memory. So it can store and recall any amount of information. Unlike human beings, it can store huge amount of data and can be retrieved when needed. 

Disadvantages of computer: 

1. No. IQ: 

It has no intelligent quotient. Hence they are slaves and human beings are the masters. It can’t take its own decisions.

2. No feelings: 

Since they are machines they have no feelings and instincts. They can perform tasks based upon the instructions given by the humans (programmers)

It is the geometric arrangement of computer system in network. Common topologies include a Linear bus, star, ring and ring.

File Transfer Protocol

Answer is Truth Table

NAND, NOR are the universal gates.

(C) \(\bar x+(\bar y+\bar z)\)

Logical expressions yield either true or false values

(d) Adeline aged 17 years is in class 12. This is information. The others are data.

Primary key uniquely identifies each record in a database.

The act of applying information in a particular context or situation is called Knowledge

Data processing is defined as a series of actions or operations that converts data into useful information.

Syntax:
data-type * pointer-variable-name;

Information is used to help people to make decision.

The data structures that are directly operated upon by machine-level instructions are called a primitive data structure.

Insert 2 zeroes in the left hand side to make the binary number in the 8 bit form 00110111 

To find the 1’s complement, change all zeroes to one and all ones to zero. Hence the answer is 11001000

 d. All of these

Index Number reveals the state of inflation and deflatilon.

Moving average Moves like a pendulum of clock and it is never ending process. 

a. Mean is not affected due to sampling fluctuations 

Variation in a time series that occurs due to chance is irregular component .

The magnitude of the class is the The difference of upper limit and lower limit

 Mean – mode = 3 (mean - median) 

H.M is defined as the reciprocal of the mean of the reciprocal of these.

Depicting of statistical data in the form of attractive shapes such as bars, circles, rectangles is called diagrammatic presentation. 

A diagram is a visual form of presentation of statistical data, highlighting their basic facts and relationship. There are geometrical figures like lines, bars, squares, rectangles, circles, curves, etc. Diagrams are used with great effectiveness in the presentation of all types of data. 

When properly constructed, they readily show information that might otherwise be lost amid the details of numerical tabulation. 

Importance of Diagrams : 

 A properly constructed diagram appeals to the eye as well as the mind since it is practical, clear and easily understandable even by those who are unacquainted with the methods of presentation. Utility or importance of diagrams will become clearer from the following points - 

(i) Attractive and Effective Means of Presentation : Beautiful lines ;full of various colours and signs attract human sight, and do not strain the mind of the observer. A common man who does not wish to indulge in figures, get message from a well prepared diagram.

(ii) Make Data Simple and Understandable : The mass of complex data, when prepared through diagram, can be understood easily. According to Shri Morane, “Diagrams help us to understand the complete meaning of a complex numerical situation at one sight only”. 

(iii) Facilitate Comparison : Diagrams make comparison possible between two sets of data of different periods, regions or other facts by putting side by side through diagrammatic presentation. 

(iv) Save Time and Energy : The data which will take hours to understand, becomes clear by just having a look at total facts represented through diagrams. 

(v) Universal Utility : Because of its merits, the diagrams are used for presentation of statistical data in different areas. It is widely used technique in economic, business, administration, social and other areas. 

(vi) Helpful in Information Communication : A diagram depicts more information than the data shown in a table. Information concerning data to general public becomes more easy through diagrams and gets into the mind of a person with ordinary knowledge.

A function very similar to that of sorting letters in a post office is  Classification

Simplest possible measure of dispersion is range.

Q₃ Is called as upper quartile.

The method of sampling, in which the choice of sample items depends exclusively on the judgement of the investigator is termed as  Judgement sampling

One dimensional diagram is Line diagram

Before analysis and interpretation, it is necessary to edit the date to detect possible errors and inaccuracies, so that accurate and impartial results may be obtained. Thus editing means the process of checking for the errors and omissions and making corrections, if necessary.

The task of editing is a highly specialized one and requires high level of skill and carefulness to attain the proper degree of accuracy. 

Editing of Primary Data : While editing primary data, the following points should be considered :- 

• Editing for consistency 
• Editing for completeness 
• Editing for accuracy 
• Editing for uniformity or homogeneity

Editing of Secondary Data : Since secondary data have already been obtained, it is highly desirable that a proper scrutiny of such data is made before they are used by the investigator. Bowley rightly points out that “secondary data should not be accepted at their face value”.

Hence before using secondary data, the investigators should consider the following aspects :-

• Whether the Data are Suitable for the Purpose of Investigation in View : Quite often secondary data do not satisfy immediate needs because they have been compiled for other purpose. The variation can be in units of measurement, variation in the date/period to which data is related etc.
• Whether the Data is Adequate for the Investigation : Adequacy of data is to be judged in the light of the requirements of the survey and the geographical area covered by the available data. For example if our object is to study ;the wage rates of the workers in sugar industry in India and the available data cover only the state of Rajasthan, it would not serve the purpose.
• Whether the Data are Reliable : The following points should be checked to find out the reliability of secondary data - 

(i) The collecting agency was unbiased. 

(ii) The enumerators are properly trained. 

(iii) A proper check on the accuracy of the field work. 

(iv) Was the editing, tabulating and analysis carefully and conscientiously done

d) All the above

 The value lying half way between the upper limit and lower limit of the class is  Mid point .