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Given:

The length of the area to be paved = 4.83 m

The breadth of the area to be paved = 5.67 m

Formula used:

Area of the space that can be paved = Length × breadth

1 m = 100 cm

Calculations:

Area of the floor = 4.83 × 100 × 5.67 × 100

⇒ 273861 cm²

If the length of the maximum tile is x then the area of 1 tile should be x²

⇒ The area of the floor must be divisible by x²

Now from the given options only 21² i.e. 441 can divide 273861 completely and give whole number as remainder

273861 ÷ 21² = 621

∴ The side of the largest possible square tile is 21 cm.

z²=2/(xy) 

d²=x²+y²+z²=x²+y²+2/(xy) 

Partial derivative relative to x : 

2x-2/(x²y)=0 

Partial derivative relative to y : 

2y-2/(xy²)=0 

Solving the equations y*(x³)=x*(y³)=1 leads to : 

x=y=1

 then z=√2 

min.distance d=2

Given function is f(x) = sec√x

By first principle of derivative, we have,

\(f'(x) = \lim\limits_{h \to 0} \frac{f(x + h) - f(x)}{h}\)

\(= \lim\limits_{h \to 0} \frac{sec\sqrt{(x + h)} - sec\sqrt{x}}{h}\)

\(= \lim\limits_{h \to 0} \cfrac{\frac{1}{cos\sqrt{(x + h)}} - \frac{1}{cos\sqrt{x}}}{h}\)

\(= \lim\limits_{h \to 0} \frac{cos\sqrt{x} - cos \sqrt{x + h}}{h\,cos\sqrt{x}\,cos\sqrt{x + h}}\)

\(= \lim\limits_{h \to 0} \cfrac{2\,sin \left(\frac{\sqrt{x} + \sqrt{x + h}}{2}\right)\, sin \left(\frac{\sqrt{x + h} - \sqrt{x}}{2}\right)}{h\,cos \sqrt{x}\,cos \sqrt{x + h}}\)

(∵ cos C - cos D = \(2\,sin \frac{C + D}{2}\) \(sin \frac{D - C}{2}\))

\(=2 \lim\limits_{h \to 0} \cfrac{sin \left(\frac{\sqrt{x} + \sqrt{x + h}}{2}\right)}{cos \sqrt{x}}\) × \(\lim\limits_{h \to 0} \frac{1}{cos\sqrt{x + h}}\) × \(\lim\limits_{h \to 0} \cfrac{sin \left(\frac{\sqrt{x + h} - \sqrt{x}}{2}\right)}{h}\)

\(\left(\because \lim\limits_{h \to 0}\,f(x) y(x) = \left(\lim\limits_{h \to 0} f(x) \right) \left(\lim\limits_{h \to 0} y(x) \right)\right)\)

\(= 2 \cfrac{sin \left(\frac{2\sqrt{x}}{2}\right)}{cos\sqrt{x}}\) × \(\frac{1}{cos\sqrt{x}}\) × \(\lim\limits_{h \to 0} \cfrac{sin\frac{\sqrt{x + h} - \sqrt{x}}{2}}{\frac{\sqrt{x + h} - \sqrt{x}}{2}} \times \cfrac{\frac{\sqrt{x + h} - \sqrt{x}}{2}}{h}\)

(Multiplying both mumerator and denominator by \(\frac{\sqrt{x + h} - \sqrt{x}}{2}\))

= 2 tan √x sec √x × 1 × \(\lim\limits_{h \to 0} \frac{\sqrt{x + h} - \sqrt{x}}{2h} \times \frac{\sqrt{x + h} + \sqrt{x}}{\sqrt{x + h} + \sqrt{x}}\)

(∵ \(\lim\limits_{x \to 0} \frac{sin\,x}{x} = 1\) and multiplying both numerator and denominator by \((\sqrt{x + h} + \sqrt{x})\))

= 2 tan √x sec √x × \(\lim\limits_{h \to 0} \frac{x + h - x}{2h(\sqrt{x + h} + \sqrt{x})}\) (∵ (a + b)(a - b) = a² - b²)

= 2 tan √x sec √x × \(\lim\limits_{h \to 0} \frac{h}{2h(\sqrt{x + h} + \sqrt{x})}\)

=  tan √x sec √x × \(\lim\limits_{h \to 0} \frac{1}{\sqrt{x + h} + \sqrt{x}}\)

\(= \frac{1}{2\sqrt{x}}\,tan \sqrt{x}\,sec \sqrt{x}\) (By taking limit)

∴ \(\frac{d}{dx} sec \sqrt{x} = \frac{1}{2\sqrt{x}}\,tan \sqrt{x}\,sec\sqrt{x}.\)

Indirect Speech: He exclaimed that it was a very beautiful view.

When the reporting verb is in the past (said) and the direct speech is in the present indefinite tense (simple present tense), then the indirect (reported) speech will change into the past indefinite tense.

Present Indefinite Tense > Past Indefinite Tense.

And if the sentence is exclamatory, we use reporting verbs like exclaimed, admired, cried etc based on the sentence.

It is a geometric progression with common ratio, r=5 ; and first term, a=0.004

the n^th term of a geometric progression is given by,

a_n = a(r)^n-1 

for the given question we have, a_n=128

Hence,            

128=0.004(5)^n-1 

32000=5^n-1 

Taking log with base 5 on both sides

6.445=n-1 

n=7.445

Since n is not a natural number we can conclude that 128 is not a term of the series.

x-y=5

xy=14

x³-y³= (x-y)(x²+xy+y²)

=(5)(x²+14+y²)

=(5)(x+y)²

=(5)(2×1×7)

=(5)(15)

=75

(i) ‘t’ is added to 100.

Ans: t + 100

(ii) 4 times ‘q’.

Ans: 4q

(iii) 8 reduced by ‘y’.

Ans: 8 – y

(iv) 56 added to 2 times ‘x’.

Ans: 56 + 2x

(v) 4 less to 9 times of ‘y’.

Ans: 9y – 4

Given:

Time taken by tap A to fill the tank = 3hrs

Time taken by tap B to fill the tank = 4hrs

Time taken by tap C to empty the tank = 6hrs

Calculation:

Amount of tank filled by A in 1hr = 1/3

Amount of tank filled by B in 1hr = 1/4

Amount of tank emptied by C in 1hr = –1/6

Amount of tank filled by A, B and C in 1hr = 1/3 + 1/4 – 1/6

⇒ (4 + 3 – 2)/12 = 5/12

∴ Together they will take 12/5 days to fill the tank

Correct answer is (b) (4/3)μF 

Truth table for NAND gate:

Truth table for NOR gate:

Correct answer is (a) 5D

Correct answer is (d) 1/3 x 10^-9

The waves in which there are a sinusoidal variation of electric & magnetic field vectors at right angles to each other & also right angle to the direction of propagation of the wave is called e.m waves.

∴ The expression for velocity of e.m. wave is

C = \(\frac{1}{\sqrt{\mu_0 \varepsilon_0}}\)

Where µ₀ → is permeability of free

space, ε₀ → is the permeability of free space.

Concept:

An embedded system is a microprocessor-based computer hardware system with software that is designed to perform a dedicated function, either as an independent system or as a part of a large system.

Explanation:

In the above given Options Smartwatch, ATM and Mobile phone are the example of the Embedded System.

Only option 3 i.e. Bank branch can't be an application of an Embedded system.

1. Embedded systems are managed by microcontrollers or digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA), GPU technology, and gate arrays.

2. These processing systems are integrated with components dedicated to handling electric and/or mechanical interfacing.

3. Some examples of embedded systems are MP3 players, mobile phones, video game consoles, digital cameras, DVD players, and GPS.

17th Dec, 2019

From 

XXXX 

YYYY

To 

Box No: WW 55164 

C/o The Hindu 

Chennai 02

Respected Sir/Madam, 

Sub: Application for the post of Secretary to M.D. With reference to your advertisement in The Hindu, dated 13th March, 20191 would like to apply for the post of secretary in your comapny. Please find enclosed my bio-data / resume to enable you to assess my suitability for the aforesaid post.

Yours sincerely, 

XXXX

Resume

Name : XXXX 

Date of Birth: 18th July, 1992 

Marital Status: Single 

Father’s Name: Mr. Ramesh Address For 

Communication: YYYY

Contact number – mobile: 9998778588 residence: 22349577 

Mother Tongue: Tamil Language 

Known: English and Tamil

Educational Background

Technical Knowledge :

1. English typewriting higher 

2. Computer MS office

Experience: 

Secretary for 4 years, K.K. Software Company, 

T.Nagar Hobbies : Dramatics, Reading, Music.

Expected Salary : 35,000/ per month

Salary Drawn : 28,000/ per month Language 

Known : English, Hindi and Tamil

I am enclosing photostat copies of my testimonials for your kind perusal.

I request that my application may be favourably considered. I sincerely assure you, sir, of my efficient service to your company, If I am selected. Looking forward to receiving your call letter.

Enel: Copies of testimonials

Declaration 

I hereby declare that the above given information is true to the best of my knowledge.

Station: YYYY 

Date : 10.03.2019

Yours faithfully 

XXXX 

Signature of the Applicant

To 

Box No: WW 55164 

C/o The Hindu 

Chennai 02

25 March 20XX 

Sujatha Kannan 37, 

Dharmapuri 

Tamil Nadu

The Principal 

Brilliant Public School 

Dharmapuri 

Sir,

Sub: Improvements in School Library

During my visit to your school in connection with P.T.A. meeting, I happened to go to the library. I would like to draw your attention to the malfunctioning of the library. I sincerely feel that it can prove more useful to the students if few steps are taken to tone it up.

I was shocked at the disorderliness in the library. Books were lying in heaps and were not restored to the proper shelves. No wonder the book which the library has is reported to be non-available by the library staff. The lack of co-operation from the library staff makes the situation worse. You may take steps to make them alert and willing workers. The shortage/ non-availability of books, if any, may be made up by buying more copies of the volumes more in demand. The old and broken tables and chairs may be repaired if not replaced.

I hope that during our next meeting we shall find the library cosy, spick and span.

Yours faithfully 

Sujatha Kannan

To 

The Principal 

Brilliant Public School 

Dharmapuri

True Indians 

Note making: 

Indians best human resources – excelled in architecture, metallurgy and medicine – five year plans – initial – agriculture development – Energy development focus – drive future – atomic energy nuclear implosion on 18th may 1974. Space also rapid strides – Indian Cosmonaut on 3rd April 1984 – Rakesh Sharma I Cosmonaut.

OR

Summary: Rough draft 

Indians have been great human resources. Since ancient times, the have excelled in various fields such as metallurgy, medicine and architecture in the ancient period itself. After 1947, the Government through five year plans attained selfsufficiency in agricultural production. Gradually the Government focused on developing atomic energy and space technology. Atomic implosion in 1974 and conquest of space in 1984 are best examples of India’s success in joining space club and energy development.

Fair draft 

Ancient Indians proved their expertise in metallurgy, medicine and architecture. After 1947, the country focused on agricultural self-sufficiency through five year plAnswer:She attained it in agricultural production. Then India joined the small band of atomic energy producing countries and by atomic explosion in 1974 proved her power. She also joined space club in 1984 by sending Rakesh Sharma to space.

25 March, 20XX 

A. Shanmugan 

Globe Sr. Sec. School 

Adambakkam 

Chennai

City Central Book Shop 

3rd Street 

Mount Road 

Chennai

Sir, 

Sub: Non-compliance of the order No. 11/RS

This is with reference to our order No. 11/RS dated 4th March, 20XX regarding the delivery of a few books for our school library.

In this respect, I regret to state that despite repeated reminders on the phone, the books have not yet been delivered to the library so far. The new session has started and the books are required urgently for reference work by the students. I am quite upset about the non-compliance and negligent attitude shown by your shop towards our order. If the specified books don’t reach us within three days from the receipt of this letter, we will conclude that you are not interested in fulfilling this order. In that case, we’ll be compelled to place the order elsewhere. A list of books ordered is being enclosed herewith. Kindly do the needful at the earliest.

Yours truly 

A. Shanmugan

(Librarian) 

Enel.—Photocopy of the book-list.

To 

City Central Book Shop 

3rd Street 

Mount Road 

Chennai

10 March 20XX 

Asokan 

5th Main Road, T. Nagar

Chennai

The Personnel Manager 

Ready Assurance Company 

Coimbatore

Sir, 

Sub: Recruitment of Management Trainee

With reference to your advertisement in The Hindu dated 5th March 20XX for management trainees to be groomed as managers for your company, I would like to be considered for the said post.

My Bio-data is enclosed for your perusal and consideration. If I am found suitable, I can appear for the interview at any time suitable to you. In case of selection, I assure you of my unstinted cooperation and devotion in the discharge of my duties.

Yours faithfully, 

Asokan

To 

The Personnel Manager 

Ready Assurance Company 

Coimbatore

Bio-Data Name : Asokan Rajan 

Father’s Name : Prof. S. Rajan 

Address : 5th Main Road, T. Nagar, Chennai 

Date of Birth : 7th August 1987 

Educational Qualifications : 1. B.Com., Madras University, 2. MBA from Madurai 

Experience : 2 years Present 

Employment : Working with Global Management, Chennai 

Marital Status : Unmarried Personal 

Details : Age 29 years, 

Height : 5.5, 

Weight : 60 kg Languages 

known : Tamil, English, Hindi, French 

Hobbies : Reading, Listening to music, Painting 

Reference : Professor Suresh Mohan, Madras University

Declaration 

I hereby declare that the above given information is true to my knowledge. 

Station : YYY 

Date : 10.03.20XX

Asokan

25th September, 2018 

K. Raman 

Modem Shoes 

TVS Nagar 

Madurai

M/s Shobha Shoes 

Pandian Nagar 

Madurai 

Dear Sirs 

Sub: Order for Men s & Women Shoes

I can express only my deep dismay and displeasure at the non-execution of the bulk order that we placed with you for the purchase of shoes on 10th August, 2018. The said order was to be executed within 10 days. However, when more than a month expired, you expressed regrets giving the strike of workers in the factory as the main reason of nonexecution. We accepted your request for executing the order within a week. We condoned the delay keeping in view of our previous good business terms. As we have not heard from you recently, we have reasons to believe that cancellation of the said order is the only way left out for us. I hope that the cancellation of the said order will not affect our otherwise good business terms in future.

Yours faithfully K. Raman

To 

M/s Shobha Shoes 

Pandian Nagar 

Madurai

(b) won’t it

Village -Tejpur
Post-Medhpur
District – Jaisalmer
PIN – 123501
21 June 2020
The Principal
Rajasthan Public School
Jaisalmer

Sub: To know about suitable courses in your school.

Madam,

I have passed secondary Examination 2020 with 93% marks. I want my career bright though my parents are poor. I want to join your school. But because of rural background, I and my family don’t have knowledge about suitability of courses for me in your school. Kindly, make available all the pieces of information about the suitable courses for me.

Thanking you

Yours faithfully

Suman

c. 24 Hz 

According to Carson’s rule, the bandwidth required is twice the sum of the maximum frequency deviation and the maximum modulating signal frequency. Or,

B=2(Δf +f_m) Hz

B= 2(Δf +12) Hz = 2 Δf + 24 Hz (1)

Assuming Δf to be constant, 

B = 2 Δf + 48 Hz (2) 

(2)-(1)= 24Hz 

Therefore the bandwidth changes by 24Hz.

1. Rebate 

2. Discount 

3. Refunds 

4. Product Combinations 

5. Quantity gift 

1. Rebate: Offering products at special prices 

2. Discount: Offering products at less than list price 

3. Refunds: Refunding a part of price paid by customer 

4. Product Combinations: Offering another product as gift along with the purchase of a product. 

5. Quantity Gift: Offering extra quantity of the product.

3. cooperating

F.W. Taylor.

Rules are specific statements that inform what is to be done. They are simplest type of plans.

4. Informal organisation

1. Transfers and 

2. Promotions (Write any one point)

Controlling means ensuring that activities in an organisation are performed as per the plans.

OR

Controlling is the process of ensuring that actual activities conform to planned activities.

Financial accounting is concerned with recording of day to day business transactions.

Accounting is an art of recording, classifying and summarizing all the transactions of monetary value in a significant manner to identify the end result. Day to day transactions are recorded in a chronological order.

2. Complement each other

Publicity is a non-personal and non paid form of communication of some favourable news presented in the mass media about a product or service. It has more credibility.

b) Disaster Management Cycle

Full form of DMC is Disaster Management Cycle.

b) Analysis

Having the ability to connect pieces of information together in order to determine what the intended meaning of the information was meant to represent is called Analysis.

b) 2005

The Disaster Management Act passed in 2005 provides for a detailed action plan right from the central government to the district and local levels to draw, implement and execute disaster management plans.

Search and rescue team.

The marketing concept implies that the firm can achieves its goals by identifying the needs of customers in a chosen market and satisfying them better than the competitors. This essentially involves that the firm must develop products and services that customers require, and not what it can make. 

Marketing functions include a series of specified activities performed in the marketing of goods and service.

(a) Gathering and analysing market information. Marketing research is the systematic investigation of the facts relevant to various aspects in marketing. Marketing research helps managers to arrive at appropriate decisions. Market information should be gathered and analysed. 

(b) Marketing planning. To achieve the marketing objectives of the organization appropriate marketing plans covering various important aspects should be developed. 

(c) Product designing and development. Product designing and development is concerned with anticipating customers’ needs. developing new products and improving the existing products so as to meet expectations of customers. A good design can improve the performance of a product and also give it a competitive advantage in the market. 

(d) Standardisation and grading. Standardisation refers to the process of setting certain standards for a commodity on the basis of its desired qualities. Grading refers to the division of products into classes made up of units possessing similar features. 

(e) Packaging and labeling. Packaging is the act of designing and producing the package for a product. A package is a wrapper or a container in which a product is enclosed. Packaging reduces the risk of spoilage, breakage, etc. in the process of storage and transportation of goods. Whereas labeling means putting identification marks on the package. 

(f) Branding. It is the process of stamping a product with some identifying name or mark or a combination of both.

Wireless Technology in Networking:

• Wireless Technology in Networking for transmission of data occurs in Local Area Network. This technology is termed as WiFi.
• It is the most popular wireless technology that allows an electronic device to exchange data or connect to the network using radio waves.
• Wi-Fi facilities are now available at many public places and commercial complex.

Comparison:

1) The proprietary software is software for which source code is not open. But the open source software is software for which source code is open.

2) In the proprietary software, users are not being given the right to open, modify or further distribute the source code of such software. But in the open source the users are granted License to use, study, modify and further redistribute it.

3) The owner of the proprietary software takes fees for granting the License for using its application while open source software is provided free.

4) Example of proprietary software are LIBSYS, VIRTUA, TRUDAN etc. while example of open source software one KOHA, New Gen Lib, ABCD etc.

Advantages of E –resources:

i. Multiple Access: Same E-resources can be accessed by many readers simultaneously. 

ii. Remote Access: A reader can read or download E-resources from the compatible devices as desktop computer, laptop etc. 

iii. Speed: The delivery of e-resources is fast. It can beaccessed from anywhere in the world. 

iv. Space: The E-resource saves physical space to store. 

v. Functionality: Searching content of e-resources can be done with the click.

Disadvantages of the E-resource:

i. Copyright: The copyright is the legal right given to the creator of the content of the information resources. It is always necessary to take permission from the owner of the resources to read, download or browse.

ii. Access to Network: E-resources are accessible through internet or any other network. In the absence of the network, it is not possible to access the resources.

iii. Skills: Searching, retrieving and making use of e-resources require a certain level of skill.

v. Cost of the Resources: The cost of e-resources is very high in comparison to printed resources.

v. Language: Very less E-resources are available in vernacular language

Explanation:

• The dish named Undhiya or upside down, in Gujrati.
• The upside down here because the pot in which this food is made placed upside down.
• Undhiya would be eaten with bajra rotis, freshly cooked on chulha.

The farmers of Gujrat are fond of these foods.