Write a recursive function in C language to calculate the sum of all digits in a long integer provided as input.

Solve the following recurrence equations:
(i) T(n) = 2T(n/2) + 0(n)
(ii) T(n) = T(n - 1) + 0(n)

For a problem P, two algorithms A and B have time complexities T1(n) = 5n² and T2 (n) = 100nlogn respectively. Find the range for n, the size of instance of the given problem P, for which A is more efficient than B.

1.Read the following passage and answer the questions that follow:
The Artist co-operates with God in making increasingly larger numbers of people see the beauty of the world which these people could never see for themselves, The world is, of course, God's artistic masterpiece; but it is the artist who lends people eyes to see it with. Browning's Fra Lippo has the last word on the subject:-
For, don't you mark, we're made so that we love
First when we see them painted, things we have passed
Perhaps a hundred times nor cared to see?
In this sense, Oscar Wilde's paradox is perfectly true: that Nature imitates Art; for the majority of men see in Nature what Art has taught them to see in Nature. The fogs of London, said Wilde, were the invention of Whistler. To love beauty therefore becomes to the artist, as an artist, his first duty. To love beauty, that is, to see it for himself first, and then to communicate it to others; for love implies at once vision and reproduction. It must be the first article in an artist's creed, as an artist, that beauty is the best interpreter of God to man; that; when he has got hold of beauty, he has got hold of the surest key to the knowledge of God. Keats has said that Beauty is Truth.
Now, this is not true. But to us here, Beauty is, as Plato said, the splendour of Truth. The artist, as an artist, must be content with the splendour and, through this splendour strive to convey the truth. Tie has no business with truth as such as the philosopher, for instance, has. He has no concern with conduct as such, as the moralist, for instance, has. It is not his function to exhort men to good works, or to prove things; but merely to exhibit then. Plato thought a picture, for instance, was just a copy of an object - a copy of the idea. It was Aristotle, Plato's pupil, who pointed out that, though a picture was in one sense certainly a copy and therefore something less
than the object, in another sense it was something more than the object. It was, briefly, the idea of the object made visible to the eye. Art, therefore, does not consist merely in line and colour, sound and image, but primarily in ideas. Beauty may not be useful. Beauty may not improve our minds. But beauty must please. Indeed, such is the inherent delightfulness of beauty that, by its magic touch, not only the ugly becomes pleasurable, but even sorrow becomes a joy. That is the explanation of the pleasure we feel in tragedy. What would shock us in actual life gives us pleasure in a tragedy. For tragedy makes experience significant; and by making it significant, it makes it beautiful; and by making it beautiful, it makes it pleasant. And yet, it does not aim at pleasing; it only aims at exhibiting. Pleasure is not its aim; it is its effect.
- Armando Menezes

1a      What does the artist do for most of us? 
1b      Why does the artist “lend” his eyes to people? 
1c      Explain: "Nature imitates Art." 
1d      What is the artist's first duty? Why? 
1e      What is the surest key to the knowledge of God? Why? 
1f       Give a suitable title to the passage. 
1g      Find words from the passage which mean the same as the following: 

i Deity       ii persons          iii Great work
iv gives     v fondness         vi The natural world
vii Pass on       viii portrayer        ix noticeable
x Important

2 Choose the correct form of the verb from within the brackets so as to make it agree with the subject.
1. The plane --- at 3.30. (arrives, will arrive)
2. I will phone you when he --- back, (comes, will come)
3. When I get home, my dog --- at the gate waiting for me. (sits, will be sitting)
4. I --- the Joshis this evening, (visit, am visiting)
5. Look at those black clouds. It ---, (will rain, is going to rain)
6. The train --- before we reach the station, (arrives, will have arrived)
7. Perhaps we --- Mahabaleshwar next month, (visit, will visit)
8. Unless we --- now we can't be on time, (start, will start)
9. I --- into town later on. Do you want a lift? (drive, will be driving)
10. The next term --- on 16th November, (begins, is beginning)

 3 Put the verbs given in brackets in the most appropriate tense:
1. The earth --- round the sun. (move)
2. My friends --- the Prime Minister yesterday, (see)
3. I --- him only one letter up to now. (send)
4. She --- worried about something, (look)
5. It started to rain while we --- tennis, (play).
6. He --- fast when the accident happened, (drive)
7. He --- asleep while he was driving, (fall)
8. I'm sure I --- him at the party last night, (see).
9. He --- a mill in this town, (have)
10. He --- here for the last five years, (work).

4. In the following sentences change the Voice: 
1. We elected Balu captain.
2. I saw him opening the box.
3. We must listen to his words.
4. Shall I ever forget those happy days?
5. By whom was this jug broken?

5. Fill in the blanks using a or an or the as may be suitable 
1. Copper is --- useful metal.
2. He is not --- honourable man.
3. --- able man has not always a distinguished look.
4. --- reindeer is a native of Norway.
5. Honest men speak --- truth.

6. Fill in the blanks with appropriate Prepositions 
1. No doubt he has achieved much, but I cannot give him credit --- all that he boasts ---.
2. The despotism of custom is everywhere the standing hindrance --- human
achievement.
3. He is indebted --- his friend --- a large sum.
4. What Dr. Arnold mainly aimed ---, was to promote the self-development of the young minds committed --- his charge.
5. He was so much enamoured --- her that he forgot his duties --- his children.
6. It is difficult to agree --- those critics who ascribe the work of Shakespeare

7. Write a about 300 words on any one of the following topics:
i Life after Covid 19
ii The Digital World: Bane or Boon?

8. In about 200 words, write a conversation between: 
i You and elder sister where you are asking her suggestions regarding what subject you should go for after completing 10+2.
OR
ii You and a cricketer where you are asking him ten questions and he is answering those ten questions.

Read the following passage and answer the questions given below:

How to Choose the Right University

Choosing which university fits your interests and academic background is an important decision that will greatly influence the success of your university study. In the UK alone, there are hundreds of choices and therefore you need to be strategic in making a shortlist of universities and narrowing down your choices into second and first choice. This involves weighing some factors such as your motivation and aspiration, your personality, your location, and your budget.

People attend university for different reasons, so ask yourself what you want from your target university and what you want to do after you graduate. Many people attend top universities because of the prestige without considering their choice of future career. If you have interest in a particular career, you should find universities with a better reputation for your career choice than others. With a degree from a university that is most respected in the profession you want to enter; it will be easy for you to get your dream job and you will be able to climb the career ladder fast.

Your personality types also play an important role in yoursuccess as a university student. A scholarly type of student usually has self-motivation to work hard to ace exams and achieve high grades. This type of person will find comfort in a highly academic environment offered by top world universities such as Oxford or Cambridge. On the contrary, if you are not a type of person who can study for hours and getting top grades is not your main priority, you better go to a university with a more laid-back academic environment so that you will not be stressful all the time and can enjoy
your life at university.

Coming home could be a good escape during your hard time at university, so think about the distance between your home and the target university. If you get homesick easily, you should not consider choosing a university outside your hometown or which takes more than a day to travel by land or water. However, if distance is not a problem for you, you might want to consider studying abroad, especially at a university whose reputation is better than the universities in your home country.

Finally, calculate your financial ability, which should cover tuition fees and cost of living. Both vary across the country and different universities, so do your homework by doing some research to find out which one fits your bills. If you cannot afford to go to the University of your Choice, you can
search for financial aid in the forms of student loans, grant, orscholarship. Doremember that if you decide to obtain a loan, you must pay for it after you finish your study.

(i) Reading comprehension questions that go with the above reading passage.
1) Why do you need to choose the right university?
A) Because it will make you happy.
B) Because it has an impact on yoursuccess at university.
C) Because life at university is difficult.
D) Because the right university is difficult to find.

2) Which university should you go to if you already have a career choice?
A) One with the lowest tuition fees.
B) One that offers you a scholarship.
C) One that has the highest prestige.
D) One that has a good reputation in your future profession.

3) What type ofstudent will enjoy a highly academic environment?
A) A student who has self-motivation to work hard.
B) A smart student who does not need to study hard for exams.
C) A student who puts the highest priority on student societies.
D) A student who does not have a part-time job.

4) Where should you study if you are prone to homesickness?
A) Abroad.
B) Outside your hometown.
C) At your local university.
D) At home.

5) What can you do if you do not have enough money to fund yourstudy?
A) Wait for a year to collect money.
B) Find a full-time job.
C) Choose to study online.
D) Find a student loan orscholarship.

(ii) Answer the following questions:
1) What can you do if you do not have enough money to fund your study?
2) Does your personality type help you to choose university? If yes, then how?
3) Why do people attend University?
4) Write synonym for ‘aspiration’. Use it in sentence.
5) Give exact word from the passage for ‘easy-going’.

Briefly enumerate the points you should keep in mind while writing a memo? What are the features of a memo?

Write a letter to a professor asking him / her if you can mention him / her as a referee in your CV and whether he / she will be willing to provide a reference for you when needed.

Include the following points:
- a reminder of who you are (professors teach hundreds of students and should be able to
remember who you are)
- request for permission to name him / her as a referee
- inform them about where you are applying – it could be an Institute of Higher Education or a
business organization

Answer the questions given below briefly using (PREPOSITION) on, in or at in your answers. The first one has been done for you:

a. When did you last go on a holiday?
Ans. In the summer.
b. When did you get to work this morning?
c. When did you last visit Agra?
d. When did you last go to the dentist?
e. When does the train reach Mumbai?
f. When does the bank open?
g. When did you last go to see a cinema?
h. When did you start this exercise?
i. When did you reach home last night?
j. When did you last go to a meeting?

What are the main features of Web 2.0? What do you understand by Web 2.0 tools? Give a few examples.

A portfolio is a (i)______________ (job-hunting/ job- getting / job-gaining) tool that you can
(ii) _____________(evolve / make / develop), that gives employers a (complete / whole / big)  picture of who you are – your education, your experience, your accomplishments, your skill sets - and whether you have the (iii)_____________ (skill / potential / strength) to become - much more than what you claim in your cover letter and resume. A portfolio is not (iv)_______________ (very / completely / absolutely) necessary. But if you want to get an edge, make an impact, or in short do everything possible to get a job, then it is a good idea to have a portfolio when (v) ____________(preparing /interviewing /showcasing) for professional positions.

Enlist at least 5 benefits of registering with Recruitment Agencies.

Example: I wrote to Mr. Sharma.
Question: Who did you write to?
1. I phoned her yesterday afternoon.
........................................................
2. He went to Cincinnati.
……………………………………..
3. No, I didn’t see the memorandum.
.........................................................
4. I spoke to the Vice-President’s secretary.
.........................................................
5. The weather was great.
.........................................................

1. It's very cold today. Do you think it ____________snow later?
2. You____________ leave your door unlocked when you go out.
3. They ____________have filled the car with petrol before they set off.
4. My motorbike broke down in the middle of nowhere, but luckily, I___________ to fix it.
5. Mum says we ____________watch TV after we've finished our homework.

Show that Bose derivation of Planck’s law for energy density is given by 

Establish the Boltzmann relation  ln  

Define phase space of the system. Draw the phase space for a linear harmonic oscillator.

Obtain an expression of single particle partition function. Hence, using this expression obtain expressions for entropy and pressure.

What is Joule-Thomson effect? Write the mathematical expression of Joule Thomson Coefficient for van der Waals’ gas. What will be the effect on gas if the intermolecular forces are strong?

Derive Clausius-Clapeyron equation for two phases to coexist in equilibrium.

Write Maxwell’s relations and using these relations derive first and second energy equations.