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1. (c) Let C(x) be the maintenance cost function, then C(x) = 5000000 + 160x - 0.04x²
2. (b) We have, C(x) = 5000000 + 160x - 0.04x²
   Now, C{x) = 160 - 0.08x
   For maxima/minima, put C'(x) = 0
   {tex}\Rightarrow{/tex} 160 = 0.08x
   {tex}\Rightarrow{/tex} x = 2000
3. (b) Clearly, from the given condition we can see that we only want critical points that are in the interval [0, 4500]
   Now, we have C(0) = 5000000
   C(2000) = 5160000 and C(4500) = 4910000
   {tex}\therefore{/tex} Maximum value of C(x) would be ₹5160000
4. (a) The complex must have 4500 apartments to minimise the maintenance cost.
5. (a) The minimum maintenance cost for each apartment woud be ₹1091.11

Danny Casey didn't come on a date

For the Motion

Good morning everyone! Respected judges, worthy opponents and the esteemed audience,
Today, I Karuna of class XII, stand before you all to speak in favour of the motion, "The Internet cannot replace a classroom teacher".
The classrooms today differ from the classrooms a decade ago in multitudinous ways. The influx of technology has opened doors, expanded minds and changed the world. However, no matter how advanced and beneficial the technology has got, it can never replace a classroom teacher. There is no denying to the fact that the internet can solve a bulk of problems and provide students all the necessary answers along with illustrations. However, it cannot replace a classroom teacher as it is devoid of any kind of emotion, which is very much required during teaching. A teacher simply does not impart knowledge or information. A teacher leads, guides, facilitates and mentors a student. He understands the emotions and sentiments of the students. He realises the positive as well as the negative feelings of the students.

A teacher faces all types of students with different mental abilities while teaching. He, thus, adjusts his teaching methodology according to them. He helps the weaker students to bloom and motivates his students accordingly. The internet cannot solve all the queries but a teacher can and that too in person. Teachers help the students to remain alert and active in the classroom during teaching, whereas a machine can never do so. Internet would never care about how much concentration, focus and attention the student is learning with. Besides, it can never beat the knowledge of human beings. In addition, it’s not necessary that all the information provided by internet is genuine. Have you ever wondered where all the information or knowledge on the internet has come from? It is only we humans who have fed it into the computers.
In conclusion, I would like to say that a machine can never replace a living and breathing knowledgeable person.

Thank you!

Against the Motion

Good morning everyone! Respected judges, worthy opponents and the esteemed audience,
Today, I Karuna of class XII, stand before you all to speak against the motion, "The Internet cannot replace a classroom teacher".
The classrooms today differ from the classrooms a decade ago in multitudinous ways. These days, a modern classroom is defined by technology. Teachers, administrators, parents and students have been told time and again that it is technology alone through which we can sharpen our education system. True personalised tech-infused learning is the future of education. In today’s age, the old school method of books and notes is no longer beneficial. Teachers have to keep themselves updated with today’s trends and have to equip themselves with the latest technology.
There is constant pressure on teachers and administrators today to implement technology in classroom. In order to fully engage the students and make them learn, a teacher will have to come out of his comfort zone and explore new ways of teaching through the internet. The internet has immense potential to upgrade today’s educational system. There may come a time soon when the role of a teacher in the classroom will considerably be diminished by the internet-based learning environment .
In near future, the teacher will not be able to function without internet and technology. The teacher will have to become a facilitator of imparting trustworthy information from electronic sources. The teachers today need to strike a balance and empower themselves through technology so as to prevent themselves from getting replaced altogether by the internet.

Thank you!

Photoelectric effect: When certain metals are exposed to a beam of light, the electrons are ejected from the metal. This phenomenon is called the photoelectric effect. The electrons ejected are called photoelectrons.

The results of this experiment were:

1. The electrons are ejected from the metal surface as soon as the beam of light strikes the surface, i.e., there is no time lag between the striking of the light beam and the ejection of electrons from the metal surface.
2. The number of electrons ejected is proportional to the intensity or brightness of the light.
3. For each metal; there is a minimum frequency, {tex}\nu_o{/tex} below which photoelectric effect is not observed.
4. K.E. of electrons {tex}\propto{/tex} frequency of light.

Equipment for studying the photoelectric effect. Light of a particular frequency strikes a clean metal surface inside a vacuum chamber. Electrons are ejected from the metal and are counted by a detector that measures their kinetic energy:

Explanation of photoelectric effect on the basis of quantum theory: When a photon of sufficient energy strikes an electron in the atom of the metal, it transfers its energy to the electron and the electron is ejected without delay. Greater the energy of the photon, greater will be the kinetic energy of the ejected electron.

1. 1. Due to greater electronegativity of sp² hybridised carbon to which carboxyl carbon is attached and greater resonance stabilization of carboxylate ion with the benzene ring, benzoic acid is a stronger acid than acetic acid.
   2. Methanal is more reactive towards nucleophilic addition reaction than ethanal because carbonyl carbon of methanal is more electrophilic than that of ethanol. Also, due to +I effect of methyl group in ethanal, reactivity of ethanal decreases.

1. China has successfully focused on Pro-poor reforms.
2. Agrarian reforms have been effectively carried out.
3. Export driven manufacturing has significantly grown, adding to the pace of GDP growth.
4. SEZ policy has proved to be a boon for FDI flow in India.

Although the loneliness of Derry dominates the play, there are evident traces of Mr. Lamb’s loneliness throughout the first scene of the play. The old man says that having heard the bees for a long time he knows that they sing, not buzz. It not only depicts how his perception was different from others but also illustrates that he was lonely and that he did not have anyone to be with.
Another evidence of his loneliness is the fact that the whole day he sat in the sun and read books. This proved that books were his only true friends.
By the end of this scene, it became even clearer that he was lonely and sad when he muttered to himself that no one came back to him after the first meeting. Likewise, he did not expect Derry to return. He was so sure that Derry would never return that he climbed the ladder to collect all the apples himself, although Derry had offered to help him after informing his mother. Ironically, the old man would have died unnoticed if Derry had not returned to fill the emptiness of his own life.

Before reaching Champaran, Gandhiji first went to Muzzafarpur to obtain complete information about the conditions of the peasants. He accordingly sent a telegram to Professor J.B. Kripalani. Gandhiji stayed for two days in the home of a government school teacher and scanned the entire situation of the peasants. He scolded the lawyers for charging exorbitant fees and resolved to free the peasants from the fear of the British rule.