If a particle move in a horizontal plane in a central force potential U® , which of the following physical quantities are conserved : ?->(Show Answer!)

1. If a particle move in a horizontal plane in a central force potential U® , which of the following physical quantities are conserved :

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MCQ->If a particle move in a horizontal plane in a central force potential U® , which of the following physical quantities are conserved :....

MCQ-> Read the following passage carefully and answer the questions based on it. Some words have been printed in bold to help you locate them while answering some of the questions.Notwithstanding the fact that the share of household savings to GDS is showing decline, still this segment is the significant contributor to GDS with 70% share. Indian households are among the most frugal in the world However, commensurate capital formation has not been taking place as a lion's share of household savings are being parked in physical assets compared to financial assets. The pattern of disposition of saving is an important factor in determining how the saved amount is utilized for productive purposes. The proportion of household saving in financial assets determines the channelisation of saving for investment in other sectors of the economy. However, the volume of investment of saving in physical assets determines the productivity and generation of income in that sector itself. Post-Independence era has witnessed a significant shift in deployment of household savings especially the share of financial assets increased from 26.39% in 1950 to 54.05% in 1990 may be on account of increased bank branch network across the country coupled with improved awareness of investors on various financial / banking products. However, contrast to common expectations, the share of financial assets in total household savings has come down from 54.05% to 50.21% especially in post reform period i.e. 1990 to 2010 despite providing easy access and availability of banking facilities compared to earlier years. The increased share of physical assets over financial assets (around 4%) during the last two decades is a cause of concern requires focused attention to arrest the trend. Traditionally, the Indians are risk-averse and prefer to invest surplus funds in physical assets such as Gold, Silver and lands. Nevertheless, considerable share of savings also owing to financial assets, which includes, Currency, Bank Deposits, Claims on Government, Contractual Savings, Equities The composition of household financial savings shows that the bank deposits (44%) continue to remain the major contributor along with the rise in the Contractual Savings, Claims on Government and Currency. Though there was gradual decline in currency holdings by the households i.e. 13.79% in 1970s to 9.30% in 2007, still the present currency holding level with households appears to be on high side compared to other countries. The primary reasons for higher currency holdings could be absence of banking facilities in majority villages (5.70 lakh villages)as well as hoarding of unaccounted money in the form of cash to circumvent tax laws. Though, cash is treated as financial asset, in reality, a major portion of currency is blocked and become unproductive. Bank deposits seemed to be the preferred choice mainly on account of its inbuilt features such as Safety, Security and Liquidity. Traditionally, the Household sector has been playing a leading role in the landscape of bank deposits followed by the Government sector. However, the last two decades has witnessed significant shift in ownership of Bank deposits. While there was improvement in Corporate and Government sectors' share by 8.30% and 7.20% respectively during the period 1999 to 2009, household sector lost a share of 13.30% in the post reform period. In the post independence era, Indian financial system was characterized by poor infrastructure and low level of financial deepening. Savings in physical assets constituted the largest portion of the savings compared to the financial assets in the initial years of the planning periods. While rural households were keen on acquiring farm assets, the portfolio of urban households constituted consumer durables, gold, jewellery and house property.Despite the fact that the household savings have been gradually moving from physical assets to financial assets over the years, still 49.79% of household savings are wrapped in unproductive physical assets, which is a cause of concern as the share of physical assets to total savings are very high in the recent years compared to emerging economies. This trend needs to be arrested as scarce funds are being diverted into unproductive segments. Of course, investment in Real estate sector can be treated as productive provided construction activity is commenced within reasonable time, but it is regrettably note that many investors just buy and hold it for speculation leading to unproductive investments. India has probably the largest fascination with gold than any other country in the world with a share of 9.50% of the world's total gold holdings. The World Gold Council believes that they are over 18000 tonnes of gold holding in the country. More impressive is the fact that current demand from India alone consumes 25% of the world's annual gold output. Large amount of capital is blocked in gold which resides in bank lockers and remain unproductive. Indian economy would grow faster if the capital markets could attract more of the nation's savings and channel them into more productive areas, especially infrastructure. If the Indian market can develop and evolve into a more mature financial system, which persuades the middle class to put more of its money into equities, the potential is mind-boggling.Which of the following statement (s) is/are correct in the context of the given passage? I. The GDS percentage to GDP has shown considerable improvement from 10% in 1950 to 33.7% in 2010, which is one of the highest globally. II. The saving rate however shows an increasing trend, marginal decline is observed under tic use hold sector. III. The share of financial assets in total household savings have come down from 54.05% to 21% especially in post reform era.....

MCQ-> Modern science, exclusive of geometry, is a comparatively recent creation and can be said to have originated with Galileo and Newton. Galileo was the first scientist to recognize clearly that the only way to further our understanding of the physical world was to resort to experiment. However obvious Galileo’s contention may appear in the light of our present knowledge, it remains a fact that the Greeks, in spite of their proficiency in geometry, never seem to have realized the importance of experiment. To a certain extent this may be attributed to the crudeness of their instruments of measurement. Still an excuse of this sort can scarcely be put forward when the elementary nature of Galileo’s experiments and observations is recalled. Watching a lamp oscillate in the cathedral of Pisa, dropping bodies from the leaning tower of Pisa, rolling balls down inclined planes, noticing the magnifying effect of water in a spherical glass vase, such was the nature of Galileo’s experiments and observations. As can be seen, they might just as well have been performed by the Greeks. At any rate, it was thanks to such experiments that Galileo discovered the fundamental law of dynamics, according to which the acceleration imparted to a body is proportional to the force acting upon it.The next advance was due to Newton, the greatest scientist of all time if account be taken of his joint contributions to mathematics and physics. As a physicist, he was of course an ardent adherent of the empirical method, but his greatest title to fame lies in another direction. Prior to Newton, mathematics, chiefly in the form of geometry, had been studied as a fine art without any view to its physical applications other than in very trivial cases. But with Newton all the resources of mathematics were turned to advantage in the solution of physical problems. Thenceforth mathematics appeared as an instrument of discovery, the most powerful one known to man, multiplying the power of thought just as in the mechanical domain the lever multiplied our physical action. It is this application of mathematics to the solution of physical problems, this combination of two separate fields of investigation, which constitutes the essential characteristic of the Newtonian method. Thus problems of physics were metamorphosed into problems of mathematics.But in Newton’s day the mathematical instrument was still in a very backward state of development. In this field again Newton showed the mark of genius by inventing the integral calculus. As a result of this remarkable discovery, problems, which would have baffled Archimedes, were solved with ease. We know that in Newton’s hands this new departure in scientific method led to the discovery of the law of gravitation. But here again the real significance of Newton’s achievement lay not so much in the exact quantitative formulation of the law of attraction, as in his having established the presence of law and order at least in one important realm of nature, namely, in the motions of heavenly bodies. Nature thus exhibited rationality and was not mere blind chaos and uncertainty. To be sure, Newton’s investigations had been concerned with but a small group of natural phenomena, but it appeared unlikely that this mathematical law and order should turn out to be restricted to certain special phenomena; and the feeling was general that all the physical processes of nature would prove to be unfolding themselves according to rigorous mathematical laws.When Einstein, in 1905, published his celebrated paper on the electrodynamics of moving bodies, he remarked that the difficulties, which surrouned the equations of electrodynamics, together with the negative experiments of Michelson and others, would be obviated if we extended the validity of the Newtonian principle of the relativity of Galilean motion, which applies solely to mechanical phenomena, so as to include all manner of phenomena: electrodynamics, optical etc. When extended in this way the Newtonian principle of relativity became Einstein’s special principle of relativity. Its significance lay in its assertion that absolute Galilean motion or absolute velocity must ever escape all experimental detection. Henceforth absolute velocity should be conceived of as physically meaningless, not only in the particular ream of mechanics, as in Newton’s day, but in the entire realm of physical phenomena. Einstein’s special principle, by adding increased emphasis to this relativity of velocity, making absolute velocity metaphysically meaningless, created a still more profound distinction between velocity and accelerated or rotational motion. This latter type of motion remained absolute and real as before. It is most important to understand this point and to realize that Einstein’s special principle is merely an extension of the validity of the classical Newtonian principle to all classes of phenomena.According to the author, why did the Greeks NOT conduct experiments to understand the physical world?
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MCQ-> Please read the passage below and answer the questions that follow:It is sometimes said that consciousness is a mystery in the sense that we have no idea what it is. This is clearly not true. What could be better known to us than our own feelings and experiences? The mystery of consciousness is not what consciousness is, but why it is.Modern brain imaging techniques have provided us with a rich body of correlations between physical processes in the brain and the experiences had by the person whose brain it is. We know, for example, that a person undergoing stimulation in her or his ventromedial hypothalamus feels hunger. The problem is that no one knows why these correlations hold. It seems perfectly conceivable that ventromedial hypothalamus stimulation could do its job in the brain without giving rise to any kind of feeling at all. No one has even the beginnings of an explanation of why some physical systems, such as the human brain, have experiences. This is the difficulty David Chalmers famously called ‘the hard problem of consciousness’.Materialists hope that we will one day be able to explain consciousness in purely physical terms. But this project now has a long history of failure. The problem with materialist approaches to the hard problem is that they always end up avoiding the issue by redefining what we mean by ‘consciousness’. They start off by declaring that they are going to solve the hard problem, to explain experience; but somewhere along the way they start using the word ‘consciousness’ to refer not to experience but to some complex behavioural functioning associated with experience, such as the ability of a person to monitor their internal states or to process information about the environment. Explaining complex behaviours is an important scientific endeavour. But the hard problem of consciousness cannot be solved by changing the subject. In spite of these difficulties, many scientists and philosophers maintain optimism that materialism will prevail. At every point in this glorious history, it is claimed, philosophers have declared that certain phenomena are too special to be explained by physical science - light, chemistry, life - only to be subsequently proven wrong by the relentless march of scientific progress.Before Galileo it was generally assumed that matter had sensory qualities: tomatoes were red, paprika was spicy, flowers were sweet smelling. How could an equation capture the taste of spicy paprika? And if sensory qualities can’t be captured in a mathematical vocabulary, it seemed to follow that a mathematical vocabulary could never capture the complete nature of matter. Galileo’s solution was to strip matter of its sensory qualities and put them in the soul (as we might put it, in the mind). The sweet smell isn’t really in the flowers, but in the soul (mind) of the person smelling them … Even colours for Galileo aren’t on the surfaces of the objects themselves, but in the soul of the person observing them. And if matter in itself has no sensory qualities, then it’s possible in principle to describe the material world in the purely quantitative vocabulary of mathematics. This was the birth of mathematical physics.But of course Galileo didn’t deny the existence of the sensory qualities. If Galileo were to time travel to the present day and be told that scientific materialists are having a problem explaining consciousness in purely physical terms, he would no doubt reply, “Of course they do, I created physical science by taking consciousness out of the physical world!”Which of the following statements captures the essence of the passage?
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MCQ-> The following questions relate to a game to be played by you and your friend. The game consists of a 4 x 4 board (see below) where each cell contains a positive integer. You and your friend make moves alternately. A move by any of the players consists of splitting the current board configuration into two equal halves and retaining one of them. In your moves you are allowed to split the board only vertically and to decide to retain either the left or the right half. Your friend, in his/her moves, can split the board only horizontally and can retain either the lower or the upper half. After two moves by each player a single cell will remain which can no longer be split and the number in that cell will be treated as the gain (in rupees) of the person who has started the game. A sample game is shown below. So your gain is Re.1. With the same initial board configuration as above and assuming that you have to make the first move, answer the following questions. Initial Board

After your move (retain left)

After your friends move (retain upper)

After your move (retain right)

After your friends move (retain lower)

If you choose (retain right) (retain left) in your turns, the best move sequence for your friend to reduce your gain to a minimum will be
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