Other Exams

Permutation  ï»¿ A permutation, also called an "arrangement number" or "order," is a rearrangement of the elements of an ordered list S into a one-to-one correspondence with S itself. The number of permutations on a set of nelements is given by n! (n factorial;  For example, there are  2!=2·1=2 permutations of {1,2}, namely {1,2}and {2,1}, and 3!=3·2·1=6 permutations of {1,2,3}, namely {1,2,3}, {1,3,2}, {2,1,3}, {2,3,1}, {3,1,2}, and {3,2,1}.  The number of ways of obtaining an ordered subset of k elements from a set of n elements is given by       You will get a detailed knowledge at the given below different links : http://www.studyadda.com/videos/jee-mathematics-lectures/permutations-combinations/factorial-1/1611 http://www.studyadda.com/videos/jee-mathematics-lectures/permutations-combinations/permutations-2/1612 http://www.studyadda.com/videos/jee-mathematics-lectures/permutations-combinations/permutations-3/1613 http://www.studyadda.com/videos/jee-mathematics-lectures/permutations-combinations/permutations-4/1614 http://www.studyadda.com/videos/jee-mathematics-lectures/permutations-combinations/permutations-5/1615 http://www.studyadda.com/videos/jee-mathematics-lectures/permutations-combinations/permutations-6/1616 http://www.studyadda.com/videos/jee-mathematics-lectures/permutations-combinations/permutations-7/1617 http://www.studyadda.com/videos/jee-mathematics-lectures/permutations-combinations/permutations-8/1618 http://www.studyadda.com/videos/jee-mathematics-lectures/permutations-combinations/permutations-9/1619 http://www.studyadda.com/videos/jee-mathematics-lectures/permutations-combinations/permutations-10/1620 http://www.studyadda.com/videos/jee-mathematics-lectures/permutations-combinations/permutations-11/1621 http://www.studyadda.com/videos/jee-mathematics-lectures/permutations-combinations/permutations-12/1622  

BuoyancyIn science, buoyancy  is an upward force exerted by a fluid that opposes the weight of an immersed object. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus a column of fluid, or an object submerged in the fluid, experiences greater pressure at the bottom of the column than at the top. This difference in pressure results in a net force that tends to accelerate an object upwards. The magnitude of that force is proportional to the difference in the pressure between the top and the bottom of the column, and (as explained by Archimedes' principle) is also equivalent to the weight of the fluid that would otherwise occupy the column,  i.e.,  the displaced fluid. For this reason, an object whose density is greater than that of the fluid in which it is submerged tends to sink. If the more...

An allylic rearrangement or allylic shift is an organic reaction in which the double bond in an allyl chemical compound shifts to the next carbon atom. It is encountered in nucleophilic substitution. In reaction conditions that favor a SN1 reaction mechanism the intermediate is a carbocation for which several resonance structures are possible. This explains the product distribution (or product spread) after recombination with nucleophile Y. This type of process is called an SN1' substitution. Alternatively, it is possible for nucleophile to attack directly at the allylic position, displacing the leaving group in a single step, in a process referred to as SN2' substitution. This is likely in cases when the allyl compound is unhindered, and a strong nucleophile is used. The products will be similar to those seen with SN1' substitution. Thus reaction of 1-chloro-2-butene with sodium hydroxide gives a mixture of 2-buten-1-ol and 1-buten-3-ol. In this video Mr. more...

As with alkenes, the addition of water to alkynes requires a strong acid, usually sulfuric acid, and is facilitated by mercuric sulfate. However, unlike the additions to double bonds which give alcohol products, addition of water to alkynes gives ketone products ( except for acetylene which yields acetaldehyde ). The explanation for this deviation lies in enol-keto tautomerization, illustrated by the following equation. The initial product from the addition of water to an alkyne is an enol (a compound having a hydroxyl substituent attached to a double-bond), and this immediately rearranges to the more stable keto tautomer. Tautomers are defined as rapidly interconverted constitutional isomers, usually distinguished by a different bonding location for a labile hydrogen atom (colored red here) and a differently located double bond. The equilibrium between tautomers is not only rapid under normal conditions, but it often strongly favors one of the isomers ( acetone, for example, more...

The Wurtz reaction, named after Charles-Adolphe Wurtz, is a coupling reaction in organic chemistry, organometallic chemistry and recently inorganic main group polymers, whereby two alkyl halides are reacted with sodium to form a new alkane:   2R–X + 2Na → R–R + 2Na+X−   Other metals have also been used to effect the Wurtz coupling, among them silver, zinc, iron, activated copper, indium and a mixture of manganese and copper chloride. The related reaction dealing with aryl halides is called the Wurtz-Fittig reaction.This can be explained by the formation of free radical intermediate and its subsequent disproportionation to give alkene. The reaction consists of a halogen-metal exchange involving the radical species R• (in a similar fashion to the formation of a Grignard reagent and then the carbon–carbon bond formation in a nucleophilic substitution reaction.) One electron from the metal is transferred to the halogen to produce a metal halide and more...

"We have never succeeded In slowing down our nuclear fusion reactors." Wilson Greatbatch, inventor In 1950 Andrei Sakharov (1921-1989) took a break from designing nuclear weapons to study plasma physics with Igor Tamm (1895-1971) for a year, during which time they developed the concept for a machine that could produce energy through nuclear fusion. Tamm went on to win the 1958 Nobel Prize in Physics; Sakharov was awarded the 1975 Nobel Peace Prize. Progress on fusion power has been slow. Nuclear fission produces energy by splitting highly radioactive atoms of uranium or plutonium. However, fission also produces waste that is dangerously radioactive for 10,000 years. Fusion, on the other hand, produces energy by combining deuterium (heavy hydrogen) into helium, with no dangerous waste. Sea water has one atom of deuterium for each 6,500 atoms of hydrogen. Deuterium atoms are twice as massive as hydrogen atoms, so they are relatively easy more...

An auto rickshaw is a form of transport which does not depend on human muscles yet is cheaper than a taxi, both to run and use. It consists essentially of a motorcycle engine mounted on a three-wheeled chassis, with space for passengers and a driver. Its single steering wheel is at the front, below the Windscreen, with the two driven wheels at the back. The passengers are well protected from the weather by a canvas hood. The driver sits in front with the engine beneath his seat. The passengers' compartment is at the back. (The life of an auto rickshaw driver is very hard. He has to bear hot winds during summer season. He has to face bone biting cold winds in the winter. Even rainy season too does not favour him. Sometimes he gets drenched and sometimes he has to face the muddy water forcing him to draw his more...

“I have little patience with scientists who... drill...holes where drilling is easy." Albert Einstein, theoretical physicist Stone Age man figured out that spinning a sharp rock on a wooden board would produce a circular hole—a useful discovery. The application of a bow to such a drill increased the rate of spinning and therefore the speed of boring the hole. By the nineteenth century, the bow had been replaced by geared machinery and the stone bit by metal, but otherwise the concept remained basically the same. Prior to the early 1860s, the standard drill bit consisted simply of a flattened, sharpened piece of metal. These "spade bits" were notoriously imprecise and also prone to rapid dulling when used on hard surfaces. American Stephen Morse believed that he could improve the standard drill bit, and, in 1861, he patented what has now become known as the twist drill. The device was the more...

"Anything that needs communications or control will be wirelessly connected." Vie Hayes Today's wireless networks owe much to one of the earliest computer networks, the University of Hawaii's ALOHAnet. This radio-based system, created in 1970, had many of the basic principles still in use today. Early wireless networks were expensive, however, and their equipment was bulky. They were used only in places where wired networks were awkward, such as across water or difficult terrain. It was not until the 1980s, with the arrival of cheaper, more portable equipment, that wireless networking began to go mainstream. There was a problem, however. By the end of the 1980s several companies were selling wireless networking equipment, but it was all incompatible. What was needed was some joined-up thinking. Step forward the Institute of Electrical and Electronic Engineers (IEEE) and in particular Vie Hayes {b. 1941). Hayes did not invent any new technology, but more...

"The telephone is a good way to talk to people without having to offer them a drink." Fran Lebowitz, writer Superheroes may use phone booths to change into spandex, prostitutes may use them to place calling cards, and hooligans occasionally abuse them as urinals, but the impetus for the first payphone initially sprang out of an individual's desperate need for the use of a telephone and not being able to find one. Conscious of this need, U.S. inventor William Gray devised the first coin-operated pay phone in 1889. It was a post-pay machine so the money was paid after the call to an attendant. Demand for .the device was not immediate, but he managed to interest telephone companies, hotels, and shops. As people traveled more, the need for public payphones grew, and Gray's idea fueled the demand for household telephones. Phone booths have undergone more design changes over the years more...