Exam Preparation Tips

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Scoring tips The following tips would certainly help you in scoring well in the exam: Go through previous years’ question papers along with solutions, and analyse the subject pattern and focus on those subjects which have maximum weightage. Books can further be divided into two categories: Books that deal with the fundamentals and focus on conceptual clarity. Here textbooks by reputed publishers are a must. Books that provide a great deal of difficult and time-consuming questions and are used essentially as practice material. Do not rely on just one book for a topic; instead consult a couple of books for the same topic. Prepare notes after completing each chapter. Practise the maximum number of questions possible on a given topic. This certainly strengthens your preparation. Keep in mind that those topics which are not in GATE syllabus could be certainly left out. Make a list of topics in which you more...

In mathematics a combination is a way of selecting several things out of a larger group, where (unlike permutations) order does not matter. In smaller cases it is possible to count the number of combinations. For example given three fruit, say an apple, orange and pear, there are three combinations of two that can be drawn from this set: an apple and a pear; an apple and an orange; or a pear and an orange. More formally a k-combination of a set S is a subset of k distinct elements of S. If the set has n elements the number of k-combinations is equal to the binomial coefficient          which can be written using factorials as   more...

Definition:  Factorial: The number of sequences that can exist with a set of items, derived by multiplying the number of items by the next lowest number until 1 is reached. In mathematics, product of all whole numbers up to the number considered. The special case zero factorial is defined to have value 0!=1, consistent with the combinatorial interpretation of there being exactly one way to arrange zero objects. The notation n factorial (n!) was introduced by Christian Kramp in 1808. Permutation: An arrangement is called a Permutation. It is the rearrangement of objects or symbols into distinguishable sequences. When we set things in order, we say we have made an arrangement. When we change the order, we say we have changed the arrangement. So each of the arrangement that can be made by taking some or all of a number of things is known as Permutation.  Combination: A Combination is more...

Definition:  Permutation: An arrangement is called a Permutation. It is the rearrangement of objects or symbols into distinguishable sequences. When we set things in order, we say we have made an arrangement. When we change the order, we say we have changed the arrangement. So each of the arrangement that can be made by taking some or all of a number of things is known as Permutation.  Combination: A Combination is a selection of some or all of a number of different objects. It is an un-ordered collection of unique sizes.In a permutation the order of occurence of the objects or the arrangement is important but in combination the order of occurence of the objects is not important.   Formula: 

• Factorial=n! = 1*2*3*...*n.
• Permutation = nPr = n! / (n-r)! 
• Combination = nCr = nPr / r! =n!/(n-r)! r!

where,       more...

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...