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Document Laplace transform of standerd functions 1)L[e^at]=1/(s-a) 2)L[e^-at]=1/(s+a) 3)L[sinat]=a/(s^2+a^2) 4)L[cosat]=s/(s^2+a^2) 5)L[sinht]=a/(s^2) 6)L[cosht]=s/(s^2-a^2) 7)L[t^n]=n!/s^(n+1) 8)L[t]=1/s^2

The organisation in which manages operates copmrises of many interrelated subsystem such as humam (social)subsystem,an administration (structural)subsystem,an informational(decision making)subsystem and an economic (technological)subsystem. The economical subsystem will concentrate on the work to be done and its cost effectiveness.The dicision making system will focus on the keys decison areas and the informational needs to keep the system operating.The main concern of the structural subsytem will be on organisational structure,authority and responsibility setup within the organisation.whreas,the humen or social subsystem will look into the motivational aspect and needs of organisational members and the type of leadership necessary. As mentioned above,when we treat the organisation as asocial comprising of many interralated subsystems,the manegement has not only to look into the internal management of the organisation but also be aware of the needs and pressures from the ex...

Concept of Pipes and Cistern Welcome students to my new blog in aptitude series. In this blog we are going to clear the concept of pipes and cistern. This topic is related to work and wages , I hope you can solve problems on it. Let's revise it. Lets revise.. There are two kind of pipes, inlet pipe and outlet pipe. Inlet pipe is the pipe that fills the tank or any reservoir and Outlet pipe is the pipe that empties the tank. Mathematically: If a pipe fills a tank in 'x' hours, then in one hour it will fill 1/x portion of tank. For e.g, if a pipe takes 4 hours to completely fill a tank of 12 liters, then in 1 hour it will fill 1/4 part of tank, means 3 liters of tank. Similarly, If a pipe empties a tank in 'x' hours, then in one hour it will empty 1/x portion of tank. For e.g, if a pipe takes 4 hours to completely empty a tank of 12 liters, then in 1 hour it will empty 1/4 part of tank, means 3 liters of tank. If we have inlet and outlet pipes both opene...

Concept Of Work and Wages Welcome students to my new blog in aptitude series. In this blog we are going to clear the concept of work and wages. Work and wages is the widely asked topic in every exam from past few years. Let's revise it. What is Work? Work is a certain set of tasks or activities to achieve result. We can write work in mathematics as: If any person complete his/her work in N days, then total amount of work done in 1 day is given by = 1/N. Similarly, if another person complete work in M days, then also total work done in 1 day is given by = 1/M. From above two situations we can conclude that those two persons complete (1/N + 1/M) amount of work in 1 day. In question if their is comparison of work and efficiency then use formula: M1*D1*H1*E1 / W1 = M2*D2*H2*E2 / W2 Where, M = Number of workers D = Number of days H = Number of working hours in a day E = Efficiency of workers W = Units of work Work done is directly proportional to the time and efficien...

What is LCM and HCF ? Hello students, welcome to my next article on Aptitude series. In this article we are going to learn about how to find LCM and HCF of any two numbers with simple trick. Lets firstly know about what is LCM and HCF. LCM The full form of LCM is Lowest Common Multiple or Lowest Common Divisor. LCM is the value which is divisible by the two given numbers. LCM is the method to find smallest common multiple between given two or more numbers. How find LCM? When we multiply any two numbers then we get value known as Multiple. For e.g, 4 is multiple of 2. LCM is calculated by simple formula. Let a & b two integers. Then formula is: LCM (a,b) = (a x b)/GCD (a,b) In case of fractional numbers the LCM is calculated by formula: LCM (a / b) = LCM (a) / LCM (b). LCM by Prime Factorisation Method Prime factorial method is a very simple method to find LCM of any two or more numbers. Suppose there are three numbers 18, 12, 24. Lets write prime factors of all this numbers ind...

Hyperbola Hello students, in this blog we are going to learn how to draw hyperbola in very easy step. According to google, Hyperbola is a symmetrical open curve formed by the intersection of a circular cone with a plane at a smaller angle with its axis than the side of the cone. Lets see how can we draw it. Question: Point F is 50 mm from a line AB. a point P is moving in a plane such that the ratio of it's distances from F and line AB remains constant and equal to 2/3. draw locus of point P. { ECCENTRICITY = 2/3 }. Solution: Procedure: Draw a vertical line AB and point F 50 mm from it. Divide 50 mm distance in 5 parts. Name 2nd part from F as V. It is 20mm and 30mm from F and AB line respectively. It is first point giving ratio of it’s distances from F and AB 2/3 (i.e 20/30) Form more points giving same ratio such as 30/45, 40/60, 50/75 etc. Taking 45,60 and 75mm distances from line AB, draw three vertical lines to the right side of it. Now with 30, 40 an...

Types of Numbers Hello students, welcome to my new series of Aptitude , in this blog we are going to learn about numbers. Numbers is the very basic thing in Aptitude learning. Numbers starts from Zero "0". Zero was firstly invented by Aryabhata. Lets learn more about numbers. Types of numbers.. Integers: All the numbers whose fractional part is zero are known as Integers. For e.g. -6, -4, 0, 1, 99, 1000, etc. Natural Numbers: All the numbers whose fractional part is zero and also they are greater than zero are termed as natural numbers. For e.g. 1, 2, 3, 4,..., upto n. Whole Numbers: All the numbers whose fractional part is zero, including zero are termed as natural numbers. For e.g. 0, 1, 2, 3, 4,..., upto n. Prime Numbers: All the numbers having only two factors, the number itself and 1, are termed as prime numbers. For e.g. 2, 3, 19, 7, etc. 1 is not prime, nor composite number. 2 is the smallest even prime number. There are total 25 prime numbers upto 100....

Ionization Energy Hello students, I hope you may know the concept of Ionization energy. In 10th standerd we have leart about Ion and Different types of energies associated with it. Lets first talk about what is Ionization Energy? The energy required to remove valence electron form an isolated state or neutral gaseous atom is reffered as Ionization Energy. The ionization energy associated with removal of the first (most loosely held) electron. Ionization is an endothermic process which means that, it is positive for neutral atoms. There are four major factors which affects on Ionization energy are as follows: Atomic Size. Nuclear Charge. Screening Effect. Type of electron removed. Lets look towards how above factors affect ionization energy. Atomic size Atomic size is a distance between nucleus and the outermost shell of an atom. Atomic size depends upon atomic number. Ionization energy is inverselt proportional to atomic size. As atomic size increases nuclear charge ...

Effective Nuclear Charge According to Wikipedia , In atomic physics, the effective nuclear charge is the actual amount of positive (nuclear) charge experienced by an electron in a multi-electron atom. The symbol of effective nuclear charge is Zeff or Z*. ENC is the net positive charge experienced by an electron in a multi-electron atom. The effective nuclear charge on an atom is given by equation- Zeff = Z – S Where, Z = The number of protons in the nucleus (atomic number). S = The number of electrons between the nucleus and the electron in question (the number of nonvalence electrons). Question: Consider a neutral neon atom (Ne), a sodium cation (Na+), and a fluorine anion (F–). What is the effective nuclear charge for each? Solution: Start by figuring out the number of nonvalence electrons, which can be determined from the electron configuration. Ne has 10 electrons. The electron configuration is 1s22s2 2p6. The valence shell is shell 2 and contains 8 valence electrons...

Normal & Tangent to Epicycloid According to Wikipedia , In geometry, an epicycloid is a plane curve produced by tracing the path of a chosen point on the circumference of a circle—called an epicycle—which rolls without slipping around a fixed circle. Question: A circle of 50 mm diameter rolls on the circumference of another circle of 180 mm diameter and outside it. Trace the locus of a point on the circumference of the rolling circle, for one complete revolution. Name the curve formed. Draw a tangent to the curve at a point on it 125 mm from the center of the directing circle. Solution: Procedure: Draw an Epicycloid according to the given data. (Don't know how to draw an epicycloid? To learn, kindly follow the given link: How to draw an Epicycloid?). On epicycloid take a point Q. Draw an arc of 25 mm on the arc passing through the center of the circle from point Q. From that point, draw a straight line to the center of the circle of having 90 mm radius (180 ...