Important Formulae for Aptitude Solving in Competitive Exams

Here is a list of formulae that are helpful for solving aptitude problems for Competitive Exams, Campus Recruitment Training, CAT, and others.


A) Profit and loss

1) Gain = (S.P.) - (C.P.)
2) Loss = (C.P.) - (S.P.)
3) Gain % = (Gain x 100)/C.P.
4) Loss % = (Loss x 100)/C.P.
5) SP = ((100 + Gain %) x C.P)/100
6) SP = ((100 - Loss %) x C.P.)/100
7) C.P. = (100 x S.P.)/ (100 + Gain %)
8 ) C.P. = (100 x S.P.)/ (100 - Loss %)
9) When a person sells two similar items, one at a gain of say x%, and the other at a loss of x%, then the seller always incurs a loss given by:
Loss % = ((Common Loss and Gain %) /10) ^2 = (x*x)/100.
10) If a trader professes to sell his goods at cost price, but uses false weights, then
Gain % = [(Error x 100) /(True Value) - (Error)]%


B ) Percentage

1) To express x% as a fraction: x%=x/100.
2) To express a/b as a percent: a/b=[(a/b)*100]%
3) (i) If the price of a commodity increases by R%, then the reduction in consumption so as not to increase the expenditure is: [(R/ (100+R))*100]%
(ii) If the price of a commodity decreases by R%, then the increase in consumption so as not to decrease the expenditure is: [(R/ (100-R))*100]%
4) Results on Population: Let the population of a town be P now and suppose it increases at the rate of R% per annum, then:
(i) Population after n years = P * (1 + R/100)^n
(ii) Population n years ago = P /(1 + R/100)^n
5) Results on Depreciation: Let the present value of a machine be P. Suppose it depreciates at the rate of R% per annum. Then:
(i) Value of the machine after n years = P *(1 - R/100) ^n
(ii) Value of the machine n years ago = P / (1 - R/100) ^n
6) If A is R% more than B, then B is less than A by:
[(R/ (100+R)) * 100]%
7) If A is R% less than B, then B is more than A by : [(R/ (100-R)) * 100]%


C) Average

1) Average = (sum of observation) / (Number of observations)
2) Suppose a man covers a certain distance at x kmph and an equal distance at y kmph. Then, the average speed during the whole journey is (2xy/(x+y)) kmph

D) Time and Work

1) If A can do a piece of work in n days, then A's 1 day's work = 1/n
2) If A's 1 day's work = 1/n, then A can finish the work in n days.
3) If A is twice as good a workman as B, then:
(i) Ratio of work done by A and B = 2:1
(ii) Ratio of times taken by A and B to finish a work = 1:2

E) Time and Distance

1) (i) Speed = Distance / Time
(ii) Time = Distance / Speed
(iii) Distance = Speed * Time
2) x km/hr = (x * 5/18) m/sec
3) x m/sec = (x * 18/5) km/hr
4) If the ratio of the speeds of A and B is a : b, then the ratio of the times taken by then to cover the same distance is 1/a : 1/b or b : a.
5) Suppose a man covers a certain distance at x km/hr and an equal distance at y km/hr. Then, the average speed during the whole journey is: [2xy/(x+y)] km / hr


F) Partnership

1) Ratio of Divisions of Gains:
(i)When investments of all the partners are for the same time, the gain or loss is distributed among the partners in the ratio of their investments.
Suppose A and B invest Rs. x and Rs. y respectively for a year in a business, then at the end of the year:
(A's share of profit) : (B's share of profit) = x : y.

(ii) When investments are for different time periods, then equivalent capitals are calculated for a unit of time by taking (capital x number of units of time). Now gain or loss is divided in the ratio of these capitals.
Suppose A invests Rs. x for p months and B invests Rs. y for q months then,
(A's share of profit) : (B's share of profit)= xp : yq.

2) Working and Sleeping Partners: A partner who manages the business is known as a working partner and the one who simply invests the money is a sleeping partner.


G) Simple Interest

1) Principal: The money borrowed or lent out for a certain period is called “the principal " or " the sum".
2) Interest: Extra money paid for using others money is called "interest".
3) Simple Interest (S.I.): If the interest on a sum borrowed for certain period is reckoned uniformly, and then it is called "simple interest".

Let Principal = P, Rate = R% per annum (p.a.) and Time = T years. Then:

(i) Simple Interest = (P*T*R)/100
(ii) P = (100*S.I.) / (R*T); R = (100*S.I.) / (P*T) ; T = (100*S.I.) / (P*R).


H) Ratio and Proportion

1) The ratio of two quantities a and b in the same units, is the fraction a/b and we write it as a : b.
2) Proportion: The equality of two ratios is called proportion.
If a : b = c : d, we write a : b :: c : d and we say that a, b, c, d are in proportion . Here a and d are called "extremes", while b and c are called "mean terms".
Product of means = Product of extremes. Thus, a : b :: c : d (b x c) = (a x d).
3) (i) Fourth Proportional : If a : b = c : d, then d is called the fourth proportional to a, b, c.
(ii)Third Proportional: a : b = c : d, then c is called the third proportion to a and b.
(iii)Mean Proportional: Mean proportional between a and b is (ab) ^0.5.
4) (i) Comparison of Ratios : We say that (a : b) > (c : d) -> a/b > c/d .
(ii) Compounded Ratio: The compounded ratio of the ratios: (a : b), (c : d), (e : f) is : (ace : bdf)
5) (i) Duplicate ratio of (a : b) is (a^2 : b^2).
(ii) Sub-duplicate ratio of (a : b) is (a^0.5 : b^0.5).
(iii) Triplicate ratio of (a : b) is (a^3 : b^3).
(iv) Sub-triplicate ratio of (a : b) is (a^1/3 : b^1/3).
(v) If a/b=c/d , then a+b/a-b = c+d/c-d [componendo and dividendo]
6) (i)We say that x is directly proportional to y, if x = ky for some constant k.
(ii)We say that x is inversely proportional to y, if xy = k for some constant k.

I) Permutations and Combinations

1) Factorial Notation: Let n be a positive integer. Then, factorial n, denoted n! is :
n! = n(n - 1)(n - 2) ... 3.2.1.
2) Permutations: The different arrangements of a given number of things by taking some or all at a time are called "permutations".
3) Number of permutations: Number of all permutations of n things, taken r at a time, is given by:
nPr = n(n - 1)(n - 2) ... (n - r + 1) = n! / (n-r)!
4) If there are n subjects of which p1 are alike of one kind; p2 are alike of another kind; p3 are alike of third kind and so on and pr are alike of rth kind,
Such that (p1 + p2 + ... pr) = n.
Then, number of permutations of these n objects is = n! / (p1!).(p2)!.....(pr!)
5) Combinations: Each of the different groups or selections which can be formed by taking some or all of a number of objects is called a "combination".
6) Number of Combinations: The number of all combinations of n things, taken r at a time is:
nCr = n! / (r!)(n - r!) = n(n - 1)(n - 2) ... to r factors / r!

J) Chain Rule

1) Direct Proportion: Two quantities are said to be directly proportional, if on the increase (or decrease) of the one, the other increases (or decreases) to the same extent.
2) Indirect Proportion: Two quantities are said to be indirectly proportional, if on the increase of the one, the other decreases to the same extent and vice-versa.

K) Numbers

1) (a + b)(a - b) = (a^2 - b^2)
2) (a + b)^2 = (a^2 + b^2 + 2ab)
3) (a - b)^2 = (a^2 + b^2 - 2ab)
4) (a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)
5) (a^3 + b^3) = (a + b)(a^2 - ab + b^2)
6) (a^3 - b^3) = (a - b)(a^2 + ab + b^2)
7) (a^3 + b^3 + c^3 - 3abc) = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ac)
8 ) When a + b + c = 0, then a^3 + b^3 + c^3 = 3abc.

Hope you will make a wise use of them.
Source : www.indiabix.com

Javascript Injection

Summary: Javascript injection is a nifty little technique that allows you to alter a sites contents without actually leaving the site. This can be very usefull when say, you need to spoof the server by editing some form options. Examples will be explained throughout.

Contents:
I. Injection Basics
II. Cookie Editing
III. Form Editing


I. Injection Basics

Javascript injections are run from the URL bar of the page you are visiting. To use them, you must first completly empty the URL from the URL bar. That means no http:// or whatever.

Javascript is run from the URL bar by using the javascript: protocol. In this tutorial I will only teach you the bare bones of using this, but if you are a Javascript guru, you can expand on this using plain old javascript.

The two commands covered in this tutorial are the alert(); and void(); commands. These are pretty much all you will need in most situations. For your first javascript, you will make a simple window appear, first go to any website and then type the following into your URL bar:
javascript:alert('Hello, World');
You should get a little dialog box that says "Hello, World". This will be altered later to have more practical uses.

You can also have more than one command run at the same time:
javascript:alert('Hello'); alert('World');
This would pop up a box that said 'Hello' and than another that says 'World'.

II. Cookie Editing

First off, check to see if the site you are visiting has set any cookies by using this script:
javascript:alert(document.cookie);
This will pop up any information stored in the sites cookies. To edit any information, we make use of the void(); command.
javascript:void(document.cookie="Field = myValue");
This command can either alter existing information or create entirely new values. Replace "Field" with either an existing field found using the alert(document.cookie); command, or insert your very own value. Then replace "myValue" with whatever you want the field to be. For example:
javascript:void(document.cookie="Authorized=yes");
Would either make the field "authorized" or edit it to say "yes"... now wheter or not this does anything of value depends on the site you are injecting it on.

It is also usefull to tack an alert(document.cookie); at the end of the same line to see what effect your altering had.

III. Form Editing

Sometimes, to edit values sent to a given website through a form, you can simply download that html and edit it slightly to allow you to submit what you want. However, sometimes the website checks to see if you actually submitted it from the website you were supposed to. To get around this, we can just edit the form straight from javascript. Note: The changes are only temporary, so it's no tuse trying to deface a site through javascript injection like this.

Every form on a given webpage (unless named otherwise) is stored in the forms[x] array... where "x" is the number, in order from top to bottom, of all the forms in a page. Note that the forms start at 0, so the first form on the page would actually be 0, and the second would be 1 and so on. Lets take this example:

Note:Since this is the first form on the page, it is forms[0]

Say this form was used to email, say vital server information to the admin of the website. You can't just download the script and edit it because the submit.php page looks for a referer. You can check to see what value a certain form element has by using this script:
javascript:alert(document.forms[0].to.value)
This is similar to the alert(document.cookie); discussed previously. In this case, It would pop up an alert that says "admin@website.com"

So here's how to Inject your email into it. You can use pretty much the same technique as the cookies editing shown earlier:
javascript:void(document.forms[0].to.value="email@nhacks.com")
This would change the email of the form to be "email@nhacks.com". Then you could use the alert(); script shown above to check your work. Or you can couple both of these commands on one line.





Source : http://nexodyne.com/archive/index.php?t-14736.html

Introduction to Automata Theory, Languages, and Computation 2nd Edition - John E. Hopcroft,Rajeev Motwani,Jeffrey D. Ullman

Introduction to Automata Theory, Languages, and Computation, 2/E
Publisher: Addison Wesley;
Author: John E. Hopcroft,Rajeev Motwani,Jeffrey D. Ullman
Edition: 2 edition (November 24, 2000)
Format: PDF
ISBN: 0201441241
EAN: 978-0201441246
No.ofPages: 521

Book Description:
It has been more than 20 years since this classic book on formal languages, automata theory, and computational complexity was first published. With this long-awaited revision, the authors continue to present the theory in a concise and straightforward manner, now with an eye out for the practical applications. They have revised this book to make it more accessible to today's students, including the addition of more material on writing proofs, more figures and pictures to convey ideas, side-boxes to highlight other interesting material, and a less formal writing style. Exercises at the end of each chapter, including some new, easier exercises, help readers confirm and enhance their understanding of the material. 

Table of Contents:
The purpose of this course is to acquaint the student with an overview of the theoretical foundations
of computer science from the perspective of formal languages.
• Classify machines by their power to recognize languages.
• Employ finite state machines to solve problems in computing.
• Explain deterministic and non-deterministic machines.
• Comprehend the hierarchy of problems arising in the computer sciences.

UNIT I :
Fundamentals : Strings, Alphabet, Language, Operations, Finite state machine, definitions, finite
automaton model, acceptance of strings, and languages, deterministic finite automaton and non
deterministic finite automaton, transition diagrams and Language recognizers.
UNIT II :
Finite Automata : NFA with Î transitions - Significance, acceptance of languages. Conversions and
Equivalence : Equivalence between NFA with and without Î transitions, NFA to DFA conversion,
minimisation of FSM, equivalence between two FSM’s, Finite Automata with output- Moore and Melay
machines.
UNIT III :
Regular Languages : Regular sets, regular expressions, identity rules, Constructing finite Automata for a
given regular expressions, Conversion of Finite Automata to Regular expressions. Pumping lemma of
regular sets, closure properties of regular sets (proofs not required).
UNIT IV :
Grammar Formalism : Regular grammars-right linear and left linear grammars, equivalence between
regular linear grammar and FA, inter conversion, Context free grammar, derivation trees, sentential forms.Right most and leftmost derivation of strings.
UNIT V :
Context Free Grammars : Ambiguity in context free grammars. Minimisation of Context Free Grammars.Chomsky normal form, Greiback normal form, Pumping Lemma for Context Free Languages. Enumeration of properties of CFL (proofs omitted).
UNIT VI :
Push Down Automata : Push down automata, definition, model, acceptance of CFL, Acceptance by final state and acceptance by empty state and its equivalence. Equivalence of CFL and PDA, interconversion.(Proofs not required). Introduction to DCFL and DPDA.
UNIT VII :
Turing Machine : Turing Machine, definition, model, design of TM, Computable functions, recursively
enumerable languages. Church’s hypothesis, counter machine, types of Turing machines (proofs not
required).
UNIT VIII
Computability Theory : Chomsky hierarchy of languages, linear bounded automata and context sensitive language, LR(0) grammar, decidability of, problems, Universal Turing Machine, undecidability of posts. Correspondence problem, Turing reducibility, Definition of P and NP problems, NP complete and NP hard problems.

 

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Mobile Communications 2nd Edition - Jochen Schiller

Publisher: Addison Wesley
Number Of Pages: 492
Publication Date: 2003-09-21
ISBN-10 / ASIN: 0321123816
ISBN-13 / EAN: 9780321123817

Product Description:

This book takes a non-mathematical, computer science approach to the introduce the field of mobile communications. A wide range of examples is combined with a strong pedagogy making the book perfect for self-study. This book explains the most current developments in mobile communications in both research and industry in a well-structured context with a detailed technical background. An up-to-date idea of the mobile/wireless communications field is provided throughout the text. People interested in learning about mobile communications from a computer scientist's perspective.

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