# Results

The important thing in any kind of Age Problem, is to decide which age – present or past or future – to be taken as ‘x’!   Let us make a simple rule for ourselves – the ‘x’ should be the present age always.    In most cases, taking the present age as ‘x’, i.e., the base
Permutation implies arrangement where order of things is important and includes word formation, number formation, circular permutation etc.  Combination means selection where order is not important and it involves selection of team, forming geometrical figures, distribution of things etc. Factorial = Factorial are defined for natural numbers, not for negative numbers. n! = n.(n-1).(n-2).........3.2.1 For example: 1) 4! = 4.3.2.1 = 24
Today, we are going to discuss a very interesting topic Simple and Compound interest. It deals with the money matters. By the end of it, we shall be familiar with the basic formulas used for the calculation of simple and compound interest and their practical applications. Various terms to be used along with their general representation are: Interest It is money paid by the borrower for using
Concepts 1) There is a relationship between speed, distance and time: Speed = Distance / Time OR Distance = Speed* Time 2) Average Speed = 2xy / x+y where x km/hr is a speed for certain distance and y km/hr is a speed at for same distance covered. **** Remember that average speed is not just an average of two speeds i.e. x+y/2. It is equal to 2xy / x+y 3)
Trick One simple technique is using days in denominator while solving questions. For example, A can do a job in 3 days and B can do the same job in 6 days. In how much time they can do the job together. Solution - 1/3 + 1/6 = 1/2, hence 2 days is the answer. Examiner can set the question in opposite way and can ask you how much
Noun Rule1 There are some nouns which are uncountable like thoughts, scenery, poetry, luggage, work etc. Such nouns are always followed by singular verbs. Example:  The scenery of forts in Rajasthan are very beautiful.
Pronoun Pronouns are the words which are used by replacing main noun so that we can avoid the repetition of that noun again and again.  Rule1 When in any sentence the subject of the verb is receiver for an action and the action is said to be reflected then such verbs are called reflective verb like enjoy,avail,adapt,pride etc.Pronouns used for such reflection are herself, himself, themselves, ourselves etc. Example:
1 Squares of numbers from 51 to 59: Where A is the unit digit of the number and A2 should be written as a two digit number.   2 Square of Numbers having unit digit 5
The term percent means “for every hundred”. It can best be defined as- “A fraction whose denominator is 100 is called a percentage, and the numerator of the fraction is called the rate percent.   E.g. A man saves 10% of his monthly income means ‘A man saves Rs 10 out of every Rs 100 of his income. Some of the important prime fractions represented in percentage terms are given below-
Natural Numbers : Numbers which are used for counting the objects are called natural numbers. They are denoted by N. N = { 1, 2, 3………………..} All positive integers are natural numbers. Whole numbers :-
Factor :  A number is said to be a factor of another number it divides the other number exactly. E.g. 2 and 3 are factors of 6. Common Factor : A common Factor of two or more numbers is a number that divides each of them
If a number ‘x’ is multiplied by itself n times, the product is called power of x and is written as . In , x is called the base and n is called the index of the power. To find the Number at Unit Place
Adjectives Rule 11: Adjectives of Same Degree If two Adjectives are joined by ‘and’, they must be in the same degrees. E. g., (A) Good and wise (B) Better and wiser
Adjectives An Adjective is a word which qualifies a Noun or Pronoun Rule 1: Order of Definite Numeral Adjectives If in a sentence all the three types of Definite Numeral adjectives are used then their order should be: Ordinal (first, second, third etc.) + Cardinal (one, two, three etc.) + Multiplicative (single, double, triple etc.).
Adjectives Rule 11: Adjectives of Same Degree If two Adjectives are joined by ‘and’, they must be in the same degrees. E. g., (A) Good and wise (B) Better and wiser (C) Best and wisest
Some Typical Adjectives         (1) Later and Latter Later is the comparative degree of late and it denotes time. Latter is an antonym of former and it denotes position Amit came later than Sumit.
Adverbs Position of Adverbs It is very important to use Adverbs at proper position. Wrong use of Adverbs may change the meaning of the sentence. E. g., Only he can read. He can only read. The meaning
Some Typical Adverbs (1) Too Too = More than enough ‘Too’ has negative sense or undesirability; so ‘too’ should not be used in place of ‘very’ or ‘much’. E. g., I am too happy to hear of your success. (Incorrect)
Inversion Inversion means putting the verb before the subject. E.g., Hardly does he come to me. Rule 1: Inversion is used in the sentences starting with “Seldom, never, hardly, rarely, scarcely”. E.g., Seldom have I seen such a beautiful sight. (Correct)
CONJUNCTIONS Conjunction is a word whose only work is to join Uses of Conjunctions Rule 1:Correlative Conjunctionsare those conjunctions which are used only in pairs.               Either………………………………..or
CONJUNCTIONS Rule 6: The reason is / The reason why Sentences beginning with ‘The reason is / The reason why’ are connected by conjunction ‘that’ and not by conjunction ‘because’, ‘due to’ or‘owing to’ e.g., The reason of his failure is that he did not study seriously. The reason why he failed is that he did not study seriously. Rule 7: As if / As though As if/ As though shows expressions having imagination
CONJUNCTIONS CONDITIONAL SENTENCES (= Functional Conjunctions /Types of Conjunctions) (1) Conjunctions of Comparison As……………as, not so/ as…………….as,(with positive degree) than, to (with comparative degree) This book is as good as that.        This book is not so/ as good as that. This book is better than that.      I am senior to him. (2) Conjunctions of Concession: Though, Although, Even if, For all,
PREPOSITIONS Pre + Position, i.e., the word or phrase which is placed before a Noun or Pronoun. Rule: Generally, prepositions are used before their objects. E.g., The book is on the table.            My daughter
Some Typical Prepositions (1) IN/INTO In = Position of rest Into = Position of motion The table is in the room.                      The ball fell into the well.
TIME AND TENSE Time is an integral part of our life while Tense representsGrammatical Form of the Verb. The Uses of Tenses (I) SIMPLE PRESENT TENSE (1) To represent Universal truth, Principle, Permanent activityor Nature.
ARTICLES Article is a form of Determiner. (Determines Noun) Kinds of Articles : 1.      Indefinite Article (A and An) 2.
Uses of Definite Article (The) Rule 1: With Definite Person(s) or Thing(s) (For that noun which is used earlier or is specific in nature) e.g.,     This is the chapter I read yesterday.             This is the car by which I go to office. Rule 2:Before those Proper
Omission of Articles Rule 1:Before Plural Noun (Generally article is not used with plural noun). e.g.,     He loves books.                                   Cars were towed. Note: But when plural noun denotes some defined or special objects/ things, article ‘The’ should be used. The cows of Haryana give much milk. The litchis of Muzaffarpur
NOUN (Part 1) “Noun is a naming word.” OR “A noun is a word used as the name of a person, place or thing.” e.g., Katrina, Marker, Jaipur, Sweetness, Copper, Cow etc. Rule 1: Nouns always Plural Following Nouns are always used in Plural Number; so plural verbs are used with them. Removing –s from these words and using them as Singular Noun is wrong. Alms, thanks, species, scissors, trousers, pants, tongs, gallows, goggles, spectacles,
NOUN (Part 2) Rule 5: Noun with Numeral Adjective Some Nouns followed by Definite Numeral Adjective are always used in plural. E.g. Pair, dozen, score, gross, hundred, thousand, million, billion etc. Six dozen pencil (correct)                             Six dozens pencils (incorrect) But if Numeral Adjective denotes Infinite Number, then the above nouns are used in Plural Number e.g., Dozens of oranges; millions of dollars; many pairs of shoes etc. Scores of houses have been gutted in
Pronoun Rule 1: In a sentence, Nominative Pronoun is used as a Subject of a Verb. I, We, You, He, She, It and They are Nominative Pronouns. E. g., I am working hard. They go to Mumbai.
Relative Pronoun Rule 1: Who ‘Who’ is used in Nominative Case for Person(s) only in both the Singular and plural Numbers. ‘Who’ is not used for animals and inanimate objects. But for ‘people’ and ‘those’, who must be used.
SYNTAX (=CONCORD or AGREEMENT)   “Agreement in Person, Number, Gender or Tense between Two or more parts of a Sentence” is called Syntax.   Subject-Verb Agreement
Rule 8: When Plural Noun represents Definite Quantity, Number, Price or Distance, the verb used is Singular in its form. e.g.,     Ten lakh rupees is a large sum. Six quintals is a heavy load for a camel. Rule 9: When the “Title of a Book” or “Name of a Country” or Name of an Organisation”
SYNTAX (=CONCORD or AGREEMENT)   Rule 16: Numerical Expressions/ Quantitative Expressions and the Verb (a)   A Number of is used for indefinite number ---
VOICE (Active & Passive Voice) Conditions which do not have passive voice (i) Those sentences which have verbs in Intransitive form (ii) Sentences of Future Continuous Tense (iii) Sentences of Perfect Continuous Tenses Important Rules of Conversion of Active Voice to Passive Voice Rule (1):Interchange of Position of Subject and Object Active: Ram loves Shyam.                            Passive: Shyam is loved by Ram .               Note: While interchanging subject
Rule (7):If Imperative Sentence denotes order, command, then in the passive voice the sentence begins with Let and ‘be’ is used before V3. Active: Shut the door                                     Passive: Let the door be shut                     Rule (8):If Imperative sentence denotes Request or Advice; then in the sentence in the Passive Voice ‘should be’ is used before V3 and sentence does not begin with ‘Let’. Active: Help the poor.                    Passive: The poor should be helped. Active: Feed the child, please.   Passive: The child should be
Time, Speed & Distance Important Formula Units conversion (1) units of
Boats and streams Let us suppose (A) Speed of boat in still water = x kmph (B) Speed of stream = y kmph Then :
Pipe and cistern concept Pipes and cisterns are almost the same as  time and work problems. There are two kinds of pipes. 1 Inlet pipe- it fills the tank. If a pipe fills a tank in x hours. Then in 1 hours, it will fill
Problem on trains 1 Suppose there are two trains A and B having length a metre and running at a speed of x m/sec and y m/sec respectively. Here two cases arise-
GEOMETRY To understand geometry there is three conceptual concept : Point, line and plane. Pointy: A circle which do not have radius is called point. But this type of circle is not possible. Therefore point does not have any ideal definition.           In other
POLYGON Definition : A closed figure formed by three or more than side is called polygon. Important facts about polygon: 1 sum of all interior angle of ‘n’ sided polygon
TRIANGLE Definition : A closed figure formed by three sides. Ø
Logical Venn Diagram Type-1 Relationship among different objects/things In this type of question an object is represented by the venn digram, and you are asked to show the relationship among the objects through the venn-diagrams. Types of Venn diagrams representing
Primary Auxiliary Verbs : Those verbs which can either be used independently or together with the main verb in the sentence are called Primary Auxiliaries. (A) Be – is /am/are/was/were (be, been, being)
Bare Infinitives (Infinitive without ‘to’) Rule 10 : Bare infinitive is used after let, bid, hear, watch, behold, see, feel, make etc.
Profit and loss Cost price : The cost at which an article is purchased is called its cost price (C.P.) Selling price : The price at which an article is sold is called its selling price (S.P.) Profit /Gain
Syllogism (Notes New) Venn Diagrams Method Step I : Draw standard representations for the statements separately. Note :
Logical Reasoning Strong & Weak Arguments (Notes New) The forcefulness of an argument (strong argument or weak argument) can be determined in four steps. In the first step, you have to make preliminary screening of the given
Mixture & Allegation (Notes) New Allegation is the rule that enables us :- (i) To find the mean or average value of mixture when the prices of two or more ingredients which may be mixed together and the proportion in which they are mixed are given (= Allegation Medial); and
Logical Reasoning Statement & Courses of Action (Notes New) * To solve questions on ‘courses of action’ first of all decide whether it is a ‘problem solution’ or ‘fact-follow up action’ type * If it is ‘Problem solution’ then accept the suggested course of action,
Alphabet Test (Notes New) 1        2        3        4        5        6        7        8        9        10      11      12      13      A       B       C       D
Alphabet Test (Notes New) 1        2        3        4        5        6        7        8        9        10      11      12      13      A       B       C       D
Dice (Notes New) Cube : Closed figure which is composed of 6 square surface is called cube. Cuboid : Closed figure which is composed of 6 rectangular surface is called cuboid. Dice : When some numbers or points are printed
Coding- Decoding (Notes New) In this type of questions, an expression is given in coded form. You have to answer the given question by decoding the code of the expression. Coding : Something written in special form in codes is called coding.
Clock (Notes) New Some Important facts * Angle made by an hour hand of a clock in 1 hour is 30°. * Angle Made by min hand of a clock in 5 minutes = 30°
Average Related to speed (Notes-2) Theorem (1) : If a person travels a distance of a speed of x km/hr and the same distance at a speed of y km/hr, then the average speed during the whole journey is given by
Height and Distance Angles of Elevation  and Depression : Suppose we are viewing an object. The line of sight or the line of vision is a straight line from our eye to the object we are viewing. * if the
Trigonometry (Note-1) Pythogoras theorem : In a right- angled triangle, the square of hypotenuse is sum of the squares of the base and the perpendicular.