# 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
CIRCLES   Area of the circle is A =  Circumference (perimeter) of the circle=  Sector of Circle
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)
Theorem Angle Sum Property of a Triangle The sum of the angles of a triangle is 1800.
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.
People who can use passive voice appropriately are considered to have a good level of English. Go through the article to learn about the correct usage of passive voice. Difference in Active and Passive voice
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
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-
Mirror Image *In mirror, left position changes to right and the right position changes to left. Mirror  image of Alphabets
Water image In case of water image, the upper position becomes the lower one and the lower position becomes the upper one. In this case, the left and right side remain the same. Water image of Alphabets
Embedded Figure The question asked from the embedded figure are of the following types :- (i) To find the answer figure in which the question figure is embedded. (ii) To find the answer figure that can be formed from the figure of the question figure. Important points :
Analogy   Analogy : When there is similarly between two or more objects, or they have certain relationship, then they are called analogous. E.g.- Paper : Book : : player : ? Captain Team Play ground
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
TRIANGLE Definition : A closed figure formed by three sides. Ø
CONGRUENCY Congruent Figures :- Congruent means equal in all respects or figures whose shape and size are both the same. For example:- Two circles of same radii are congruent, also two squares of the same sides are congruent. Congruent Triangle
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
Bare Infinitives (Infinitive without ‘to’) Rule 10 : Bare infinitive is used after let, bid, hear, watch, behold, see, feel, make etc.
Some relationships :- 1. Mother’s side – Maternal 2. Father’s side – Paternal 3. Parent’s brother – Uncle 4.  Parent’s sister – Aunt
B- Brackets O-Orders (powers and roots) D-Division M-Multiplication A-Addition S-Subtraction
News = Make four directions, namely north, East, West, and South. Based on their combination, there are four more directions, namely, North-East, North-West, South-East and South-West.
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