| CAT Preparation

Sunday, 18 March 2012

Pronouns

Pronouns are words that take the place of a noun. Pronouns are used instead of a noun. If we didn't have pronouns, we would have to repeat a lot of nouns!

Types of Pronouns

Personal Pronouns

I, me, mine
you, your, yours
she, her, hers,
it, its
we,us, our, ours
they, them, their,
theirs
myself
yourself

Interrogative Pronouns

who
whom
what
which
whose

Demonstrative Pronouns

this
that
these
those

Indefinite Pronouns

anybody
each
either
none
someone, one

Reflexive Pronouns

myself, yourself
himself, herself
ourselves, itself

Verb

Verb is a word that expresses action or otherwise helps to make a statement. Every sentence must have a verb.
Kinds of verbs

Action verbs which express physical or mental action. Example: He rode the horse to victory.
Linking verbs which make a statement by connecting the subject with a word that describes it or explains it. Example: He has been sick. NEXT

Adjective

Adjective is a word that modifies or describes a noun or pronoun.

Adjectives are invariable: They do not change their form depending on the gender or number of the noun.
Where a number of adjectives are used together, the order depends on the function of the adjective. The usual order is: Value/opinion, Size, Age/Temperature, Shape, Colour, Origin, Material. However, this is not strictly followed.

Examples

He is a lonely man (Quality)
This clock is German (Origin)
My coat is very old (Age)
This is a very long film (Size)
He wore a red shirt (Colour)
A square envelope (Shape)
Grammar is boring (Judgement)

Subject Verb Agreement

Basic Principle: Singular subjects need singular verbs; plural subjects need plural verbs. My brother is a nutritionist. My sisters are mathematicians.

The indefinite pronouns anyone, everyone, someone, no one, nobody are always singular and, therefore, require singular verbs.
Phrases such as together with, as well as, and along with are not the same as and. The phrase introduced by as well as or along with will modify the earlier word (mayor in this case), but it does not compound the subjects (as the word and would do).
The pronouns neither and either are singular and require singular verbs even though they seem to be referring, in a sense, to two things.
The conjunction or does not conjoin (as and does): when nor or or is used the subject closer to the verb determines the number of the verb. Whether the subject comes before or after the verb doesn't matter; the proximity determines the number.
The words there and here are never subjects.
Sometimes modifiers will get betwen a subject and its verb, but these modifiers must not confuse the agreement between the subject and its verb.
Words such as glasses, pants, pliers, and scissors are regarded as plural (and require plural verbs) unless they're preceded the phrase pair of (in which case the word pair becomes the subject).
Fractional expressions such as half of, a part of, a percentage of, a majority of are sometimes singular and sometimes plural, depending on the meaning. (The same is true, of course, when all, any, more, most and some act as subjects.)
If your sentence compounds a positive and a negative subject and one is plural, the other singular, the verb should agree with the positive subject.

Saturday, 25 February 2012

Probability

Probability is the likelihood or chance of an event occurring.

Some Concepts

When we toss a coin, then either a Head (H) or a Tail (T) appears.
A dice is a solid cube ,having 6 faces,marked 1, 2, 3, 4, 5, 6 respectively. When we throw a die, the outcome is the number that appears on its upper face.
A pack of cards has 52 cards. It has 13 cards of each suit, namely spades, clubs, hearts and diamonds. Cards of spades and clubs are balck cards. Cards of hearts and diamonds are red cards. There are four honours of each suit. These are Aces, Kings, Queens and Jacks. These are called Face cards.

The probability of a certain event occurring can be represented by P(A). The probability of a different event occurring can be written as P(B). Therefore, for two events A and B,

$\displaystyle P(A) + P(B) - P(A\cap B) = P(A\cup B)$

Mutually Exclusive Events

Events A and B are mutually exclusive if they have no events in common. If two events are mutually exclusive,

$\displaystyle P(A) + P(B) = P(A\cup B)$

Independent Events

Two events are independent if (and only if)

$\displaystyle P(A\cap B) = P(A)P(B)$

Conditional Probability

Conditional probability is the probability of an event occurring, given that another event has occurred.

$\displaystyle P(A|B)$ means the probability of A occurring, given that B has occurred.

For two events A and B,

$\displaystyle P(A\cap B) = P(A|B)P(B)$

$\displaystyle P(A\cap B) = P(B|A)P(A)$

Permutation & Combination

Combination & Permutation deals with arrangement of thing. If the order doesn't matter, then it is called Combination. If the order does matter, then it is a Permutation.

In other words, Permutation is an ordered Combination.

Permutation

${^nP_r} = {n! \over {(n-r)!}$

There are basically two types of permutation:

When repetition is allowed
No repetition

1. Permutations with Repetition
To choose r things from n when repetition is allowed, the permutations are:

n × n × ... (r times) = n^r

(Because there are n possibilities for the first choice, then there are n possibilites for the second choice, and so on.)

Combinations

Number of ways objects can be selected from a group.
${^nC_r} = {{^nP_r} \over r!}$ NEXT

Logarithms

$\therefore \log x = \log b^y$
$\log x = y \log b$
${{\log x} \over {\log b}} = y$
$\log_b x = y$
Therefore,
$\text{ if }x = b^y,\text{ then }y = \log_b (x)$

Logarithmic Identities

$\log_b(xy) = \log_b(x) + \log_b(y)$
$\log_b\!\left(\begin{matrix}\frac{x}{y}\end{matrix}\right) = \log_b(x) - \log_b(y)$
$\log_b(x^d) = d \log_b(x)$
$\log_b\!\left(\!\sqrt[y]{x}\right) = \begin{matrix}\frac{\log_b(x)}{y}\end{matrix}$
$x^{\log_b(y)} = y^{\log_b(x)}$
$c\log_b(x)+d\log_b(y) = \log_b(x^c y^d)$
$\log_b(1) = 0$
$\log_b(b) = 1$
$b^{\log_b(x)} = x$
$\log_b(b^x) = x$
$\log_a b = {\log_c b \over \log_c a}$ NEXT