SETS

General formulae:

n(A B) = n(A) + n(B) – n(A B)

n(A B C) = n(A) + n(B) + n(C) – n(A B)

– n(B C) – n(A C) + n(A B C)

1. Where used:

Permutation Combination

Arrangement Selection

Digits Choose

Letters of the alphabet Committee

Standing in a line / row Group

Seating in a Circle Geometry

2. Multiplication Principle

Dependent operations can be done in (m x n) ways.

3. Addition Principle

Independent operations can be done in (m + n)

ways.

Permutation: General Formulae:

4) nPr = (|n ) / (|n – r )

5) Number of permutations of n different things

taken all at a time = n!

6) Permutation of n things where P1 are alike of one

type, P2 are alike of second type, P3 are alike of

3rd type is given by (n!) / ( P1! P2! P3! )

7) Number of permutations of ‘n’ different things

taken ‘r’ at a time repetition allowed = n r

8) Arranging n people on a circular table = ( n – 1) !

9) Combination: General Formulae:

nCr = |n / |r |n – r

10) nCr = nCn – r

nCr + nCr-1 = n+1Cr

11) Selection of zero or more things out of ‘n’

different things taken some or all at a time

= nC0 + nC1 + nC2 + …….. + nCn = 2n

12) The total number of combinations of (p + q +

r+..) things of which ‘p’ are alike of one kind, ‘q’

alike of a second kind, ‘r’ alike of a third kind,

and so on, taking any number at a time is

= (p+ 1) (q +1) (r + 1)…… –1

13) Number of ways of dividing (m + n) different

things in two groups containing m and n things

is = m + nCn = (m + n)! / m! n!

PROBABILITY

1) P(E) = No. of Favorable outcomes

Total No. of outcomes

2) If A and B be two mutually exclusive events,

then P(A and B) = 0

3) Theorem of additions of probability:

If A and B are two mutually exclusive events,

then P(A or B) = P(A) + P(B)

If two events A and B are not mutually exclusive,

then P(A or B) = P(A) + P(B) - P(A and B)

4) Multiplication Theorem:

If A and B are two independent events, then the

probability of the occurrence of both is equal to

the product of their individual probabilities. i.e.

P(A and B) = P(A) x P(B)

5) NOTE: .AND. & .OR. Usage

P(A) .AND. P(B) = P(A) x P(B)

P(A) .OR. P(B) = P(A) + P(B)

Even functions: f(x) = f(-x)

Properties of even functions

a) The sum, difference, product and quotient

of an even function is also an even function

b) The graph of an even function is

symmetrical about the y – axis

Odd functions: f(x) = - f(-x)

Properties of odd functions

a) The sum and difference of an odd function is

an odd function.

b) The product and quotient of an odd function

is an even function

c) The graph of an odd function is symmetrical

about the origin and necessarily passes

through it.

BASIC

CONVERSIONS

A. 1 metre = 100 cm = 1000 mm

1 km = 1000 m = 5/8 miles

1 inch = 2.54 cm

B. 1 metre = 39.37 inches

1 mile = 1760 yd = 5280 ft

1 nautical mile (knot)

c. 100 kg = 1 quintal

10 quintal = 1 tonne = 1000 kg

1 kg = 2.2 pounds (approx)

d. 1 litre = 1000 cc

1 acre = 100 sq m

1 hectare = 10000 sq m

For further information

contact:

INFOSYS, WIPRO, SATYAM, CTS, TCS, HCL