Post on 14-May-2017
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