Wednesday 30 September 2015
Tuesday 29 September 2015
Monday 28 September 2015
Sunday 27 September 2015
Friday 25 September 2015
Ranking or Ordering
Important
TRICKS:
1. Total number = Rank from TOP + Rank from BOTTOM -1.
2. Total number = Rank from LEFT + Rank from RIGHT -1.
3. For Interchange of
position: FOCUS on that position for which rank is given from both the end and
then use the concept above ( 1 or 2) Trick.
4. Position of 1st
is given from 1st end and position of 2nd is given from 2nd
end given, then Answer will be : either
Total = L+R+n or
Total = L+R-n-2
Note: when both are available
in answer, then choose: answer cannot be determined.
SOLVED EXAMPLE:
Model1: To find the total number of
person in the row, when position of person if given from any one end.
Q1. Babul rank 9th
from TOP and 38th from bottom in a class. What is the total number
of students?
Ans: Total number = Rank from TOP + Rank from BOTTOM -1.
Total number = 9 +38 -1 = 46
Model2: To find out the position of a
person in the row from Left side or Right side:
Q2. There are 12 Person in a row. The position of Ram is 7th from
Left. What is his position from the right end?
Ans:
Total number = Rank from Left + Rank from Right -1.
12 = 7 + Rank from Right -1
Rank from Right= 12+1-7
= 6
Q3.
In a class of 36 students, if Ashish ranks
from the TOP is 12 and Vaibhav ranks 3 place above him. What is Vaibhav rank
from Top?
Ans: Vaibhav rank from TOP = (12-3) = 9
Vaibhav rank from BOTTOM = X (let)
Total
number = Rank from TOP + Rank from BOTTOM -1.
Rank from BOTTOM= Total number - Rank from
TOP + 1.
= 36 -9 +1 =
37-9 = 28
Rank from BOTTOM = 28
Model3: For Interchange of position
TRICK: FOCUS on that position for which rank is
given from both the end
Q4.
In a row of girls, Dipa is 7th from
Left and Madhu is 12th from right. If they interchange their
position, Dipa becomes 22nd from Left , what is the total number of
girls in the row?
Ans: FOCUS on position of Dipa
After interchange Dipa becomes 22nd
from Left.( This position is same as earlier position of Madhu .ie. Madhu is 12th
from right)
Hence, for Dipa:
Position from Left = 22 (after
interchange)
Position from right = 12 (Madhu’s
original position)
Now,
Total
number = Rank from Left + Rank from Right -1.
= 22+12-1 = 33.
Model4: Position of 1st is given from 1st
end and position of 2nd is given from 2nd end:
Q5.
Prakash
is 14th from left end and Qureshi is 7th from right end
in a row of boys. What is the total number of boys in the row, if there
are 4 boys between them.
Ans: either Total = L+R+n or
Total = L+R-n-2
Total = L+R+n = 14+7+4
= 25
Or, Total = L+R-n-2 = 14+7-4-2 = 15
Hence, Answer is 25 or 15 [choose that
option which given in question. If both are there in option then, choose:
cannot be determined option.]
Model5: Finding option by elimination of Wrong
option:
Q6.Ritesh is taller than Anup but shorter
than Seema. Kapil is taller than Pooja but shorter than Anup.Deepak is taller
than kapil but shorter than Seema.Who among them is tallest?
Ans: Traditional Method: Time consuming
S>R>A>k>P and D>K and
D< S, hence K<D<S: Seema is
tallest
Shortcut
Method: Eliminate the wrong option
( here, eliminate the 5 persons who
cannot be tallest.)
Ritesh is taller than Anup ( Anup X)
Ritesh
is shorter than Seema(Ritesh X).
Kapil is taller than Pooja (Pooja X)
Kapil is shorter than Anup.(kapil X)
Deepak is taller than kapil . .(kapil X)
Deepak is shorter than Seema.( Deepak X)
Hence, Seema is tallest ( as all other options are
now eliminated).
Model6: Ordering: Statement and meaning :
a) A is neither taller nor equal to B : A< B
b) A is neither shorter nor equal to B: A> B
c) A is neither shorter nor taller than B: A =B
d) A is not taller than B: A< =B
e) A is not shorter than B: A> =B
f) A is as tall as B : A<B
g) A is not as tall as B: A<B
h) A is only shorter than B : A< B
Model7: Statement containing”ONLY” and its meaning:
a) A is shorter than B: A<B
b) A is shorter than ONLY B: A<B and it also mean B is tallest and A is 2nd tallest in group
c) A is taller than B: A>B
d) A is taller than ONLY B: A>B and it also mean, B is shortest and A is 2nd shortest in group.
Thursday 24 September 2015
Tuesday 22 September 2015
Monday 21 September 2015
Permutation:
“Permutation means ARRANGEMENT”
Each of the different arrangement which can be made by taking
some or all of a number or things is called a Permutation.
Note: The word arrangement is used, if the order of things is considered.
Mathematically, The number of ways of arranging ‘n’ distinct objects , taking ‘r’at a time .
It
is denoted by: nPr
nPr = n (n-1)(n-2)(n-3)……(n-r+1)
nPr = n! / (n-r)!
Solved Examples:
Q1. Find 75P2
= ?
Ans: nPr = 75P2
= 75!/ (75-2)! =75!/73!
= (75x 74x 73!) / 73! = 75x 74 =5550
Q2. Find
4P4 =?
Ans: nPr = 4P4 = 4!/ (4-4)! =
4!/0! = 4!/1 = 4! =4x 3x 2x 1 = 24.
Q3. How many different signals can be made
by using 5 flags from 8-flags of
different colours?
Ans. Number of ways taking 5 flags out of
8-flag: n = 8 and r = 5.
nPr = 8P5 = 8!/ (8-5)! = 8! /3!
= (8 x 7 x 6 x 5 x 4x 3!)/ 3! = 6720.
Q4.How many words can be made by using
the letters of the word “SIMPLETON” taken all at a time?
Ans. There
are ‘9’ different letters of the word “SIMPLETON”
n = n and r = 9.
Number of Permutations
taking all the letters at a time
nPr = 9P9 =
9!/ (9-9)! = 9!/0! = 9! = 362880.
Q5.How many words with
or without meaning can be formed by using all the letters of the word, PUNJAB’
Ans: Required number of
words = 6P6
nPr =6P6
= 6!/ (6-6)! = 6!/ 0! = 6!/1 = 6x 5 x 4 x 3 x 2 x1 =
720.
Q6. In how many ways
can the letters of the word ‘LOVELY’ be arranged?
Ans: The word ‘LOVELY’
contains 6 letters:
L = 2 times, O = 1 time,
V= 1 time, E = 1 time and Y= 1 time.
Required number of
words = 6!/ (2! X 1! X 1! X 1! X 1!)
(Please note, 2! In denominator, because
L is repeated 2 times )
Sunday 20 September 2015
Geometric Progression (G.P.)
Geometric Progression (G.P.):
A Geometric Progression
is a set of quantities arranged in such a way that the ratio (known as Common ratio, r ) between consecutive terms remains the same.
General form of GP: a, ar ar2 , ar3 ,ar4……..
Example: 3, 6,12, 24, 48…..……… is an Geometric progression
with common ratio 2.
n-th term of
Geometric Progression is given
by:
an = a r(n-1) .
Here, an is n-th
term, a is 1st term , n is total number of term, r is common ratio.
The sum (Sn) of
the first n terms
of an Geometric progression is
given by
When r >1
S
= a(rn – 1)/
(r – 1)
When 0<r <1
S
= a (1– rn) /
(1 – r)
For infinite number of terms (0<r <1)
S∞
= a/ (1 – r)
Solved Examples:
Q1.What will be the 11 th term of the geometric sequence 3,
6, 12, 24, ...
Ans: Sequence has a common ratio of 2. The values of a and r are:
a = 3 and r = 2.
a = 3 and r = 2.
a11 = 3x 2(11-1)
.
a11 =
3 × 210 = 3 × 1,024 = 3,072
Q2. What is the sum of the first eight terms of the geometric sequence
5, 15, 45,... ?
Ans: Sequence has a common ratio of 3.The values of a, r and n
are:
a = 5, r = 3 and n = 8 (for first 8 terms).
a = 5, r = 3 and n = 8 (for first 8 terms).
When r >1
S = a(rn – 1)/ (r – 1)
S= 5(38–1)/(3–1)
= 5(6561–1)/2 = 16400
Q3. The 1st term
of a GP is 5 and the 6th term is 160.What is the common ratio?
The first term a = 5 and the common ratio r
Use the formula for the n'th term: an = a r(n-1)
The sixth term = 160 = ar6 - 1= 160 ⇒ ar5 = 160
But a = 5 .
Use the formula for the n'th term: an = a r(n-1)
The sixth term = 160 = ar6 - 1= 160 ⇒ ar5 = 160
But a = 5 .
Therefore 5r5= 160 ⇒ r5= 160 ÷ 5 = 32
r= 2.
-----------------------------------------------------------------------------------------
Arithmetic Progression (A.P.)
Arithmetic
Progression: An arithmetic
progression is a sequence of numbers such that the difference of any two
successive members is a constant. The constant difference is called the Common Difference.
General form of AP: a, a+d, a+2d, a+3d……
Example:
3,5,7,9,11……… is an
arithmetic progression with common difference 2
7,5,3,1,-1,-3….. is an
arithmetic progression with common difference -2.
Arithmetic
series means
the sum of the elements of an arithmetic progression.
n-th term of Arithmetic Progression is given by:
an =
a +
(n - 1)d
Here, an is n-th term,a is 1st
term , n (e.g. n=1,2,3…) is
total number of term and d is common difference.
The sum (Sn) of the first n terms
of an arithmetic progression is given by :
Sn
= n/2 {2a + (n-1)d}
Solved
Examples:
Q1. Is the row 1,11,21,31... an arithmetic progression?
Ans: Yes, it is an arithmetic progression. Its first term is
1 and the common difference is 10.
Q2. Find the 12th term of the AP: 3,7,11,15……
Ans:
Q3. Find.Find the
sum of the first 10 numbers of this arithmetic series: 1, 11, 21, 31...
Ans: Sn = n/2 {2a + (n-1)d} = 10/2 { 2*1 +(10-1)*10} = 5*92 = 460.
Q4. The first five terms
of an arithmetic sequence are given: 4,3,2,1,0,… What is the next term in
the sequence?
Ans: In any arithmetic sequence,
each term is equal to the previous term plus the common difference, the common difference is −1.
Next term = 0+(-1) = -1.
Saturday 19 September 2015
Friday 18 September 2015
Thursday 17 September 2015
Wednesday 16 September 2015
Monday 14 September 2015
Friday 11 September 2015
Word list- 3 : News paper terminologies (Words compiled from “THE HINDU”)
|
Word
|
Meaning
|
|
Fanatics
|
Extreme enthusiasm
|
|
Atheists
|
Who do not
believe in existence God
|
|
Agnostic
|
Doubtful,
noncommittal
|
|
Rationalist
|
Positivist
|
|
Exodus
|
A departure of a large number of people.
|
|
Denizen
|
An inhabitant
|
|
Transcend
|
To move
upward and beyond something.
|
|
Ethnicity
|
Ethnic
character, background
|
 |
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