NTSE-2015
Friday, 28 August 2015
Standard Notations for Sets of Numbers
Standard Notations for Sets of Numbers
ℕ - Natural Number
ℕk - Natural Numbers less than or equal to k
I - Integers
I0 - Integers excluding
0
ℤ - Integers
ℤ+ - Positive Integers
ℤ- -
Negative Integers
ℚ - Rational Numbers
ℚ+ - Positive Rational Numbers
ℚ0 - Non-zero Rational Numbers
ℝ - Real Numbers
ℝ+ - Positive Real Numbers
ℝ0 - Non-zero Real Numbers
ℂ - Complex Numbers
ℂ0 - Non-zero Complex Numbers
W - Whole Numbers
Mathematics GK
A young Indian
mathematician, Nikhil Srivastava, has been named a joint winner of the
prestigious George Polya Prize for finding proof of a riddle that had eluded
mathematicians for more than half a century.
Srivastava of Microsoft Research India and Adam W. Marcus and
Daniel A. Spielman from Yale University will be presented the 2014 George
PA³lya Prize at the July 7-11annual meeting of the Society for Industrial and
Applied Mathematics (SIAM), in Chicago.
The trio had announced the proof of what is known as the
Kadison-Singer conjecture, first proposed by Richard Kadison and Isadore Singer
in 1959, pertaining to the mathematical foundations of quantum mechanics about
a year ago.
Measurements-Weights-Linear-Square-Land Measurements
MEASUREMENTS
WEIGHTS
10
Milligrams = 1
Centigram
10
Centigrams = 1 Decigram
10
Decigrams = 1 Gram
10
Grams = 1
Decagram
10
Decagrams = 1 Hectogram
10
Hectograms = 1 Kilogram
100
Kilograms = 1 Quintal
10
Quintals = 1 Ton
1000
Kilograms = 1 Ton
LINEAR
MEASURE
12
Inches = 1
Foot
3
Feet = 1
Yard
22
Yards = 1 Chain
10
Chains = 1 Furlong
10
Furlongs = 1 Mile
SQUARE
MEASURE
144
Sq. inches = 1 Sq. Foot
9
Sq. Feet = 1 Sq.
Yard
1210
Sq. Yards = 1 Rood
4
Roods = 1 Acre
640
Acres = 1 Sq.
Mile
Land Measurement
3
ft 3 inch = 1 sq Metre
10,000
sq Metre = 1 Hectare
107,639
sq ft = 1 Hectare
43,600
sq ft = 1 Acre
2.46878
acre = 1 Hectare
In Uttar Pradesh:
1
Bigha = 20 Bishwa = 60 Decimal = 2428.80 m2 (20 x 125 m2)
1
Biswa = 125 m2 or 154.32 yd2
1
Bigha = 0.25 Hectare (or 2500 m2 or 301 yd2
In Bihar:
1
Katha = 720 sq ft or 1/20 of a Bigha
1
decimal = 435.6 sq ft
1
Kattah = 1600000 sq ft
1
Kattah = 8000 sq meter
20
Kattah = 1 Bigha
3
Bighas = 1 Acre approx. (4800 square yards)
In Nepal:
1
Bigha = 20 Kattha (about 6,772.63 m² or 72900 sq. ft.)
1
Kattha = 20 Dhur (about 338.63 m² or 3,645 sq. ft.)
1
Dhur = 16.93 m² or 182.25 sq. ft.
1
Kanwa = 1/16 Dhur
1
Kanaee = 1/16 Kanwa
1
Bigha = 13.31 Ropani
1
Ropani = 16 aana (about 508.72 m² or 5476 sq. ft.)
1
Aana = 4 paisa (about 31.80 m² or 342.25 sq. ft.)
1
Paisa = 4 daam (7.95 m²)
MESSAGES by Famous MATHEMATICIANS
MESSAGES on MATHEMATICS
1.
A mathematician knows how
to solve a problem he cannot solve it. – Milne
2.
Analysis and natural
philosophy owe their most important discoveries to this fruitful means which is
called induction. Newton was indebted to it for his theorem of the Binomial and
the Principle of universal gravity. –
Laplace
3.
Everybody of discovery is
mathematical in form because there is no other guidance we can have. – Darwin
4.
Geometry as a logical
system is a means and even the most powerful means to make children feel the
strength of the human spirit that is of their own spirit. – H Freudenthal
5.
In these days of conflict
between ancient and modern studies, there must surely be something to be said
for a study which did not begin with Pythagoras and will not end with Einstein,
but is the oldest and the youngest. – G
H Hardy
6.
Let the relation of
knowledge to real life be very visible to your pupils and let them understand
how by knowledge the world could be transformed. – Bertrand Russell
7.
Mathematics is a most
exact science and its conclusions are capable of absolute proofs. – C P Steinmetz
8.
Mathematics is both the
queen and the hand maiden of all sciences. – E T Bell
9.
Mathematics is the art of
saying many things in many different ways. – Maxwell
10. Mathematics is the indispensable instrument of all physical
research. – Berthelot
11. Mathematics is the queen of Sciences and Arithmetic is the queen
of Mathematics. – Gauss
12.
Statistics may be
rightly called the science of averages and their estimates. – A L Bowley & A L Boddington
13. There are few things which we know which are not capable of
mathematical reasoning and when these cannot, it is a sign that our knowledge
of them is very small and confused. – Arthenbot
14. Where a mathematical reasoning can be had, it is as great a
folly to make use of any other, as to grope for a thing in the dark, when you
have a candle in your hand. – John
Arbuthnot
15. With the calculus as a key, mathematics can be successfully
applied to the explanation of the course of nature. – Whitehead
16. We will all laugh at gilded butterfly. – Shakespeare
Famous Mathematicians
Famous Mathematicians
1.
George Cantor (1845-1918)
2.
G W Leibnitz (1646-1716)
3.
Arya Bhatt (476-550)
4.
G Plano (1858-1932)
5.
W R Hamilton (1805-1865)
6.
Jacob Bernoulli
(1654-1705)
7.
Blasé Pascal (1623-1662)
8.
Rene Descartes (1596-1650)
9.
Apollonius (262 B C -190 B
C)
10. Leonhard Euler (1707-1783)
11. Sir Isaac Newton (1642-1727)
12. Karl Pearson (1857-1936)
13. Kolmogrov (1903-1987)
14. George Boole (1815-1864)
Analysis of IIT-JEE 2015
Analysis of IIT-JEE 2015
According
to the latest pattern, JEE is conducted for the admission to Undergraduate
Engineering Programs at NITs, IIITs and other CFTIs. This is a two phase exam,
the first phase JEE (Main) is designed almost on previous AIEEE Pattern. The second phase conducts JEE (Advanced),
which is based on the eligibility criteria set by the IITs. This phase is meant
for the serious candidates who aspire to enter the most sought after premier
institutions like IITs. JEE (Advanced) is conducted in same lines with that of
IIT-JEE.
The trend of questions in papers of JEE (Main & Advanced)-2015
JEE
(Main)
·
Objective
(Single Correct Answer Type)
·
Reasoning
(Assertion-Reason Type ) questions with equal weightage to PCM
JEE
(Advanced): Paper-1
·
Single
Digit Integer (One
digit numeric answer)
·
One or
More than One Correct Option
(More than one correct answer)
·
Match List
Type (2 columns
listing different entries to be matched with each other and to choose only one
correct answer from the choices)
JEE
(Advanced): Paper-2
·
Single
Digit Integer (One
digit numeric answer)
·
One or
More than One Correct Option
(More than one correct answer)
·
Paragraph
Type (2 to 3 MCQs
based on one passage)
Candidates Registered, Appeared & Qualified in JEE (Main)-2015
As
per Joint Apex Board of CBSE- the conducting body of JEE (Main), around 13 lakh
students had registered for the JEE (Main) 2015 which held in April 4 in
offline mode and on April 10 & April 11 in online mode. Last year, the
corresponding figure was 13.56 lakh as compared to around 14.62 lakh in 2013.
·
Total
candidates Registered for Paper: 12,92,711
·
Candidates
Appeared for Offline Exam: 11,05,021
·
Candidates
Appeared for Online Exam: 1,87,690
·
Candidates
Qualified for JEE (Advanced): 1,52,401 (Out of which top 1.5 lakh students were
eligible for JEE (Advanced).
The results of the JEE (Main)
2015 were declared on 27 April 2015, Monday conducted by the Central Board of
Secondary Education (CBSE) on their official website (www.jeemain.nic.in). Question
paper of JEE (Main) 2015 was of total 360 marks.
Category-wise JEE (Main) 2015 Cut-off marks for appearing in JEE
(Advanced)-2015
|
Category
|
Cut-Off Marks
|
|
GEN
|
105
|
|
OBC-NCL
|
70
|
|
SC
|
50
|
|
ST
|
44
|
Category-wise distribution of “top” candidates
|
Category
|
% of Total No. of Candidates
|
No. of Top Candidates
|
Total
|
|
GEN
|
50.5
|
73,478
|
75,750
|
|
GEN-PwD
|
|
2,272
|
|
|
OBC-NCL
|
27
|
39,285
|
40,500
|
|
OBC-NCL-PwD
|
|
1,215
|
|
|
SC
|
15
|
21,825
|
22,500
|
|
SC-PwD
|
|
675
|
|
|
ST
|
7.5
|
10,912
|
11,250
|
|
ST-PwD
|
|
338
|
Within each of these four major categories, 3 % horizontal reservation is available for PwD candidates.
JEE (Main) 2015 All
India Ranking (AIR)
The JEE (Main) All India Ranking
(AIR) were declared on 1st week of July, 2015 by Central Board of
Secondary Education on JEE (Main) official website: www.jeemain.nic.in. The JEE
(Main) All India Ranks will be used by central institutes i.e. NITs, IIITs and
other prestigious institutes in India. The JEE (Main) All India Ranking 2015
were declared by combining 55% weightage of JEE (Main) Scores and 45% weightage
of Class XII result in General Category and 60% weightage of JEE (Main) Scores
and 40% weightage of Class XII result in all other categories.
Revised Qualifying
Marks for JEE (Advanced) 2015
The total marks obtained in
mathematics will be the marks awarded for mathematics in Paper-1 and Paper-2.
The total marks obtained in physics and chemistry will also be calculated in
the same way. The aggregate marks will be calculated as the sum of the marks
obtained in mathematics, physics and chemistry. Candidates have to satisfy the
subject-wise as well as the aggregate qualifying marks to be included in a rank
list.
Maximum
aggregate marks: 264 (Paper-1) + 240 (Paper-2) = 504
Maximum
marks in Physics: 88 (Paper-1) + 80 (Paper-2) = 168
Maximum
marks in Chemistry: 88 (Paper-1) + 80 (Paper-2) = 168
Maximum
marks in Mathematics: 88 (Paper-1) + 80 (Paper-2) = 168
Minimum Percentage of
Marks for Inclusion in a Rank List in JEE (Advanced)-2015
Rank List Minimum % of marks in each subject Minimum
% of aggregate marks
Common 7.00 24.500
OBC-NCL 6.30 22.050
SC 3.50
12.250
ST 3.50
12.250
OPEN-PwD 3.50 12.250
OBC-NCL-PwD 3.50 12.250
SC-PwD 3.50 12.250
ST-PwD 3.50 12.250
Preparatory Course 1.75 06.125
Candidates Qualified in JEE (Advanced)-2015
The results for the Joint Entrance Examination (JEE) Advanced
2015 were declared on 18 June 2015, Thursday on http://jeeadv.iitb.ac.in/ . The JEE (Advanced)
Exam was held on 24 May 2015, Sunday.
According
to the statistics released by IIT-Bombay, around
1.24 lakh candidates registered for the JEE (Advanced) 2015 and 26456 candidates qualified out of approx 1.17 lakh
(appeared) for admission to ISM, Dhanbad and all IITs. From the 26,456
qualified candidates, 16,230 candidates are from the common merit list, 5911
candidates are on the OBC-NCL merit list, 2570 candidates are on the SC merit
list and 1745 candidates are on the ST merit list.
In all, the 16
IITs, the Indian Institute of Technology Palakkad, the Indian Institute of
Technology Tirupati and the Indian School of Mines (ISM) Dhanbad have 10006 seats, which have been allocated
as 4900 for the general category, 2619 for other backward castes
category, 1454 for scheduled caste
candidates and 733 for candidates
from the scheduled tribes.
Number of Registered, Appeared and Qualified candidates in
JEE (Advanced)-2015
|
Category
|
No. of Registered
Candidates
|
Category Total
|
Appeared for both Paper-1 & 2
|
Category Total
|
No. of Qualified
Candidates
|
Category Total
|
|
GEN
|
47,832
|
48,501
|
46,585
|
47,186
|
16,045
|
16,230
|
|
GEN-PwD
|
669
|
601
|
185
|
|||
|
OBC-NCL
|
46,245
|
46,800
|
43,075
|
43,570
|
5,809
|
5,911
|
|
OBC-NCL-PwD
|
555
|
495
|
102
|
|||
|
SC
|
20,576
|
20,667
|
18,670
|
18,746
|
2,554
|
2,570
|
|
SC-PwD
|
91
|
76
|
16
|
|||
|
ST
|
8,734
|
8,773
|
7,704
|
7,736
|
1,742
|
1,745
|
|
ST-PwD
|
39
|
32
|
3
|
|||
|
Total
|
124,741
|
|
117,238
|
|
26,456
|
|
Gender-wise Result analysis in JEE (Advanced)-2015
|
Gender
|
Registered
|
Appeared
|
Qualified
|
|
Male
|
102,385
|
96,895
|
23,407
|
|
Female
|
22,355
|
20,342
|
3,049
|
|
Third
|
1
|
1
|
0
|
|
|
124,741
|
117,238
|
26,456
|
Zone-wise distribution of top candidates
|
Zone
|
Topper
|
Number
of candidates within the
|
All
qualified
|
||
|
Top
10
|
Top
100
|
Top
500
|
|||
|
IIT Bombay
|
Bharat Khandelwal
(AIR 5)
|
1
|
34
|
151
|
6838
|
|
IIT Delhi
|
Janak Agrawal
(AIR 2)
|
2
|
12
|
70
|
4511
|
|
IIT Guwahati
|
Ayush Ranjan (AIR
94)
|
0
|
1
|
10
|
1445
|
|
IIT Kanpur
|
Satvat Jagwani
(AIR 1)
|
1
|
5
|
43
|
3085
|
|
IIT Kharagpur
|
Rohit Kumar Jena
(AIR 57)
|
0
|
3
|
40
|
3115
|
|
IIT Madras
|
Kamana Nagendra
Reddy (AIR 4)
|
5
|
28
|
127
|
4928
|
|
IIT Roorkee
|
Himanshu Gupta
(AIR 7)
|
1
|
17
|
59
|
2534
|
Total No. of Seats at various IITs
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