Showing posts with label exam. Show all posts
Showing posts with label exam. Show all posts

24 May 2011

30,000 degree students of Vinoba Bhave University (VBU) would be using computerized answer sheets at their degree Part III examination


For the first time, nearly 30,000 degree students of Vinoba Bhave University (VBU) would be using computerized answer sheets at their degree Part III examination commencing from Tuesday.

Although college authorities fear that the students from rural background may not be able to fill the required information on the computerized first page of the answer books, the university has made elaborate arrangement to ensure that everything passes off peacefully.

The university has distributed dummy copies of the first page of the computerized answer sheet along with admit card to the students well in advance to avoid any last-minute trouble at the examination hall.
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Dravyansh Sharma of Delhi Public School, Meerut Road Ghaziabad with an overall aggregate of 98.6 per cent stood first in the overall merit list of students who appeared in class 12th examinations conducted by Central Board of Secondary Education (CBSE) from Uttar Pradesh and Uttarakhand

Dravyansh Sharma of Delhi Public School, Meerut Road Ghaziabad with an overall aggregate of 98.6 per cent stood first in the overall merit list of students who appeared in class 12th examinations conducted by Central Board of Secondary Education (CBSE) from Uttar Pradesh and Uttarakhand and the results for which were declared on Monday.

Sharma was closely followed in the second spot by Sachin Kumar of DAV Centenary Public School, Haridwar with an aggregate of 98 per cent followed by Kalyani Chaudhary of Army Public School, NOIDA, Gautam Buddh Nagar with 97.6 per cent.The fourth spot went to Sanchit Gangwar of Ben Hur Public School, Pilibhit with 97.6 percent while Paridhi Gupta of DPS Shastripuram , Agra with 97.4 percent bagged the fifth spot.
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The Chennai region has topped the rest of the country in pass percentage with 91.32% in the Central Board of Secondary Education's CBSE class 12 board exams this year 2011

Releasing the Class XII results on Monday, CBSE said 91.32% of students who took the exam in the region had passed, well above the national average of 81.71%.

The region, which scored over the national average on almost all parameters, however, saw a dip when compared to the performance in 2010. The pass percentage saw a dip from last year as did the individual pass percentages of boys and girls.

CBSE does not release the list of top rankers nor the top marks. In Chennai, at least five students notched aggregate scores of 487 and above. Among the high scorers were S Divya of Modern Senior Secondary School in Nanganallur with 98.4% and K A Sumana of PS Senior Secondary School in Mylapore with 98.2%.

School heads said that while there didn't seem to be much change in the number of centums in maths from last year, the number of centums in physics had gone down. Students had said earlier that physics exam was tough.
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26 April 2011

The government is replacing all engineering entrances, including Indian Institutes of Technology-Joint Entrance Examination (IIT-JEE) and All India Entrance Examination for Engineering (AIEEE), with one National Aptitude Test (NAT).

The reform is likely to benefit more than 10 lakh students every year, who at present have to take multiple examinations to get into engineering courses.
In a meeting, which was attending by the directors of IIT Delhi, Kanpur and other engineering institutions, the government broadly agreed on “one nation one examination” policy. Dr T Ramaswamy, secretary, department of science and technology was entrusted the job to re-look at the test methodology of selecting students and have a common system for admission. According to sources, NAT will be similar to the single medical entrance test that the Medical Council of India (MCI) will conduct from next year.
The state governments may not approve the idea of NAT and the IITs do not want the JEE system to be destroyed. “You already have a good system working, why destroy it,” an IIT director said.
During the last meeting of the IITs council, there was no consensus on having a single entrance examination for admissions. Seven out of 15 IITs favoured having a separate “add-on” examination in addition to the NAT. However, HRD minister Kapil Sibal is of the view that if IITs have an additional exam then nothing stops other institutions like planning and architecture colleges etc to have their own exams.
The Science Advisory Council to the Prime Minister in its recommendations has also favoured a single entrance examination for engineering.
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24 March 2011

Akshit Jayesh Dhruv, a Class V student become the youngest student to equal the world record of obtaining full 1,000 marks in an online computer exam conducted by US-based multinational Microsoft Corp.

RAJKOT: A city boy has become the youngest student to equal the world record of obtaining full 1,000 marks in an online computer exam conducted by US-based multinational Microsoft Corp.

Akshit Jayesh Dhruv, a Class V student, appeared in the exam on March 16 and obtained full marks, said Chirag Kothari, Centre Head of Inside Tomorrow Computer Academy, where the 11-year-old studied.
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03 March 2011

Jammu University -Master of Education( M Ed) 1st Semester (DDE/Private) Exam 2010 Results online

Jammu University M Ed I Semester (DDE/Private) Exam 2010 Results Declared
Jammu University, located in Jammu & Kashmir, on Tuesday i.e. March 1, 2011, has declared the results of Master of Education (M Ed) I Semester (DDE/Private) exam. The exams were held in 2010. To know more about the results, candidates can visit the university's official website: http://www.jammuuniversity.in/.
Jammu University is located in Jammu & Kashmir. It is one of the renowned universities of the region accredited with ‘A’ grade by the National Assessment and Accreditation Council (NAAC), Bangalore. The university offers education at different degree level in a wide variety of disciplines - Life Sciences, Arts / Oriental Languages, Sciences, Education, Commerce, Management Studies, Behavioral Science, Law, Social Science, Medicine, Engineering and Music & Fine Arts.
Date of Results Declaration
March 1, 2011
Category of Exam
Education - Master of Education (M Ed) I Semester (DDE/Private) Exam
Where to Go for Result

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Rajasthan Technical University (RTU), Kota, Rajasthan Science/Engineering - Master of Technology (M Tech) I Semester Main Exam result online

RTU Kota M Tech I Semester Main Exam Results Declared
Rajasthan Technical University (RTU), Kota, Rajasthan, on Tuesday i.e. March 1, 2011, has declared the results of Master of Technology (M Tech) I Semester Main exam. To know more about the results, candidates can visit the university's official website: http://www.rtu.ac.in/.
Located in Kota, Rajasthan Technical University (RTU) is one of the premier technical universities of the state. It was set up in 2005 by Govt. of Rajasthan to enhance technical education in Rajasthan. Presently, 60 Engineering Colleges, 08 M Tech Colleges, 21 MCA Colleges, 69 MBA Colleges and three Hotel Management and Catering Institute are affiliated to the university.
Date of Results Declaration
March 1, 2011
Category of Exam
Science/Engineering - Master of Technology (M Tech) I Semester Main Exam
Where to Go for Result

Contact address:
Rajasthan Technical University

Rawathbhata Road.
Kota - 324 010
Rajasthan
Phone: +91-744-2473001, 2473004
Fax: +91-744-2473006
infortu@mail.com
www.rtu.ac.in/
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02 March 2011

The sixth teachers' registration examination test-2010 result available on the websites of Non Government Teachers' Registration and Certification Authority (NTRCA)

The results of the sixth teachers' registration examination test-2010 have been published.

A total of 42,641 candidates passed the test, showing a pass percentage of 19.34.

Education minister Nurul Islam Nahid announced the results at a press conference on Wednesday.

The results are available on the websites of Non Government Teachers' Registration and Certification Authority (NTRCA) and government-run mobile company Teletalk.

The number of successful candidates for colleges is 15,280 or 19.81 percent, while that for schools is 27,361 or 19.08 percent.

The exam was held on Dec 10 and 11 last year, with 220,517 candidates taking part in it.

The minister said that NTRCA would gradually be developed to recruit teachers. It will be established like Public Service Commission (PSC).

"It helps make the list of meritorious candidates," Nahid added.
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Sri Krishnadevaraya University (SKU), Anantapur. UG Semester I (Lateral Entry) examination result online

SKU UG Semester I (Lateral Entry) Exam Sept 2010 Result Declared On February 28, 2011 results of UG Semester I (Lateral Entry) examination was declared by Sri Krishnadevaraya University (SKU), Anantapur. For knowing more about the results one can visit the University’s official website: www.skuniversity.org

Sri Krishnadevaraya University (SKU) is a public university in Anantapur in the state of Andhra Pradesh. It has earned its name as a centre of academic excellence and it is also accorded with a four star status by the National Assessment and Accreditation Council (NAAC). The University was founded in the year 1968, however, in 1987 it was conferred the status of an affiliating University. Presently, it provides course at various faculties via its numerous affiliated colleges / institutes.



Date of Results Declaration
February 28, 2011

Where to Go for Result

www.skuniversity.org

Contact address:
Sri Krishnadevaraya University
Anantapur - 515 003
Andhra Pradesh
Phone: +91-8554-55367-73 / 255231 / 255700
Fax: +91-8554-255244 / 255805 / 25
www.skuniversity.org
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Visvesvaraya Technological University (VTU), Belgaum, Karnataka, BE/B Tech 3 (III) Semester Exam Results Online

VTU Belgaum BE/B Tech III Semester Exam Results Declared
Visvesvaraya Technological University (VTU), Belgaum, Karnataka, on March 1, 2011, has declared the results of Bachelor of Engineering (BE)/Bachelor of Technology (B Tech) III Semester exam. The results have been announced for Belgaum, Gulbarga and Mysore region. To know more about the results, candidates can visit the university's official website: http://www.vtu.ac.in/.
Located in Belgaum, Karnataka, Visvesvaraya Technological University (VTU) is one of the largest technical universities in India. The university offers engineering and technology courses at various levels. Currently, the university has more than 200 departments across the affiliated colleges recognized as Research Centres.
Date of Results Declaration
March 1, 2011
Category of Exam
Science/Engineering - Bachelor of Engineering (BE)/Bachelor of Technology (B Tech) III Semester Exam
Where to Go for Result

Contact address:
Visvesvaraya Technological University

Jnana Sangama
Belgaum - 590 014
Karnataka
Phone: +91-831-2498197
info@vtu.ac.in
www.vtu.ac.in
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The Punjab Technical University (PTU) has declared the online result of Bachelor of Technology (B Tech) examinations.

 The results have been uploaded on the official website of the University.
The students will have to upload their registration number/Roll number to download the results.

We are providing below the links for the official site.
You can connect to the official website after clicking on the following links.
http://www.ptu.ac.in/
http://ptuexam.com/
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The top performers on the 2010 Regents Latin test. Included are the top districts and public high schools in Western New York and the Rochester Area, as determined by Business First’s analysis of newly released test results. Read more: Results of 2010 Regents Latin exam | Business First

Western New York (districts)

• 1. Orchard Park CSD
• 2. Clarence CSD
• 3. Albion CSD
• 4. Hamburg CSD
• 5. Williamsville CSD
• 6. Niagara-Wheatfield CSD
• 7. East Aurora UFSD
• 8. Lockport City SD
• 9. LeRoy CSD
• 10. Amherst CSD

Western New York (public high schools)

• 1. Orchard Park HS (Orchard Park)
• 2. Clarence SHS (Clarence)
• 3. Williamsville North HS (Williamsville)
• 4. Charles D'Amico HS (Albion)
• 5. Hamburg HS (Hamburg)
• 6. Niagara-Wheatfield SHS (Niagara-Wheatfield)
• 7. East Aurora HS (East Aurora)
• 8. Lockport HS (Lockport)
• 9. LeRoy JSHS (LeRoy)
• 10. Amherst Central HS (Amherst)

Rochester Area (districts)

• 1. Pittsford CSD
• 2. Gates Chili CSD
• 3. Penfield CSD
• 4. Geneva City SD
• 5. Rochester City SD
• 6. West Irondequoit CSD

Rochester Area (public high schools)

• 1. Pittsford Sutherland HS (Pittsford)
• 2. Gates Chili HS (Gates Chili)
• 2. Pittsford Mendon HS (Pittsford)
• 4. Penfield HS (Penfield)
• 5. School of the Arts (Rochester)
• 6. Geneva HS (Geneva)
• 7. Irondequoit HS (West Irondequoit)
• 8. Joseph C. Wilson Magnet HS Commencement Academy (Rochester)
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28 February 2011

The question paper of an all-India examination for the post of assistant administrative officer of Life Insurance Corporation of India (LIC) was leaked in Delhi on Sunday ahead of the test.

The question paper of an all-India examination for the post of assistant administrative officer of Life Insurance Corporation of India (LIC) was leaked here on Sunday ahead of the test.
Delhi Police has taken into its custody a youth, who allegedly sold the papers for Rs five lakh each and is believed to be the main conspirator.
The police swung into action after the crime branch officials got hold of the copies of the question papers for both morning and afternoon sessions from some persons much ahead of the scheduled time of the examination.
The test is being conducted in two sessions in 160 centres across India. There are 16 centres for the test in New Delhi.
An LIC spokesperson said Educational Consultants India Limited (EDCIL), a public sector company, is conducting the entire examination process.
He further said that there is no report of leakage of question papers from any other part of India.
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Nagpur University (RTMNU) Science/Engineering Online Result - Bachelor of Engineering (BE) III Semester Winter 2010 Exam

Nagpur University (RTMNU) BE III Semester Winter 2010 Exam Results Declared
Rashtrasant Tukadoji Maharaj Nagpur University (RTMNU), formerly known as Nagpur University, located in Nagpur (Maharashtra), on Sunday i.e. February 27, 2011, has declared the results of Bachelor of Engineering (BE) III Semester Winter 2010 exam. To know more about the results, candidates can visit the university's official website: http://www.nagpuruniversity.org/.
Rashtrasant Tukadoji Maharaj Nagpur University (RTMNU), formerly known as Nagpur University, which is located in Nagpur (Maharashtra), is considered as one of the prominent universities in the state of the Maharashtra. It conducts several undergraduate and postgraduate level programmes.
Date of Results Declaration
February 27, 2011
Category of Exam
Science/Engineering - Bachelor of Engineering (BE) III Semester Winter 2010 Exam
Where to Go for Result

Contact address:
Nagpur University
Rashtrasant Tukadoji Maharaj
Rabindranath Tagore Marg
Nagpur - 440 001
Maharashtra
Phone: +91-712-2525417
Fax: +91-712-2532841
vc@nagpuruniversity.org
http://www.nagpuruniversity.org/
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27 February 2011

Gulbarga University Online Results 2011 available for B.Com Semester 3, B.A Semester 5, B.Sc Semester 3, Semester 5 and BCA Semester 3

Gulbarga University UG Exam Nov 2010 Results Announced Gulbarga University, Karnataka, has announced the results of UG (undergraduate), held in November 2010. Students can check the results are made available in the University’s official website: http://www.gulbargauniversity.kar.nic.in/


Gulbarga University Results are available for B.Com, BA, B.Sc and BCA. To view the results one must enter Register No. and Select Course & Year/Semester to get results in the given link:

Gulbarga University Results 2011 are available for B.Com Semester III, B.A Semester V, B.Sc Semester III, Semester V and BCA Semester III.

For knowing more about the results one can visit the University’s official website.

Contact address:
Gulbarga University,
Jnana Ganga
Gulbarga - 585 106
Karnataka
Phone: +91-8472-263202
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26 February 2011

Rajasthan University IT - BCA (Bachelor of Computer Applications) Part III (Supplementary) Exam Result 2010 online with full detail and contact address

University of Rajasthan (UOR), popularly known as Rajasthan University, Jaipur, is one of the oldest universities of the state. The University has been accredited with ‘A+’ grade by National Accreditation and Assessment Council (NAAC), Bangalore, for its academic excellence. The University is an excellent quality higher education in the state. Presently, the University has 36 post graduate departments, 15 recognized research centers, 6 constituent colleges and 500 constituent colleges, spread across 6 districts of Rajasthan.


Date of Results Declaration
February 25, 2011

Category of Exam
IT - BCA (Bachelor of Computer Applications) Part III (Supplementary) Exam

Where to Go for Result
www.uniraj.ernet.in

Contact address:
University of Rajasthan
Rajasthan University,
JLN Marg
Jaipur - 302 055
Rajasthan
Phone: +91-141-2711070, 2708824
nkjain@uniraj.ernet.in
www.uniraj.ernet.in/
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Pune University Master of Science (M Sc - Computer Science) October 2010 Exam Results online and contact address

Pune University, formerly known as University of Poona, is situated in Pune, Maharashtra. It is one of the renowned universities offering quality education in the region. The university imparts education in wide range of disciplines via its various affiliated colleges / institutes.

Date of Results Declaration
February 24, 2011
 
Category of Exam
Science - Master of Science (M Sc) Computer Science Exam
 
Where to Go for Result

Contact address:
Pune University,
Ganeshkhind Road
Pune - 411 007
Maharashtra
Phone: +91-20-25601099 / 25696061 / 25690062 / 25696064 / 25696065
regis@unipune.ernet.in
www.unipune.ernet.in
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Institute of Company Secretaries of India (ICSI) CS Exam December 2010 Results on website and email with institute address

The Institute of Company Secretaries of India (ICSI) was constituted under an Act of Parliament i.e. the Company Secretaries Act, 1980 (Act No. 56 of 1980). It is the only recognized professional body in India to develop and regulate the profession of Company Secretaries in India. The Institute of Company Secretaries of India awards the certificate of bestowing the designation of Company Secretary (CS) to a candidate qualifying for the membership of the Institute.



Institute of Company Secretaries of India (ICSI), New Delhi, declared the results of CS December 2010 examination today i.e. on February 25, 2011 at 12.00 noon. The results will be made available in the institute’s official website: www.icsi.edu/
Candidates will be able to check their CS December 2010 examination results in the aforementioned official website, once declared.
One can also get the results through email by visiting the following link:
http://www.icsi.edu/icsiweb/email/resemail.asp.
For that candidate must select :
  1. Syllabus / Course (From the Given Options), 
  2. enter their Email and 
  3. Roll No in the space provided and 
  4. click in the Submit Button in the aforementioned link.

Contact address:

Institute of Company Secretaries of India
New Delhi,
Delhi
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26 September 2010

20 Important Maths Shortcuts, Formula and Tips & Tricks with example for speedy calculations in various exams and enterance tests like CAT, GMAT, GRE, BANK exams


1) 2^2n-1 is always divisible by 3
2^2n-1 = (3-1)^2n -1
= 3M +1 -1
= 3M, thus divisible by 3

2) What is the sum of the divisors of 2^5.3^7.5^3.7^2?
ANS : (2^6-1)(3^8-1)(5^4-1)(7^3-1)/2.4.6
Funda : if a number 'n' is represented as
a^x * b^y * c^z ....
where, {a,b,c,.. } are prime numbers then

Quote:
(a) the total number of factors is (x+1)(y+1)(z+1) ....
(b) the total number of relatively prime numbers less than the number is n * (1-1/a) * (1-1/b) * (1-1/c)....
(c) the sum of relatively prime numbers less than the number is n/2 * n * (1-1/a) * (1-1/b) * (1-1/c)....
(d) the sum of factors of the number is {a^(x+1)} * {b^(y+1)} * ...../(x*y*...)

  http://hallosushant.blogspot.com/
3) what is the highest power of 10 in 203!
ANS : express 10 as product of primes; 10 = 2*5

divide 203 with 2 and 5 individually
203/2 = 101
101/2 = 50
50/2 = 25
25/2 = 12
12/2 = 6
6/2 = 3
3/2 = 1
thus power of 2 in 203! is, 101 + 50 + 25 + 12 + 6 + 3 + 1 = 198

divide 203 with 5
203/5 = 40
40/5 = 8
8/5 = 1

thus power of 5 in 203! is, 49

so the power of 10 in 203! factorial is 49

4) x + y + z = 7 and xy + yz + zx = 10, then what is the maximum value of x? ( CAT 2002 has similar question )
ANS: 49-20 = 29, now if one of the y,z is zero, then the sum of other 2 squares shud be equal to 29, which means, x can take a max value at 5

5) In how many ways can 2310 be expressed as a product of 3 factors?
ANS: 2310 = 2*3*5*7*11
When a number can be expressed as a product of n distinct primes,
then it can be expressed as a product of 3 numbers in (3^(n+1) + 1)/2 ways

6) In how many ways, 729 can be expressed as a difference of 2 squares?
ANS: 729 = a^2 - b^2
= (a-b)(a+b),
since 729 = 3^5,
total ways of getting 729 are, 1*729, 3*243, 9*81, 27*27.
So 4 ways
Funda is that, all four ways of expressing can be used to findout distinct a,b values,
for example take 9*81
now since 9*81 = (a-b)(a+b) by solving the system a-b = 9 and a+b = 81 we can have 45,36 as soln.

7) How many times the digit 0 will appear from 1 to 10000
ANS: In 2 digit numbers : 9,
In 3 digit numbers : 18 + 162 = 180,
In 4 digit numbers : 2187 + 486 + 27 = 2700,
total = 9 + 180 + 2700 + 4 = 2893

8 ) What is the sum of all irreducible factors between 10 and 20 with denominator as 3?
ANS :
sum = 10.33 + 10.66 + 11.33 + 11.66 + 12.33 + 12.66 + 13.33 + 13.66…….
= 21 + 23 + ……
= 300

9) if n = 1+x where x is the product of 4 consecutive number then n is,
1) an odd number,
2) is a perfect square

SOLN : (1) is clearly evident
(2) let the 4 numbers be n-2,n-1,n and n+1 then by multing the whole thing and adding 1 we will have a perfect square

10) When 987 and 643 are divided by same number 'n' the reminder is also same, what is that number if the number is a odd prime number?
ANS : since both leave the same reminder, let the reminder be 'r',
then, 987 = an + r
and 643 = bn + r and thus
987 - 643 is divisible by 'r' and
987 - 643 = 344 = 86 * 4 = 43 * 8 and thus the prime is 43
hence 'r' is 43

11) when a number is divided by 11,7,4 the reminders are 5,6,3 respectively. what would be the reminders when the same number is divided by 4,7,11 respectively?
ANS : whenever such problem is given,
we need to write the numbers in top row and rems in the bottom row like this

11 7 4
| \ \
5 6 3

( coudnt express here properly Evil or Very Mad)
now the number is of the form, LCM ( 11,7,4 ) + 11*(3*7 + 6) + 5
that is 302 + LCM(11,7,4) and thus the rems when the same number is divided by 4,7,11 respectively are,

302 mod 4 = 2
75 mod 7 = 5
10 mod 11 = 10

12) a^n - b^n is always divisible by a-b

13) if a+b+c = 0 then a^3 + b^3 + c^3 = 3abc
EXAMPLE: 40^3-17^3-23^3 is divisble by
since 40-23-17 = 0, 40^3-17^3-23^3 = 3*40*23*17 and thus, the number is divisible by 3,5,8,17,23 etc.
  http://hallosushant.blogspot.com/
14) There is a seller of cigerette and match boxes who sits in the narrow lanes of cochin. He prices the cigerattes at 85 p, but found that there are no takers. So he reduced the price of cigarette and managed to sell all the cigerattes, realising Rs. 77.28 in all. What is the number of cigerattes?

a) 49
b) 81
c) 84
d) 92

ANS : (d)
since 77.28 = 92 * 84, and since price of cigarette is less than 85, we have (d) as answer
Quote:

i have given this question to make the funda clear


15) What does 100 stand for if 5 X 6 = 33
ANS : 81
SOLN : this is a number system question,
30 in decimal system is 33 in some base 'n', by solving we will have n as 9
and thus, 100 will be 9^2 = 81

16) In any number system 121 is a perfect square,
SOLN: let the base be 'n'
then 121 can be written as n^2 + 2*n + 1 = (n+1)^2
hence proved

17) Most of you ppl know these, anyways, just in case
Quote:
(a) sum of first 'n' natural numbers - n*(n+1)/2
(b) sum of the squares of first 'n' natural numbers - n*(n+1)*(2n+1)/6
(c) sum of the cubes of first 'n' natural numbers - n^2*(n+1)^2/4
(d) total number of primes between 1 and 100 - 25 Monsieur GreenMonsieur Green


18 ) See Attachment Twisted Evilto know how to find LCM, GCF of Fractions
Quote:
CAT 2002 has 2 questions on the above simple concept


19) Converting Recurring Decimals to Fractions

let the number x be 0.23434343434........

thus 1000 x = 234.3434343434......
and 10 x = 2.3434343434.........
thus, 990 x = 232
and hence, x = 232/990

20) Reminder Funda

(a) (a + b + c) % n = (a%n + b%n + c%n) %n
EXAMPLE: The reminders when 3 numbers 1221, 1331, 1441 are divided by certain number 9 are 6, 8, 1 respectively. What would be the reminder when you divide 3993 with

9? ( never seen such question though Monsieur Green)
the reminder would be (6 + 8 + 1) % 9 = 6

(b) (a*b*c) % n = (a%n * b%n * c%n) %n
EXAMPLE: What is the remainder left when 1073 * 1079 * 1087 is divided by 119 ? ( seen this kinda questions alot Monsieur GreenMonsieur Green)
1073 % 119 = ?
since 1190 is divisible by 119, 1073 mod 119 is 2
and thus, "the remainder left when 1073 * 1079 * 1087 is divided by 119 " is 2*8*16 mod 119 and that is 256 mod 119 and that is (238 + 18 ) mod 119 and that is 18 Monsieur Green

Glossary : % stands for reminder operation



find the number of zeroes in 1^1* 2^2* 3^3* 4^4.............. 98^98* 99^99* 100^100

the expresion can be rewritten as (100!)^100 / 0!* 1!* 2!* 3!....99!


Now the numerator has 2400 zeros

the formular for finding number of zeros in n! is

[n/5]+[n/5^2]...[n/5^r]
where r is such that 5^r<=n<5^(r+1)

and [..] is the grestest integer function

for the numerator find the number of zeros using the above formulae..

for 0!...4! number of zeros ..0
5!...9!.number os zeros ..1
9!...14!... 2
15!..19!..................3
20!..24!..................4!
now at 25! the series makes a jump to 6
25!...29!.................6
30!...34!.................7
this goes on and again makes a jump at 50!
and then at 75!

so the number of zeros is...

5(1+2....19) + 25+ 50+ 75

the last 3 terms 25 50 and 75 are because of the jumps..

this gives numerator has 1100 zeros

now total number of zeros in expression is no of zeros in denominator - no of zeros in numerator
2400 - 1100

the Answer 1300
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Maths Shortcuts and formula for speedy calculations in various exams and enterance tests like CAT, GMAT, GRE, BANK exams



  • To find the number of factors of a given number, express the number as a product of powers of prime numbers.

In this case, 48 can be written as 16 * 3 = (24 * 3)

Now, increment the power of each of the prime numbers by 1 and multiply the result.

In this case it will be (4 + 1)*(1 + 1) = 5 * 2 = 10 (the power of 2 is 4 and the power of 3 is 1)

Therefore, there will 10 factors including 1 and 48. Excluding, these two numbers, you will have 10 – 2 = 8 factors.


  • The sum of first n natural numbers = n (n+1)/2

The sum of squares of first n natural numbers is   n (n+1)(2n+1)/6

The sum of first n even numbers= n (n+1)

The sum of first n odd numbers= n^2


  • To find the squares of numbers near numbers of which squares are known

To find 41^2 , Add 40+41 to 1600 =1681

To find 59^2 , Subtract 60^2-(60+59)  =3481

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  • If an equation (i:e f(x)=0 ) contains all positive co-efficient of any powers of x , it has no positive roots then.
eg: x^4+3x^2+2x+6=0 has no positive roots .
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  • For an equation f(x)=0 , the maximum number of positive roots it can have is the number of sign changes in f(x) ; and the maximum number of negative roots it can have is the number of sign changes in f(-x) .
Hence the remaining are the minimum number of imaginary roots of the equation(Since we also know that the index of the maximum power of x is the number of roots of an equation.)
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  • For a cubic equation ax^3+bx^2+cx+d=o

sum of the roots = - b/a
sum of the product of the roots taken two at a time = c/a
product of the roots = -d/a
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  • For a biquadratic equation ax^4+bx^3+cx^2+dx+e = 0

sum of the roots = - b/a
sum of the product of the roots taken three at a time = c/a
sum of the product of the roots taken two at a time = -d/a
product of the roots = e/a
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  • If for two numbers x+y=k(=constant), then their PRODUCT is MAXIMUM if
x=y(=k/2). The maximum product is then (k^2)/4
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  • If for two numbers x*y=k(=constant), then their SUM is MINIMUM if
x=y(=root(k)). The minimum sum is then 2*root(k) .
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  •  |x| + |y| >= |x+y| (|| stands for absolute value or modulus )
(Useful in solving some inequations)
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  •  Product of any two numbers = Product of their HCF and LCM .
Hence product of two numbers = LCM of the numbers if they are prime to each other

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  • For any regular polygon , the sum of the exterior angles is equal to 360 degrees
hence measure of any external angle is equal to 360/n. ( where n is the number of sides)

For any regular polygon , the sum of interior angles =(n-2)180 degrees

So measure of one angle in

Square                    =90
Pentagon                =108
Hexagon                 =120
Heptagon                =128.5
Octagon                  =135
Nonagon                 =140
Decagon                  = 144


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  •  If any parallelogram can be inscribed in a circle , it must be a rectangle.

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  •  If a trapezium can be inscribed in a circle it must be an isosceles trapezium (i:e oblique sides equal).

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  •  For an isosceles trapezium , sum of a pair of opposite sides is equal in length to the sum of the other pair of opposite sides .(i:e AB+CD = AD+BC , taken in order) .
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  •  Area of a regular hexagon : root(3)*3/2*(side)*(side)
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  • For any 2 numbers a>b

a>AM>GM>HM>b (where AM, GM ,HM stand for arithmetic, geometric , harmonic menasa respectively)

 (GM)^2 = AM * HM
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  •  For three positive numbers a, b ,c

(a+b+c) * (1/a+1/b+1/c)>=9

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  •  For any positive integer n

2<= (1+1/n)^n <=3

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  • a^2+b^2+c^2 >= ab+bc+ca
If a=b=c , then the equality holds in the above.

 a^4+b^4+c^4+d^4 >=4abcd
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  • (n!)^2 > n^n (! for factorial)
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  • If a+b+c+d=constant , then the product a^p * b^q * c^r * d^s will be maximum
if a/p = b/q = c/r = d/s .
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  • Consider the two equations

a1x+b1y=c1
a2x+b2y=c2

Then ,
If a1/a2 = b1/b2 = c1/c2 , then we have infinite solutions for these equations.
If a1/a2 = b1/b2 <> c1/c2 , then we have no solution for these equations.(<> means not equal to )
If a1/a2 <> b1/b2 , then we have a unique solutions for these equations..
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  • For any quadrilateral whose diagonals intersect at right angles , the area of the quadrilateral is
0.5*d1*d2, where d1,d2 are the lenghts of the diagonals.
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  •  Problems on clocks can be tackled as assuming two runners going round a circle , one 12 times as fast as the other . That is ,
the minute hand describes 6 degrees /minute
the hour hand describes 1/2 degrees /minute .

Thus the minute hand describes 5(1/2) degrees more than the hour hand per minute .

 The hour and the minute hand meet each other after every 65(5/11) minutes after being together at midnight.
(This can be derived from the above) .
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  • If n is even , n(n+1)(n+2) is divisible by 24

If n is any integer , n^2 + 4 is not divisible by 4


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  • Given the coordinates (a,b) (c,d) (e,f) (g,h) of a parallelogram , the coordinates of the meeting point of the diagonals can be found out by solving for
[(a+e)/2,(b+f)/2] =[ (c+g)/2 , (d+h)/2]

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  • Area of a triangle
1/2*base*altitude = 1/2*a*b*sinC = 1/2*b*c*sinA = 1/2*c*a*sinB = root(s*(s-a)*(s-b)*(s-c)) where s=a+b+c/2
=a*b*c/(4*R) where R is the CIRCUMRADIUS of the triangle = r*s ,where r is the inradius of the triangle .

In any triangle
a=b*CosC + c*CosB
b=c*CosA + a*CosC
c=a*CosB + b*CosA
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  • If a1/b1 = a2/b2 = a3/b3 = .............. , then each ratio is equal to
(k1*a1+ k2*a2+k3*a3+..............) / (k1*b1+ k2*b2+k3*b3+..............) , which is also equal to
(a1+a2+a3+............./b1+b2+b3+..........)
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  • In any triangle
a/SinA = b/SinB =c/SinC=2R , where R is the circumradius
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  • x^n -a^n = (x-a)(x^(n-1) + x^(n-2) + .......+ a^(n-1) ) ......Very useful for finding multiples .For example (17-14=3 will be a multiple of 17^3 - 14^3)
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  •  e^x = 1 + (x)/1! + (x^2)/2! + (x^3)/3! + ........to infinity
 2 < e < 3
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  •  log(1+x) = x - (x^2)/2 + (x^3)/3 - (x^4)/4 .........to infinity [ Note the alternating sign . .Also note that the ogarithm is with respect to base e ]
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  •  In a GP the product of any two terms equidistant from a term is always constant .
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  •  For a cyclic quadrilateral , area = root( (s-a) * (s-b) * (s-c) * (s-d) ) , where s=(a+b+c+d)/2
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  •  For a cyclic quadrilateral , the measure of an external angle is equal to the measure of the internal opposite angle.

 (m+n)! is divisible by m! * n! .
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  •  If a quadrilateral circumscribes a circle , the sum of a pair of opposite sides is equal to the sum of the other pair .
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  • The sum of an infinite GP = a/(1-r) , where a and r are resp. the first term and common ratio of the GP .
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  • The equation whose roots are the reciprocal of the roots of the equation     ax^2+bx+c is cx^2+bx+a
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  •  The coordinates of the centroid of a triangle with vertices (a,b) (c,d) (e,f)
is((a+c+e)/3 , (b+d+f)/3) .
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  •  The ratio of the radii of the circumcircle and incircle of an equilateral triangle is 2:1 .
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  •  Area of a parallelogram = base * height
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  • APPOLLONIUS THEOREM:

In a triangle , if AD be the median to the side BC , then
AB^2 + AC^2 = 2(AD^2 + BD^2) or 2(AD^2 + DC^2) .

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  • For similar cones , ratio of radii = ratio of their bases.

 The HCF and LCM of two nos. are equal when they are equal .

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  • Volume of a pyramid = 1/3 * base area * height
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  • In an isosceles triangle , the perpendicular from the vertex to the base or the angular bisector from vertex to base bisects the base.

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  •  In any triangle the angular bisector of an angle bisects the base in the ratio of the
other two sides.
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  • The quadrilateral formed by joining the angular bisectors of another quadrilateral is
always a rectangle.

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  • Roots of x^2+x+1=0 are 1,w,w^2 where 1+w+w^2=0 and w^3=1

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  • |a|+|b| = |a+b| if a*b>=0
else |a|+|b| >= |a+b|
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

  •  2<= (1+1/n)^n <=3
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  •  WINE and WATER formula:

If Q be the volume of a vessel
q qty of a mixture of water and wine be removed each time from a mixture
n be the number of times this operation be done
and A be the final qty of wine in the mixture

then ,
A/Q = (1-q/Q)^n
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  •  Area of a hexagon = root(3) * 3 * (side)^2
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

  •  (1+x)^n ~ (1+nx) if x<<<1
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

  •  Some pythagorean triplets:

3,4,5 (3^2=4+5)
5,12,13 (5^2=12+13)
7,24,25 (7^2=24+25)
8,15,17 (8^2 / 2 = 15+17 )
9,40,41 (9^2=40+41)
11,60,61 (11^2=60+61)
12,35,37 (12^2 / 2 = 35+37)
16,63,65 (16^2 /2 = 63+65)
20,21,29(EXCEPTION)
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  • Appolonius theorem could be applied to the 4 triangles formed in a parallelogram.
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  •  Area of a trapezium = 1/2 * (sum of parallel sids) * height = median * height
where median is the line joining the midpoints of the oblique sides.
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  •  when a three digit number is reversed and the difference of these two numbers is taken , the middle number is always 9 and the sum of the other two numbers is always 9 .
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  •  ANy function of the type y=f(x)=(ax-b)/(bx-a) is always of the form x=f(y) .
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  •  Let W be any point inside a rectangle ABCD .
Then
WD^2 + WB^2 = WC^2 + WA^2

 Let a be the side of an equilateral triangle . then if three circles be drawn inside
this triangle touching each other then each's radius = a/(2*(root(3)+1))
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  •  Let 'x' be certain base in which the representation of a number is 'abcd' , then the decimal value of this number is a*x^3 + b*x^2 + c*x + d
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  • when you multiply each side of the inequality by -1, you have to reverse the direction of the inequality.
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  • To find the squares of numbers from 50 to 59

For 5X^2 , use the formulae

(5X)^2 = 5^2 +X / X^2

Eg  ; (55^2) = 25+5 /25
                     =3025
         (56)^2 = 25+6/36
                      =3136
          (59)^2 = 25+9/81
                      =3481
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  • Many of u must b aware of this formula, but the ppl who don't know it must b useful for them.
a+b+(ab/100)

this is used for succesive discounts types of sums.
like 1999 population increses by 10% and then in 2000 by 5%
so the population in 2000 now is 10+5+(50/100)=+15.5% more that was in 1999

and if there is a decrease then it will be preceeded by a -ve sign and likeiwse
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