Mathematician From Jammu Kashmir -- Rajeev Motwani

 Dear Friends

This is Day - 2 of the Quiz - Mathematician from Jammu- Kashmir

Today, you will learn about computer wizard - Rajeev Motwani. 

Please go through the following web page to know about Mr Motwani.

https://en.wikipedia.org/wiki/Rajeev_Motwani

There is another beautiful article published by his alma mater - IIT Kanpur

https://iitk.ac.in/dora/profile/Late-Prof-Rajeev-Motwani

Most of the questions on Mr Rajeev Motwani was prepared by - SUNNY TANDON, a teacher from JK and a member of Expert committee of All India Ramanujan Maths Club.

Some of the highlighted questions of the quiz are --- 

1. In 1998 Rajeev Motwani along with Sergey Brin ,Larry Page and Terry Winograd Published the Paper Tittled “What Can You Do with A Web in your Pocket”.In this Researh Paper all of them announced that we have used our Research Paper ‘Page Rank’ to develop a Novel Search Engine .What is the Name of  that Search Engine?

2. Who was the  PhD Advisor of Rajeev Motwani ?

Keep Learning

Don't forget to share in groups.

                                               Link of Quiz

Please write your views in the comment box.

MATHEMATICIANS FROM STATES

 DEAR FRIENDS

From June 1, I shall start a quiz series that will last at least for 29 days. This quiz will be unique as I shall take one mathematician each day from a state. I promise to cover all states and Union territories in this mega event.

Hope you will enjoy the quiz.

Friends, in the last year, I had conducted 4 sets of quiz on Ramanujan, Indian Mathematicians, History of Mathematics and Indian Mathematics. The quiz was well participated by students across India. More than 26 thousands students participated in the quiz.

This is my small effort  make all Indians aware about the mathematicians born in India, their contributions ,to make us feel happy. I would be happy if you would enjoy during the LOCKDOWN period by learning something new.

I request you all to please share the information to different groups so that maximum people can get benefitted and a culture of research is born with such efforts.

Please read about the mathematician mentioned here.

 June 1, 2:- 

State : Jammu - Kashmir                      

Mathematicians:- Vatesvara and Chander Kanta Gupta

                            Link will be OPENED TILL 1st June (11PM) itself.

LINK FOR QUIZ IS HERE . PLEASE CLICK THE LINK BELOW

                                    MATHEMATICIANS FROM JK

QUESTIONS AT A GLANCE:- 

1. The astronomical book of Vatesvara is divided into 15 chapter containing ---- verses

2. Vatesvara's book - Vatesvara siddhanta is still available at ---- 

3. Name the Persian mathematcian who had referred the work of  Vatesvara in his book

Keep reading and enjoy the lockdown period.

Dr Rajesh Kumar Thakur

QUADRATIC EQUATION - K BHANUMOORTHY

  

“Keep exploring. Keep dreaming. Keep asking why. Don’t settle for what you already know. Never stop believing in the power of your ideas, your imagination, your hard work to change the world.

------- Barack Obama.

The general form of QE is ax^2+bx+c =0, where a≠0, a, b, c €R. The equation is of second degree with variable x. The equation has two roots, may be distinct, equal, complex, depend on the discriminant of equation. (D= b^2 -4ac) There are conditions for the kinds of roots. In this article let me write on applications QE.

Sridhar Acharya , an Indian mathematician born in 8th Century in India. He was a Sanskrit scholar and a mathematician. His father Baldev Acharya was also a Sanskrit Scholar. Sridhar Acharya was the first mathematician who derived the formula of quadratic equation. The above formula is due to Sridhar Acharya. Sridhar Acharya wrote - Pati Ganit, Trisatika and Pati ganit Sara.

Quadratic Equations are applied in our daily life, such as throwing a ball/stone, figuring out gain or loss, to find the speed of boat in a river, so on. Few applications are discussed.

1.      A river flows at 3kmper hour A boat goes 10km upriver and back again. A trip takes 2 hours to go and return. Find the speed of the boat.?

We can use the formula Time =Distance / Speed. Let us assume the speed of the boat be X Km per hour. As per given data we can form statement: Speed of the boat against the current of water is (X-3) km/hr, in the direction of flow of water is (X+3) Km per hour.

 Hence  

(10 / X-3) + (10/ X+3) = 2 hours total time taken. 

By solving we get the equation 2X^2 -20X -18= 0,

 i.e.  X^2 – 10X-9 = 0, we will get X = 10.83Km per hour. Speed of the boat is 10.83km /hour (up to two decimal places)

2.    2.  A ball is thrown straight up from 9 m above the ground  with velocity of 12m/sec. When does hit the ground? (Air resistance being ignored).

 Let ‘t’ denote time, h denotes height, g denotes gravitational force.

 To use the formula S = ut + ½ gt^2. G = 9.8mper Sec ^2, initial velocity is given as 12m/sec. ½ g be approximated to be 5. instead of 4.9. ultimately the required statement is h= 9 + 12t-5t^2.

Rewriting the equation as 5t^2 -12t-9=0, By solving we get t = 3, other value of t is negative, not possible. Hence the answer is 3. 

We can draw the graph and verify. The graph shall be parabola.

 

3.       From the given diagram find the area of A and B. The total area is given as 42Sq cm.

  We know Area of Rectangle = Length x Breath

Given A + B = 42Sqcm, where area A= 4 × x,

Area B=(3x+1) × x

A =4x, B = 3x^2+x, we get, A+B= 4x+3x^2+x=3x^2+5x; given total area as 42, so 3x^2+5x=42,

si.e., 3x^2+5x-42 = 0, by solving we get x= 3, the other value is neglected being negative. The factors are (x-3) and 3x+14). Hence A= 12Sq cm, and B= 30Sqcm.

 

4.In a circuit diagram two resistors are connected in parallel. The total resistance is measures as 3ohms.One of the resistors is given to be 8 ohms more than the other, what are the values of two resistors.?

  Since connected in parallel, we can use the formula 1 / R = (1/ R₁₎ +( 1 / R₂₎ where R denotes total resistance, R₁ and R₂ be two resistors. As per given data since one resistor more than the other by 8, R₂ = R₁ + 8.

Forming the equation, we get 1 / 3 = (1 /R₁) + (1/ (R₁ +8)

3(R₁ + R₁ + 8) = R₁ (R₁ + 8), 6 R₁ + 24 = R₁^2 + 8 R₁, after simplification we get an equation as   

R₁ ^2 + 2R₁ -24 = 0, factors are (R₁ +6) and (R₁ - -4), hence R₁ = 4, the other value is neglected. two resistors’ values are 4 ohms and 12 ohms.

5.      If SinA, CosA are the roots of equation 12X^2 +5X-7 =0, Find what is Sin 2A

Sum of the roots SinA + cosA = --5 / 12, product of roots SinA Cos A = --7 / 12.

 Sin 2 A = 2sin A CosA   = 2 ×-- 7 / 12 = -- 14 / 12.

 

(just a linkage with trigonometry, we shall see some more in the next posting, to be continued)

 

 About the Author:- K Bhanumoorthy is a retired KV Principal. He lives in Bangluru. He is the Director of All India Ramanujan Maths Club (South Zone) and a recipient of Ramanujan Award. He is actively involved in Mathematics training and writing mathematical blogs.

Application of Linear Equations -- Mr K Bhanumoorthy

                                                                                                                 ----     Continued .

Application of Linear Equations

“Tell me and I forget 

  Teach me and I remember 

   Involve me and I learn” …………Fenjamin Franklin 

Before introducing variables, say x, y, z, a, b, c,.to form a statement of an equation, let me share few lines, how to introduce, guide lines/suggestions, to form a statement, further  an equation from the given data.

Algebra is generalized arithmetic. Few examples be given, be discussed, in brief to be conversant   with statement. At the beginning some numerical.

e.g.: 1. Kunal’s present age is 20years. What was his age before 7 years? What will be his age after /hence 5 years? The students are to be drilled to give the correct answer knowing the operation to be carried out. Answers: 13 years, 25 years. (operation; subtraction, addition)

2.In the same way, Rajan’s present age is 25 years, his father’s age is 2 times of his age. Find Rajan’s father’s present age ?  The ANSWER IS 2 × 25 = 50 YEARS. {OPERATION IS([MULTIPLICATION)

This would facilitate students, to think, and decide the kind of operation to be carried out. Let me Proceed further in solving age related questions.

 

1. The sum of present ages of father and son is 54 years.6 years ago father was 6 times age of his son. Find the present ages of son and father.

Let age of son be x years, father be y years, then, as per given data, x + y = 54, where y = 54 - x.

6 years ago, son   x - 6 years, while father was 54 -x- 6, i.e.  y = 54 -x - 6 = 48 -x years.

As per data   48 -x = 6 (x – 6), by solving we will get x = 12, y = 42, hence age of son is 12yrs, father is 42yrs.

II. 5% of what is 20?      

Let 5 % of x be equal to 20, (5/100) × x = 20, x = 20 × (100 / 5) = 400.

Hence the answer; 400.

III What % of 400 is 20.

Let us assume x % of 400=. 20, (x/ 100) × 400= 20, solving we will get the answer 5 .

Iv. The distance covered by a train in 3 hours is 180 kms Find the speed of the train. Assume train covers equal distance in equal intervals of time.

We can use the formula, Distance = speed x time. If, distance is d, speed is s, time as t then  

d=s x t or s = d / t, using the formula we get speed is 60 Km per hour. Ans: 60km / hour.

v. The sum of digits of a two-digit number is 9. If digits are reversed the number is decreased by 9. Find the number. 

  Let the number be XY, X in ten’s place, Y be in one ’s place. The sum of digits is 9, 

 X + Y = 9. ……. I. value of number is 10X + Y; as per given data, the digits are reversed, ie YX, the value of the number is 10Y+ X. But given, the number is decreased by 9.

So 10X+ Y - 9 = 10Y +X., ie 9X— 9Y = 9, so X- Y = 1…..  II, solving between I and II we get  the solution as X = 5 and Y = 4.

Hence the number is 54 the answer.

vi. There are two industries engage workers. one industry say A pays Rs 240 per hour, and the other say B pays Rs.6000.per week. They have to work for 30 hours. Which is advantage for the worker? 

For industry B: 6000 = 30 × X (X being the amount per hour), So X = Rs.200. We can easily conclude industry A is beneficial.

  

Next topic: Quadratic Equation

                                                                 -------               be continued.

Mr. K Bhanumoorthy is a retired KVS Principal and recipient of Ramanujan Award. He lives in Bengaluru.

Please do comment your views in the comment box given below.

 

NATIONAL MATHEMATICS OLYMPIAD 2021

AIRMC NATIONAL MATHEMATICS OLYMPIAD 2021

About the Organization

AIRMC- All India Ramanujan Maths Club is a National Mathematics club established in the year 1993. Its head office is in Gujarat. The main aim of this club is to make mathematics a friendly subject. In the last 27 years of its journey, the club has organized 14 National and 14 State level Convention where thousands of students participate and show their talents and win medals, mementos and certificates. Participation in the National Events is free of cost. The club provides FREE boarding and lodging facilities to all the participants during the State and National Convention.

This is a fund raiser campaign to build a library in Jalgaon District in Maharashtra where free land has been donated by a lady to build a library, museum and seminar hall. We will build an e- library in near future where students can freely access the books, mathematical journals in online as well as off line mode. Donation to the Club is exempted (50%) under Income Tax Rule.

The club organizes Mathematics Olympiad and the winner gets Cash Prizes, e-Certificates and Direct entry to the National Convention held every year. 

Cash Prizes and Award: - This year the Cash prizes in Each category are Rs. 2500, Rs 1500 and Rs 1000.  Besides that, the Topper of each category will get a chance to visit and interact with the scientists of  ISRO museum and Science City Gujarat. The club will bear the cost of safe stay of the winner and ticketing to the museum. No travel support for this purpose will be provided by the club.

20 Consolation Prizes in each category will be given to students. A certificate with ranking in the specific class and All India Rank will be provided to the winner.

Top 25 from each category will be given 6-8 FREE ZOOM CLASSES for National Maths Olympiad, VVM, GMO,

2 years membership of the Club is free for Top 20 students in each category. If a student secures top position in 3 consecutive years, he/she will be given membership of the club up to class 12 and will be entitled to participate in the National Mathematics Convention directly.

Note: If  more than 50 students register from a school then a certificate (Hard copy) will be sent to the respective schools.

Exam Fee: - Rs 100 per student (Gateway Charges included) through online transaction 

Level of Exam: - There will be ONLY ONE stage of Exam.  

Mode of Examination: - Online mode through Web Browser/ Mobile App

Registration of Exam :- Through Mobile App/ Web Browser

How to register For Exam

1. Download the App from Google Play Store by clicking the following link in your mobile.

GOOGLE PLAY STORE APP LINK

Registration can also be done through browsers..

https://airmcolympiad.proctur.com/

Note: Every individual has to register separately.

2. Register as a New User by providing information and putting the OTP Sent to your registered mobile number.

3. Add the class for which you are applying, in your cart.

4. Pay Rs. 100 through gateway. 

4. After the payment is done, you will get confirmation mail into your account.

What do you get after registration?

3 Free Zoom Classes on Crypt Arithmetic, Vedic Maths and Indian Mathematics before EXAM. 

Tentative Syllabus of Examination: -

Kaprekar group – For Students of class 3, 4 and 5

70% course based on NCERT syllabus, 15 % on Crypt arithmetic, 15% on General Reasoning

Aryabhatta group: - For Class 6, 7 and 8

60% course based on NCERT syllabus, 10% on Video based questions. 20% Crypt arithmetic & reasoning and 10% History of Indian Mathematics ( MCQ on Life Sketch of Kaprekar and Aryabhata).

Ramanujan group: - For students of Class 9, 10

50% course based on NCERT syllabus, 10% paragraph-based question, 10% on Video based question. 20% Crypt arithmetic & reasoning and 10% History of Indian Mathematics. ( MCQ on Life Sketch of Ramanujan, Bhaskaracharya, Varahmihir and Aryabhata)

Bhaskaracharya group :- For class 11 and 12

50% course based on NCERT syllabus, 10% paragraph-based question, 10% on Video based question. 20% Crypt arithmetic & reasoning and 10% History of Indian Mathematics. ( MCQ on Life Sketch of P C Vaidya, Hemchandra, Sharadchandra Shankar Shrikhande and Brahmagupta)

Number of Questions:- 75 Time: -90 minutes

Date of Examination: - 11th July 2021

Last date of Registration: - 3rd July 2021

Mock test will be done through Mobile app/Web Browser on 3RD/4TH JULY 2021

A MAIL WILL BE SENT TO YOU IN ADVANCE REGARDING MOCK TEST

Keep checking our Facebook Page for more details

FACEBOOK PAGE LINK - DR RAJESH KUMAR THAKUR

FACEBOOK PAGE- MATHS ADDA

AIRMC FACEBOOK PAGE

Ramanujan Remembrance Day Quiz

 Dear Friends

Today is the death anniversary of Mathematical Genius Srinivasa Ramanujan Iyengar. You all have read and learnt a lot about this mathematical genius in the quiz that I conducted last year. I am overwhelmed with the response I got in 3 quiz I conducted on the life of Srinivasa Ramanujan. Nearly 30 thousands students, teachers and researcher across the globe participated in the quiz.

I got many WhatsApp messages from my friends and emails from many of the participants requesting me to conduct quiz on Ramanujan's death anniversary. I do hope you will enjoy the quiz. 

Click the link to play the quiz

You can watch the PPT of 1st round of quiz consisting of 60 questions on the life of Srinivasa Ramanujan.

watch the quiz on Youtube

Thanks a lot 

Dr Rajesh Kumar Thakur

Application of Mathematics :- Sh. K. Bhanumoorthy

 

Topic: Application of Mathematics

 

In school curriculum mathematics is one of the subjects being taught .We are fully aware mathematics is queen of all sciences. It’s applications are vast used in all branches of sciences, all branches of Engineering, Accountancy, Manufacturing Industries, business, food preparation, arts, music, religion etc. We do find in nature, arrangement of petals in flowers, nodes in fruits. More than that applied in our daily life. To site an example even in preparation of food, say rice, there is fixed quantity of water to be poured. Sometimes quantity of water differ to the kind of rice what we use. Preparation of sweets, there is fixed ratio how much sugar, in gradients to be added/mixed. Many more examples to narrate in this way preparation of eatables at home.

The syllabus is graded right from class one to higher classes .There is vertical integration from class to class with a chain of continuity. No doubt there is a linkage to other subjects too. Teachers during their teaching, they could spell out the linkage creating interest in the subject and the reasons why to learn mathematics. In this article, would like to share the duty of teachers to discuss the utility of chapters/ units in our daily life. Let me put across the applications of Linear equations. Linear equations are invented by Irish mathematician Sir William Rowan Hamilton in the year 1843.

Students learn from. Class VII. The teachers have to mention where and all, it’s applications are used. Education is not simply, only knowledge based, it has to be skill oriented. We are preparing students to meet the challenges and use presence of their mind to find the solution rather solve the problem. The solution does not mean the solution for problems in mathematics only, what one has learnt, to apply in real life situations, to overcome the difficulties and find solution what we face in real life. Education is the preparation of one’s life.

Linear equations:  Applied in age related questions; Time, speed ,distance questions; Time and work; daily wages; predicting gain/profit in  business so on.

(------to continue)

 

Mr. K Bhanumoorthy

(The author is a retired Kendriya Vidyalaya Principal. He lives in Bengaluru. He can be reached through Facebook.

https://www.facebook.com/bhanumoorthy.krishnamoorthy