### CLASS XII MATHS ANSWER KEY

### HAPPY BIRTHDAY TO GREATEST INDIAN MATHEMATICIAN -- SRINIVASA RAMANUJAN

The Indian mathematician Srinivasa Ramanujan Aiyangar (1887-1920) is best known for his work on hyper geometric series and continued fractions.

Srinivasa Ramanujan, born into a poor Brahmin family at Erode on Dec. 22, 1887, attended school in nearby Kumbakonam. By the time he was 13, he could solve unaided every problem in Loney's *Trigonometry ,*and at 14 he obtained the theorems for the sine and the cosine that had been anticipated by L. Euler.

Ramanujan became so absorbed in mathematics that when he entered the local government college in 1904 with a meritscholarship, he neglected his other subjects and lost the scholarship. Ramanujan married in 1909, and while working as a clerk he continued his mathematical investigations.

In January 1913 Ramanujan sent some of his work to G. H. Hardy, Cayley lecturer in mathematics at

far beyond, some of the latest conclusions of Western mathematicians.

In 1914 Ramanujan went to

In 1918 Ramanujan was elected a fellow of the Royal Society and a Fellow of Trinity College,

However, the story goes that , Ramanujan’s health deteriorated greatly while he was in

### APNO GHAR TRIP ON 4 DEC 2010

### CLASS XI - ENRICHMENT ASSIGNMENT - I

### First Intra-School Maths Olympiad

###
**
Dear all
**

**
Dear all
**

**The school's Mathematics Department is organising the First Intra-School Mathematics Olympiad for all the classes (I - XII) on Tuesday, 9 November 2010 in the school.**

**All the students of classes I-XII who have scored at least 75% marks in mathematics in their previous class are eligible to participate in the Olympiad. (And all those students who are interested but do not satisfy the eligibility criteria may also participate, provided they submit a recommendation letter from their respective mathematics teacher.)**

**The questions may be expected from**

*non-routine math*of various topics of school mathematics. The question paper will only contain multiple choice questions.

**THERE IS NO ENTRY/REGISTRATION FEE.**

**DATE OF EXAM: 09 NOVEMBER 2010 (Tuesday)**

**DURATION OF EXAM: 1 HOUR AND 30 MINUTES**

**LAST DATE TO APPLY: 30 OCTOBER 2010 (Saturday)**

**FOR OTHER DETAILS, CONTACT YOUR MATHEMATICS TEACHER.**

Link to question papers,answer key and the result.

Amit Sir

### Solve it - Question no. 15

### PROUD TO BE A TEACHER

### What is the best way to study mathematics

### Dear All

Mathematics is Fun

### MATH FUN

### Dear All

Just do the following multiplication :

13837 x Your Age x 73 = ? ? ?

You get very interesting resut, let me know.

You get the same result if you multiply 10001 * your age * 101

How is that?

### INTERSTING NUMBER 37

### NUMBER 37 IS AN INTERESTING NUMBER:

111/(1+1+1)=37

222/(2+2+2)=37

333/(3+3+3)=37

444/(4+4+4)=37

555/5+5+5=37

666/(6+6+6)=37

777/(7+7+7)=37

888/(8+8+8)=37

999/(9+9+9)=37

### Setting Goals after Board Results

__Setting Goals after Board Results__

There are certain basic *fundas* that you need to know while setting your goals :

**A)** **Write down all your goals separately**. Writing is described as the act of inscribing characters or shapes on a surface to convey thoughts and ideas. Have you ever wondered why this symbolic, mechanical act is considered so important in the goal-achievement process?

It is important because putting pen to paper gives body to our thoughts. It transfers non-verbal cues into tangible, concrete expressions. The writing becomes your signed testimonial. You can look at it, physically from a distance and it will remind you of what you promised yourself a year ago.

This act of using your eye in co-ordination with your hand, while holding a pen, will make a firm impression on your mind, so while you are reading or re-reading a particular phrase, a sentence or a book section, this impression consolidates and slips deeper into our subconscious.

**B)** **Define goals in terms of specific activities and specific processes**. Without specifics, the whole exercise is futile and meaningless. So split your goals in terms of specific actions and prioritise those actions.

**C)** **Prioritise and re-prioritise your goals**. This will help you make the maximum use of your time resource, so that nothing important gets left out.

**D)** **Identify your obstacles**. These could be internal, as well as external. Decide what additional knowledge you need to gather before you can set out to achieve your goals.

**E)** **Define your goals and start working backwards from those goals**. Affirmative commands are excellent for time management. Keep repeating to yourself, “I am always punctual”, “I am well-organised”, “I use my time productively.” Repeat these commands in your spare time. Act or pretend as if you have already begun to follow these commands.

In short, fake it until you make it.

**To solve a problem or to reach a goal, you...don't need to know all the**

**answers in advance. But you must have a clear idea of the problem or**

**the goal you want to reach.**

### DIFFERENT KINDS OF NUMBERS NUMBERS

** Deficient number** -number whose proper divisors add up to less than itself. For example, 16 is a deficient number as sum of its proper divisors {1, 2, 4, 8} = 15.

** Abundant number** -number whose proper divisors add up to more than the number itself. For example, 18 is a abundant number as 1+2 +3 +6 +9 = 21. Can you find the smallest abundant number?

** Happy number** -number for which the sum of the squares of the digits eventually equals 1.For example, 203 is happy because 2² +0² +3² = 13; 1² +3² = 10; 1² +0² = 1

Can you think of another happy number? An unhappy number?

### Solve it - Question 14

Solve the following question:

well, we have a quick respose by Prabhat. Well done!

I will appriciate if you could give your responses in the comment section of the post. Anyways, here is the solution:

### DIFFERENT KINDS OF NUMBERS NUMBERS

**Dear All**

Do you know any perfect human being! May be NO... But, in mathematics there are the numbers which are perfect. Let us consider the following definition:

**Perfect number**-number whose divisors (except itself) add up to itself. For example,. 28 is a perfect number. Its proper divisors are {1, 2, 4, 7, 14} and 1 +2 +4 +7 +14 = 28.

Well, Can you find the smallest perfect number?

All perfect numbers less than 500.

Is 360 a perfect number?

Find out more about perfect numbers and explore the beautiful world of numbers!

### Math Joke

hungry so he stopped at a nearby pizza place and ordered a large pizza. When it was ready, the pizza guy asked him if he wanted it cut into six or eight pieces. The Math major replied, “Cut it

into six—I don’t think I could eat eight pieces.”

### SOLVE IT - QUESTION 13

Today, I am posting a very interesting problem. Waiting for your responses...

QUESTION:

### Solve it - Question 11

### Solve it - Question 10

### HAPPY NEW YEAR 2010

I wish Happy New Year 2010 to all of you. May God fulfill your dreams of life to be true and keep you healthy, give you wealth, family prosperity, happiness, free from all worries, achieve your goal, and other good wishes.