## Category Archives: IITJEE Foundation Math IITJEE Main and Advanced Math and RMO/INMO of (TIFR and Homibhabha)

### Maths will rock your world — a motivational article

keep dreaming the applications of math…try to count every thing….

Jan 23 2006

A generation ago, quants turned finance upside down. Now they’re mapping out ad campaigns and building new businesses from mountains of personal data

Neal Goldman is a math entrepreneur. He works on Wall Street, where numbers rule. But he’s focusing his analytic tools on a different realm altogether: the world of words.

Goldman’s startup, Inform Technologies LLC, is a robotic librarian. Every day it combs through thousands of press articles and blog posts in English. It reads them and groups them with related pieces. Inform doesn’t do this work alphabetically or by keywords. It uses algorithms to analyze each article by its language and context. It then sends customized news feeds to its users, who also exist in Inform’s system as — you guessed it — math.

How do you convert written words into math? Goldman says it takes a…

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### A motivation for Math and some Math competitive exams in India

what motivates you to keep going in math?

Sometime back, there was a tremendous publicity in the Indian media to two Fields medallists of Indian origin. They also talked about what motivated them towards Math when they were young. One should  not do Math just lured by its glamorous applications in IT or other engineering disciplines. But, one can develop both aptitude and attitude  towards it if one works from a young age.

What you need is intrinsic motivation. In this context, I like to quote the following words of a famous mathematician:

“And, a final observation. We should not forget that the solution to any worthwhile problem very rarely comes to us easily and without hard work; it is rather the result of intellectual effort of days or weeks or months. Why should the young mind be willing to make this supreme effort? The explanation is probably the instinctive preference for certain values, that is, the attitude…

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### Skill Check I: IITJEE Foundation Maths

1. Simplify: $(+1) \times (-1) + (+1) \div (-1) -()-1 +(-1) \div (-1) \times (-1) +(-1)$
2. Simplify: $\{ 7 \hspace{0.1in} of \hspace{0.1in} 6 \div 2 - 4(8 \times 12 \div 3 + \overline{-3 \hspace{0.1in} of \hspace{0.1in}+6 -2 })\} \div (-3)$
3. Simplify: $24 \div (-8) + 3 \times (-3)$
4. Simplify: $(+7) - (-3) + (+4) \times (-3) \div (+3) of (-2)$
5. Simplify: $(-3) of (-5) \div (-3) \times (-2) + (-5) - (-2) \div (+2)$
6. Simplify: $(-7) + (-8) - (-3) \hspace{0.1in} of \hspace{0.1in} (-6) \div (+2) - (-4) \times (-4) \div (+2)$
7. Simplify: $(+24) \div (-3) \hspace{0.1in} of \hspace{0.1in} (+4) - (-25) \times (-6) \div (-3) + (-15) \div (-3) \times (-10)$
8. Simplify: $(-3) \hspace{0.1in} of \hspace{0.1in} (-8) \div (-6) - (-8 +4-3)$
9. Simplify: $(-5) [ (-6) - \{ -5 + (-2 + 1 - \overline{3-2}) \} ]$
10. Simplify: $(-3) [ (-8) - \{ +7 - (4-5 - \overline{2-5-1})\}] \div (-11)$
11. Simplify: $(+8) \times (-3) \times (+2) \div [ -1 - \{ -3 + 8 - (6 -2 - \overline{3+5-4}) \} ]$
12. Simplify: $(+32) \div (+2) of (-4) \div [(-7) of 3 \div \{4 - 5(3 - \overline{4 of 2 - 2 of 5}) \}]$
13. Simplify: $(-30) + (-8) \div (-4) \time 2$
14. Simplify: $(-3) \times (-6) \div (-2) + (-1)$
15. Simplify: $56 \div (16 + \overline{4-6}) + (6-8)$
16. Simplify: $(7+6) \times [19 + \{ (-15) + \overline{6-1}\}]$

Regards,

Nalin Pithwa

Purva building, 5A
Flat 06
Mumbai, Maharastra 400101
India

### Math Basics Division by Zero

the eleventh commandment of Moses: Though shall not divide by zero !!

Let’s pause Geometry for a little time and start thinking of some basic rules of the game of Math. Have you ever asked “why is division by zero not allowed in Math?” Try to do 1/2 in a calculator and see what you get!!

This was also a question an immortal Indian math genius, Srinivasa Ramanujan had asked his school teacher when he was a tiny tot. Note the following two arguments against the dangers of division by zero:

(a) Suppose there are 4 apples and two persons want to divide them equally. So, it is 4/2 apples per person, that is, 2 apples per person. But, now consider a scenario in which there are 4 apples and 0 persons. So, how can you divide 4 apples amongst (or by) 0 persons? You can think of any crazy answer and keep on arguing endlessly about it!!!!

(b) The cancellation law…

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### Math from scratch

Most important out of all blogs…explains what is math and the nature of its rigour

Math from scratch!

Math differs from all other pure sciences in the sense that it can be developed from *scratch*. In math jargon, it is called “to develop from first principles”. You might see such questions in Calculus and also Physics.

This is called Axiomatic-Deductive Logic and was first seen in the works of Euclid’s Elements (Plane Geometry) about 2500 years ago. The ability to think from “first principles” can be developed in high-school with proper understanding and practise of Euclid’s Geometry.

For example, as a child Albert Einstein was captivated to see a proof from *scratch* in Euclid’s Geometry that “the three medians of a triangle are concurrent”. (This, of course, does not need anyone to *verify* by drawing thousands of triangles and their mediansJ) That hooked the child Albert Einstein to Math, and later on to Physics.

An axiom is a statement which means “self-evident truth”. We accept…

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### Binomial Theorem : Tutorial Problems II: IITJEE Mains practice

I. Find the $(r+1)6{th}$ term in each of the following expansions:

1. $(1+x)^{-\frac{1}{2}}$
2. $(1-x)^{-2}$
3. $(1+3x)^{\frac{1}{3}}$
4. $(1+x)^{-\frac{2}{3}}$
5. $latex(1+x^{2))^{-3}$
6. $(1-2x)^{-\frac{3}{2}}$
7. $(a+bx)^{-1}$
8. $(2-x)^{-2}$
9. $\sqrt[3]{a^{2}-x^{2}}$
10. $\frac{1}{\sqrt{1+2x}}$
11. $\frac{1}{\sqrt[3]{(1-3x)^{2}}}$
12. $\frac{1}{\sqrt[n]{(a^{n}-nx)}}$

Find the greatest term in each of the following expressions:

1. $(1+x)^{-r}$ when $x=\frac{4}{15}$
2. $(1+x)^{\frac{11}{2}}$ when $x=\frac{2}{3}$
3. $(1-7x)^{-\frac{11}{4}}$ when $x=\frac{1}{8}$
4. $(2x+5y)^{12}$​ when $x=8, y=3$
5. $(b-4x)^{-7}$ when $x=\frac{1}{2}$
6. $(3x^{2}=4y^{3})^{-n}$ when $x=9, y=2, n=15$

Find to five places of decimals the value of:

1. $\sqrt{98}$
2. $\sqrt[3]{998}$
3. $\sqrt[3]{1003}$
4. $\sqrt[4]{2400}$
5. $\frac{1}{\sqrt[3]{128}}$
6. $(\frac{601}{50})^{\frac{1}{3}}$
7. $(630)^{-\frac{2}{3}}$
8. $(3128)^{\frac{1}{4}}$

Regards,

Nalin Pithwa.