Munna Bhaiya Study Tips :: Part I

Every day I answer student’s queries related to how they should prepare for IITJEE; how much to study; what to study; when to study and so on.

I have been answering these question since last 13 years when I started teaching Mathematics for IITJEE.

So I decided to start a series of study tips “IITJEE Simplified” where I will write about the best approaches to follow while preparing for IITJEE exam. In this series, I will also answer most common questions that an IITJEE aspirant can come across.

Here is today’s tip:

How many hours should I study at home?

Some of you out there must be toppers of your class or among the top 10% of your class. But that is just a performance in your class or best at a school level. It means till now you have been competing among a small student base of 50 - 1000 students.

But once you start preparing for IITJEE or AIEEE entrance, the competition is huge. This year in 2008, over 3.2 lakh students appeared in IITJEE and over 9 lakh in AIEEE. So my advice is that you seriously need to scale up your efforts to face the competition.

Are you ready for this?

You need to prepare yourself mentally as well as physically to face this competition. Mentally, you need to think wide when you think of competition you are facing. Remember there are more than 10000 schools (just CBSE) in India. So don’t get defocused and remember that you have to compete with unknowns.

Most of you would have scored well in your school level examinations by not even spending 20 hours on studies at home. This is not going to be enough with such a huge competition. You need to scale up your efforts and set a target of 50-55 hours studies at home every week.

But just sitting in front of the books for these 50-55 hours is not enough. You have to study with full concentration, no disturbance, and continuously for 3 hour sessions. The idea is to simulate real exam conditions. While studying, you have to create an atmosphere as if you are sitting in exam. Avoid doing following during a 3 hours session:

• Study on a desk if you have it at home. Avoid studying while lying down on a bed.
• Don’t get up from your desk during 3 hours of study session. Even not for drinking water.
• Don’t listen music during studies. If you have a habit, then slowly come out of it by reducing it day by day.
• No phone calls and no SMS during studies.
• Study with 100 percent concentration as if you are sitting in exam.

Note: to make up 50-55 hours you need to study 6-7 hours every day during the week and remaining 20-25 hours over the weekend.

Crazy Questions at Google Job Interview

Many are open ended with several right answers and many I haven't been able to answer, therefore I did not provide the answers.

1. How many golf balls can fit in a school bus?....(Good Question)

2. You are shrunk to the height of a nickel and your mass is proportionally reduced so as to maintain your original density. You are then thrown into an empty glass blender. The blades will start moving in 60 seconds. What do you do?

3. How much should you charge to wash all the windows in Seattle?....(Good Question)

4. How would you find out if a machine’s stack grows up or down in memory?

5. Explain a database in three sentences to your eight-year-old nephew....(not relevant for us enough!)

6. How many times a day does a clock’s hands overlap?

7. You have to get from point A to point B. You don’t know if you can get there. What would you do?

8. Imagine you have a closet full of shirts. It’s very hard to find a shirt. So what can you do to organize your shirts for easy retrieval?

9. Every man in a village of 100 married couples has cheated on his wife. Every wife in the village instantly knows when a man other than her husband has cheated, but does not know when her own husband has. The village has a law that does not allow for adultery. Any wife who can prove that her husband is unfaithful must kill him that very day. The women of the village would never disobey this law. One day, the queen of the village visits and announces that at least one husband has been unfaithful. What happens?

10. In a country in which people only want boys, every family continues to have children until they have a boy. if they have a girl, they have another child. if they have a boy, they stop. what is the proportion of boys to girls in the country?

11. If the probability of observing a car in 30 minutes on a highway is 0.95, what is the probability of observing a car in 10 minutes (assuming constant default probability)?

12. If you look at a clock and the time is 3:15, what is the angle between the hour and the minute hands? (The answer to this is not zero!)

13. Four people need to cross a rickety rope bridge to get back to their camp at night. Unfortunately, they only have one flashlight and it only has enough light left for seventeen minutes. The bridge is too dangerous to cross without a flashlight, and it�s only strong enough to support two people at any given time. Each of the campers walks at a different speed. One can cross the bridge in 1 minute, another in 2 minutes, the third in 5 minutes, and the slow poke takes 10 minutes to cross. How do the campers make it across in 17 minutes?....(remember class 10th quiz)

14. You are at a party with a friend and 10 people are present including you and the friend. your friend makes you a wager that for every person you find that has the same birthday as you, you get $1; for every person he finds that does not have the same birthday as you, he gets $2. would you accept the wager?(My answer....No)

15. How many piano tuners are there in the entire world? (piano tuners...????)

16. You have eight balls all of the same size. 7 of them weigh the same, and one of them weighs slightly more. How can you find the ball that is heavier by using a balance and only two weighings?...simple

17. You have five pirates, ranked from 5 to 1 in descending order. The top pirate has the right to propose how 100 gold coins should be divided among them. But the others get to vote on his plan, and if fewer than half agree with him, he gets killed. How should he allocate the gold in order to maximize his share but live to enjoy it? (Hint: One pirate ends up with 98 percent of the gold.)....already posted

2=1 ?

First Way to prove it.
(n+1)^2 = n^2 + 2n + 1
or, (n+1)^2 - (2n+1) = n^2
subtracting n(2n+1),
or, (n+1)^2 - (n+1)(2n+1) = n^2 - n(2n+1)
or, (n+1)^2 - (n+1)(2n+1) + 1/4(2n+1)^2 = n^2 - n(2n+1) + 1/4(2n+1)^2
or, (n - 1/2)^2 = (n + 1/2)^2
or, (n - 1/2) = (n + 1/2)
or, -1/2 = +1/2
or, 1 = 0
or, 2 = 1 !!


Second Way

4*4 = 4 + 4 + 4 + 4

:. 4*4= 4 + 4 +… 4 times.

:. x*x = x + x + … x times.

Differentiating,

2*x = 1 + 1 + 1 … x times.

:. 2*x = x

Hence 2 = 1!!!

Third Way

Every1 here knows the pretty little Binomial thorem going as :

(a+b)n = an + n*b*an-1 + ... + n*bn-1*a + bn
Observing we find that leaving the first and last term, all other terms are a multiple of n.
For some wierd results, let us put n = 0 ;
LHS = (a+b)0 = 1
RHS = a0 + 0 ... + 0 + b0
= 1 + 0 ... 0 + 1
= 2
:. since LHS = RHS
2 = 1

Fourth Way
- 1 = - 1
or, sqrt(-1) = sqrt(-1)
or, sqrt(-1/1) = sqrt(1/-1)
or, sqrt(-1)/sqrt(1) = sqrt(1)/sqrt(-1)
or, i/1 = 1/i
or, i2 = 1
or, -1 = 1
or, 2 = 0
or, 1 = 0
or, 2 =1

Fifth Way

The very interesting infinitie series :

0 = 0 + 0 + 0 + 0 ...

For those who don't find it so interesting, follow me.

0 = ( 1 - 1 )
:. 0 = ( 1-1 ) + ( 1-1 ) + ( 1-1 ) ...

Now all of you would have paid attention in primary school when we were taught the associative law of addition.
Interestingly applying that here,

0 = ( 1-1 ) + ( 1-1 ) ...
or, 0 = 1 + (-1+1) + (-1+1) ...
or, o = 1 + 0 + 0 + 0 + 0 + ...
or, 0 = 1
or, 1 = 2

Sixth Way

- 20 = - 20

or, 25 - 45 = 16 - 36

or, 5² - 5*9 = 4² - 4*9

or, 5² - 5*9 + 81/4 = 4² - 4*9 + 89/4

or, (5 - 9/2)² = (4 - 9/2)²

or, (5 - 9/2) = (4 - 9/2)

or, 5 = 4

or, 2 = 1

The question is, Can you find another way of proving it?