Two good syllabus questions

1

Quadratic Equations

If α, β, γ, δ are the four positive roots of the equation x⁴ -12x³+ax²+bx +81=0, then find “a” and “b”.

2

Permutations and Combinations

Find all possible arrangements of the word "COMBINATORICS" such that all the vowels are in alphabetical order and consonants are also in alphabetical order.

Note: Consonants and vowels to be considered separately.

Note: These are not puzzles but JEE-level questions

What's probable & what's not?

!!Please comment on the correctness of this question!!

In a lucky draw competition, a contestant had to draw 3 tickets from a pile of well-shuffled tickets. If the numbers on these tickets were in arithmetic progression, he would be adjudged the winner of the contest. If the numbers were not in arithmetic progression, he would return them to the pile. The tickets were numbered from 1 to 201. What is the minimum number of contestants to ensure that at least one of them wins the contest? If 100 people took part in the lucky draw, do you think we could take for granted that at-least one contestant would win the prize?

The Consecutive Numbers

A Math teacher, in order to keep two of her students occupied thought of two consecutive numbers in the range 1 to 10, and told one of the students Alex one of the numbers and the other student, Sam the other.

Sam and Alex then had the following conversation:

Alex: I don't know your number.
Sam: I don't know your number, either.
Alex: Now I know!

How many such sets of numbers can you find? Can you find all the sets which could have been thought up by the Math teacher?

Sequence 2

Find the next term of the sequence:
1, 2,6,12,25, _


Hint: The answer is in 40's or 50's

Please give the logic as well as logic only would decide the correctness of the answer.

Lets go on with the Puzzles..

I hope you have done your AP, GP and (HP) Chapter well. If you have ::
Find the next term of the sequence..

2, 3, 10, 12, 13, 20, 21, 22, _

Bad Hint :: Its not related with Fibonacci

Mayank, if you remember the answer please do not post it.

{Level: Medium}

Some more CJ's, SJ's, JC's to make you CRY

I think you are familiar with the term CJ, ie, "Chhonkar Joke" another name for low level(extrreeeeemely low level) sastas..

I have posted these on the blog "Puzzle Spot" because they also involve certain(very different) kind of thinking and presence of mind

Note:Comments are necessary for this post.
I would like you to consider my decisions which I have made upon the level of a PJ after much technical review. However if there are any discrepancies I would consider them.

Here are some. Some are better than CJ so consider them as SJ(Shikhar Joke) and some are even better so you can consider them as JC(Jain Comments)..


Question: An elephant was in love with a she-elephant. But the she-elephant
went and got married to some other elephant. So our elephant was very
Depressed. One of his friends felt sorry for him, and took him to a park to
cheer him up. In the park, they sat on a see-saw, but the see-saw broke.
Now, which song would our hero sing?(CJ)





Ans: "See-saw ho ya dil ho, aakhir toot jaata hai."



Question: Two hairs on a bald man's head fall in
love with each other and want to get married, but
cannot. Why?(SJ)






Ans: Because under Indian laws, "baal vivaah" is
illegal.


Question: One fine morning, Ravan felt guilty day
for all his bad deeds. He felt that he should go an
apologise to Ram for all the problems he had caused. So he went to Ram's
house and knocked on the door. Ram opened the door and was surprised to
find Ravan standing there. Ravan just kept staring and thinking but
didn't say a word. What was he thinking?(JC)





Ans: "Kis mooh se maafi maangoon?"


Question: How do you "cut" roads?(CJ)






Ans: By laughing... because "Haste haste cut jaye
raaste".


Question: Luv and Kush are going to a village and pass by a well. Luv falls
into the well. Why?(SJ)






Ans: Because Luv is blind.


Question: Now, Kush also jumps in. Why?(CJ)






Ans: Because Luv ke liye saala Kush bhi karega!



Question: Jackie Chan ki saas ka naam kyahai? Socho, socho. Nahi pata?(JC)






Ans: D'Cold; Because... Chan ki saans - D'Cold


Question: Chalo ab batao, Jackie Chan ki bahu ka
naam kya hai??(CJ)









Ans: D'Cold again... Kyunki saans bhi kabhi bahu thi


A railway station beggar meets another beggar. A software engineer meets
another software engineer.
Both of them ask the same question to each other.
What is the question?(DJ)-Dipanshu Joke







"So, which platform are you working on?"

A large ssssssssss noise should be produced right at this moment


Question: What do you call a person who is leaving
India?(CJ)




Ans: Hindustan Lever.


Question: What do you call a person who leaves India, but doesn't travel
much?(DJ)





Ans: Hindustan Lever Limited.



Question: In an elephant school, some loafer elephants were hanging around
in the canteen. A sexy female elephant passes by. What do the loafer
elephants say about her?(CJ)






Ans: Look yaar, 36000 - 24000 - 36000!!


Question: Kalidas ka ek bhai joote banata tha. Uska
naam kya tha?(DJ)






Ans: Adidas.


Question: Prasad asks Kumble to bring a Pepsi. Kumble brings a bottle, but
takes it directly to Tendulkar. Why?(JC)





Ans: Because Tendulkar is an opener.


Question: What is the similarity between Satynarayan pooja and the Indian
cricket team?(AGRJ)-understandable






Ans: Dono ke ant me "Prasad" aataa hai.

Question: Who is Joe?(CJ/DJ)







Ans: Kambakth ishq... Because "Kambakth ishq hai
Joe!"


Question: The Madrasi said, I want to see the movie "my heart is an
umbrella'. Which movie did he really want to see?(AGRJ)







Ans: Dil Chhaata Hai.


Woh kaun sa hindi geet hai jis main "Internet Explorer" ka zikar kiya gaya
hai???(DJ)


Hint: The heroine also refers to herself as Internet Explorer.







The answer is... Maine Pyar Kiya.

And the song goes....

Aajaa shaam hone IE (Internet Explorer)
Mausam ne lee angada IE
To kis baat ki hai lada IE
Tu chal........ Main IE !!!




Once 5 CHIPKALIs (house lizards) :
Phulwa,RaamPyaari, RaamDulari,RaamPuri and
RaamChuri were crawling on the wall when all of a sudden, Phulwa started to
sing a song. the moment Phulwa stopped singing the song, RaamPyaari,
RaamDulari, RaamPuri and RaamChuri fell down from the wall !!!... WHY ???(SJ)









coz, they all started clapping !!!!


PJ Isse kehte hain.........

Gattu ek lecture attend karta hai. lecture ke baad use bhookh lagti hai. so
he goes to the canteen. Canteen mein gattu ek pav leta hai. jaise hi woh
pav khane ke liye uthata hai to dekhta hai ki uski plate mein "jannat"
likha hai.

To janaab ab aapko yeh batana hai ki gattu jiska lecture attend karke aa
raha hai, us proffessor kanaam kya hai??? guess(JC)









The answer is

Ishq Ki Chhaon.

Jinke "Sir" ho "Ishq ki Chhaon"
"Pav" ke neeche "Jannat" hogi....

Don't scratch ur head this is a song from film "Dil Se"









What wud u call a Gal who never laughs ????(CJ)










....and the Answer is..........

HASINA !


Once all the scientists die and go to heaven. They decide to play
hide-n-seek. Unfortunately Einstein is the one who has the den. He is
supposed to count up to 100 ...and then start searching. Everyone starts
hiding except Newton. Newton just draws a square of 1 meter and stands in
it rightin front of Einstein. Einsteins counting....
97,98,99.....100........


He opens his eyes and finds Newton standing in front.
Einstein says "newtons out..newtons....out....." Newton denies and says i
am not out. He claims tht he is not Newton. All the scientists come out
and he proves tht he is not Newton...... how ????(JC)



lesson from this PJ- use of physics is not limited








His proof:

Newton says:


I am standing in a square of area 1m square. That means I am Newton per
meter square. Hence I am Pascal....since Newton per meter square = Pascal

Think Free – Your Office Online!!

ThinkFree Online is an Internet-based file sharing and storage ( Java Application).
You'll get 1Giga for free to storage any file you need. (up to10MB for a file)

The platform allows you to:

1. Create Microsoft Office compatible word processing, spreadsheet and presentation files or edit existing documents.
2. Access your most important documents and applications from any computer anytime.
3. Share your inspiration with others - Set the privilege for each person, allowing them either read only or read and edit.
4. Document revision history and rolling back-ThinkFree Online tracks previous versions of a document.
5. Publish live documents within your blog or publish your files to a location on the internet. Send private message/email to your friends when you publish new documents.
6. Add to your work: images, graphs, charts and input from others. Moreover, you can add images from Flickr to your documents.
7. Create your own guest book.
8. Add comments and Tags.

Unfortunately the application is a bit heavy because of the Java but the results are pretty good and the interface is pleasant to use.

ThinkFree Office is compatible with Windows, Macintosh, Unix and Linux systems.

The CocoNut Problem

Five sailors survive a shipwreck and swim to a tiny island where there is nothing but a coconut tree and a monkey. The sailors gather all the coconuts and put them in a big pile under the tree. Exhausted, they agree to go to wait until the next morning to divide up the coconuts.

At one o'clock in the morning, the first sailor wakes up. He realizes that he can't trust the others, and decides to take his share now. He divides the coconuts into five equal piles, but there is one coconut left over. He gives that coconut to the monkey, hides his coconuts (one of the five piles), and puts the rest of the coconuts (the other four piles) back under the tree.

At two o'clock, the second sailor wakes up. Not realizing that the first sailor has already taken his share, he too divides the coconuts up into five piles, leaving one coconut over which he gives to the monkey. He then hides his share (one of the five piles), and puts the remainder (the other four piles) back under the tree. At three, four, and five o'clock in the morning, the third, fourth, and fifth sailors each wake up and carry out the same actions. In the morning, all the sailors wake up, and try to look innocent. No one makes a remark about the diminished pile of coconuts, and no one decides to be honest and admit that they've already taken their share. Instead, they divide the pile up into five piles, for the sixth time, and find that there is yet again one coconut left over, which they give to the monkey.

The Question: What is the smallest amount of coconuts that there could have been in the original pile?

You can also generalize the answer for n number of sailors by devising a C++ program.

Once Again, the Same Puzzle

Find the number of integral solutions to the following equation.
1/x + 1/y = 1/12

The Tourist : Lateral Thinking Puzzle

this is one of the standard L.T. puzzles: Enjoy!!!
the tourist from spain used to suffer from stomach pains regularly. Years ago his doctor had been born in goa. When he came back to his hotel, what was the landlady from israel watching on TV?

Level: Medium


I have a nice clue....request in comments if wanted.