KATBABA

2009-09-20T00:14:00.001+05:30

here are a few papers for u r practise...........so go download them

"my stuff"

2009-09-20T00:05:00.001+05:30

great websites to improve your vocabulary try out them..............

MNEMONIC DICTIONARY-----technique to remember words

WORDZA---become the word czar

cat 09--the surprise factor

2009-09-13T23:56:00.000+05:30

Everybody knows that CAT is one of the most unpredictable exams held in India and abroad. Every year it presents a new surprise. The biggest one for 2009 or rather the biggest till date is the news that CAT 09 is going to be computer-based.

However, it would be wrong to assume that this will be the only surprise in store. MBA aspirants who have prepared themselves with information about past CATs wil find it easier to develop flexible time management strategies, thus eliminating the effects of a changed CAT pattern.

Towards this end, examination experts at www.TCYonline.com have done a critical analysis of the previous CATs by measuring the three most crucial factors that remain tricky in all CATs. These are:

Number of questions and their break up into the Quant, Verbal and DI sections
Total time and its break up into sub-sections
Difficulty level of the questions

It has been observed that whatever CAT one takes for analysis, the interplay of these three factors has consistently been responsible for the 'surprise' factor.

Let us try to identify what were the indicators of the difficulty level of any section of CAT in the past. We recognise the fact that the level of difficulty is a quite a subjective experience. A section that is difficult for one candidate may be the only score getter for another. Still, a sprinter must know what the real obstacles are in his sprint so that he may adjust his pace and concentration in order to conquer them. Hence, a comprehensive knowledge of a different combination of the three factors -- which eventually boil down to TDS ie time, difficulty and speed -- will help us know the approximate dimensions of our obstacles (over and above those offered by its computer-based , which are discussed at http://getahead.rediff.com/report/2009/apr/29/cat-online-challenges-myths.htm) in CAT 2009.

When we look at all the possible ways the experts explored to define "difficulty" in a CAT, we found that most times it is the interplay of the total time available, the number of questions and length and complexity of their statement that decide whether a particular set of questions were easy, moderate or difficult. Hence, the importance of analysis and daily ranking (www.TCYonline.com/subscription) cannot be over emphasised.

Additionally, it can be seen that the questions are getting easier but trickier with each CAT since CAT 2004. This, together with the fact that Prometric -- the company who will administer CAT 09 -- has a track record of presenting trickier and lengthy statement-based questions in Quant as well as Verbal, has left no option for test-takers but to concentrate on each and every question that they come across throughout the year. The key is not to do more questions but to repeatedly do a balanced set of questions with optimum representation of all areas. One must understand that CAT 09 preparation is not a mere MOCK CAT game; rather one needs to know one's performance everyday and should get a chance to compare it with the best of the nation in each test.

At this crucial juncture, the FREE online CAT course offered by TCYonline.com (http://www.tcyonline.com/cat2009/cat_preparation.php) and the online tools like Test Generator (www.TCYonline.com/CreaTest) and Challenge Zone (www.TCYonline.com/LetUsChallenge) come handy for a CAT 2009 aspirant. These offerings can contribute for the missing technology-link that exists between the traditional CAT prep ways and the demands of the new computer-based CAT.

source:-rediff.com and tcyonline

technique of remembering words

2009-09-13T23:53:00.000+05:30

recondite-secret,profound(re+con+dite-----keep something inside(diet inside)...thats a secret)

redlinquish-abandon(red+link+ish.....red means stopor danger.....which is linked to abandon the place)

pariah-untouchables..............i hate angeles

torpor-inactive..laathkhor pati bhasae

abet--misleading to do something wrong(a+bet.....betting is evil)

abhor---dislike or hating(boring person is disliked)

cadavar-----dead body,corpse..........cadet+war......a cadet got killed in a war.........so his corpse remains....

paragon-----perfection,excellence............par+a+gone...........equal not present

yore------long past,long ago...............yore rhymes witth bore.and we generally bored by age old things.

caulk-----to make watertight.........caulk sonds like cork........cork is used to make things worktight

cache-----hiding place............cache sounds like cash.......so u have to hide it somewhere

laudatory---------praising..........we applaud to praise........applaid rhymes with laud....so worth applauding

machiavellian-----crafty..........fro machiavelli's rule of cunning way of gaining power

onus--burden............comes frm "ON US".......U R BURDEN ON US

loquacious-----talkative.....haveing the ability rto grab the attention of others through speech......lok means people.......loksabha here mps speak and speak.......trying to ocatch attetion of others and speaker espc

venerate------sacred/adore..........venus-----symbol of love.......is reespected as such

abash-----embrassed......AB+ASH........THEIR marriage...caused embrassement to vivek and sallu.who couldnt get her

ulterior--------hidden intentionally.........ultra+interior....thing is at depths of depth.....so is thre due to someone hiding it there

aargh---used to show anger.........aagh(fire)...expresses rage

obeisance.......willingness to obey............obey+saints....we obey saints as we held them as elders

palliavate------sothe...u r pal always tries to sothe u when ur in distress

watershed-----turningpoint,high area dividing the regions drained by differnt by differrent rivers......shed frm rainfall can be turning point to ur miseries added by rain.......u may find a girl alone there standing under the shed..............!!!!!!!!

tryst-----a secret meeting between two lovers.........trust bonds two lovers and so they meet

NUMBER THEORY-basics

2009-09-13T23:50:00.000+05:30

_________________________________________________________________________________________________

Number Theory

Cyclicity

At times there are questions that require the students to find the units digit in case of the numbers occurring in

powers. If anyone asks you to find the unit digit of 33, you will easily calculate it also you can calculate for 35

but if any one ask you the unit digit of 17399, it will be hard to calculate easily.

But it’s very simple if we understand that the units digit of a product

is determined by whatever is the digit at the units place irrespective

of the number of digits. E.g. 5 × 5 ends in 5 & 625 × 625 also ends in 5.

Now let’s examine the pattern that a number generates when it occurs in

powers of itself.

See the last digit of different numbers.

Unit Digit Chart

TABLE SHOWING THE UNIT DIGIT OF A NUMBER FOR DIFFERENT EXPONENTS

N1 N2 N3 N4 N5 N6 N7 N8 N9

1 1 1 1 1 1 1 1 1 1

2 2 4 8 6 2 4 8 6 2

3 3 9 7 1 3 9 7 1 3

4 4 6 4 6 4 6 4 6 4

5 5 5 5 5 5 5 5 5 5

6 6 6 6 6 6 6 6 6 6

7 7 9 3 1 7 9 3 1 7

8 8 4 2 6 8 4 2 6 8

9 9 1 9 1 9 1 9 1 9

From the above table we can conclude that the unit digit of a number repeats after

an interval of 1, 2 or 4. Precisely we can say that the universal cyclicity of all the

numbers is 4 i.e. after 4 all the numbers start repeating their unit digits.

Therefore, to calculate the unit digit for any exponent of a given number we have

to follow the following steps

Step 1: Divide the exponent of the given number by 4 and calculate the remainder.

Step 2: The unit digit of the number is same as the unit digit of the number raise to

the power of calculated remainder.

Step 3: If the remainder is zero, then the unit digit will be same as the unit digit of N4.

Let us consider an example

Ex.1 Find the last digit of (173)99.

Sol. We notice that the exponent is 99. On dividing, 99 by 4 we get 24 as the quotient & 3 as the remainder.

Now these 24 pairs of 4 each do not affect the no. at the units place So, (173) 99 ≈ (173)3. Now, the

number at the units place is 33 = 27.

Find the last digit of

(232)222 + (173)99?

Last two digits

For 25N = 25

For 76N = 76

Know me

4 is the universal

cyclicity for finding

the unit digit of any

number

_________________________________________________________________________________________________

Factors

A factor is a number that divides another number completely. e.g. Factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24.

Number of Factors

If we have a number, N = pa × qb × rc

Where p, q, and r are prime numbers and a, b, and c are the no. of times each

prime number occurs , then the number of factors of n is found by (a + 1) (b +

1)(c + 1).

Example:

Find the number of factors of 24 × 32.

Number of factors = (4 + 1) (2 + 1) = 5(3) = 15

Number of Ways of Expressing a Given Number as a Product of Two Factors

When a number is having even number of factors then it can be written as a product of two numbers in

( )( )( )

a + 1 b + 1 c + 1

ways.

But if a number have odd number of factors then it can be written as a product of two different numbers in

( )( )( )

a + 1 b + 1 c + 1 −1

ways and can be written as a product of two numbers (different or similar) in

( )( )( )

a + 1 b + 1 c + 1 + 1

ways.

Examples:

1. 148 can be expressed as a product of two factors in

6 or 3 ways.

{Because (p + 1) (q + 1) (r + 1) in the case of 148 is equal to 6}.

2. 144 (24.32) can be written as a product of two different numbers in

( )( )

4 + 1 2 + 1 −1

i.e. 7 ways

Sum of the factors of a number:

If a number N is written in the form of N = ap.bq.cr ,where a, b & c are prime numbers and p, q & r are positive

integers, then the sum of all the factors of the number are given by the formula

Sum of factors = ( )( )( )

(a 1)(b 1)(c 1)

ap 1 1 bq 1 1 cr 1 1

− − −

+ − + − + −

Factorial

Factorial is defined for any positive integer. It is denoted by or !. Thus “Factorial n” is written as n!

n! is defined as the product of all the integers from 1 to n.

Thus n! = 1.2.3. …. n. (n! = n(n – 1)!)

Finding the Highest power of the number dividing a Factorial

Ex.2 Find the largest power of 3 that can divide 95! without leaving any remainder.

Find the largest power of 3 contained in 95!.

Sol. First look at the detailed explanation and then look at a simpler method for solving the problem.

FUNDA

All the perfect

squares have odd

number of factors

and other number

have even number of

factors

_________________________________________________________________________________________________

When we write 95! in its full form, we have 95 × 94 × 93 ….. × 3 × 2 × 1. When we divide 95! by a power

3, we have these 95 numbers in the numerator. The denominator will have all 3’s. The 95 numbers in

the numerator have 31 multiples of 3 which are 3, 6, 9….90, 93.Corresponding to each of these

multiplies we can have a 3 in the denominator which will divide the numerator completely without

leaving any remainder, i.e. 331 can definitely divide 95!

Further every multiple of 9, i.e. 9, 18, 27, etc. after canceling out a 3 above, will still have one more 3

left. Hence for every multiple of 9 in the numerator, we have an additional 3 in the denominator. There

are 10 multiples of 9 in 95 i.e. 9, 18….81, 90. So we can take 10 more 3’s in the denominator.

Similarly, for every multiple of 33 we can take an additional 3 in the denominator.

Since there are 3 multiples of 27 in 91 (they are 27, 54 and 81), we can have three more 3’s in the

denominator.

Next, corresponding to every multiple of 34 i.e. 81 we can have one more 3 in the denominator. Since

there is one multiple of 81 in 95, we can have one additional 3 in the denominator.

Hence the total number of 3’s we can have in the denominator is 31 + 10 + 3 + 1, i.e., 45. So 345 is the

largest power of 3 that can divide 95! without leaving any remainder.

The same can be done in the following manner also.

Divide 95 by 3 you get a quotient of 31. Divide this 31 by 3 we get a quotient of 10. Divide this 10 by 3

we get a quotient of 3. Divide this quotient of 3 once again by 3 we get a quotient of 1. Since we cannot

divide the quotient any more by 3 we stop here. Add all the quotients, i.e. 31 + 10 + 3 + 1 which gives

45 which is the highest power of 3.

Add all the quotients 31 + 10 + 3 + 1, which give 45.

{Note that this type of a division where the quotient of one step is taken as the dividend in the

subsequent step is called “Successive Division”. In general, in successive division, the divisor need

not be the same (as it is here). Here, the number 95 is being successively divided by 3.

Please note that this method is applicable only if the number whose largest power is to be found out is

a prime number.

If the number is not a prime number, then we have to write the number as the product of relative

primes, find the largest power of each of the factors separately first. Then the smallest, among the

largest powers of all these relative factors of the given number will give the largest power required.

Ex.3 Find the largest power of 12 that can divide 200!

Sol. Here we cannot apply Successive Division method because 12 is not a prime number. Resolve 12 into

a set of prime factors. We know that 12 can be written as 3 × 4. So, we will find out the largest power of

3 that can divide 200! and the largest power of 4 that can divide 200! and take the LOWER of the two

as the largest power of 12 that can divide 200!.

3 9 5

3 31 ---> Quotient

3 10 ---> Quotient

3 3 ---> Quotient

1 ---> Quotient

_________________________________________________________________________________________________

To find out the highest power of 4, since 4 itself is not a prime number, we cannot directly apply the

successive division method. We first have to find out the highest power of 2 that can divide 200!. Since

two 2’s taken together will give us a 4, half the power of 2 will give the highest power of 4 that can

divide 200!. We find that 197 is the largest power of 2 that can divide 200!. Half this figure-98-will be the

largest power of 4 that can divide 200!.

Since the largest power of 3 and 4 that can divide 200! are 97 an 98 respectively, the smaller of the

two, i.e., 97 will be the largest power of 12 that can divide 200! without leaving any remainder.

Ex.4 What is the last digit of 234 × 334 × 434

Sol. Given = (24)34

Last digit of 4n is 6, if n is even. ⇒ Answer 6

Ex.5 What is the right most non zero digit of (270)270

Sol. The required answer is the last digit of 7270.

Last digit of 7 powers repeat after every 4.

So, the last digit of 7270 is the last digit of 72 = 9.

Ex.6 How many factors do 1296 have?

Sol. 1296 = 4 × 324

= 4 × 4 × 81

= 24 × 34

Number of factors = (4 + 1) (4 + 1) = 25.

Ex.7 If x is the sum of all the factors of 3128 and y is the no of factors of x and z is the number of

ways of writing ‘y’ as a product of two numbers, then z = ?

Sol. 3128 = 4 × 782

= 4 × 2 × 391

= 23 × 17 × 23

∴ x = ⎟

⎟

⎠

⎞

⎜ ⎜

⎝

⎛

−

⎟ ⎟

⎠

⎞

⎜ ⎜

⎝

⎛

−

⎟ ⎟

⎠

⎞

⎜ ⎜

⎝

⎛

−

23 1

17 1

2 1

24 1 2 2

= 15 × (17 + 1) (23 + 1)

= 3 × 5 × 9 × 2 × 8 × 3

= 24 × 34 × 5

∴ y = (4 + 1) (4 + 1) (1 + 1)

= 2 × 52

∴ z =

1 { (1 + 1) (2 + 1) } = 3

Ex.8 How many cofactors are there for 240, which are less than 240?

Sol. 240 = 16 × 15

= 24 × 3 × 5

Number of co primes to N, which are less than N

= N − − − − ⎟⎠

⎞

⎜⎝

⎛ − ⎟⎠

⎞

⎜⎝

⎛ −

1 1

_________________________________________________________________________________________________

if N = ab × bq × - - - - (a, b, - - - - are Prime no.s)

∴ Number of co primes to 240 = ⎟⎠

⎞

⎜⎝

⎛ − ⎟⎠

⎞

⎜⎝

⎛ − ⎟⎠

⎞

⎜⎝

⎛ −

1 1

240 1 1

= 240 × 64

1 × × =

Ex.9 What is the sum of all the co primes to 748? Which are less than N?

Sol. 748 = 4 × 187

= 22 × 11 × 17

Number of co primes = 748 ⎟⎠

⎞

⎜⎝

⎛ − ⎟⎠

⎞

⎜⎝

⎛ − ⎟⎠

⎞

⎜⎝

⎛ −

1 1

748 × 1 × × = 320.

Sum of all the co primes to N. which are less than N is

N (number of co primes to N, which are less

than N.

∴ Sum = 320

748 ×

= 119680

Ex.10 In how many ways 5544 can be written as a product of 2 co primes?

Sol. If N = ap × bq × - - - -, where a, b, - - - - are prime numbers

N can be written as a product of two co primes in 2n-1 ways, where n is the number of prime factors to

∴ 5544 = 11 × 504

= 11 × 9 × 56

= 11 × 9 × 8 × 7

= 23 × 32 × 7 × 11

∴ Answer: = 24-1 = 23 = 8. (Because, 2, 3, 7 & 11 are four different prime factors).

Ex.11 If n! have 35 zeroes at the end. What is the least value ‘n’ will take?

(1) 110 (2) 120 (3) 130 (4) 140 (5) 145

Sol. Since the number of zeroes are 35, 535 should exactly divide n! by trail & error, take n = 140.

So, there are 34 zeroes.

∴ The answer should be 145. Answer: (5)

5 140

_________________________________________________________________________________________________

Ex.12 ‘N’ is a five digit number. The last digit of N35 is 2. What is the last digit of N?

(1) 2 (2) 3 (3) 7

(4) 8 (5) Cannot be determined

Sol. The last digit repeats after every 4th power.

Since the last digit of N35 is 2

⇒ The last digit of N3 is 2

Which is possible only for 8. Answer: (4)

Ex.13 What is the right most non zero digit in 20

Sol. 20

40 = ( ) 60 20

20 20

80 40

2 10

2 10 = ×

The required answer is the last digit of 260 = 6

VERBAL TEST-1

2009-09-13T23:45:00.000+05:30

DIRECTIONS for questions 1 to 4: Each question has a word that has been used in a sentence that gives its contextual usage. From the choices, choose the word that is the most appropriate substitue for the question word, in the context.

1. Scoffed(at): A 20% growth in exports is not something to be scoffed at.

(1) tanned (2) appreciated (3) devalued (4) followed

2. Flamboyance: Mr. Sarkar is known for his flamboyance but little else.

(1) exaggeration (2) flagellation (3) industry (4) ostentation

3. Reiterate: The minister in his speech has reiterated the established policy stance.

(1) repeated (2) opposed (3) supported (4) encouraged

4. Corroborative: It is not always possible to obtain corroborative evidence in insurgency cases.

(1) authentic (2) misleading (3) spurious (4) confirmative

DIRECTIONS for questions 5 to 8: For each word given below, a contextual usage is provided. From the alternatives given, pick the word that is the most inappropriate substitute for the question word, in the given context.

5. Jaundiced: The disillusioned prisoners of war developed a jaundiced view of the UN’s peace intiatives.

(1) cynical (2) puerile (3) pessimistic (4) disenchanted

6. Desecrated: The suburb was tense after an idol had seen desecrated by hooligans.

(1) vandalized (2) violated (3) defaced (4) impaired

7. Winding: Driving down the winding ghat roads requires great caution and skill.

(1) serpentine (2) aligned (3) sinuous (4) tortuous

8. Straitened: The sudden death of the patriarch left the family in straitened circumstances.

(1) penurious (2) destitute (3) dire (4) impoverished

DIRECTIONS for Questions 9 to 12: In each question, the word at the top of the table is used in four different ways, numbered 1 to 4.Choose the option in which the usage of the word is INCORRECT or INAPPROPRIATE.

9. Shadow

1 The children were having fun chasing each other’s shadow.

2 Though I tried hard, her work put mine in the shadow.

3 People live under the shadow of fear in a military regime.

4 I knew beyond a shadow of doubt that he was lying.

10. Bill

1 Post the bill quickly lest anyone should notice it.

2 His suffering from severe cold can be easily made out from his bill.

3 Look how sharp the bill of that woodpecker is.

4 The bill was passed by 290 votes to 85.

11. Concerned

1 We should make no compromise where safety is concerned.

2 Parents are concerned about excessive violence on television.

3 They were more concerned about how the speaker was dressed than about what she was saying.

4 She has started making a concerned effort to find a job.

12. Flag

1 Unless we flag him without food for two more days, he will not speak the truth.

2 Though indefatigable, he began to flag before the match ended.

3 Can you flag all the relevant pages in this book?

4 No other flag can be hoisted here except ours.

DIRECTIONS for questions 13 to 16: Select the correct word/words from the choices that complete the given sentence. Please note that more than once choice may fit in to make a syntactically correct sentence but select the choice that is logical in the context of the

sentence.

13. An experienced politician, who knew better than to launch a campaign in troubled political waters, she intended to wait for a more

______ occasion before she announced her plans.

(1) propitious (2) provocative (3) questionable (4) perfect

14. The judge ruled that the evidence was inadmissible on the grounds that it was not ______ to the issue at hand

(1) useful (2) germane (3) manifest (4) inchoate

15. To seek ______ from the ______ summer of the plains, many people prefer going to cooler climes during the summer months.

(1) refuge . . . scalding (2) shelter . . . boiling (3) respite . . . scorching (4) solace . . . blazing

16. The columnist was almost ______ when he mentioned his friends but he was unpleasant and even ______ when he discussed people who irritated him.

(1) recalcitrant . . . sarcastic (2) reverential . . . acrimonious

(3) sensitive . . . remorseful (4) insipid . . . militant

DIRECTIONS for questions 17 to 21: Fill the blanks in the passages below with the most appropriate word from the options given for each gap. The right words are the ones used by the author. Be guided by the author’s overall style and meaning when you choose the

answers.

Twenty-five years ago, when Mauritius gained independence from Britain, this nation of 1.1 million seemed like anything but paradise.With ----17--- unemployment and one of the fastest growing populations in the world, Mauritius looked as if it were ----18--- heading for disaster. Yet over the past decade, the island has witnessed an extraordinary economic boom. Mauritius today is a success and one of the few ----19--- democracies in Africa.

17. (1) chronic (2) lingering (3) characteristic (4) incessant

18. (1) irrefutably (2) irresistibly (3) irrationally (4) irretrievably

19. (1) malfunctioning (2) performing (3) functioning (4) farfetched

Turning out concise, cliched paragraphs, with little ----20--- but at high speed, is a talent that is greatly prized by international news agencies - along with a stomach for filthy coffee and the ability to work round the clock. Nothing will kill off a natural writing gift quite so well as a ----21--- news-agency training.

20. (1) orthodoxy (2) originality (3) authenticity (4) organization

21. (1) widespread (2) superficial (3) thoughtful (4) thorough

HOW TO IMPROVE YOUR VOCABULARY

2009-06-05T03:06:00.000+05:30

This is my first post.let us start with som voc. fundas..........for english portion of CAT.Following are a few methods for expanding your vocabulary with words you will feel comfortable using. Try one or more of these at your convenience. The ones that seem most appealing will probably work best for you.

1. Make a list of subjects that fascinate you most. The more you enjoy a topic, the easier to learn about it. Now go to your local library and search for a dictionary of words specific to one of these topics. If you like Baseball you may find a dictionary of baseball words for example. Not every topic will have its own dictionary of relevant words but you? I be surprised how many do. Once you have found a dictionary for one of your favorite topics, thumb through it looking for words that you have never heard or words you have heard that you don? know the meanings of. The sheer joy of having found the words and their meanings will help them sink into your memory. Since they relate to a favorite topic, you will likely practice and use them regularly with all the commitment needed to make them a part of regular conversation.

2.In different parts of the country people favor different words. Try picking up or subscribing to a newspaper from another part of the country. Or enlist a friend or relative from another area to join in on vocabulary improvement and offer to send them a copy of your heaviest big city newspaper in exchange for yours. Or go online and read such a newspaper on line for free.

3. To make learning easier and more productive, use flash cards in a new and more effective way to master several words at once. Instead of putting separate words on separate cards with separate meanings. Pick four words that all have the same or similar meanings and write them on one side with their meanings clearly identified on the other. Since you will be learning the same or very closely related word meanings for four words, you will be learning four words and one definition with slightly subtle changes. This brings it all together as one task in which you learn 4 times as much in about the same time.

4. Object words are easier because your are learning the definition of a word which is also a tangible item that you can picture in your mind. Go to a unique curio shop, specialty store or science or other obscure type of museum you have never been too before. Keep any brochures or other documentation that describes what you are seeing. Let the mental pictures drive the names of these items and their descriptions deep into your mind for recall later.

5. You learn much more by being humble than by being proud. Just as when driving you should be willing to stop and ask for directions, you shouldn't? be afraid to do some digging when there? a word you don? understand. Look it up or even have the courage to ask. Go on a word hunt. Write down what you didn't? understand and quickly. Hound that word and its meaning with your own research until you find it. The satisfaction of victory over your ignorance of that one word will bolster your confidence that you can learn many other words if you want to badly enough