Let f(t) = t/(3 - t), t 3. If y = f(x), then x can be expressed as

3f (3/y)

-3f (3y)

-3f (-3y)

3f (3y)

3f (-3y)

A bag contains printed articles of 4 different kinds: periodicals, novellas, newspapers and hardcovers. When 4 articles are drawn from the bag without replacement, the following events are equally likely:

the selection of 4 periodicals the selection of 1 novella and 3 periodicals the selection of 1 newspaper, 1 novella and 2 periodicals and the selection of 1 article of each kind

What is the smallest number of articles in the bag satisfying these conditions?

19 21 18 More than 46 46

There are two boxes, one containing 50 red balls and the other containing 21 green balls. You are allowed to move the balls between the boxes so that when you choose a box at random and a ball at random from the chosen box, the probability of getting a red ball is maximized. This maximum probability is

1/2 + 49/140 1/2 + 20/140 50/71 1/2 + 20/70

The IT giant Tirnop has recently crossed a head count of 150000 and earnings of $8 billion. As one of the forerunners in the technology front, Tirnop continues to lead the way in products and services in India. Sharuk, a developer at Tirnop, has implemented an efficient search algorithm for web content and stored the resulting code in the file sharukkahan . Worried about data corruption, he decides to take some backups of this file. Thus he makes 12 copies of sharukkahan and wants to store the 13 identical files in three different directories of which two are on the network and one is local. He realises that there are a zillion different ways of doing this and is curious about the exact count. Can you help him count the number of ways in which the 13 (identical) files can be stored in the 3 directories? What would your answer be? (note: In the options below, choose (n,k) = n!/(k! (n-k)!) is the standard binomial coefficient)

105

91

152

choose (13,3)

313

On the planet Oz, there are 8 days in a week- Sunday to Saturday and another day called Oz day. There are 36 hours in a day and each hour has 90 min while each minute has 60 sec. As on earth, the hour hand covers the dial twice every day. Find the approximate angle between the hands of a clock on Oz when the time is 9:40 am.

11

29 36 191

smitha is traveling from India to Japan on a business trip for 3 months. She needs to change some Indian rupee (INR) to Japanese yen (Y) and finds that the exchange rate between INR and Y is 1 INR = 4Y smitha changes 2000 rupees to Japanese yen at this rate. At the end of 3 months she finds that she has 4000 yen left. But by this time the exchange rate has changed to 1INR = 3Y. She changes her yen to rupees at this new rate. Is it in smitha's advantage that the exchange rate has changed from 4Y to 3Y during her 3month trip?

No, since smitha gets only 1000 Rupees under the new exchange rate instead of 1333.33 Rupees if the exchange rate had been unchanged.

No, since smitha gets only 1333.33 Rupees under the new exchange rate instead of 2333.33 Rupees if the exchange rate had been unchanged.

Yes, since smitha gets 1250 Rupees under the new exchange rate instead of 1000 Rupees if the exchange rate had been unchanged.

Yes, since smitha gets 1333.33 Rupees under the new exchange rate instead of 1000 Rupees if the exchange rate had been unchanged

Alice and Bob play the following chip-off-the-table game. Given a pile of 178 chips, Alice first picks at least one chip but not all the chips. In subsequent turns, a player picks at least one chip but no more than the number picked on the previous turn by the opponent. The player to pick the last chip wins. Which of the following is true?

In order to win, Alice should pick one chip on her first turn. Alice has no winning strategy.

In order to win, Alice should pick two chips on her first turn. In order to win, Alice should pick 44 chips on her first turn.

Given two undefined elements "efs" and "awks", and the four postulates: P1: Every ef is a collection of awks. P2: Any two efs have exactly one awk in common. P3: Each awk is a member of exactly two efs. P4: There are exactly 4 efs. Consider the three theorems T1: There are exactly 6 awks. T2: There are exactly 3 awks in each ef. T3: For each awk there is exactly one other awk that is not in the same ef with it. The theorems that are deducible from the postulates are

T1 and T2 none of them T1 and T3 T2 and T3 T1, T2 and T3

A non-zero digit is chosen in such a way that the probability of choosing digit d is log10(d+1) log10d . For which of the sets below is the probability of choosing a digit from that set maximum?

{1}

{9} {4, 5, 6, 7} {2, 3, 4} {5, 6, 7, 8}

saif is older than parveen. He notices that if he switches the two digits of his age (which is an integer) he gets parveen's age. Also, the difference between the squares of their ages is a square of an integer. Then the difference between their ages is

36 27 18 9 67

Let x = 20. What is the value of x after the following code is executed? for (i from 0 to 7) { if ( i is odd) { x = x*2 } if (i is even) { x = x/2 } }

10

40

5

20

Given a collection of points P in the plane, a 1-set is a point in P that can be separated from the rest by a line; i.e. the point lies on one side of the line while the others lie on the other side. The number of 1-sets of P is denoted by n1(P). The minimum value of n1(P) over all configurations P of 32 points in the plane in general position (i.e. no three points in P lie on a line) is

5 32 3 16

Al Stevens goes to his hometown Cincinnati on a straight line path, which is at a distance of 30 km. While returning, he uses a circuitous route that is actually a semi-circle whose diameter equals the distance of his onward journey. What is the total distance covered by Al Stevens?

94.29 77.14 60 188.57

A chocolate drink is 6% pure chocolate by volume. If 13 litres of pure milk are added to 25 litres of this drink, the percent of chocolate in the new drink is approximately

3.95 24 6 43.51

In a tennis tournament, n women and 2n men play and each player plays exactly one match with everyone else. If there are no ties and the ratio of the number of matches won by women to the number of matches won by men is 7/5, then n equals

6 3 2 4 5

Ravi used the sieve of Eratosthenes to enumerate all prime numbers from 2 to 1122 using the following procedure (i) Write down all the numbers from 2 to 1122. Let p ( = 2) be the smallest number in this list. (ii) Circle p and cross out all multiples of p (except p itself) in the list. (iii) Find the smallest number that is neither circled nor crossed out. Call this p. (iv) Repeat steps (ii) and (iii) until all numbers in the list are either circled or crossed out. At the end of this procedure, the circled numbers are the primes and the crossed out numbers are composite. However, while crossing out multiples of 2, Ravi accidentally crossed out two odd numbers, 15 and 29, in addition to all the even numbers (besides2). Otherwise he executed the steps correctly. Which of the following are true when Ravi completes the procedure? Note that in the options below, N is the number of primes between 2 and 1122 (including 2), 225 = 15*15 and 841 = 29*29.

Both 225 and 841 will get circled and the number of circled values will be N - 1. 225 will get circled and the number of circled values will equal N. 841 will get circled and the number of circled values will equal N.

Neither 225 nor 841 will get circled and the number of circled values will be N - 1. Both 225 and 841 will get circled and the number of circled values will be N+1.

A collection of 14 bags containing tennis balls is to be distributed among some players. The bags are labeled "bag_1", "bag_2", ..., "bag_14" and the bag labeled "bag_n" contains exactly n tennis balls. The bags are sealed and cannot be opened prior to distribution. What is the minimum number of players to whom the bags can be distributed if each player gets the same number of balls and no player gets all the bags?

14 4 5 3 2

A m x n grid is an array of mn squares arranged in m rows and n columns. A 2 x 3 grid is shown below as an example. A straight line is drawn across a 5 x 3 grid. What is the maximum number of squares intersected by the line?

5

8 7 9 6

At her usual rate Paati rows 24km downstream in 8 hours less than it takes her to return. If she doubles her speed, the time downstream is only one hour less than the time upstream. The speed of the stream's current in Km/hr is

15/2 6 7 8 13/2

A book has pages numbered 1 to 192 (totally 96 sheets). Some 21 sheets are pulled out of it at random. Which of the following cannot be the sum of these 42 page numbers?

987 983 903 882

dhanya is working as a cashier in a public sector bank. One day while checking the petty cash she counts t ten rupee coins, f five rupee coins, w two rupee coins and n one rupee coins.

Later she discovered that 8 of the two rupee coins were counted as ten rupee coins and 8 of the five rupee coins were counted as one rupee coins. To correct her mistake she has to

subtract 32 from the original total add 32 to the original total add 8 to the original total subtract 4 from the original total

The equation | x + 10| - | x + 5| = 0 has

no solutions 5 solutions. 10 solutions. 1 solution. 2 solutions

A group of engineers work on a software project. Each person has to work in exactly two out of three shifts; morning, afternoon or evening. If 100 engineers worked in the morning shift, 60 in the afternoon shift and 110 in the evening shift, totally how many engineers worked on the project? You may assume that once the shifts are chosen by a person, they cannot be changed during the project.

135 180

There is insufficient information to determine the answer. 270 90

You are given 82 coins all of different weights. You are given a machine that allows you, with one weighing, to determine for any 10 coins, the one with the maximum weight. What is the least number of weighings required to find the coin with maximum weight among the 82 given coins?

9 8 10 11 infinite; it is imposible to find the coin with maximum weight using this machine

Find the number of 5 digit numbers consisting only of even digits.

3125 2500 90000 1024

At different times during the day Dhruva gets emails in his yahoo account. When he has time, Dhruva goes to his inbox and reads the most recent unread mail. If there are 5 emails in all and they are delivered to Dhruva in the order 1 2 3 4 5, which of the following could not be the order in which Dhruva reads them?

25431 12345 54321 13452 35412

If y < 0, then |y - (y - 1)2| equals

1

2y - 1

1 + 2y

1 - 2y

-2y - 1

When a census was taken in 2011, it was found that, compared to 2006, the population of Alhambra had gone up by 32% while that of Nalanda had gone down by 16%. Also it turned out that in 2011, the populations of Alhambra and Nalanda were equal. In 2006, what percentage of the population of Nalanda was the population of Alhambra?

87.88 123.53 12.12 63.64