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1. Trains are traveling between stations A and B situated 120 km apart. There are 3 more stations between A and B. Each train halts at each station for 2 min. What should be the minimum no. of trains, if the trains are traveling at 40kmph and a regular interval of 6mins is to be maintained b/w the departure of two trains from both the stations?

a. 31 b. 30 c. 62 d. 63 e. None of these 2. A and B can each run at a uniform speed along a circular track. To cover the whole track, A need 5

seconds less than B. If they start simultaneously from the same place and run in the same direction, they meet 30 seconds later. At how many points will they meet if they run in the opposite directions?

a. 9 b. 12 c. 13 d. 16 e. None of these 3. A man leaves office daily at 7pm, when a driver comes to pick him up from his home. One day he gets

free at 5:30 and instead of waiting for the driver, he starts walking towards his home. On the way, he meets the car and returns home. He reaches home 20mins earlier than usual. Had he become free at 6:00, how much early would he have reached?

a. 11 min b. 13 min c. 40

min3

d. 40

min7

e. None of these

4. Two buses B1 and B2 start from A and B respectively towards each other. B2 departs 30mins after B1

does. B1, after traveling for 2 hours, is separated from B2 by 19/30th of the distance betweenw A and B. If B1 reaches B half hour later as compared to when B2 reaches A, how much time will each take to cover the distance?

5. A woman is walking down a downward-moving escalator and steps down 10steps to reach the bottom.

Just as she reaches the bottom of the escalator, a sale commences on the floor above. She runs back up the downward moving escalator at a speed five times that which she walked down. She covers 25 steps in reaching the top. How many steps are visible on the escalator when it is switched off?

6. There is a escalator and 2 persons move down it. A takes 50 steps and B takes 75 steps while the

escalator is moving down. Given that the time taken by A to take 1 step is equal to time taken by B to take 3 steps, find the no. of steps in the escalator while it is stationary?

7. A and S walk up an escalator. The escalator moves at a constant speed A takes 9 steps for every 16 of

S's steps. A gets to the top of the escalator after having taken 30 steps while S, because of his faster pace, ends up taking 40 steps to reach the top. If the escalator was turned off, how many steps wud they have to take to walk up?

8. A man leaves office daily at 7pm.a driver with car comes from his home to pick him from office and bring

back home. One day he gets free at 5.30 and instead of waiting for driver he starts walking towards home. In the way he meets the car and returns home on car. He reaches home 20 minutes earlier than usual. In how much time does the man reach home usually? a. 1 hr 20 min b. 1 hr c. 1 hr 10 min d. 55 min

9. which of the following is true, if 1logloglog

=++abc

cabc

babc

acba

a. 1=++ cba cba b. 1=++ cba cba c. abccba cba =+ 111 d. 1111 = cba cba

10. if cbaabcx ++= and abc 0,then x1

is



a. log(base (a + b + c))(abc) b. log(base(a + b + c))(ab + bc + ca) c. log(base(abc))(a + b + c) d. log(base(ab + bc + ca))(a + b + c) e. 2 log(base(abc))(a + b + c)

11. A and B pick up a card at random from a well shuffled pack of cards one after the other ,replacing it

every time till one of them gets a queen .If A starts the game, then the probability that B wins the game is

a. 1213

b. 113

c. 1325

d. 225

e. 1113

.

12. A and B have to clear their respective loans by paying 3 equal annual installments of rs30000 each. A

pays @10% pa of SI while B pays 10%pa CI. What is the difference in their payments? 13. Rs 100000 was invested by mohan in a FD @10%pa at CI.however every yr he has to pay 20% tax on

the CI. how much money does mohan have after 3 yrs? 14. The annual sales of a company in yr2000 was rs 1000 and in the yr 2005 was rs 2490.find the CAGR in

the given period of the same company? 15. A bought a rectangular plot of land 5 yrs ago at the rate of rs1000 per m^2.the cost of plot increases by

5% in every 6 yrs and the worth of a rupee falls down at thereat of 2% in every 5 yrs. what is the approximate value of the land per m^2 25 yrs hence?

16. A takes a loan of rs10500 at 10%pa compounded annually which is to be repaid in 2 equal annual

instalments. 1 at the end of 1 yr and the other at the end of 2nd yr. what is the value of each instalment?

17. A test consists of 4 sections each of 45 marks as their maximum. Find the number of ways in which one

can score 90 or more. a. 36546 b. 6296 c. 64906 d. none 18. There are 5 botles of sherry and each has its own cap. How many ways are there so that not a single

cap is not on the correct bottle.

a. 44 b. 155 c. 55 d. none 19. A number when divided by 100 leaves a quotient (Q) and a remainder (R). How many three-digit

natural numbers are there such that Q + R is divisible by 11? a. 9 b. 99 c. 80 d. 81 e. 90

20. g(P) represents the product of all the digits of P, e.g. g(45) = 4 5. What is the value of

g(67) + g(68) + g(69) + ..... + g(122) + g(123)? a. 1381 b. 1281 c. 1481 d. 1181 e. None of these

21. The HCF of (n + 3) and (7n + 48) is k, where n is a natural number. How many values of k are

possible? a. 4 b. 5 c. 1 d. 2 e. 3 22. Given that Q =1!+ 2!+ 3!+ 4!+ ......+ (n -1)!+ n!. For how many values of n, Q is a perfect square? a. 1 b. 2 c. 3 d. 4 e. More than 4



23. How many three-digit numbers are there such that no two adjacent digits of the number are consecutive?

a. 592 b. 516 c. 552 d. 600 e. 596

24. All win went to the market and bought some chikoos, mangoes, and bananas. Allwin bought 42 fruits in

all. The number of bananas is less than half the number of chikoos; the number of mangoes is more than one-third the number of chikoos and the number of mangoes is less than three-fourths the number of bananas. How many more/less bananas did All win buy than mangoes? a. 3 b. 6 c. 11 d. none of the foregoing

25. In an organisation there are 40 employees belonging to different departments A, B and C. each

department has more than 7 employees. The organisation decides to pay a bonus of 15000, 10000 and 7000 to each of the employees of department A, B, C respectively. If total bonus paid is 429000, then the total employee in department C is a. 16 b. 17 c. 15 d. 14 e. 12

26. Ramu started adding digits of the page numbers of a book starting from first page. After he finished his

addition, He obtained a sum of 1023.He missed adding d digits of one page number. what could be the maximum no of pages in the book? a. 121 b. 125 c. 123 d. 128 e.127

27. (Related to privous question), Which of the following could be the page number which ramu has missed? a. 21 b. 22 c. 23 d. 24 e. 25 28. Answer the questions on the basis of the information given below.

There are 5 distinct real numbers. All triplets are selected and the numbers are added. The different sums that are generated are: ( 8, 1, 3, 5, 7, 8, 10, 16, 19 and 23).

a). The smallest number among the 5 numbers is

a. 10 b. 9 c. 8 d. 7 e. 6

b). The third largest number is a. 1 b. 0 c. 1 d. 2 e. 7

29. Consider the following two curves in the x-y plane 2y x 6x 8= + and 2y x bx c.= + + If the maxima of one curve is the minima of the other curve, then what is the value of b? a. 6 b. 5 c. 3 d. 8 e. 7

30. How many integers exist such that not only are they multiples of 20082008 but also are factors of 20202008 ?

a. 12 b. 481 c. 587 d. 200812 e. 637 31. K is a set of five consecutive prime numbers such that the sum of all the elements in K is greater than

200 and less than 300. Which of the following cannot be the sum of the elements in the set K? a. 221 b. 263 c. 243 d. 271 e. 287



32. The sum of the reciprocals of the integers a and b is equal to the sum of twice the reciprocal of c and reciprocal of 10 a. What is the value of (a+b) where a, b, c are 3 distinct integers between 0 and 10.

1 1 1 1theEquationwillbe 2

a b c 10a

+ = +

a. 2c-1 b. 2c c. 2c+1 d. 2c+3 e. None of these 33. There are 10 students out of which three are boys and seven are girls, in how many different ways can

the students be paired such that no pair consists of two boys?

a. 42 b. 1260 c. 630 d. 1890 e. None of these 34. In a soccer tournament n teams play against one another exactly once. The win fetches 3 points, draw 1

each and loss 0. After all the matches were played, it was noticed that the top team had unique number of maximum points and unique least number of wins. What can be the minimum possible value of n? a. 5 b. 6 c. 7 d. 8 e. none of these

35. How many integral values of x satisfy the in equality |[x+ 3]| < 5 {Here, [x] denotes the greatest integer less than or equal to x}

a. 6 b. 7 c. 8 d. 9 e. 10 36. How many four digit perfect squares "abcd" are possible such that "dcba' is also a four digit perfect

square and is also a factor of "abcd"? (given a is not equal to zero) a. 0 b. 1 c. 2 d. 3 e. More than 3

37. Find the highest power of 3 in N=1(factorial)*2(factorial)*3(factorial)..............99(factorial)

a. 2260 b. 2280 c. 2240 d. 2220 e. 2300 38. a, b, c, d and e are five natural numbers in an arithmetic progression. It was noted that

3xedcba =++++ and 23 ydax = where, x and y are natural numbers. What is the minimum possible value of c? a. 525 b. 675 c. 2025 d. 3375 e. 225

39. In a three digit number with only odd digits, Exactly two of the digits are equal. The number is divisible

by 11. a) The digits which are equal must be a. First two b. last two c. First and Last d. cannot be determined e. none of these.

b) How many values can the number assume? a. 3 b. 4 c. 1 d. 2 e. 5

40. Find the total no of ways in which 30 identical prizes can be distributed among 4 boys such that each

boy gets an odd number of prizes and one boy gets 3k prizes, where k is a natural number? a. 185 b. 212 c. 441 d. 60 e. 316

41. In a parliament of 100 members, a bill was stuck (50 for it and 50 against it)due to cross voting on

either side, viz. the government and the opposition. If every member voted and cross voting were integral percent (



b) The percent cross voting occurred on government side? a. 5 b. 10 c. 15 d. 20

c)The percent cross voting occurred on the opposition side is a. 5 b. 10 c. 15 d. 20

42.N girls and 2N boys played a chess tournament. Every player played every other player exactly once.

The boys won 7/5 times as many matches as the girls (and there were no draws). Then which among the following is definitely false? (Assume 1 point for a win and 0 for a loss)

a. Boys pocketed prime number of points against girls b. Girls always won twice or more matches than boys won against them c. The sum of the scores of top 3 individual players was not between 25 and 33 d. The sum of the scores of top 3 individual players was 69 e. none of the foregoing

43. Akhil, Bunty, Chameli, Disha and Eku are working upon a project, which is divided into phases such that

only one person works on each phase. The work done per phase by them is inversely proportional to their age in years. Akhil has worked on 4 phases of the project whereas Bunty has worked on 5 phases. Eku and Disha have worked on 8 phases each and the rest of the phases were worked upon by Chameli, who received the honour of having worked upon 40% of the project. If the ages of these 5 persons are 36 yrs, 18 yrs, 9 yrs, 72 yrs and 24 yrs respectively, then on how many phases of the project did Chameli work?

a. 3 b. 4 c. 5 d. 6 e. 7

44. 'A' starts in car from Mumbai towards Bangalore. After some time he realizes that he will cover only

th43

of the distance in the scheduled time. He, therefore, doubles his speed immediately and thus he

manages to reach Bangalore exactly on time. Find the time from the start, after which 'A' changed his speed, given that he would have been late by 3 hours if he had not changed his speed.

a. 4hr 30min b. 6hr c. 7hr 30min d. 8hr The positive integer n divides 3030 in base 31. Find the total number of possible values of n if n is factor of 30.

45. If x satisfies the equation ,3274 22 +=+ xxxx then a. x>1 b. x< -3 c. -3< x< 1 d. No real x is possible

46. For the equation ( ) ( )2 22x 3 3x 7log 6x 23x 21 log 4x 12x 9 4+ ++ + + + + = , find the number of solutions and values of x satisfying:



47. The no. of positive integers satisfying 3 2n 16n 4n 64 0 + is a. 0 b. 1 c. 3 d. 4 e. None of these

48. For how many values of p does the equation 2px 4px 1 0+ + = have exactly 1 solution?

a. 0 b. 1 c. 2 d. 3 e. None of these

49. C is a natural no. and both 2x 4px c 0+ + = and 2x 4x c 0+ = have rational roots. The number of possible values of C is:


50. If x, y are real and y = ( )2x 12x 35 + find the range of x, given that y< x - 2 a. x b/w (31/8,infinity) b. x not b/w (31/8,infinity) c. x b/w (2,infinity) d. x not b/w (2,infinity) e. None of these

51. if -1



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53. Find the least value of 3x + 4y for positive values of x and y subject to the condition ( ) ( )2 3x y 6= a. 10 b. 32 c. 40 d. 50 e. None of these

54. Find the number of integral solutions for |x| + |5y| < 100


55. Each cell in a 2x4 grid is to be filled with tiles of one of the four colours-red blue green or yellow, such that, no two sqrs are tiled with the tiles of the same colour in the same row or in the same column. find the no. of ways to do this?

a. 4! 3! b. 4! 4! c. 23 3! d. 9 4! e. 4 4!

56. In a class of 120 students, for every 2 students taking up physics there are 4 students taking up

chemistry. Further for every student taking Physics, there are 3 students taking up maths as well as 1 student taking up Biology. Then the maximum no. of students taking up all the four subjects will be: a. 30 b. 40 c. 50 d. none of these e. can't be determined

57. find the no. of roots of ( )2nx b 0. =

Find the value of K, if the product of the roots of the equation

( ) y2log k2x 2 3k x 4y 0 + + = is 256 a. 8 b. +-8 c. 4 d. +-4 e. cannot be determined.

58. Find the sum of the terms

a. 100.104 + 101.108 + 102.112 + 103.116 + 104.120 + ... 10 terms b. 4.1 + 5.2 + 6.4 + 7.8 + 8.16 + 9.32 .... 15 terms

59. In Triangle PQR the in circle touches the sides of QR, RP, PQPQ at T, U, S respectively. If the radius of in

circle is 4 units and QT, RU, PS are consecutive integers, what is the area of the triangle a. 42 b. 84 c. 64



d. 96 60. A vertical lamppost OP stands at the centre O of a square ABCD let h and b denote the length of OP and

AB respectively. Suppose angle APB = 60 then relationship between h and b can be expressed as a. 2b2=h2 b. 2h2=b2 c. 3b2=2h2 d. 3h2=2b2

61. If f(x) = x2 + 12x + 30, then the value of x satisfying f(f(f(f(f(x))))) = 0 is

Choose one answer.

a. 1326 6

b. 1

166 6 c. none of these

d. 1

166 6+ 62. X &Y are playing a game. There are eleven 50 paise coin on the table and each player must pick up at

least one coin but not more than five. The person picking up the last coin loses, X starts. How many should he pick up at the start to ensure a win no matter what stratergy X employs.

a. 4 b. 3 c. 2 d. 5

63. if ( )5 2log x y 5a 2b= + and ( )2 5log x y 2a 5b= + find log(xy) in terms of a and b

a. a+b

b. ab

c. 2 2a b+

d. ab

e. ( )2a b+

64. If 2 2 0.06251

log P 2log Q 1 log 2,2

+ = + which of the following is always true?

a. 2

8p

8q

=

b. 8

2p

8q

=



c. 2 8p q 8=

d. 8 2p q 8= e. pq=4

65. If 13

10 10 y3log y log y 8log 10, = find y

a. 100

b. 1

100

c. 10

d. Either (b) or (c)

e. Either (a) or (b)

66. A contractor undertook to do a job in 55 days and employees 48 men for it. In 11 days only 1/6th of the task was completed. How many more men he would have employed to complete work in time? 67. Three circles touch one-another externally. The tangents at their point of contact meet at a point whose

distance from any point of contact is 4. Find the ratio of the product of radii to the sum of radii of circles.

a. 14

b. 132

c. 321

d. 41

e. 161

68. Balls are arranged in rows to form an equilateral triangle. The first row consists of one ball, the second

row of two balls and so on. If 669 more balls are added then all the balls can be arranged in the shape of a square and each of the sides then contains 8 balls less than each side of the triangle did. Determine the initial numbers of the ball.

a. 1540 b. 1541 c. 1538 d. 1542 e. 1543

69. If N is a natural number such that

k31 2aaa a

1 2 3 kN p p p ......p=

Where p1, p2, p3,.pk are distinct prime numbers, then

a. logN k log5= b. logN k log2 c. logN k log3 d. logN k log2 e. logN k log4

70. If p, q be the roots of ax^2 + 2bx + c = 0 and (p+r), (q+r) be those of Ax^2 + 2Bx +C=0, then

a. ( )( )

2 2

2

b a c AaB A C

=



b. ( )( )

2 2

2

b a c aAB A C

=

c. ( )( )

2

2

b a c aAB A C

=

d. ( )( )

2

2

b a c BbB A C

=

e. ( )( )

2 2

2

b a c bBB A C

=

71. Find the number of triangles that can be formed with the angular points of a polygon of a polygon of n sides. What will be the corresponding number of triangles if none of the sides are to be the sides of the polygon?

a. ( ) ( )n n 4 n 5

6

b. ( ) ( ) ( )n 2 n 4 n 5

12

c. ( ) ( )n n 1 n 2

3

d. ( ) ( )n n 5 n 6

12

e. ( ) ( ) ( )n n 3 n 4 n 16

12

72. A function is defined as follows:

( ) n 1 n 2 n 3 01 2 3 n 1 2 3 nf a ,a ,a ,.....a a 2 a 2 a 2 ..... a 2 = + + + + Where a is any positive integer. The above function is repeated until the value of function reduces to a single digit number.

What is the value of f [f(888222) + f(113113)]:

a. 6 b. 7 c. 8 d. 9 e. 10

73. If 6 x

1log 2log 2

2 136 ,2

+ = then x is

a. 136

b. 36 c. 6 d. 16

e. 216



74. If 3ylog x is the same as 3xlog y, then find the value of 3xlog y

a. 13

b. 13

c. 23

d. either (a) or (b) e. none of these

i got (a)1/3 but the answer given is (4).

75. If logx log343 logy

,log4 log49 log64

= = then find x + y.

a. 520 b. 640 c. 880 d. 240 e. cannot be determined

no. of positive non integral solutions of {abc = 30} is ? 76. 10 105 log x 5log y,+ = express x in terms of y.

a. 5x 5y=

b. 5y

x10

=

c. 2 5x 10y=

d. ( )5x 10y= e. 5

yx

10=

77. Two 300 m circular tracks 1 and 2 cut each other such that the centre of each track lies on the

circumference of the other track. A and B respectively are running on the track 1 and 2 at the speed of 8 m/s and 10 m/s respectively. If they start running away from each other from a common point so that they cover relatively outer part of the track first, after how many seconds do they meet at the other intersection?

a. 20 sec b. 25 sec c. 40 sec d. 100 sec e. None

78. There is a number a(1111) such that a(1111) is sum of squares of consecutive odd numbers. Find a. 79. Two brothers inherited a rectangular plot from their father which was to be divided equally among

the two. But there was a small rectangular patch of barren land somewhere in that field. So the two brothers decided that each of them should get equal area of land with equal distribution of its barren patch. Also they want that their share of land must have exactly 4 straight edges. Help them to do this herculean task as they think.



80. Prove that 1 1 3 5 2009 1

.....64 2 4 6 2010 44

<



At what time would B and C meet for the second time, if all the three of them run in the clockwise direction? a. 10 : 03 : 50 a.m b. 10 : 04 : 35 a.m. c. 10 : 05 : 10 a.m. d. 10 : 06 : 25 a.m. e. None

87. A and B run in opposite directions from a point P on a circle with different but constant speeds. A runs in the clockwise direction. They meet for the first time at a distance of 900 m in the clockwise direction from P and for the second time at a distance of 800 m in the anticlockwise direction from P. If B is yet to complete 1 round, then the circumference of the circle is a. 1200m b. 1250 m c. 1300m d. 1700m e. None

88. 9 points are marked on a straight line and 10 points are marked on another line which is parallel to

the first line. How many triangles can be formed with these points as vertices? a. 950 b. 360 c. 765 d. 405 e. 800

89. 10 points are plotted in a plane such that no 3 of them lie on a straight lin,4 of these points are

joined to each of the remaining 6 points and each of the remaining 6 points is joined to exactly 5 points. how many line segments are formed? a. 27 b. 25 c. 29 d. 24 e. 32

90. Solve the equation 10x 5 = 9[x] on the set of real numbers (where [x] stands for the greatest integer not greater than x). Find the total number of real solutions for x.

91. The number of sides of a polygon is doubled. For how many polygons will the sum of the angles of

the new polygon be a multiple of the sum of the angles of the original polygon? 92. The sides of a rectangle are a and b. Two congruent circles are placed in a rectangle so that they

have no interior point in common. What is the ratio of the sides of the rectangle if the diameter of

the largest possible circles is ? 93. On Christmas Eve two candles, one of which was one inch longer than the other, were lighted. The

longer one was lighted at 4:30 and shorter one at 6:00. At 8:30 they were both the same length. The longer one burned out at 10:30, and the shorter one burned out at 10:00. How long was each candle originally?

94. In a math class that contains both 11th and 12th graders, each student must do a class

presentation on a famous mathematician. Each student may do the presentation alone or with a class partner. An 11th graders partner must be a 12th grader and a 12th graders partner must be an 11th grader. If two-thirds of the 11th graders and three-fifths of the 12th graders work with partners, what proportion of the class works alone?



95. Two cars (A and B) start at the starting line at the same time on a 3-mile long circular track, going in opposite directions. As they drive around the course, they pass each other many times. Exactly one hour after starting, they pass each other for the 33rd time. At this point car A has completed exactly 20 laps. What is the average speed of Car B?

96. Find all integers for which the value of the expression 6x2 - 167x - 4823 is

a) a prime number; b) the smallest possible integer.

97. To boost the sales of a certain kind of sweets, the manufacturing company encloses gift vouchers in some of the boxes. The managers consider that the campaign will be efficient and costs will be bearable if the probability for a customer buying 10 boxes of sweets to find at least 1 voucher is about 50%. One in how many boxes should contain a voucher to achieve that?

Direction for Question 20 to 22: For mechanical engineer, number of people for whom the details of feature are available are as below : (Total Mechanical Engineer = 42000)

Name 42000 Age 35700 Address 29400 Experience 39900 Phone number 25200 Email 33600

98. The number of mechanical engineers, for whom the details of exactly four of six features are available, is at least? a. 2100 b. 6300 c. 10500 d. 21000 e. None of These

For Professor, number of people for whom the details of feature are available is are as below (Total Professor=10000) Address - 75000 Phone Number - 85000 Email id 95000 99. The number of professor for whom at least two of the three features, address phone number and

e-mail ID are available, is at least a. 8000 b. 7500 c. 6000 d. 6500 e. 5000

For CAs, number of people for whom the details of feature are available are as below: (Total CA = 2600) Name 2600 Age 2080 Address 1300 Experience 1040 Phone number 1300 Email 2340 100. For at most how many of the CAs are the details of exactly five of the six features available?


101. Find the reminder when ( ) 1777716!38 is divided by 17 a. 1 b. 16 c. 8 d. 13 e. None of these



102. For how many positive integers x between 1 and 1000, both inclusive, is 4x6 + x3 + 5 is divisible by 7?

a. 11 b. 36 c. 0 d. 4 103. Let S be the set of all 5 digit numbers with distinct digits that can be formed using the digit

1,2,4,5 and 8 such that exactly two odd positions are occupied by the even digits. find the sum of the digits in the rightmost position of all the numbers in S. a. 256 b. 316 c. 296 d.329 e. None of these

104. For how many prime numbers p, is 4 2p 15p 1+ also a prime number? 105. A certain number of students of a school participated in the chess tournament of their annual

sports meet. Each player played 1 game against each of the other player. it was found that in 66 games both the players were girls, and in 240 games one was a girl and the other was a boy. The number of games in which both the players were boys is a. 190 b. 95 c. 210 d. 380 e. 110

106. Find the no. of ways of dividing 16 different books equally (a)among 4 boys

a. 4

16!

4!

b. 3

16!

4!

c. 5

16!

4!

d. 44! e. 16! (b) into 4 parcels

a. 4

16!

4!

b. 3

16!

4!

c. 5

16!

4!

d. 44! e. 16!

107. A group of friends reserve 2 circular tables in a restaurant for a dinner. one table has 4 chairs and the other has 6 chairs. In how many ways can the group seat themselves for the dinner?



a. 10!4!6!

b. 10!4!

c. 10! D. 3!5! e. 10!6!

108. From a group of 10 professors and 6 assistant professors, a management institute desires to send

a delegation of 8 persons consisting of 5,professors and 3 assistant professors to the IIMs annual meet. If Prof. Balamurali , a science Professor refuses to be in the delegation if assistant Prof. Sheshadri, an arts professor is included in the delegation , then in how many ways can the delegation be formed? a. 9 44 3C C

b. 9 45 2C C

c. 10 6 9 55 3 4 2C C C C d. 9 4 9 44 3 5 2C C C C e. None of these

109. Find the remainder when 55555555.................(93 times) is divided by 98

110. Julia is as old as John will be when Julia is twice as old as John was when Julia's age was half the sum of their present ages. John is as old as Julia was when John was half the age he will be 10 years from now. The Question: How old are John and Julia?

111. "Between two and three o clock yesterday," said Colonel Crackham, "I looked at the clock and mistook

the minute hand for the hour hand, and consequently the time appeared to be fifty-five minutes earlier than it actually was. What was the correct time?

112. If you add the square of Tom's age to the age of Mary, the sum is 62; but if you add the square of

Mary's age to that of Tom, it is 176. Can you say what the ages of Tom and Mary are? 113. Nine boys and three girls agreed to share equally their pocket money. Every boy gave an equal sum to

every girl, and every girl gave another equal sum to every boy. Every child then possessed exactly the same amount. What was the smallest possible amount that each then possessed?

114. A man went into a bank to cash a check. In handing over the money the cashier, by mistake, gave him

dollars for cents and cents for dollars. He pocketed the money without examining it, and spent a nickel on his way home. He then found that he possessed exactly twice the amount of the check. He had no money in his pocket before going to the bank. What was the exact amount of that check?

115. In how many ways can 4 letters be selected from the letters of the word ADDRESSEE? a. 126 b. 28 c. 65 d. 120 e. 30

116. How many four digit numbers, that are divisible by 3, can be formed, using the digits 0,1,2,3 and 8 if no digit is to occur more than once in each number? a. 36 b.18 c. 54 d. 78 e. 42

117. given that p,q,r are the length of three sides of a scalene triangle. if the question

22

2 2k5p3x x 2p 0p q r

+ + =+ + has distinct and real roots, then which of the following is a possible value of k? a. -0.55 b. -0.45 c. 0.6 d. 0.75 e. 1



118. if all the roots of the equation, nx n m

mn 0m x+ + = nx +n/m +m/x mn =0 are negative, then

which of the following is a possible value of 2

5m

n?

a. 18

, when n= -2 ,

b. 18

, when m = -2 ,

c. 18

, when m = -2,

d. 18

,when n=2 ,

e. none of the above

119. a set P consists of the first 25 natural numbers. How many minimum numbers should one pick from the set P so that there is always at least one pair (x,y) among them satisfies 3x=2y? a. 13 b. 16 c. 17 d. 18 e. 20

120. 4: if (x - 2y + w) : (y + 2z - 2x): (z w + y) = 3:2:1, then find the value of (5x - 2y - 2z - w): (3z - x). {w, x, y, z are real numbers} a. 1:6 b. 1:3 c. 1:2 d. 2:3 e. 5:6

121. N = (3333333..333 up to 51 digits) * (6666666..666 up to 51 digits). What is the 52nd digit of N from right? a. 8 b. 7 c. 1 d. 2 e. 3

122. When the digits of a two number digits are reversed, the number formed is 75% than the original number. By what percent is the unit digit of the original number more/less than the tenth digit?

123. How many divisors of the number 7 5 4N 2 3 5= have unit digit equal to 5? 124. how many non-negative integral solutions does the equation 1 2 3 4x x x x 10+ + + = have?(

1 2 3 4x ,x , x , x are distinct values) a. 286 b. 86 c. 35 d. 165 e. 270

125. 6 points are located on a circle and lines are drawn connecting these points, each pair of points connected by a single line. What can be the maximum number of regions into which the circle is divided? a. 22 b. 29 c. 32 d. 31

126. 43444 + 34333 is divisible by......... a. 9 b. 11 c. 2 d. 5



127. 6 boxes numbered 1 -6 are arranged in a row. Each is to be filled by either a green or a blue colour ball such that no two adjacent boxes contain green coloured balls. In how many ways can the boxes be filled with the balls? a. 15 b. 16 c. 20 d. 21 e. 28

128. Which of the following integers does NOT have a divisor greater than 1 that is the square of an integer? a. 75 b. 42 c. 32 d. 25 e. 12

129. An advertisement board is to be designed with seven vertical stripes using some or all of the colours red, black, yellow and blue .In how many ways can the board be designed such that no two adjacent stripes have the same colour?

a. 972 b. 2916 c. 729 d. 2187 e. 1865

130. A security agency assign a 2-digit code with distinct digits to each of its members using the digits

0, 1, 2...9 such that the first digit of the code is not 0. However the code printed on a badge can potentially create confusion when read upside down. For example, the code 18 may appear as 81.How many codes are there for which no such confusion can arise? a. 69 b. 71 c. 81 d. 65 e. 75

131. How to find the digital sum of a factorial.......say 100! 132. 1 and 8 are first 2 natural numbers for which 1 + 2 + 3 +....+ n is a perfect square. Which is 4th such no? 133. Find the remainder when 139 + 239 + 339 + 439 + ... + 1239 is divided by 39

a. 38 b. 12 c. 1 d. 0

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