Section Test 2

This test consists of 18 questions each of 3 marks, please deduct 1 mark for each wrong attempt. Time allotted : 40 minutes

1. A given three digit number when subtracted from other three digit number which is obtained by reversing the digits of the given three digit number (both should be two digits), the resultant so obtained is 396. How many such three digit numbers are possible.

1. 10

2. 25

3. 50

4. 6

2. Find the remainder when (3)^53! Is divided by 80?

1. 0

2. 1

3. 2

4. Cannot be determined

3. If p is a prime number and p² + 3 is also a prime number. How many different values p can assume?

1. 3

2. 2

3. 1

4. Cannot say

4. If p and q are the roots of the quadratic equation x² + px + q = 0, then find the values of p and q?

1. p = 1; q = -2

2. P = -1; q = 2

3. p = q = 1

4. P = q = 2

5. The sum of all the roots of the equation 2(x-3)² + (x-3)- 6 = 0?

1. 4

2. 6

3. 8

4. 2

Direction (6 – 8):- Questions are followed by two statements as (I) and (II). You have to decide if these statements are sufficient to conclude the answer of the question.

Choose (1) If statement (I) alone is sufficient to give the answer of the question but statement (II) is not Sufficient or VICE- VERSA

(2) If Statement (I) & statement (II) together sufficient but neither of the two alone is sufficient to answer the question.

(3) If either statement (I) or statement (II) alone is sufficient to answer the question

(4) Both statements are not sufficient to answer the question.

6. Is n odd?

(I) n is divisible by 3, 5, 7, 9

(II) n is between 10 and 500

7. What is the price of apples?

(I) Price of mangoes is 5 more than the price of apples

(II) Price of mangoes is 5 less than the price of banana which is three times the price of apple

8. What are the percentage classes attended by Radha in the course?

(I) 20% of the classes was attended by Radha and Mira together.

(II) Number of classes attended by Radha without Mira is 3/5 of the total number of classes attended by Radha.

9. Profit of selling 10 tubes equals selling price of 3 bulbs. While loss on selling 10 bulbs equals selling price of 4 tubes. Also, profit percentage equals to loss percentage and cost of tube is half that of the bulb. What is the ration of the selling price of the tube and the bulb?

1. 5:4

2. 3:2

3. 4:5

4. 3:4

10. If a/(b+c) = b/(a+c) = c/(b+a) and a + b + c ≠ 0 then the value of

b/(a+ b+c) ?

1. ½

2. 1/3

3. ¼

4. 1

11. There are 10 bogies in a train which carries on an average 20 passengers per compartment. If at least 12 passengers were sitting in each compartment and no an compartment has equal number of passengers then maximum how many passengers can be accommodated in any compartment?

1. 64

2. 45

3. 56

4. None of these

12. From the container of milk, Ram kept out 15L of the milk and replaced it with water. He again repeated the same process. Thus in three attempts the ratio of milk and water becomes 343 : 169. The initial amount in the container was?

1. 75L

2. 100L

3. 150L

4. 120L

13. ABCD is a trapezium such that AB, DC is parallel and BC is perpendicular to them. If angle (DAB) = 45⁰, BC = 2cm and CD = 3cm, then find the length of AB?

1. 6cm

2. 4cm

3. 3cm

4. 5cm

14. Find the number of positive integral solution of the equation 3x + y = 42?

1. 12

2. 13

3. 14

4. 15

15. A, B and C can complete a piece of work in 15, 30 and 40 days respectively. They started the work together and A left 2 days before the completion of work and B left 4 days before the completion of work. In how many days was the work completed?

1. 73/10 days

2. 152/15 days

3. 307/30 days

4. None of these

16. A & B are running a circular track in opposite directions. They meet at a point 450m from the starting point and continued running. They now meet at a point 300m from the starting point, but in the opposite direction as before. What is the length of the track?

1. 1000m

2.1350m

3. 1250m

4. 1500m

17. If y = min(x^2+ 2, 6-3x), find the maximum value of y for x > 0?

1. 3

2. 2

3. 1

4. 4

18. How many five digit numbers can be made with three 0 and two 5?

1. 4

2. 6

3. 10

4. 12

Logical reasoning based Data Interpretation Test 2

This test consisting of 27 question and each question if of 3 marks and for every wrong answer 1 marks will be deduced.

Instructions for questions 1 to 4: In a class of 50 students, a game of logic is to be played. The students were given a basket with many different colored balls numbered from 0 to 9 (as 0-red, 1-pink, 2-green, 3-yellow, 4-blue, 5-white, 6-black, 7-grey, 8-brown and 9-orange). Now students need to select a ball with a minimum possible number such that the square of his roll number when multiplied with the ball number would result with the unit’s digit of his roll number. Assume that all the students are roll numbered from 1 to 50 and there is sufficient number of balls for each type.

1. How many students picked green ball?

   1. 0

   2. 1

   3. 5

   4. 10

   5. None of the above

2. What is the ratio of the number of students picking red and yellow balls?

   1. 1:1

   2. 1:2

   3. 2:1

   4. 1:3

   5. data incomplete

3. If the condition of minimum number is changed to any number but minimum then which ball will not be picked at all?

   1. Blue

   2. Green

   3. Pink

   4. Yellow

   5. None of these

4. If all the girls happened to pick pink color then what is the ratio of boys and girls in the class?

   1. 1:4

   2. 3:7

   3. 7:3

   4. 4:1

   5. 2:3

Instructions for questions 5 to 8: In a society of hostel of 190 students, all the students do at least one of these: smoking, drinking and doping. Some additional information regarding the hostel is as follows:

• Number of students smoking is 20 more than the number of the students who drink.

• Number of students who either drink or dope or both is 148.

• Number of students who either smoke & drink, drink & dope and those who dope & smoke are in AP, but necessarily in that order. And moreover they have a common difference of 2. Moreover, number of students who smoke and drink is minimum

• Number of students who only drink is equal to number of students who drink as well as dope but not smoke

5. If 60 students dope then how many of them are involved in smoking?

   1. 42

   2. 58

   3. 60

   4. 76

   5. Can not be determined

6. What can be the maximum number of students, who do dope?

   1. 98

   2. 102

   3. 112

   4. 118

   5. Can not be determined

7. If none of the students can dope alone then how many of them are involved in all of the activities?

   1. 48

   2. 52

   3. 74

   4. Either 52 or 74

   5. Either 48 or 52 or 74

8. Which of the following information is required to enable us to find the exact number of all the activities?

   1. 112 students dope

   2. 70 students dope but not smoke

   3. 24 students are involved in all three

   4. Either of the above 3

   5. None of these

Instructions for questions 12 to 16: In a one-day cricket tournament, where in first round is round robin league where in all the teams play against each other exactly once. And top two teams will reach the finals. And all the matches are typical 50 over matches.

Net run rate is defined as the difference of the two team’s scores divided by total over to be played per team. For example, India wins first match by 33 runs and lose next match by 49 runs then their net run rate will be (+33-49)/100=(-0.16).

Now the following table gives the net run rate of a tournament at different point in times as recorded, but some of the run rates are missing because of technical error.

	After 1st match	After 2nd match	After 3rd match
India	+0.8		+0.6
Pakistan		-0.4
Bangladesh	+1	+0.25	+0.066
Sri Lanka		-0.5

Following additional information is also known

• No match ended in a tie or draw

• All teams played their respective 50 over and in all the games, team playing first won their respective matches

• At the end of the tournament, if there are more than one team with same number of wins then team with higher run rate will get a better rank

12. What was the result of second match played by India?

    1. Lost by 25 runs

    2. Won by 25 runs

    3. Lost by 38 runs

    4. Won by 38 runs

    5. Can not be found

13. Against which country, Bangladesh played their first game?

    1. India

    2. Pakistan

    3. Sri Lanka

    4. Either Pakistan or Sri Lanka

    5. Can not be found

14. How many matches ended with a win of more than 50 runs

    1. 1

    2. 2

    3. 0

    4. 3

    5. None of these

15. If the team which ranked second in the round robin matches won the final, then which team won the tournament

    1. India

    2. Pakistan

    3. Bangladesh

    4. Srilanka

    5. Pakistan or Srilanka

16. Against which country, Pakistan played their last game?

    1. India

    2. Bangladesh

    3. Sri Lanka

    4. Either India or Bangladesh

    5. Either Bangladesh or Sri Lanka

Instructions for questions 17 to 20: Four friends Ramu, Kallu, Billu and Lallu are very fond of beer and collect beer bottles. They have collected beer bottles of Kingfisher (A), Heaward (B), Toofan (C), Knock out (D), Heineken (E), Carlsberg (F) and Budweiser (G)

Following table gives a ratio of different number of bottles of each type with all of them. Go through the table and then answer the questions that follow:

	Ramu	Kallu	Billu	Lallu
A:B:C	1:2:3	2:3:4	3:4:5	1:2:4
C:D:E	3:4:5	4:5:6	5:6:7	4:5:7
E:F:G	5:6:7	6:7:8	7:8:9	7:8:10

17. What can be the minimum number of bottles with them if Ramu has highest number of bottles and Billu has minimum number of bottles?

    1. 210

    2. 220

    3. 250

    4. 270

    5. None of the above

18. What can be the maximum number of bottles with them if none of them has more than 1000 bottles?

    1. 3900

    2. 3925

    3. 3950

    4. 3975

    5. 4000

19. If all of them have collectively less than 1000 bottles then what can be the maximum number of bottles with them?

    1. 892

    2. 900

    3. 999

    4. Can have more than one answer

    5. None of the above

20. What can be the maximum number of bottles with Billu if he has fewer bottles than Ramu?

    1. 170

    2. 142

    3. 150

    4. 340

    5. None of the above

Instructions for questions2 1 to 24: Ramu is very fond of whiskey and rum cocktail. Therefore, as a rule, he never drinks either of them alone rather he always drinks both of them, one after the other or mixed. Once he went to Bewafa Bar to drink his daily quota. Available drinks at Bewafa Bar are

	Type of drink	Content	Price
1	Mixed drink	1 peg of Whiskey+ 2 peg of rum	230
2	Pure drink	3 peg of whiskey	210
3	Pure drink	4 Peg of rum	240
4	Mixed drink	2 peg of Whiskey + 3 peg of rum	250

Now, Ramu was deciding what to drink and how to order his drinks in order to minimize his budget.

21. Ramu has decided to go for only pure drinks and also to consume 15 pegs. So, what will be his budget for the day?

    1. 930

    2. 1050

    3. 960

    4. 1000

    5. None of the above

22. If he has decided to consume only 25 pegs and will consume only mixed drinks. Then what can be his minimum expenditure for the day?

    1. 1840

    2. 1590

    3. 1920

    4. 1440

    5. None of These

23. If Ramu has decided to consume 15 peg of whiskey and 25 peg of rum, then what can be his minimum possible expenditure?

    1. 1590

    2. 2120

    3. 2620

    4. 2400

    5. None of these

24. If Ramu need to consume at least 16 peg of rum, then what can be his minimum expenditure?

    1. 1180

    2. 960

    3. 840

    4. 1250

    5. 1590

Instructions for questions 25 to 30: IIM A has decided to host an inter B-School sports competition. Now IIM A is deciding on teams to be invited. Apart of IIM A, which will obviously participate in the competition, there are total of 10 external teams which are being discussed to be called. These teams are IIM B, IIM C, IIM L, IIM I, IIM K, IIM S, XLRI, FMS, SP Jain, IIFT.

• Only one of IIM K, XLRI and FMS is to be called because last time, when all these teams came for the same competition then there were fights between these colleges and IIM A does not want these things to repeat this time.

• Only one of IIM L and IIM S should be invited as there are certain conflicts between the two managements. Another option is not to call either of the two.

• If IIM B is to be invited then IIM C must be called as well, as other wise none of the two will come for the competition

• FMS, SP Jain and IIFT also share some good rapport among themselves and thus all of the three should be invited together or neither of the three should be invited

• IIM C and IIM I can not be called together as they do not share a good rapport.

• IIM C and SP Jain does not want to compete with each other as both of them have their ego issues and they have created many problems in other events that have happened this year

Number of teams to be invited is not fixed and is tentative, but the competition should be conducted peacefully. Now answer the following questions based on the information given.

25. If IIM B is to be invited for sure then what can be the number of teams to be invited?

    1. 6

    2. 3

    3. 4

    4. 7

    5. 5

26. If IIM I is invited then in how many ways, participating teams can be selected?

    1. 3

    2. 4

    3. 5

    4. 6

    5. 7

27. What can be the largest number of participating teams for the competition?

    1. 4

    2. 5

    3. 6

    4. 7

    5. 8

28. Which of the following can be a participating team if a total of 5 teams are invited?

    1. IIM B

    2. IIMC

    3. IIM L

    4. IIM K

    5. XLRI

29. Which of the following can not be a participating team if a total of 3 teams are invited?

    1. IIMC

    2. IIM L

    3. IIM K

    4. IIM I

    5. IIM S

30. If at least 6 teams are to be invited then what can be the minimum number of teams to be invited?

    1. 6

    2. 7

    3. 8

    4. 9

    5. Not possible to invite more than 5 teams

Logical Reasoning Based Data Interpretation Test 1

Question 1-3 Three men (Tom, Peter and Jack) and three women (Eliza, Anne and Karen) are spending a few months at a hillside. They are to stay in a row of nine cottages, each one living in his or her own cottage. There are no others staying in the same row of houses. Anne, Tom and Jack do not want to stay in any cottage, which is at the end of the row. Eliza and Anne are unwilling to stay besides any occupied cottage.. Karen is next to Peter and Jack. Between Anne and Jack's cottage there is just one vacant house. None of the girls occupy adjacent cottages. The house occupied by Tom is next to an end cottage.

1. Which of the above statements can be said to have been derived from two other statements ? (a) Statement 1 (b) Statement 2 (c) Statement 3 (d) Statement 5 (e) Statement 6

2. How many of them occupy cottages next to a vacant cottage ? (a) 2 (b) 3 (c) 4 (d) 5 (e) 6

3. Which among these statement(s) are true ? Anne is between Eliza and Jack. At the most four persons can have occupied cottages on either side of them. . Tom stays besides Peter (a) I only (b) II only (c) I and III only (d) II and III only (e) I, II and III

Questions 4 - 7 An employee has been assigned the task of allotting offices to six of the staff members. The offices are numbered 1 - 6. The offices are arranged in a row and they are separated from each other by six foot high dividers. Hence voices, sounds and cigarette smoke flow easily from one office to another. Miss Robert's needs to use the telephone quite often throughout the day. Mr. Mike and Mr. Brown need adjacent offices as they need to consult each other often while working. Miss. Hardy, is a senior employee and has to be allotted the office number 5, having the biggest window. . Mr. Donald requires silence in the offices next to his. Mr. Tim, Mr. Mike and Mr. Donald are all smokers. Miss Hardy finds tobacco smoke allergic and consecutively the offices next to hers to be occupied by non-smokers. Unless specifically stated all the employees maintain an atmosphere of silence during office hours.

4. The ideal candidate to occupy the office furthest from Mr. Brown would be (a) Miss Hardy (b) Mr. Mike (c) Mr. Tim (d) Mr. Donald (e) Mr. Robert

5. The three employees who are smokers should be seated in the offices. (a) 1, 2 and 4 (b) 2, 3 and 6 (c) 1, 2 and 3 (d) 1, 2 and 3 (e) 1, 2 and 6 Questions 6 - 7 refers to the following table: PERCENT CHANGE IN DOLLAR AMOUNT OF SALES IN CERTAIN RETAIL STORES FROM 1977 TO 1979 Percent change 6. In 1979, for which of the stores was the dollar amount of sales greater than that of any of the others shown? (a) P (b) Q (c) R (d) S (e) It cannot be determined from the information given. 7. In store T, the dollar amount of sales for 1978 was approximately what percent of the dollar amount of sales for 1979? (a) 86% (b) 92% (c) 109% (d) 117% (e) 122% Questions 8 - 9 refers to the following Figure: 8. Of every dollar received by the federal government, how much (in cents) is from corporate sources? (a) 32 (b) 70 (c) 30 (d) 35 (e) 29 9. what percentage of the federal revenue is derived from borrowings? (a) 0.2% (b) 0.02% (c) 2.7% (d) 1.2% (e) 2.5% Questions 10 - 11 refers to the following table: DIRECTIONS: The following question are based on the bellow table, which shows per capita Mean Expenditure, Per capita Food expenditure, Number of Households and Per capita cereal consumption, in both quantity and value, for different expenditure classes of rural India. The sampled 41597 households are divided into 12 expenditure classes, starting from less than Rs.65 per month per capita and ending at more than Rs.385 per capita per month. 10. According to the results of this sample survey, what is the proportion of total expenditure on food to total expenditure for all the sampled households taken together? (a) 58% (b) 36.7% (c) 63.3% (d) 71% (e) Cannot be determined 11. What is the difference, approximately, between the gross expenditure of the sampled households in the Rs.95-110 expenditure class and in the Rs.180-215 expenditure class? (a) 372000 (b) 448000 (c) 496000 (d) 93.8 (e) 52.3 Ans : (a) Questions 12 - 13 refers to the following Graph: GRAPH SHOWS EXPENDITURE ON ARMS BY DIFFERENT COUNTRIES (VALUE IN DOLLARS '000 MILLIONS) 12. The amount spent by country C in 1983 is what percentage more than the amount spent by Countries A and B together in 1977? (Find approximately) (a) 50% (b) 179% (c) 75% (d) 13% (d) 70% 13. Which of the following statements must be true? Country A spends minimum amount of its budget on arms. Throughout, Country C has spent the maximum amount on arms during the years shown. An examination of the information for the last 3 years reveals that generally all 3 countries are reducing their expenditure on arms. (a) i only. (b) i and ii only (c) i and iii only (d) ii and iii only (e) None of the statements above.

Logical Reasoning based Data Interpretation 3

In a multinational company RQR, no person joined or left the company from 1^st January 2007 to 31^st August 2008.

“E” is defined as the total duration (in months) for which an employee has stayed in the company.

The following table gives information about the number of employees and their values of “E” at five different dates between 1^st January 2007 and 31^st August 2008 (both inclusive).

Assume that the value of “E” for each of the employees is an integer and increases on the last day of every month.

	P()	Q()	R()	S()
1st January 2007	24	31	43	56
1st October 2007	28	23	59	48
1st December 2007	18	27	45	51
1st April 2008	17	37	51	67
31st August 2008	31	44	57	73

1. Out of the employees who were in category R on 1^st January 2007, at least how many employees remained in category R on 1^st October 2007?

1. 2

2.3

3.4

4.5

5.6

2. The total number of employees in the multinational company RQR on 1^st May 2008 is at least

1.261

2.260

3.259

4.258

5.257

3. On January 21^st 2007, the number of employees who have a value of “E” less than 20 is

1.29

2.30

3.32

4.31

5. Cannot be determined.

4. If the total number of employees in the company on 31^st August 2008 is 265, then the number of employees who have a value of “E” less than 20 on 31^st August 2008 is

1.1

2.2

3.5

4.3

5.4

Logical Reasoning based Data Interpretation 2

In a factory outlet shirts are sold. All the shirts available in the factory outlet are either large (L) or extra large (XL) in size. Also, all the shirts are either of brand Addidas or Reebok. The shirts are available in two colours blue and white. The shirts either cost Rs. 400 or Rs. 600. The shirts either have half sleeves or have full sleeves. The shirts either have collar or do not have collar. The shirts are either made of cotton or made of polyester. The shirts are designer or non – designer.

The following table gives information about the number of shirts that are available in the factory outlet.

Number of Large shirts: Number of Extra Large shirts	2: 3
Number of shirts of brand Addidas: Number of shirts of brand Reebok	1: 6
Number of blue shirts: Number of white shirts	5: 7
Number of shirts that cost Rs. 400: Number of shirts that cost Rs. 600	2: 7
Number of shirts that have half sleeves: Number of shirts that have full sleeves	6: 1
Number of shirts with collar: Number of shirts without collar	3: 1
Number of cotton shirts: Number of polyester shirts	5: 3
Number of designer shirts: Number of non – designer shirts	4: 1

Each of the given ratios is true in each of the other given ratios.

For, example the ratio of Large Addidas shirts to Large Reebok shirts is 1:6.

1. Which of the following can be the total number of shirts in the factory outlet?

1. 2540

2. 5120

3. 7560

4. 8240

9. None of these.

2. What is the ratio of the number of white cotton large shirts with collar to the number of blue polyester extra large shirts with collar?

1. 14: 9 2. 7: 3 3. 5:1 4. 10: 3

5. None of these.

3. If the total number of half sleeves shirt without collar is 4320, then the number of large polyester blue shirts with collar costing Rs. 600 is

1. 715 2. 720 3. 725 4. 730 5.735

4. If the number of cotton designer shirts is equal to ‘X’, then which of the following is more than ‘X’?

1. Number of polyester non designer shirts.

2. Number of whites shirts that cost Rs. 600.

3. Number of half sleeves shirt without collar.

4. Number of large shirts of brand Reebok.

5. None of the above.

MIND BLOWING 1

1. Find the side length of the smallest equilateral triangle in which
three discs of radii 2, 3, 4 can be placed without overlap.

2. The quadrilateral ABCD is inscribed in a circle. The lines AB
and CD meet at E, while the diagonals AC and BD meet at F.
The circum circles of the triangles AFD and BFC meet again at H.
Find angle (EHF)?

3. A 7 x 7 chessboard is given with its four corners deleted.
(a) What is the smallest number of squares which can be colored
black so that an uncolored 5-square (Greek) cross cannot be
found?
(b) Prove that an integer can be written in each square such that
the sum of the integers in each 5-square cross is negative while
the sum of the numbers in all squares of the board is positive.

4. Starting at (1; 1), a stone is moved in the coordinate plane according
to the following rules:
(i) From any point (a; b), the stone can move to (2a; b) or (a; 2b).
(ii) From any point (a; b), the stone can move to (a - b; b) if a > b,
or to (a; b - a) if a < b.
For which positive integers x; y can the stone be moved to (x; y)?

5. Each diagonal of a convex pentagon is parallel to one side of the
pentagon. Prove that the ratio of the length of a diagonal to that of
its corresponding side is the same for all five diagonals, and compute
this ratio.

6. For each positive integer n, and the greatest common divisor of n!+1
and (n + 1)!.

7. Let A and B be opposite vertices of a cube of edge length 1. Find
the radius of the sphere with center interior to the cube, tangent to
the three faces meeting at A and tangent to the three edges meeting
at B.

8. A function f is de fined on the positive integers satis fies f(1) = 2010
and
f(1) + f(2) + ............ + f(n) = (n^2)f(n) (n > 1):
Calculate f(2010).

9. Let n be a natural number. A cube of side length n can be divided
into 1996 cubes whose side lengths are also natural numbers.
Determine the smallest possible value of n.

10. The numbers from 1 to 37 are written in a line so that each number
divides the sum of the previous numbers. If the first number is 37
and the second number is 1, what is the third number?

Logical Reasoning based Data Interpretation SET 1

A man observe some children playing ’cycle game’ in front of his house every Sunday. He observes that children come in groups and after every 15 minutes, one child from each group leaves their group and form a new group. When same number of groups with same size occurred again , ‘cycle’ has occurred. For example, let initially 3 children in a single group, regrouping 2, 1 and again regrouping 2,1 means cycle occurred. The following table gives the data of seven Sundays as

Sundays........Initial number of groups..........Number of children.........Final number of groups

Sunday 1.................... --- .........................................15 ..........................................---
Sunday 2 .................... 2 ......................................... --- .......................................... 6
Sunday 3 .................... --- ......................................... --- ....................................... 7
Sunday 4 .................... --- .........................................4 ..........................................---
Sunday 5 .................... 2 .........................................10 .......................................... 4
Sunday 6 .................... 5 .........................................18 ..........................................---
Sunday 7 .................... 2 ......................................... --- .......................................... ---


On the basis of the above data, answers the following Questions.

1. How many of the given Sundays, cycle does not occur?
(1) 1 (2) 2 (3) 4 (4) It occurs all the 7 Sundays

2. How many children were there on 3rd Sunday?
(1) 25 (2) 22 (3) 36 (4) 28

3. If six children comes at 9:00 am on 7th Sunday, at what time it is known that
Cycle has occurred first time?
(1) 9:45 am (2) 10:00am (3) 10:15am (4) 10:30am

4. The minimum time to know that ‘cycle’ has occurred first time on 5th Sunday?
(1) 45 minutes (2) 1 hr 15 minutes
(3) 1 hr (4) 2 hr 15 minutes

SECTION TEST 1

1. Find the last two digits of the expression 7324⁵⁴⁶⁷?

1. 24

2. 76

3. 36

4. 74

2. A given two digit number is added to another two digit number obtained by reversing thedigits of the given number (both should be two digits), the sum so obtained is a perfect square. How many such two digit numbers are possible.

1. 4

2. 6

3. 8

4. 10

3. Find the number of zeroes at the end of the expression

1³⁰ x 2²⁹ x 3²⁸ x …… x 28³ x 29² x 30¹

1. 77

2. 83

3. 87

4. 95

4. In a school, the number of female students are F such that 60%<65%

number of students in the class. What can be the minimum number of female students in the class?

1. 5

2. 8

3.17

4. 31

5. Vessel A contains milk and Vessel B contains water. Initially milk in Vessel A and waterIn Vessel B is in ratio 2 : 3. 20% of the volume of the vessel A is poured in Vessel B and then half of the final volume of Vessel B is poured in Vessel A. The process repeated again. Find the ratio of water in Vessel A to Vessel B?

1. 3 : 7

2. 7 : 3

3. 7 : 43

4. 43 : 7

6. If a = 2009, b = 2010 & c = 2011, then find the value of a³ + b³ + c³ – 3abc?

1. 12,090

2. 18,090

3. 15,190

4. 16,090

7. A can built a wall in 20 days, B can built it in 25 days, C can destroyed the complete wall in 40 days. They stars work in alternate days in such a way that, A start the work, followed by B next day, then by C next day, then by A next day and so on. How many ways it will take to complete the wall at first time?

1. 44.5 days

2. 45 days

3. 44 days

4. 45.5 days

8. The average age of A, B & C is 82 years, the average age of A, B & D is 79 years,

the average age of A, C & D is 83 years and the average age of D, B & C is 81 years.

Who among the A, B, C & D is the eldest?

(1) A

(2) B

(3) C

(4) 4

9. Ram, Sham and Mohan travel from Chandigarh to Amritsar. They have a single Bi-Cycle which is only drive by Mohan and only two persons sit at it at a time. The distance between Chandigarh and Amritsar is 240 Km and all of them can walk at a speed of 12 kmph but to reach Amritsar simultaneously also they started their journey simultaneously. (Ram took one among them and the second one walked. Left the first one at any point and return to pick the another one). If the speed of the Bi-cycle is 48mph, them find the total distance that Bi-cycle travel?

1. 336 km

2. 360 km

3. 320 km

4. 400 km

10. Ran while diametrically across a semicircular playground takes 5 minutes less than if he walked round the circular path. If he walks 100 m in 1 minute, what is the diameter of the playground.

1. 500m

2. 525 m

3. 625 m

4. 475 m

11. Find the sum of the infinite series

11 . 4 + 14 .7 + 17 . 10 + 110 . 13 + ……. ∞

1. 1/3

2. 1

3. ½

4. 2/3

12. Find the number of real roots of the equation (x – 6)² + (x – 7)² + (x – 8)² = 0

1. 0

2. 1

3. 2

4. 3

13.For what value of k, then difference between the roots of the equation x² + kx + 8 = 0 is 2?

1. ±2

2. ±4

3. ±6

4. ±8

Direction (14 – 15):- Questions are followed by two statements as (I) and (II). You have to decide if these statements are sufficient to conclude the answer of the question.

Choose

(1) If statement (I) alone is sufficient to give the answer of the question but statement (II) is not

Sufficient or VICE- VERSA

(2) If Statement (I) & statement (II) together sufficient but neither of the two alone is sufficient

to answer the question.

(3) If either statement (I) or statement (II) alone is sufficient to answer the question

(4) Both statements are not sufficient to answer the question.

14. What is the maximum value of (a/b)?

(I) a, a + b and a + 2b are three sides of a triangle

(II) a and b both are positive

15. Five integers A, B, C, D and E are arranged in such a way that there are two integers between B and C and B is not the greatest. There exists one integer between D and E and D is smaller than E. a is not the smallest integer. Which one is the smallest?

(I) E is the greatest integer

(II) There exists no integer between B and E.