Hcu-Previous Year Papers

HCU-PREVIOUS YEAR PAPERS

1 INFOMATHS/MCA/MATHS/

HCU-2013

PART A

1.Which letter in the word RUTHLESS has a position from the beginning of the word that is half s much as its position when seen in the alphabet?

(a) L (b)E(c) H(d) U

2.A wire of some length is bent in circular form and has an area of 308 sq. cm. If the same length of wire is straightened out and bent in the form of a square, the approximate area of the square in sq. cm may be

(a) 242(b) 121 (c) 308 (d) 69.29

3.Consider a square circumscribed by a circle with a radius of 4 units. The area of the square in square units is

(a) (b) 16(c) 32(d) 64

4.A man returns after shooting and catching birds in his bag. He was asked how many birds he had in his bag. He said, “They are all house sparrows but six, they are all pigeons but six, and all doves but six.” The number of birds he had in all were?

(a) 18(b) 36(c) 9(d) 27

5.Suppose as an ant is placed on one corner of a sugar cube, which has equal sides of 1.5 cm each. If the ant may walk only along the edges of the cube, what is the maximum distance the ant may walk on the cube without retracting its path?

(a) 9 cm (b) 18 cm

6.When the big hand of the clock is exactly at the 12 o’ clock position, an ant starts to crawl in a counter clockwise direction from the 6 o’clock position at a constant speed. On reaching the big hand of the clock, the ant turns around and at the same speed, starts to crawl, in the opposite direction. Exactly 45 minutes after the first meeting with the big hand the ant crosses the big hand for the second time and dies. How long has the ant been crawling?

(a) 51 min. (b) 54 min.

7.One third of Shrihari’s marks in Math equal half of his English marks. Shrihari noticed that in these two subjects his marks totaled 150. What did Shrihari score in English?

(a) 60(b) 15(c) 30(d) 90

8.The sum of two digits of a number is 15. If 9 is added to the number then the digits get reversed. Which of the following is FALSE about the number

(a) The number has the two digits separated by a difference of one

(b) The number is divisible by 3

(d) The number is divisible by 9

9.An ant is at a point P in a planar square field. It was observed that P is 13 feet from the corner A, and 17 feet from corner B (diagonal to A), and finally 20 feet from a third corner. The area in square feet of the field is

(a) 89(b) 231(c) 369(d) 169

10.Consider the triangle ABC with sides AB = 20 cm., AC = 11 cm., and BC = 13 cm. Then the length in cm. of the diameter of the semi-circle inscribed within ABC, which lies on AB, and has sides AC and BC as tangents is given by

(a) 11(b) 9(c) 10(d) 10.5

11.It takes 6 technicians a total of 10 hours to install a new equipment from scratch, with each working at the same rate, with each working at the same rate. If six technicians start to install the same equipment at 11:00 am, and one technician per hour is added beginning at 5:00 p.m, at what time will the equipment installation be complete?

(a) 6:40 pm (b) 7:00 pm (c) 7:20 pm (d) 8:00 pm

12.In how many ways is it possible to choose a white square and a black square on a chess board so that the squares must not lie in the same row or column?

(a) 56(b) 896(c) 60(d) 768

13.Gopal’s Shop sells small cookies in boxes of different sizes. The cookies are priced at Rs. 2 per cookies up to 200 cookies. For every additional 20 cookies, the price of the whole lot goes down by 10 paise per cookies. What should be the maximum size of the box (in terms of number of cookies it can hold) that would maximize the revenue?

(a) 240(b) 300(c) 400(d) None of these

14.3 small pumps and a large pump are filling a tank. Each of the three small pumps works at rd the rate of the large pump. In what fraction of the time that all 4 pumps working together will fill the tank in comparison to the time taken by the large pump alone?

(a) 4/7(b) 1/3(c) 2/3(d) 3/4

15.Four cows are tethered at four corners of a square plot of side 14 meters so that the adjacent cows can just reach one another. There is a small circular pond of area 20 m2 at the centre. The area left ungrazed is:

(a) 22 m2(b) 42m2(c) 84m2(d) 168m2

Answer questions 16 and 17 using the following information: 8 trees, viz. mango, guava, papaya, pomegranate, lemon, banana, raspberry and apple are planted in two rows, of four each aligned East-West. Lemon is between mango and apple but just opposite to guava. Banana is either at the end of a row and is just immediately to the right of guava, or Banana is just next to Guava. Raspberry is at the end of a row, and mango is at the other end of the opposite row.

16.Which of the following is always true

(a) Papaya is just next to Apple

(b) Apple is just next to Lemon

(d) Pomegranate is diagonally opposite to Banana

17.Which of these is directly opposite Banana?

(a) Mango (b) Pomegranate

18.How many number of times will the digit 7’ be written when listing the integers from 1 to 1000?

(a) 271(b) 300(c) 252(d) 304

19.There are 10 positive real number n1 < n2 < n3 ….. < n10. How many triplets of these numbers (n1, n2, n3), (n2, n3, n4), ….. can be generated such that in each triplet the first number is always less than the second number; and the second number is always less than the third number?

(a) 45(b) 90(c) 120(d) 180

20.There were two women amongst other men who took part in a chess tournament. Every participant played two games with every other participant. The number of games which only men played was exactly 104 games more than those played which involved a women. The total number of participants is

(a) 11(b) 13(c) 14(d) 15

Answer questions 21 and 22 using the following information : In the English alphabet there are 11 symmetric letters that appear the same when looked at in a mirror. Other 15 letters in the alphabet are asymmetric letters.

21.How many four-letter computer passwords can be formed using only the symmetric letters (no repetition allowed)?

(a) 7920(b) 330(c) 14640(d) 419430

22.How many three-letter computer passwords (no repetition allowed) can be formed with at least one symmetric letter?

(a) 990(b) 2730(c) 12870(d) 15600

23.On a straight road XY, 100 meters long, five heavy stones are placed 2 meters apart beginning at the end X. A worker, starting at X, has to transport all the stones to Y, by carrying only one stone at a time. The minimum distance he has to travel (in meters) is:

(a) 422(b) 480(c) 744(d) 860

24.Given that abca = abca, where all a, b, c are integers, then which of the following is true

(a) a = 1 (b) c = 9 (c) b = 4 (d) none of these

25.Instead of walking along two adjacent sides of a rectangular field, a boy took a short cut along the diagonal and saved a distance equal to half the longer side. Then the ratio of the shorter side to the longer side is :

(a) 1/2(b) 2/3(c) 1/4(d) 3/4

HCU-2012 B

PART A

1. The numbers 1 to 100 are written in a10  10 grid. The multiples for each ofthe first few odd numbers - 3, 5, 7, 9,11 and 13 - are coloured gray. Themultiples of which number form a continuous line at 135 in the grid? Anglesare measured in the conventionalanti-clockwise way from the horizontal line given by the bottom row of thegrid.

(a) 13(b) 5(c) 9(d) 11

2. A part of the divisibility test for 11 is:sum up alternate digits (starting fromunits place) and if the difference betweenthem is 0, the number is divisibleby 11. E.g., 1047673 gives 3 + 6 +4+1. (=14) and 7 +7 + 0 (=14), andtherefore is divisible by 11. Now, sumup alternate pairs of digits (startingfrom units place) and if the differencebetween them is 0, then the numberis divisible by X. E.g., 46662 gives 62 + 04 (=66) and 66, and therefore isdivisible by X.

What is X?

(a) 101(b) 11(c) 21(d) 22

3. In any year, if April 1 is a Wednesday then so is

(a) January 1(b) July 1

4. If (12*22*35)/p is an integer, which ofthe following CANNOT be the valueof p?

(a) 15(b) 21(c) 28 (d) 50

5.There are two cubes on a table inwhich the volume of the second is halfthat of the first. If the first cube occupiesa certain area (Y) on the table,how much area (approximately) doesthe second occupy?

(a) (b) (c) (d)

6.The age of a grandfather in years is thesame as that of his grand-daughter'sin months. If their ages differ by 55years, the age of the grand-daughteris

(a) yrs (b)months

7.Paper sizes are given by A0, A1, A2,etc. such that A0 is two times larger(in area) than A1, A1 is two times larger than A2 and so on. The longerdimension of each smaller size is equalto the shorter dimension of the larger size. For example, the longer dimensionof A2 is the same as the shorterdimension of A1. In this scheme if A4is 210 mm 297 mm in size, what arethe dimensions of A0 in mm?

(a) 840594(b) 420594

9.On Planet X, a year has 400 days witha leap year of 401 days every 4 years.Also, a year ending in '00' is a leapyear only if the year is divisible by 400,e.g, 2000 is a leap year but 3000 is not.Such a calendar is exact and needs nomore corrections.

The length of the year on Planet X is

(a) 400.2425 days(b) 400.2475 days

10. Given that D is younger than F andolder than G. A is younger than I andolder than C. I is younger than G andolder than J. J is younger than C andolder than E. F is younger than B andolder than H. H is older than D. Theyoungest of all of the above is

(a) E(b) D(c) A(d) C

11.A military general needs to take histroop of 100 soldiers across a riverfrom the bank A to bank B. He engagesa boat with two boys, both ofwhom can row, at the bank A. Butthe boat can take only upto two boysor only one soldier. What is the minimum number of round trips that the boat has to make, to transfer all the100 soldiers and the general to bankB and come back to bank A?

(a) 404(b) 200(c) 202(d) 403

12.Mr.X lies only on Saturday, Sundayand Tuesday and speaks only truth onthe remaining days. On a particularday he said, "Today being a Sunday,it is a rest day and tomorrow beinga Wednesday I will go to the market".What is the day on which this was spoken by Mr.X?

(a) Monday(b) Tuesday

13.A square whose side is 2 meters, has its corners cut away so as to form an octagon will all sides equal. Then the length of each side of the octagon, in meters is

(a) (b)

14.How many different 4-letter words can be formed (the words need not be meaningful) using the letters of the word "MEDITERRANEAN" such that the first letter is N and the last letter is R?

(a) 60(b)59(c) 58(d)56

15.The number of diagonals of a polygon having 14 sides is

(a) 66(b)72(c) 77(d)79

16.There are 6 boxes labeled from A to F. Each box is to be filled up either with a red or a green ball in such a way that at least 2 boxes contain a green ball. What is the total number of ways the boxes can be arranged such that the first and sixth box is always a box containing a green ball?

(a) 70  4(b)10  4

17. There is a vertical stack of booksmarked 1, 2, and 3 on Table A, with1 at the bottom and 3 on top. Theseare to be placed vertically on TableB with 1 at the bottom and 2 on thetop, by making a series of moves fromone table to the other. During a move,the topmost book, or the topmost twobooks, or all the three, can be movedfrom one of the tables to the other.If there are any books on the other table,the stack being transferred shouldbe placed on top of the existing books,without changing the order of books inthe stack that is being moved in thatmove. If there are no books on theother table, the stack is simply placedon the other table without disturbingthe order of books in it. What is theminimum number of moves in whichthe above task can be accomplished?

(a) One(b) Two(c) Three(d) Four

18.Ten points are marked on a straight line and eleven points are marked on another straight line parallel to the first. How many triangles can be constructed with vertices from among these points on the two lines?

(a) 2475(b)1045(c) 550(d)495

19.Consider the following two statements:

I.The Meteorological department has issued a statement mentioning deficient rainfall during monsoon in many parts of the country.

II.The Government has lowered the estimated GDP growth from the level of earlier estimates.

(a) Statement I is the cause and statement II is its effect.

(b) Statement II is the cause and statement I is its effect.

(d) Both the statements I and II are effects of independent causes.

20.P, Q, R and S made the following statements. Only one told the truth. Who is the thief?

P : Q is the thief
Q : P is the telling a lie
R : I saw P stealing
S : I am not the thief

(a)P(b)Q(c)R(d)S

21.Consider a number 23571113... madeby placing in ascending order, all theprime numbers between 2 and 30. Ifthis number were divided by 16, theremainder would be:

(a) 1(b) 9(c) 8(d) 7

22. A clock loses 1% time during the firstweek and then gains 2% time duringthe next one week. If the clock wasset right at 12 noon on a Sunday, whatwill be the time that the clock willshow exactly 14 days from the timeit was set right?

(a) 1: 36: 48(b) 1: 40: 48

23. A gives B a start of 10 metres in a100 metre race and still beats him by1.25 seconds. How long does B take tocomplete the 100 metre race if A runsat the rate of 10 m/sec?

(a) 8 seconds(b) 10 seconds

24.If a, b  0, then x =

(a) 7/2(b) 2(c) 1(d) 1/2

25. A large number of people die everyyear due to drinking polluted water during the summer.

Given the two courses of action below,which of the answers A ...D is APPROPRIATE?

I. The government should make adequatearrangements to providesafe drinking water to all its citizens.

II. The people should be educatedabout the dangers of drinkingpolluted water.

(a) Both I and II follow

(b) Only I follows

(d) Neither I nor II follows

HCU-2012A

PART A

HCU-2012

(a) 13(b) 5(c) 9(d) 11

2. There is a vertical stack of booksmarked 1, 2, and 3 on Table A, with1 at the bottom and 3 on top. Theseare to be placed vertically on TableB with 1 at the bottom and 2 on thetop, by making a series of moves fromone table to the other. During a move,the topmost book, or the topmost twobooks, or all the three, can be movedfrom one of the tables to the other.If there are any books on the other table,the stack being transferred shouldbe placed on top of the existing books,without changing the order of books inthe stack that is being moved in thatmove. If there are no books on theother table, the stack is simply placedon the other table without disturbingthe order of books in it. What is theminimum number of moves in whichthe above task can be accomplished? HCU-2012

(a) One(b) Two(c) Three(d) Four

3. A clock loses 1% time during the firstweek and then gains 2% time duringthe next one week. If the clock wasset right at 12 noon on a Sunday, whatwill be the time that the clock willshow exactly 14 days from the timeit was set right? HCU-2012

(a) 1: 36: 48(b) 1: 40: 48

4. A part of the divisibility test for 11 is:sum up alternate digits (starting fromunits place) and if the difference betweenthem is 0, the number is divisibleby 11. E.g., 1047673 gives 3 + 6 +4+1. (=14) and 7 +7 + 0 (=14), andtherefore is divisible by 11. Now, sumup alternate pairs of digits (startingfrom units place) and if the differencebetween them is 0, then the numberis divisible by X. E.g., 46662 gives 62 + 04 (=66) and 66, and therefore isdivisible by X.

What is X? HCU-2012

(a) 101(b) 11(c) 21(d) 22

5. In any year, if April 1 is a Wednesday then so is

HCU-2012

(a) January 1(b) July 1

6. If (12*22*35)/p is an integer, which ofthe following CANNOT be the valueof p? HCU-2012

(a) 15(b) 21(c) 28 (d) 50

7.There are two cubes on a table inwhich the volume of the second is halfthat of the first. If the first cube occupiesa certain area (Y) on the table,how much area (approximately) doesthe second occupy?

HCU-2012

(a) (b) (c) (d)

8.The age of a grandfather in years is thesame as that of his grand-daughter'sin months. If their ages differ by 55years, the age of the grand-daughteris

HCU-2012

(a) yrs (b)months

9.Paper sizes are given by A0, A1, A2,etc. such that A0 is two times larger(in area) than A1, A1 is two times larger than A2 and so on. The longerdimension of each smaller size is equalto the shorter dimension of the larger size. For example, the longer dimensionof A2 is the same as the shorterdimension of A1. In this scheme if A4is 210 mm 297 mm in size, what arethe dimensions of A0 in mm? HCU-2012

(a) 840594(b) 420594

10.If a, b  0, then x = HCU-2012

(a) 7/2(b) 2(c) 1(d) 1/2

11.In a country with three major scootermanufacturers, Brand C sells threetimes as many as Brand A while BrandA sells half as many as Brand B. Itimplies that Brand C holds a marketshare of about

HCU-2012

(a) 50%(b) 33%(c) 66%(d) None of these

12.On Planet X, a year has 400 days witha leap year of 401 days every 4 years.Also, a year ending in '00' is a leapyear only if the year is divisible by 400,e.g, 2000 is a leap year but 3000 is not.Such a calendar is exact and needs nomore corrections.

The length of the year on Planet X is HCU-2012

(a) 400.2425 days(b) 400.2475 days

13. A gives B a start of 10 metres in a100 metre race and still beats him by1.25 seconds. How long does B take tocomplete the 100 metre race if A runsat the rate of 10 m/sec? HCU-2012

(a) 8 seconds(b) 10 seconds

14. A large number of people die everyyear due to drinking polluted water during the summer.

Given the two courses of action below,which of the answers A ...D is APPROPRIATE?

I. The government should make adequatearrangements to providesafe drinking water to all its citizens.

II. The people should be educatedabout the dangers of drinkingpolluted water.

HCU-2012

(a) Both I and II follow

(b) Only I follows

(d) Neither I nor II follows

15. Given that D is younger than F andolder than G. A is younger than I andolder than C. I is younger than G andolder than J. J is younger than C andolder than E. F is younger than B andolder than H. H is older than D. Theyoungest of all of the above is