University of Hyderabad

University of Hyderabad

Entrance Examination (June 2007)

Master of Computer Application (MCA)

Time : 2 Hours Max. Marks: 75

Hall Ticket Number

INSTRUCTIONS

(a) Write your Hall Ticket Number in the above box AND on the OMR Sheet.

(b) Fill in he OMR sheet, the Set Code B given above at the top left corner of this sheet. Candidates should also read and follow the other instructions.

All the answers should be marked clearly in the OMR answer sheet only.
This objective type test ha two parts: Part A with 25 questions and Part B with 50 questions. Please make sure that all the questions are clearly printed in your paper.
Every correct answer carries 1 (one) mark and for every wrong answer mark will be deducted.
Do not use any other paper, envelope etc for writing or doing rough work. All the rough work should be done in your question paper or on the sheets provided with the question paper at the end.
During the examination, anyone found indulging in copying or have any discussions will be asked to leave the examination hall.
Use of non-programmable calculator and log-tables in allowed.
use of mobile phone is not allowed inside the hall.
Submit both the question paper and the OMR sheet to the invigilator before leaving the examination hall.

Part A

1.The English words for two numbers are scrambled and the letters reassembled to give two different words for two different numbers. When these two numbers are added together, it is found that their sum in the same as that of the original numbers. One of the four number is HYDERABAD-2007

(a) 11(b) 13(c) 5(d) 7

2.The minimum number of weights needed to weigh objects ranging form 1kg. To 364 kg. in a two-pan balance is HYDERABAD-2007

(a) 5(b) 6(c) 9(d) 8

3.What is the smallest 3-digit integer number that can be expressed as the sum of two squares in three different ways: HYDERABAD-2007

(a) 625(b) 325(c) 425 (d) 369

4.Which of the following 10-digit numbers containing each digit once so that the number formed by the first n digits is divisible by n for each value of n between 1 and 10? HYDERABAD-2007

(a) 3816574290(b) 2436581790

5.How many numbers between 100 and 9800 are exactly divisible by 13? HYDERABAD-2007

(a) 749(b) 746(c) 747 (d) 777

6.Given that all Indians are cricket fans, some cricket fans are hockey fans and some hockey fans are tennis fans, which of the following is ALWAYS TRUE? HYDERABAD-2007

(a)All cricket fans are Indians

(b)Some Indians are tennis fans

(c)No Indian is a tennis fan

(d)Some Indians are hockey fans

7.Whenever it is possible to find a pair of numbers neither of which contains any 0’s and whose product is of the form 10k, then at least HYDERABAD-2007

(a)one of them MUST end in a 2

(b)one of them MUST end in a 4

(c)one of them MUST end in a 5

(d)one of them MUST end in an 8

8.Multiply your phone number (without area code) by 8. Write the following three numbers:

Your phone number
8
The product of phone number with 8

Add all the digits in the three numbers. If the sum is more than one digit, add again until a single digit it reached. What is this digit? HYDERABAD-2007

(a) 0(b) 8(c) 9

(d) Depends on he phone number

9.Place 4 dice on the table and arrange them so that all four top numbers are the same. Turn any tow dice upside down and then add the top numbers. What is the sum? HYDERABAD-2007

(a) 16(b) 18(c) 20 (d) 14

10.Let be a set of companies that offer lotteries in Hyderabad. During a given year, let N be the set of numbers of the tickets. Define w: L  N such that w (x) is the mapping from name of he company from name of the company to the number of the winner of the first prize. Which do you think is the more probable of the following choices for w?

HYDERABAD-2007

(a) w sis not a function (b) w is one-to-one

11.A, B, C, D are related to the numbers 1, 2, 3 and 4 according to the following relations:

If A is 1, then B is not 3
If B is not 1, then D is 4
If C is 3, then D is not 2
If C is not 2, then D is 2
If D is 3, then A is not 4

A valid assignment for A is HYDERABAD-2007

(a) 1(b) 2(c) 3

(d) There are no valid assignments

12.Numbers 0 to 9 are assigned to the letters so that we get a correct mathematical problem. What is “ONE” in the following addition:

ONE

+ONE

------

=TWO HYDERABAD-2007

(a) 375(b) 408(c) 256 (d) N.O.T

13.Five shops sell cakes, electrical goods, greengrocery, hardware and shoes. Each decided to take on two young assistants, one of each sex. The initials of the assistance are not the same as that of the shop where they work. The assistants in the same shop cannot have the same first initial in their names. Hema, Shyam and Ekalavya are three of the assistants. Eshwari does not work with Hari nor does she work in the shoe shop. Hari does not work in the cake shop. Gopi does not work in the hardware shop. Gayatri is Into in the shoe shop. Neither Chakri nor Seema work in the greengrocer’s. If Chandrika works in the hardware shop, who works for the electrical shop? HYDERABAD-2007

(a) Hari, Gayatri (b) Gop, Hema

14.A box contains two coins. One coin is double-headed and the other is a normal one with a head and a tail. A coin is drawn from the box and it is found that one side is head. What is the probability that the other side is also a head? HYDERABAD-2007

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

15.Raju and Ravi wanted to take a vacation. They were debating how they could get to their hotel in the fastest manner. Raju said “We should go by train”. But, Ravi said “No, the train reaches the end of the line halfway to the hotel. We would have to walk the rest of the way. We should bike to the hotel instead.” Raju disagree. So, Ravi biked the whole way to the hotel while Raju took the train for the first half of the journey and walked the remainder. The speed of the train turned out to be four times that of the bike’s speed. The bike’s speed turned out to be two times faster than the walker’s speed. Who got to the hotel first and was early by how much time given that the walking speed is given to be 0.1km/min and the total distance traveled is 16 km? HYDERABAD-2007

(a)Raju by 20 min

(b)Ravi by 10 min

(c)Both reach at the same time

(d)Raju by 30 min

16.We have three containers which hold, when filled to the brim with water, exactly 8, 5 and 3 litres respectively. By starting off with the largest one full, we can pour from one to the other and without wasting a drop, divide the water into two equal portions. The minimum number of steps required is

HYDERABAD-2007

(a) 8(b) 7(c) 6

(d) 5(e) None of the above

17.A, B, C, D and E are distinct numbers from 1 to 5 satisfying the equations: A + B = 6, E + B = C, E + B + C = 8. Then, which of the following statements is true?

C has to be 4
A or B must be 1
A or E must be 5
D is 3 HYDERABAD-2007

(a) I, II and III are true (b) I, II and IV are true

18.Determine which of the following function(s) is/are one-to-one:

To each person on the Earth, assign the number which corresponds to his age
To each country in the world, assign the latitude and latitude of its capital
To each book with only one author, assign the author to the book HYDERABAD-2007

(a) I, II and III (b) I, III only (c) II, III only

(d) None of the three (e) II only

19.A positive whole number M less than 100 is represented in base-2 notation, base-3 notation and base-5 notation. It is found that in all three cases, the last digit is , while in exactly two out of the three cases, the leading digit is 1. Them M equals

HYDERABAD-2007

(a) 31(b) 63(c) 75 (d) 91(e) N.O.T

20.Let g(x) = max (5 – x, x + 2). The smallest possible value of g(x) in R is HYDERABAD-2007

(a) 4.0(b) 4.5(c) 1.5 (d) 0(e) N.O.T

21.How many even integers n, where 100  n  200, are divisible neither by even nor by nine?

HYDERABAD-2007

(a) 39(b) 38(c) 40 (d) 37(e) N.O.T

22.A student takes an 48-question multiple choice exam with four choices per question. Suppose the student makes and “educated” guess of the choices. Find the expected number E(X) of correct answers and the standard deviation . HYDERABAD-2007

(a) E(X) = 16,  = 3(b) E(X) = 12,  = 3

(e) None of the above

The questions 23-25 are based on the following passage given here

In Department of Computer and Information Sciences the following subjects are taught by the experts for the MCA course AI, DAR, SP, CIP, IP, and MC. Six professors AA, HM, BLD, PNG, CB, AN conduct lectures of these subjects on six working days from Monday to Saturday. Every day only one lecture is conduced by only one professor.

HYDERABAD-2007

(a)IP lecture is neither on Saturday nor on Tuesday, while on Friday neither AI nor MC lectures take place. PNG takes lectures take place. PNG takes lectures on SP on every Wednesday.

(b)HM is not available after Tuesday while AA is available only on Mondays.

(c)AN is an expert teacher of DAR and he delivers his lecture on every Friday.

(d)The AI teacher is available only one Thursday.

(e)CB teaches the subject of CIP. He takes his lecture on the last day of the week.

23.AI is taught by HYDERABAD-2007

(a) BLD(b) PNG(c) HM

(d) AN(e) None of the above

24.Which of the following statements is TRUE?

HYDERABAD-2007

(a)SP is neither taught by CB nor by PNG

(b)AA teaches IP

(c)AN takes his lecture on every Saturday

(d)MC lecture is scheduled on every Thursday

25.Which of the following combination is correct?

HYDERABAD-2007

(a) Friday-AN-MC(b) CIP-Monday-PNG

Part B

26.Let A be a set with 10 elements. The total number of relations that can be defined on. A which are both reflexive and symmetric is HYDERABAD-2007

(a) 245(b) 255(c) 1055(d) ()(e) N.O.T

27.Two classes A and B with respective strengths of 30 and 40 have an arithmetic mean of 50 and 60 respectively and standard deviation of 2 and 4 respectively. The respective group mean and standard deviation of the two classes are:

HYDERABAD-2007

(a) 55.7, 3.3(b) 55.0, 3.0(c) 55.0, 3.0

(d) 55.7, 3.0(e) None of the above

28.An n  m-matrix A is of rank 5, and 5 < n and 5 < m. Identify the statement which is NOT TRUE.

HYDERABAD-2007

(a)All the determinants of sub-square matrix of order k  k(k < 5) are zero.

(b)There exists a set of k rows (k < 5) which are linearly independent

(c)The set of any k(k > 5) rows are linearly dependent

(d)All the determinants of sub-square matrix of order k  k (k>0) are zero

(e)There exists a 5  5 submatrix whose determinants is non-zero

29.Which of the following statements is TRUE?

HYDERABAD-2007

(a)if a relation is not reflexive then it is irreflexive

(b)if a relation is irreflexive then it is asymmetric

(c)if a relation is asymmetric then it is irreflexive

(d)if a relation is not symmetric then it is asymmetric

(e)None of the above

30.If then at x = 0,

HYDERABAD-2007

(a) 0(b) (c) 1(d) -(e) N.O.T

31.The mean (m) and standard deviation (sd) of the binomial distribution with n = 48 and p = .75 is

(a) m = 36, sd = 9 (b) m = 12, sd = 0

(e) None of the above

32.A function f is defined on the whole of R as follows: for some k(0 < k < 1),

Then is

HYDERABAD-2007

(a) 1(b) 0(c) (d) -(e) N.O.T

33.The number 2300 * 5600 * 4400 ends in how many zeros? HYDERABAD-2007

(a) 300(b) 600(c) 400 (d) 700(e) N.O.T

34.A set A contains (2n + 1) elements. The number of subsets of A which contain at most N elements is

HYDERABAD-2007

(a) 2n(b) 2n + 1 (c) 2n – 1

(d) 22n (e) None of the above

35.Let A = {p, q, r, s} and B = {1, 2, 3, 4, 5, 6}. How many one-to-one functions are possible from A to B?

HYDERABAD-2007

(a) 46(b) 64(c) 24 (d) 360(e) N.O.T

36.Set A contains 3 elements and set B contains 4 elements. The number of onto functions from A to B is HYDERABAD-2007

(a) 2(b) 3(c) 6 (d) 5(e) N.O.T

37.Let A, B, C be disjoint subsets of a sample space S and E, F form a partition o S. Let P(A) = a, P(B) = b, P(C) = c, P(E) = e, P(F) = f, P(A/E) = x, P(A/F) = y. given that

a + b + c = 1
e + f = 1
aP(E/A) = xe

which of the following is TRUE? HYDERABAD-2007

(a) II and I (b) III and I (c) II and III

(d) I only (e) None of the above

38.If A = Then A6 is HYDERABAD-2007

(a) A(b) A2(c) A3(d) I(e) N.O.T

39.The value of a for which the system of equations

a3x + (a + 1)3y + (a + 2)3z = 0

ax + (a + 1)y + (a + 2)z = 0

x + y + z = 0

has a non-zero solution is HYDERABAD-2007

(a) 1(b) -1(c) 0

(d) 2(e) None of the above

40.If A = Then A cannot be

HYDERABAD-2007

(a) Symmetric (b) Skew-symmetric

(e) None of the above

41.If 1 and 2 are the eigen values of 2-rowed square matrix A and I2 is the unit, matrix of order 2, then A3 is equal to HYDERABAD-2007

(a) 6A + I2(b) 6A – I2 (c) 7A + 6I2

(d) 7A- 6/2(e) N.O.T

42.A and B are 3  3 matrices and A is invertible. Let eigen values of AB be 1, 2 and 3. Then, eigen values of BA are HYDERABAD-2007

(a) 1, 2, 3(b) 1/1, 12, 1/3

(e) None of the above

43.A man has seven relatives. Four of them are ladies and three are gentleman. His wife has seven relatives. Three of the mare ladies and four are gentlemen. In how many steps ca n they throw a dinner party of three ladies and three gentlemen so that there are three o of husband’s relatives and three of wife’s relatives? HYDERABAD-2007

(a) 485(b) 465(c) 475 (d) 490(e) N.O.T

44.What are the values of $  and  such that $ + $ + $ +  = $ + $ +  +  +  =  +  and  - $ = 6?

HYDERABAD-2007

(a)  = 14, $ = 8,  = 4 (b)  = 41, $ = 18,  = 4

(e) None of the above

45.Imagine a 3  3  3-inch opaque cube divided into 27 1-inch cubes. What is the maximum number of 1-inch cubes that can be seen by one person from any point in space? HYDERABAD-2007

(a) 9(b) 19(c) 18 (d) 6(e) N.O.T

46.In the expression below, what digits do the three letters represent?

(MCCA)base8 – (MCCA)base5 = (MCCA)base?

HYDERABAD-2007

(a) M = 2, C = 1, A = 1 (b) M = 1, C = 3, A = 2

(e) None of the above

47.The nullity of the matrix is

HYDERABAD-2007

(a) 3(b) 2(c) 1(d) 0(e) N.O.T

48.If 0  90 such that tan  = then, is equal to HYDERABAD-2007

(a) 231/377(b) –231/377(c) 231/337

(d) –213/377(e) None of the above

49.The angle of elevation of an aeroplane flying vertically above the ground as observed from two consecutive stones 1 km apart is 45 and 60. The height of the aeroplane above the ground in KM is :

HYDERABAD-2007

(a) (b) (c)

(d) (e) None of the above

50.The angle of elevation of the top of a tower as observed from a point on the horizontal ground is x. If we move a distance d towards the foot of the tower, the angle of elevation increases to y. The height of the tower is: HYDERABAD-2007

(a) (b) d(tan y – tan x)

(e)

51.Solution for the first order differential equation

is such that

The solution surface is exponential in both x and y

HYDERABAD-2007

(a)The solution surface is exponential in x

(b)The solution surface passes through the origin

(c)The solution surface is exponential in y

(d)None of the above

52.If f(x) is a polynomial satisfying f(x). f(1/x) = f(x) + f(1/x) and f(3), 28, then f(4) is given by

HYDERABAD-2007

(a) 63(b) 67(c) 65(d) 68(e) N.O.T

53.f(x) = x2 + 1, g(x) = 2x and h = f og(x). Then, the following statement is NOT TRUE.HYDERABAD-2007

(a)Minimum value of h is 1

(b)H(x) is always positive

(c)h-1(17) = {2}

(d)h(x) is symmetric about y-axis

(e)The graph of h(x) does not touch the line y = x

54.The volume V of the tetrahedron with a = [2, 0, 3], b = [0, 6, 2], c = [3, 3, 0] as edge vectors is

HYDERABAD-2007

(a) 10(b) 12(c) -60 (d) 11(e) N.O.T

55.The angle between the resultant r of the forces a = [3, 2, 0] and b = [-1, 4, 0] and the x-axis is

HYDERABAD-2007

(a) arcos 0.31623 (b) arcsin 0.31623

(e) None of the above

56.If = then

HYDERABAD-2007

(a)f is continuous at x = - 2

(b)f is differentiable at x = - 2

(c)f is neither differentiable nor continuous at x =-2

(d)f is continuous at x = - 2 but not differentiable

(e)None of the above

57.Which of the following statements is true given that the conditional probabilities are equal: Pr(A|B) = Pr(B|A) HYDERABAD-2007

(a)Pr(A  B) = Pr(A) + Pr(B)

(b)Pr(A  B) = Pr(A) * Pr(B)

(c)Pr(A) = Pr(B)

(d)Pr(A  B) = Pr(A) + Pr(B) – Pr(A) * Pr(B)

(e)None of the above

58.A box has 3 black and 4 red balls. A ball is drawn (first draw) at random Two new balls of the same color as the first drawn ball are dropped into the box. A bal is then drawn at random (second draw). What is the probability of the color of he second drawn ball being black? HYDERABAD-2007

(a) 12/63(b) 15/63(c) 18/63(d) 27/66(e) N.O.T

59.The geometric mean of the roots of a sixth degree polynomial P(x) with P(0) = 729, P(1) = P(2.846) = P(3) = P(5) = P(6) = 0 is HYDERABAD-2007

(a) 6(b) 2(c) 3

(d) 4(e) inadequate information

60.The following is what seems to be a mathematical proof that 10 equals 9.999999… What’s wrong with it?

A = 9.999999 . .

10a = 99.999999…

10a – a = 90

9a = 90

a = 10 HYDERABAD-2007

(a) rounding of error (b) approximation error

(e) None of the above

61.The curve y = ax3 + bx2 + cx + 5 touches the x-axis at P(-2,0) and cuts the y-axis at a point Q where its gradient is 3. The values of a, b, c are

HYDERABAD-2007

(a)a = ½, b = ¾, c = 3

(b)(b) a = - 1/2, b = - 3/4,c = 3

(c)a = - 1/2, b = -3/4, c = - 3

(d)a = - 1/2, b = 3/4, c = 3

(e)None of the above

62.How many times on average must a six-aided dice be tossed before every number from one to six comes up at least once? HYDERABAD-2007

(a) 14 (b) 13.7 (c) 12 (d) 14.7

(e) None of the above

63.If A, B are tow matrices and AB = 0, it implies

HYDERABAD-2007

(a)BA = 0

(b)A and B are orthogonal matrices

(c)Definitely either A = 0 or that B = 0

(d)Does not imply either A = 0 or B = 0

(e)None of these

64.The following statement is NOT TRUE:

HYDERABAD-2007

(a)The function tan x is one-to-one from [-1, 1] to R

(b)The function tan x : [-1, 1]  R is not onto

(c)The functions tan x and sin x intersect at infinitely many points along the real line

(d)Tan x is a periodic function of period 2

(e)tan x is asymptotic to x = for all n  N

65.The result of the subtraction FD16 – 8816 in base 2 is

HYDERABAD-2007

(a) 01110101(b) 10011001(c) 01101001

(d) 10011110(e) None of the above

66.If f(x) = = the value of at x = 0 is

HYDERABAD-2007

(a) –1(b) 0 (c) 1 (d) undefined (e) None of the above

67.If a  p, b  q, c  r and

then the value of is

HYDERABAD-2007

(a) 0(b) 0 (c) 1(d) 3 (e) -2

68.Let X be a set containing n elements. If two subsets A and B of X are picked at random, the probability that A and B have the same number of elements is

HYDERABAD-2007

(a) (b) (c)

(d) (e) None of the above

69.Suppose m boys and m girls take their seats randomly round a circle. In the following situation, the probability of their seating arrangement is HYDERABAD-2007

(a)When two boys sit together

(b)When two girls sit together

(c)When boys and girls sit alternately

(d)When m girls and one boy sit together

(e)None of the above

70.If A and B are acute positive angles satisfying the equations 3 sin2 A + 2sin2B = 1 and 3 sin2A – 2 sin2 B = 0, then A + 2B = HYDERABAD-2007

(a) (b) (c) (d) (e) N.O.T

71.If p and q are chosen randomly from the set {1, 2, 3, 4, 5, 6} with replacement, the probability that the roots of the equation x2 + pq + q = 0 are real is:

HYDERABAD-2007

(a) .53(b) .25(c) .75 (d) 0.3(e) N.O.T

The questions 72-75 are based on the flow chart given here

72.On the input array [3, 1, 2, 1, 4, 3, 1, 100] at the instance when j = 4 the value that B holds is

HYDERABAD-2007

(a) 2(b) 1(c) 4

(d) 3(e) None of the above

73.On any input array, the number of times that the value of B gets updated is equal to

HYDERABAD-2007

(a) X(b) Y(c) J

(d) Y-1(e) None of the above

74.Which of the following statements is TRUE?

HYDERABAD-2007

(a)If the array contains distinct elements, then, the value of Y is maximum

(b)If the array contains identical elements, then the value of Y is minimum

(c)If the value of Y is 0, then the array contains identical elements

(d)The value of X denotes the number of updations on B

(e)All of the above are false

75.Suppose the input array is [2, 2, 2, 2, 1, 1, 1, 1, 0, 0, 0, 0, 3, 3, 3, 3] then, the output of the flow chart is

HYDERABAD-2007

(a) 0, 0(b) 0, 12(c) 0, 9

(d) 0, 16(e) None of the above