Vellore Institute of Technology

VIT

Vellore Institute of Technology

Deemed University

Vellore – 632014. Tamil Nadu

ENTRANCE EXAMINATION FOR ADMISSION TO

MCA DEGREE PROGRAMME (ORIGINAL PAPER 2006)

QUESTION PAPER

Maximum Marks : 100Time : 10.00 am – 12.00 noon

Instructions :

1)Candidate must write the Registration Number, Examination Centre, Question Paper code and his / her name in the space provided in the Response Sheet besides signing in the approximate place and get it attested by the Invigilator.

2)There are 100 questions followed by 4 alternative answers. The candidate has to choose the most approximate answer and darken the corresponding circle in the Response Sheet given along with the question paper.

Eg.: ‘c’ is the most appropriate answer, then the following applies

3)Use only BH Pencil / Black Ballpoint pen. More than one circle shall not be darkened for a given question.

4)No marks will be deducted for wrong answers.

5)Response sheet must be handed over to the Invigilator before candidate leaves the examination hall.

MCA Entrance Examination 2006

Comprehension – Read the following passage and answer the question below:

When a person in a low – profile public servant in a government organization or a high-profile business manager in a multinational company, almost everyone may be asked to write reports at some point of time or the other. A technician may have to write technical report that provides technical data, whereas the sales manager of a company may need to prepare weekly sales reports to answer questions about how effectively sales targets are being achieved. Reports are important because in most organizations, executive decision making is based almost entirely on them.

Reports may vary from one-page informal trip report summarizing the events of a business trip to a 250 page formal annual report of an organization. They may be presented orally, electrically or in a written form. They may also vary inform, content approach and purpose. It may contain facts of situation, project; an analysis and interpretation of data, events and records; or suggestions and recommendations. Although reports may include a variety of topics and objectives, they al help in the process of decision making and improving situations.

1.The Passage deals with

(a)different types of reports

(b)nature and significance of report writing

(c)reasons for writing reports

(d)none of the above

2.A report is

(a)an information bureau

(b)written / spoken account of an event

(c)a formal document for specific audience

(d)a description of something

3.Reports actually make people to

(a)move towards an effective solution

(b)complicate the process

(c)dilute the situation

(d)none of the above

4.Report writing is used extensively by

(a) scientists (b) students

5.Reports are termed effective, based on

(a)the information presented

(b)the approval of the readers

(c)the acceptance of the higher officials

(d)none of the above

Each of the following questions has four underlined parts one of which is grammatically incorrect. Place the incorrect answer in the answer booklet.

6. of the basic differences nuclear arms, India and Pakistan together for the welfare of the subcontinent.

7.If you me that , I certainly contacted you boared there.

8.When crackers , the sound that I the

9.I my mother was late from college and he he played.

10.He advised .

11.If we add the age of three brothers Sunil, Sanjay and Sonu, then it becomes 60 years today. If 6 years ago Sonu was half the age of Sanjay and one-third the age of Sunil, then the present age of Sanjay is

(a) 10(b) 14(c) 18(d) 22

12.Honey was twice as old as vani 10 years ago. How old is Vani today if Honey will be 40 years old 10 years hence?

(a) 10(b) 14(c) 15(d) 30

13.Vandana’s mother is twice as old as her brothr. She is 5 years younger to her brother but 3 years older to her sister. If her sister is 12 years of age, how old is her mother?

(a) 35(b) 40(c) 45(d) 50

14.Sonu is 4 years younger to Manu while Dolly is 4 years younger to Sumit but one-fifth times as old as sonu. If Sumit is eight years old, how many times as old is Manu as Dolly?

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

15.5 years ago, the combined age of Ritu mother and her was 40 years. Now the ratio of their age is 4:1. How old is Ritu mother.

(a) 10(b) 40(c) 60(d) 30

For Questions 16-20

The diagram show below represents four types of literates who knows English, Hindi, Punjabi and Urdu. If we are given values for A, B, C, D such that A = 40, B = 2A, C = and D = 2E. Based on above information, solve question which follows

16.People who can read and write Hindi, Urdu and Punjabi are represented by

(a) D(b) K(c) E(d) B

17.People who can read and write all the languages except Urdu are represented by

(a) L(b) A(c) I (d) M

18.People who cannot read and write Urdu and Punjabi, but are conversant with English and Hindi both are represented by

(a) M(b) B(c) J (d) K

19.How many people can read and write only one language except Punjabi?

(a) 120(b) 140(c) 160(d) 200

20.How many people know Urdu or Punjabi?

(a) 20(b) 40(c) 60(d) 65

Directions : In each of the following questions there are four terms, marked A to D while three of the terms are similar and form a separate class, one of them does not belong to that class. Select the term that does not belong to the class.

21.(a) Five rupee note(b) ten rupee note

22.(a) Bucket (b) Hat

23.(a) State Bank of India (b) Punjab National Bank

24.(a) Physician (b) Lawyer

25.(a) Bharat Ratna (b) Padmashri

Directions : Select from answer choices an appropriate number to replace the question mark and continue the series.

26.3, 3, 6, 5, 9, 7, 12 ?

(a) 9 (b) 15(c) 18 (d) 13

27.2, 5, 12, 27, 58?

(a) 76(b) 77(c) 116(d) 121

28.11, 23, 48,99, 202 ?

(a) 268(b) 368(c) 405(d) 409

29.7, 15, 31, 63?

(a) 91(b) 107(c) 127(d) 137

30.15, 15, 11, 13, 17, 11?

(a) 16(b) 11(c) 12(d) 3

Directions : Questions 31-35 are based upon coding pattern: If ‘EFGHIJK’ are coded letters representing ‘VUTSRQP’ choose the right code for the words given in capital letters from the answer choice (A – D) given under each?

31.LIMIT

(a) KNRNC(b) ORNRG

32.POCKET

(a) KLXPVG(b) KXLPVG

33.GROUP

(a) TILEL (b) TILFK

34.HIGH

(a) STRS (b) SRTS

35.GRZQ

(a) AJIT(b) JAIT

For questions 36-38: Mr. And Mrs. Gupta have two children, Asha and Shashi. Shashi married Lakshmi daughter of Mrs. Mahajan. Suresh, son of Mrs. Mahajan married Ritu. Sonu and Vicky are born to suresh and Ritu. Uma and sudha are daughters of Shashi and Lakshmi.

36.What is Sudha’s relation to Asha?

(a) Sister (b) Aunt

37.How is Sonu related to Mr. Mahajan?

(a) Grandson (b) Son

38.How is Asha related to Lakshmi?

(a) Mother-in-law(b) Aunt

Directions : In each of the following questions there are 4 choices (A – D) of words with their letters jumbled up, three of them look alike and one is different. Find out the odd one.

39.(a) ONOM (b) UTRNAS

40.(a) DLEHNA (b) CNAIH

41.(a) NORI(b) RECOPP

42.(a) ITS(b) TIH

43.(a) RAICH(b) TEPRAC

44.(a) FIWE(b) LAML

45.(a) YNDSUA (b) MDOANY

46.A and B are two sets having 3 and 5 elements respectively and having two elements in common. Then the number of elements in A  B is

(a) 6(b) 36(c) 15(d) none of these

47.The number of subjective functions from A = {1, 2, ……, n}, n  2, onto B = {a, b} is

(a) nP2(b) 2n – 2

48.The following consecutive terms of a series are in

(a) Arithmetic progression(b) Geometric progression

49.In a progression (p + q)th term is m and (p – q)th term is n then pth term is

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

50.The sum of first n terms of the series 12 + 2.22 + 32 + 2.42 + 52 + 2.62 + ….. is , when n is even. When n is odd the sum is ______

(a) (b)

51.If the cube roots of unity are 1, , 2 then the roots of the equation (x – 1)3 + 8 = 0 are

(a) –1, 1 + 2, 1 + 22(b) –1, 1 - 2, 1 – 22

52.If then A + B + C = ___.

(a) 26(b) 18(c) 5(d) 9

53.If

; ;

then the value of is equal to _____

(a) (b) (c) (d) none of these

54.The region of Argand diagram defined by | z – 1 | + | z + 1 |  4 is

(a)Interior of an ellipse

(b)Exterior of a circle

(c)Interior and boundary of an ellipse

(d)None of these

55.If 1, , 2 are cube roots of unity then

(a) 0(b) (c) 2(d) 3

56.If x + iy = cosh (u + iv) then x2 sec2 v – y2 cosec2 v = _____

(a) 0(b) 1(c) 2(d) none of these

57.

(a) 2(b) 3(c) 4(d) None of these

58.If then a is equal to

(a) 0(b) 1(c) e(d) 0.5

59. n is an integer for

(a)all value of n

(b)for no value of n

(c)only negative values of n

(d)only positive value of n

60.If

(a) 0(b) 1(c) 2(d) does not exist

61.The set of all points of discontinuity of the function f(x) = contains

(a) (b)

62.Let f(x) = | x – 2 | + | x – 5 |. Then

(a)f(x) is continuous for all values of x

(b)f(x) is non-differentiable at x = 2

(c)f(x) is non-differentiable at x = 5

(d)all the above

63.If y = e-x sin x then is

(a) e-x (sin x – cos x) (b) 2e-x (cos x – sin x)

64.If y = then

(a) (b)

65.The derivative of sin-1x with respect to cos-1

(a) (b) cos-1 x

66.If y = then at is

(a) -2(b) 2(c) 2(d) none of these

67.If y = a cos (log x) + b sin (log x) then x = ______

(a) y(b) 2y(c) -y(d) –2y

68.The function f(x) = x (x + 3) satisfy all conditions of Rolle’s theorem in the interval [-3, 0]. Then the value of C = _____.

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

69.The value of c of the mean value theorem if f(x) = x (x – 1)(x – 2); a = 0, b = is

(a) 1(b) -1(c) (d)

70.If y = a log |x|+ bx2 + x has its entremum values at x = - 1 and x = 2 then

(a) a = 2, b = -1(b) a = 2, b =

71.The minimum distance from the point (4, 2) to the parabola y2 = 8x is

(a) (b) (c) 2(d)

72.

(a) –cot(xex)+c(b) tan (xex)+c

73.

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

74.

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

75.

(a) (B)

76.Using trapezoidal rule and talking n = 4 the value of is

(a) 1.1167(b) 1.1176

77.Simpson’s rule for evaluations of requires the interval (b0a) to be divided into

(a) 3n intervals (b) 2n intervals

78.The relationship between mean, median and mode for a moderately skewed distribution is

(a)Mode = median – 2 mean

(b)Mode = 2 median – mean

(c)Mode = 2 median – 3 mean

(d)Mode = 3 median – 2 mean

79.Mean of 100 items is 49. If was discovered that three items which should have been 60, 70, 80 were wrongly read as 40, 20, 50 respectively. The correct mean is

(a) 48 (b) 50 (c) 60 (d) 68

80.A measure of dispersion is an indicator of the reliability of

(a) an average (b) variability

81.For a frequency distribution, the mean deviation about mean is computed by

(a) (b)

82.The standard deviation of first n natural numbers is

(a) (b)

83.If Cov(x, y) = -16.5, Var (x) = 2.89, Var (y) = 100 the coefficient of correlation yxy =

(a) –0.97(b) 0.97(c) –0.87(d) .87

84.The regression coefficient of y on x is and of x on y is If the acute angle between the regression lines is , then tan  =

(a) 1/18(b) 1/19(c) 1/9(d) 2/9

85.The equation of two regression lines are 4x + 3y + 7 = 0 and 3x + 4y + 8 = 0. The coefficient of correlation between x and y is

(a) 0.75(b) –0.75(c) 0.25(d) –0.25

86.If P(A  B) = P(AB) then

(a) A = B (b) P(A B) = 1

87.Out of 13 applicants for a job, there are 5 women and 8 men. It is desired to select 2 persons for the job. The probability that at least one of the selected persons will be a women is ____

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

88.If A and B are evens such that (P (A) > 0 and P (B)  1, then P is equal to

(a) (b)

89.A bag X contains 2 white and3 red balls. Another bag Y contains 4 white and 5 red balls. One ball is drawn at random from one of the bags and it is found to be red. What is the probability that it was drawn from bag Y.

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

90.A random variable X has the following probability function

X / 0 / 1 / 2 / 3 / 4 / 5 / 6 / 7
P(x) / 0 / K / 2k / 2k / 3k / K2 / 2K2 / 7k2+k

Then the value of K = ______

(a) 1/10(b) 3/10(c) 7/10(d) 9/10

91.If the mean and variance of a binomial distribution is 3 and 1.5, what is the probability of obtaining at least 4 successes?

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

92.The mean and variance of a Poisson distribution are

(a) equal (b) not equal

93.Which of he following is true?

(a)the mean, median and mode of a normal distribution coincide

(b)mean = 2 median + mode

(c)mean = - 2 median + mode

(d)None of these

94.The triangle joining the points (2, 7), (4, -1), (-2, 6) is

(a) equilateral (b) right angled

95.A (6, 3), B(-3, 5), C(4, -2) and D(x, 2x) are 4 points. If DBC = ABC = 1:2, then x is equal to

(a) (b) (c) 5(d) 5

96.The extremities of a diagonal of a parallelogram are the points (3, -4) and (-6, 5). If third vertex is (-2, 1) then fourth vertex is

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

97.If each of the points (a, 4), (-2, b) lies on the line joining the points (2, -1), (5, -3) then the point (a, b) lies on the line

(a) 6x + 6y – 25 = 0 (b) x + 3y + 1 = 0

98.The line segment joining the points (1, 2) and (-2, 1) is divided by the line 3x + 4y – 7 = 0 in the ratio

(a) 3:4 (b) 4:3(c) 9:4(d) 4:9

99.The equation of the line passing through (1, 2) and is perpendicular to x + y + 1 = 0 is

(a) y – x + 1 = 0 (b) y – x – 1 = 0

100.The equation of the straight line whose slope is 3 and which bisects the join of (-2, 5) and (3, 4) is

(a) x – 3y + 1 = 0 (b) 6x – 2y + 3 = 0

101.Foot of perpendicular drawn from (0, 5) to the line 3x – 4y – 5 = 0 is

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

102.Equation of straight-line which passes through the point (1, -2) and cuts off equal intercepts from axes will be

(a) x + y = 1 (b) x – y = 1

103.The distance between parallel lines y = 2x + 4 and 6x = 3y + 5 is .

a. b. 1c. d.

104.The locus of a point equidistant from the points (a + b, a - b) and (a – b, a = b) is.

bx + ay = 0
ax – by = 0
bx – ay = 0
None of these

105.A line passes through the intersection of the lines x + y – 1 = 0 and 2x – y + 3 = 0 and is perpendicular to one of the following equation.

a. 3x - 3y + 7 = 0b. 2x + 6y – 7 = 0

c. 2x – 2y + 7 = 0d.x + 2y – 1 = 0

106.If the two lines 3x + 4y + 7 = 0 and ax + 3y – 6 = 0 are perpendicular to each other than the value of a is.

a. –4b. –3c. 4d. 3

107.The equation of a circle passing through the point (4, 5) having the center at (2, 2) is.

x2+ y2 + 4x + 4y = 0
x2+ y2 - 4x - 4y + 5 = 0
x2+ y2 - 4x - 13 = 0
x2+ y2 - 4x - 4y + 5 = 0

108.Equation of the circle through origin which cuts intercepts of length and b on axes is.

a. x2+ y2 - 4x + ax + by = 0

b. x2+ y2 -ax - by = 0

c. x2+ y2 + bx + ay = 0

d. None of these

109.Equation of the circle whose diameter is line joining the points (-4, 3) and (12, -1) is.

a x2+ y2 - 8x - 2y - 51 = 0

b. x2+ y2 - 4x - y - 51 = 0

c. 2x2+ 2y2 - 8x - 2y - 51 = 0

d. None of these

110.Four distinct points (2k , 3k), (1, 0) (0,1) and (0,0) lie on a circle for .

All integral values of k
0 < k < 1
k < 0
k = 5 / 13