HYDERABAD - 2008
1 INFOMATHS/MCA/HCU-2008
INSTRUCTIONS
- (a) Write your Hall Ticket Number in the above box AND on the OMR Sheet.
(b) Fill in the 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.
BEST OF LUCK
PART A
1.A teacher when giving an assignment, instructed the students that a student can exchange notes but only with those who are taller than him/her. In a class of 40 students, how many exchanges are possible?
HCU-2008
(a) 780(b) 40(c) 39(d) 0
2.Seven digits from 0, 1, 2, 3, 4, 5, 6, 7, 8 & 9 are represented by a different letter in the figure below. The products A B C, B G E and D E F are equal. What digit doesG represent?
A D
B G E
C F
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(a) 4(b) 2(c) 8(d) 1
3.Two objects are weighed using a faultybalance that either over- or under-weighs every object by a constantamount. The first object weighed50kg and the second weighed 25kg onsuch a balance. When they both areweighed together they weighed 77kg. What is the true weight of the firstobject?
HCU-2008
(a) 52kg(b) 27kg(c) 51kg(d) 49kg
4.Big Baazar is celebrating its 10thanniversary by offering a 20% discountfor the whole 1stweek of April. OnApril 5, which is the date of inauguration, they offer an additional discountof 15% (on discounted price). What isthe overall discount?
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(a) 35%(b) 32%(c) 5%(d) 23%
5.Three dozen lemons cost as many rupees as one can have lemons for Rs. 16. How much does a dozen lemonscost?
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(a) Rs. B(b) Rs. 16(c) Rs. 1(d) Rs. 24
6.10 cards numbered 0 to 9 are arrangedin a stack in such a way that: whilesaying out loud Z,E,R, we move thecards from the top to the bottom ofthe stack and when saying 'O'we turnthe card face up and we get 0. We thenremove this card from the stack. Wenow repeat the above procedure withO,N,E and get '1' and so on... Whatis the top card?
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(a) 7(b) 2(c) 1(d) 4
7.Rakesh will eat eh orange if Roopa does not cook. Based only on the information above, which of the following must be TRUE?
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(a) Rakesh will not eat the orange if Roopa cooks.
(b) If Rakesh did not east the orange, Roopa did cook.
(c) If Rakesh eats the orange, then Roopa did not cook.
(d) If Roopa does not cook, Rakesh will not east the orange.
8.A large steel ball is placed inside a cubic box such that its height equals the diameter of the ball. An identical box is then filled with 216 smaller steels balls (each with the diameter of the large ball). Which of the following statement is TRUE?
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(a) The two boxes are of equal weight
(b) The second box is heavier
(c) The first fox is heavier
(d) Depends on the exact amounts of space left in the box.
9.Given a 5 5 grid, in how many ways can the cells be filled with the numbers 1, 2, 3, 4 and 5 in such a way that no number is repeated in any row or column?
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(a) 120(b) 153(c) 25(d) 62
10.Find the total number of ways a child can be given at least one rupee from four 25 paise coins, three 50 paise coins and two one-rupee coins
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(a) 53(b) 51(c) 54(d) 55
11.A sensitive instrument can measure lengths upto 10-10 metre. A square. A square sheet of paper of side 1 metre is repeatedly folded into halves. What is the maximum number of folds that can be made such that the instrument can still successfully measure it?
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(a) 10(b) 20(c) 30(d) 40
12.If (a1, a2, a3) = (100, 0, 1) and (b1, b2, b3) = (1, 100, 00) then find a sequence s1, s2, …., sk of numbers from 1, 2, 3 such that as1 as2 …. ask = bs1 bs2 … bsk. (For example 13 is not a solution as a1a3 = 1001 and b1b3 = 100)
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(a) 1322132(b) 1322322
(c) 1311322(d) 1312312
13.What is the value of the ten’s digits in the sum 1! + 2! + 3! + …… + 2008!
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(a) 0(b) 1(c) 9(d) 40
14.A four digit number a3a2a1a0 is formed from digits 1 … 9 such that i = 0, 1, 2
is the smallest integer larger than a and is the largest integer smaller than a. The smallest value that a3 can have is
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(a) 5(b) 7(c) 9(d) 1
15.How many 5-digit prime numbers can be formed using the digits 3, 5, 7, 2 and 1 once each?
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(a) 1(b) 5! – 4! (c) 0(d) 5!
16.Swarup takes 5 hrs 45 min in walking to a certain place and riding back. He would gained 2 hrs by riding both ways. The time he would take to walk both ways is
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(a) 3 hrs 45 min (b) 7 hrs 45 min
(c) 7 hrs 30 min (d) 11 hrs 45 min
17.A number when divided by 783, gives a remainder 48. What remainder would be obtained by dividing the same number by 29?
HCU-2008
(a) 29(b) 27(c) 19(d) None of these
18.Four students have to be chosen – 2 girls as captain and vice – captainand 2 boys as captain and vice – captain. There are 15 eligible girls and 12 eligible boy. In how many ways can they be chosen if Sunitha is sure to be captain?
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(a) 114(b) 1020(c) 360(d) 1848
19.If there are 20 possible lines connecting non-adjacent points of a polygon, how many sides does it have?
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(a) 12(b) 10(c) 8(d) 9
20.From 5 different green balls, four different blue balls and three different red balls, how many combinations of balls can be chosen taking atleast one green and one blue ball?
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(a) 60(b) 3720(c) 4096(d) None of these
21.From city A to B, there are 3 different roads. From B to C there are 5 and from C to D there are 2 different roads. Laxman has to go from A to D attending to some work in B and C on the way and has to come back in the reverse order. In how many ways can he complete his journey if he does not take the exact same path while coming back?
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(a) 250(b) 870(c) 90(d) 100
22.If the sum of the least and greatest of 55 consecutive integers is 154, then the average of the 55 consecutive integers is
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(a) 155(b) 77(c) 50(d) 110
23.A 3-inch cube is colored red on all sides. The cube is cut into small 1 inch cubes. The number of cubes which have atleast two sides colored red is
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(a) 19(b) 21(c) 22(d) 20
24.Whenever Anoop sings, Bobby gets a headache and Rohit groans. If Rohit is not groaning, which of the following statements must be TRUE?
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(a) Anoop is singing and Bobby has a headache.
(b) Bobby has a headache but Anoop is not necessarily singing.
(c) Anoop is singing, but Bobby does not necessarily have a headache.
(d) Anoop is not singing.
25.Find the probability that a leap year will contain either 53 Tuesdays or 53 Wednesday.
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(a) (b) (c) (d)
Part B.
26.Let R be a relation on the set of positive integers defined as follows: a R b iff 4a + 5b is divisible by 9 then R is
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(a) Reflexive only
(b) Reflexive and symmetric but not transitive
(c) Reflexive and transitive but not symmetric
(d) An Equivalence relation.
27.If f(x) = a loge|x| + bx2 + x has the extrema at x = 1 and x = 3 then
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(a) (b)
(c) (d) None of these
28.The number of even proper factors of 1008 is
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(a) 24(b) 22(c) 23(d) 25
29.If and f(0) = 0 then f ' (0) is
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(a) 0(b) 1(c) e(d) None of these
30.It is given that square matrix A is orthogonal and also that det A is not equal to 1. Then,
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(a) |A| is zero
(b) |A| > 1
(c) |A| cannot be determined
(d) None of the above
31.Which of the following numbers has the largest number of ‘1’s when represented in binary
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(a) 8192(b) 4099(c) 1031(d) 63
32.Suppose x and y are sides of a right angled triangle and x is increased by dx, y is decreased by dy, then the hypotenuse h of the triangle is changed by dh =
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(a) (b)
(c) (d)
33.Let S be a set of strings with length n (n is odd) using symbols 0, 1, 2. Define an equivalence relation R on S such that two elements of S are related to each other if they have the same central element. The size of equivalence class induced by R of elements having central element 1 is
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(a) 3n(b) (c) 3n/3(d) 3n-1
34.The probability that atleast one of A and B occurs is 0.6. If A and B occur simultaneously with probability 0.3, then P(A') + P(B') is
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(a) 0.9(b) 1.15(c) 1.1(d) 2
35.If the
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(a) unbounded (b) lies between 1 and
(c) 0(d) lies between and
36.The sum of two positive real numbers is 2a. The probability that product of these two numbers is not less than times the greatest possible product is
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(a) (b) (c) (d)
37.If f(0) = f '(0) = 0 and f " (x) = tan2 x then f(x) is
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(a) (b)
(c) (d) None of the above
38.If set A has 6 elements, B has 4 elements and C has 8 elements, the maximum number of elements in (B – C) (A B) C is
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(a) 18(b) 12(c) 16(d) 24
39.Let , be the roots of the equation (x – a) (x – b) = c, c 0, then the roots of the equation (x + ) (x + ) + c = 0
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(a) a, – b (b) – a, b (c) –a, – b (d) a, b
40.The set having only one subset is
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(a) {}(b) {0}(c) {{}}(d) None of these
41.A cubic f(x) vanishes at x = - 2 and has relative minimum / maximum at x = - 1 and x = 1/3. If the cubic f(x) is
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(a) x3 + x2 + x + 6 (b) x3 – x2 – x + 10
(c) x3 + x2 + x + 2 (d) x3 + x2 – x + 2
42.Let for all real x and y. If f ' (0) exists and equals – 1 and f(0) = 1, then, f(2) is
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(a) -1 (b) 2(c) 0(d) 1
43.The sides of the rectangle of the greatest area that can be inscribed in the ellipse x2 + 2y2 = 8, are given by
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(a) (b) (c) (d)
44.Find the base in which the number seven thousand, six hundred and forty two is represented by the symbol 1234
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(a) 19(b) 18(c) 17(d) 20
45.Which measure is used for determining the average annual percent increase in sales from one period to another
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(a) Arithmetic mean (b) Harmonic mean
(c) Mode (d) Geometric mean
46.If f(x) = sin(log x), then, the value of is
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(a) 0(b) – 1 (c) 1(d) – 2
47.Consider the function on ℝ. Let x1 and x2 be two real values such that f(x1) = f(x2). Then x1 – x2 is always of the form
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(a) n : n ℤ(b) 2n : n ℤ
(c) : n ℤ(d) : n ℤ
48.Value of (for n, a positive integer) depends on
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(a) value of A (b) Value of n
(c) neither A nor n (d) both A and n
49.Two persons are standing at different floors of a tall building and are looking at a statue that is 100 metres far from the building. Angle of inclination of the person at higher floor is 60 and that of the person at lower floor is 45. What is the distance between the two persons?
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(a) (b)
(c) (d)
50.If R and S are equivalence relations on a set A, then
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(a) R S is an equivalence relation
(b) R S is an equivalence relation
(c) Both A and B are true
(d) Neither A nor B is true
51.Let A and B be sets and the cardinality of B is 6. The number of one-to-one functions from A to B is 360. Then the cardinality of A is
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(a) 5(b) 6
(c) 4(d) cannot be determined
52.The equation of the circle having the chord x – y = 1 of the circle x2 + y2–x – 3y – = 0 as a diameter is
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(a) x2 + y2 – 3x – y + = 0
(b) x2 + y2+3x + y + = 0
(c) x2 + y2 – x – 3y + = 0
(d) x2 + y2 – 3x –y – = 0
53.Let A be a set with 10 elements. The total number of relations that can be defined on A that are both reflexive and asymmetric is
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(a) 245(b) 255(c) (d) None of these
54.If and then A8 equals to
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(a) 64B (b) 128B (c) – 128B (d) – 64B
55.If A is a 3 3 matrix and AtA = I and |A| = 1 then the value of |(A – I)| =
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(a) 1(b) – 1 (c) 0(d) None of these
56.If a, b, c are the roots of x3 + px2 + q = 0, then
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(a) p(b) p2(c) p3(d) q
57.If , and = 3 then + u + v is
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(a) 6(b) 9(c) 1(d) 0
58.The eigen vectors of a real symmetric matrix corresponding to different eigen values are
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(a) Singular (b) Orthogonal
(c) Non-Singular (d) None of the above
The questions 59 – 61 are based on the flow chart given here.
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59.If the sequence of numbers read is 1, 5, 7, 9, 17, 23, 45, 56, 63, 99, 101, 109, 121, 130, 142, 146, 150, how many times is the comparison I J done before the key 130 is found.
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(a) 3(b) 4(c) 2(d) 5
60.For the same sequence of numbers as above, if the key being searched is 17, the final values of (I, J) are
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(a) 3, 7 (b) 4, 8 (c) 5, 5 (d) 3, 8
61.If 8192 numbers are read and the key is a number that is not present in the sequence read, how many times is the comparison I J done before it prints KEY NOT FOUND?
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(a) 4096 (b) 8192 (c) 13(d) 8191
62.Equation of a circle passing through (3, 2) and (9, 10) with a radius of 5 is
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(a) x2 + y2 + 4yx – 55y – 39 = 0
(b) x2 + y2 = 44x – 54y – 37 = 0
(c) x2 + y2 – 12x – 12y + 47 = 0
(d) x2 + y2 + 12x + 12y + 47 = 0
63.The value of x for which the volume of parallelepiped formed by the vectors i + xj + k, j + xk and xi + k is minimum is
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(a) – 3 (b) (c) (d)
64.Loci of a point equidistant to (2, 0) and x = - 2 is
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(a) y2 = 8x (b) y2 = 4x (c) x2 = 2y (d) x2 = 16y
65.Given two fixed points A(-3, 0) and B(3, 0), with AB = 6, the equation of the locus of point P which moves such that PA + PB = 8 is
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(a) (b)
(c) (d)
66.Let , and are three non-zero vectors, no two of which are collinear. If is collinear with and is collinear , then is
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(a) (b) parallel to
(c) parallel to (d) parallel to
67.The following system of equations
6x + 5y + 4z = 0
3x + 2y + 2z = 0
12x + 9y + 8z = 0
has
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(a) no solution
(b) a unique solution
(c) more than one but finite number of solutions
(d) infinite solutions
68.Which of the following functions cannot define a probability distribution:
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(a) for x = 3, 4, 5, 6
(b) for x = 0, 1, 2, 3, 4
(c) for x = 0, 1, 2, 3, 4, 5
(d) for x = 0, 2
69.If and is a vector satisfying and then
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(a) 0(b) (c) (d)
70.Let
be a 2 2 matrix such that A3 = 0. The sum of all the elements of A2 is
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(a) 0(b) a + b + c + d
(c) a2 + b2 + c2 + d2(d) a3 + b3 + c3 + d3
71.According to the IEEE standard, a 32-bit, single precision, floating point number N is defined to the N = (-1)S 1.F 2E-127 where S is the sign bit, F the fractional mantissa and E the biased exponent. A floating point number is stored as S : E : F, where S, E and F are stored in 1 bit, 8 bits and 28 bits respectively. What is the decimal value of the floating point number C1 E00000 in hexadecimal notation.
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(a) 26(b) – 13 (c) – 26(d) – 28
72.The number of positive real roots for the following polynomial P(x) = x4 + 5x3 + 5x2 – 3x – 6 is
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(a) 0(b) 1(c) 2(d) 3
73.Given a series of values of X as 1, 3.5, 4.5, 6, 7.5, 8, 9, 10.5, 12, what is the value of the sum of the deviations taken from the mean?
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(a) 16.5(b) 6.5(c) 7.5(d) None of these
74.(341)16 can be represented in base 7 as
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(a) 2311(b) 2300(c) 3200(d) 2003
75.What does the above flowchart do?
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(a) Computes Least Common divisors
(b) computes Least Common Multiple
(c) Computes Greatest Common Divisor
(d) None of these
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1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10A / B / A / B / A / A / B / A / A / C
11 / 12 / 13 / 14 / 15 / 16 / 17 / 18 / 19 / 20
A / C / B / D / C / B / C / D / A / B
21 / 22 / 23 / 24 / 25 / 26 / 27 / 28 / 29 / 30
B / B / D / D / D / D / C / C / A / D
31 / 32 / 33 / 34 / 35 / 36 / 37 / 38 / 39 / 40
D / A / D / C / D / A / A / B / C / A
41 / 42 / 43 / 44 / 45 / 46 / 47 / 48 / 49 / 50
D / A / B / A / B / A / A / C / A / B
51 / 52 / 53 / 54 / 55 / 56 / 57 / 58 / 59 / 60
C / D / D / B / C / C / B / B / B / C
61 / 62 / 63 / 64 / 65 / 66 / 67 / 68 / 69 / 70
C / C / B / A / D / A / D / B / D / A
71 / 72 / 73 / 74 / 75
D / B / D / B / B
1 INFOMATHS/MCA/HCU-2008