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INFOMATHS
HYDERABAD CENTRAL UNIVERSITY - 2009
1.
2.
3.
4.
5.
6.
7.
8.
9.
The value of a certain two digit number is decreased
is, “how many such lucky numbers are there between
by 54 when the digits are interchanged. How many
‘1’ and ‘9999’ (both inclusive)?”
such 2-digit numbers are possible.
(a) 10
(b) 12
(c) 121 (d) 1111
HCU-2009 10. A tiling of a plane is an arrangement of plane figures
(a) 0
(b) 1
(c) 4
(d) 9
that fills the plane with no overlaps and no gaps. For
example, a square shape can tile a plane because it is
easy to see that a grid arrangement satisfies the
definition above. On the other hand, a circle cannot
tile a plane. Consider the shapes given below:
Which of the following statements is true?
(a) Only (b) and (c) can tile the 2D plane
(b) Only (a) and (b) can tile the 2D plane
(c) Only (a), (b) and (c) can tile the 2D plane
(d) All the shapes above can tile the 2D plane
11. That the sum of the firs 100 odd is namely 1 + 3 + …
+ 197 + 199 = x sum of the first 100 even integers, 2
+ 4 + …. + 198 + 200 is
Consider the shapes given in the figure. If these
(a) 2x + 1 (b) x + 100 (c) 2x – 1 (d) x – 100
shapes are folded as cubes, which among them will
12. What is the value of 22009 – 22008 – 22007?
have a dotted ring around the cube?
(a) 2
(b) 22008 (c) 22007 (d) 21004
(a) I only
(b) I, III and IV only
13.
Into
which
pocket will the cue ball ‘C’ roll into if it
(c) I, II and IV only
(d) All of them
is
hit
such
that
it bounces off the point ‘p’ as shown
An experiment consists of tossing a fair coin 5 times
in the figure? Assume that the ball rolls in a straight
are noting the result of each toss. How many of the 32
line, follows simple laws of reflection and that there
possible outcomes have exactly 3 heads?
is no spin or other forces acting on the ball.
HCU-2009
(a) 1
(b) 6
(c) 10
(d) 18
A student’s average mark after 8 results was 54. This
dropped to 49 when he received his ninth result which
was for Maths. How many marks did he get in
Maths?
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(a) 49
(b) 44
(c) 14
(d) 9
Imagine placing a mirror horizontally across the
middle of the following English words so that the
bottom half of the word is a reflection of its top half
in the mirror. Which of the words remains
(a) 2
(b) 1
(c) 4
(d) 5
unchanged in such a situation?
14. How often between 11 ‘o’ clock and 12 ‘o’ clock,
(a) HIDE (b) COME(c) NOSE (d) MEOW
the difference between the positions of the hour hand
A ball with a diameter of 40 centimeters is lying on
and minute hand will have an integer number of
the ground, tight against a wall. What is the diameter
minutes between them?
of a ball that can pass through the gap between ball,
(a) 5 positions
(b) 3 positions
ground and wall.
(c) 1 position
(d) 2 position
(a) 3.43 cm
(b) 6.86 cm
(c) 5.68 (d)
15. Which of the following pairs are not rotations of
9.86cm
each other?
An object appears inverted if we look at it through a
convex lens; a mirror reverses the left and right
directions. Assume that the time is 2.40 but the clock
is seen through a system that contains a convex lens
and a mirror. What 'time' does one see in such an
image?
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(A) 4.50 (B) 8.50 (C) 4.10 (D) 8.10
12 – 22 + 32 – 42 + ………… - 19982 + 19992 =
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(a) 1,990,990
(b) 1,009,909
(d) 1,999,000
(d) 1,000,999
The people of India in general consider ‘9’ a lucky
number and like to get vehicle numbers where the
digits add up to ‘9’. For example, numbers such as
‘54’, ‘702’, etc. are considered lucky. The question
1
INFOMATHS/MCA/MATHS/
INFOMATHS
50
square inches
(b) 52.5 square inches
3
(c) 50 square inches
(d) 47.5 square inches
23. Ramesh’s watch is ten minutes slow but he thinks it
is five minutes fast. Suresh’s watch is five minutes
fast but he thinks that it is ten minutes slow. One
day, they plan to catch a train leaving exactly at 4
p.m. Then which of the following is true?
(a) Suresh misses the train
(b) Ramesh misses the train
(c) Both will catch the train
(a) (a)
(b) (c)
(c) (d)
(d) (b)
(d) Both bill miss the train
If you have 3 weights, each with an integer value,
you can measure food parcels weighing from 1 kg – 24. In a race of 1260 meters, P can beat Q by 60 meters,
while in a race of 840 meters, Q can beat R by 140
13 kg (also integers). What are the possible value of
meters. By what distance does P beat R in a race of
the three weights (in ascending order)?
630 meters.
(a) 1, 5, 8
(b) 1, 2, 8
(a) 380 meters
(c) 1, 4, 8
(d) 1, 3, 9
(b) 500 meters
Mr. X found that in stead of throwing away the stubs
(c) 160 meters
of used candles, you could melt them down and
(d) 130 meters
again turn them to new candles. It turned out that one
new candle could be made out of 3 used candle 25. Following are the statements and conclusions. Find
out which conclusions follow the statements.
stubs. Mr. X bought his candles as pack of 27. How
i.
All bottles are plates
many new candles he is able to make from each pack
ii. Some bottles are glasses
of candles?
Conclusions:
(a) 13
(b) 11
(c) 9
(d) 10
i.
Some plates are glasses
Suppose the current month is X. The result of adding
ii.
Some bottles are plates
the date of the last Monday of last month and the
iii. Some glasses are bottles
date of first Thursday of next month is 38. Both the
(a) Only (i) and (ii) follow
dates belong to the same year. What is X?
(b) Only (ii) and (iii) follow
(a) February
(b) May (c) July (d) August
(c) Only (i) and (iii) follow
In a forest, three friends X, Y and Z decided to stand
(d) All three follow
and watch at night. On the first night itself one of the
three overslept and lost his watch. Find out who
PART B
overslept and lost his watch from the following
2
2
2
2
statements.
26. Let A    x dx , B    x  dx where [ . ] is
1
1
i.
If x stood his watch, then Y overslept
greatest integer function, then which of the following
ii. If Y stood his watch, then Z overslept
is true?
iii. If X overslept then only Z stood his watch
(a) A > B
(a) X
(b) Y
(c) X
(b) A = B
(d) No conclusion can be drawn
(c) A < B
There is a cylinder of height 10 cm and radius 1 cm.
(d) Cannot say
A string is tightly wrapped around the cylinder from
27.
Suppose
r and s are two real roots of the equation x 2
the top to bottom in five equally spaced loops around
+ ( - 4)x + (2 - 3 +3) = 0. If r2 + s2 = 6 then  = ?
the cylinder. What is the length of the string?
(a) 1  3
(b) 1  3
(a) 10
(b) 2  2  1
(a)
16.
17.
18.
19.
20.
(c) 1  3
(d) None of the above
(c) 10  2  1
(d) 2(10 + 1)
n
21. Two cars start travelling from two different points 28. An n   the function 2 grows faster than
and in opposite directions in a circuit race at constant
(a) n but slower than n
speeds. The cars cross for the first time at point A,
(b) n but slower than n2
second time at point B, third time at point C and
(c) n2 but slower than 2n
fourth time again at point A. How much faster one
car is going than the other?
(d) 2n , but slower than n2
(a) Both cars are going at the same speed
29. Directrix of the Parabola y = x2 – 4x + 2 is
(b) One car is going twice as fast as the other
7
7
(a) y 
(b) y 
(c) One car is going thrice as fast as the other
4
4
(d) Cannot be determined from the given data
9
9
22. The big square has an area of hundred square inches.
(c) y 
(d) y 
4
4
The area of the small square is
2
INFOMATHS/MCA/MATHS/
INFOMATHS
(a) 43983
(b) -43983
30. Equation of the ellipse with vertices (4, 0) and foci
(c) 2147527631
(d) N.O.T
(2, 0) is
39. The system of equations given below
(a) 3x2 + 4y2 = 48
(b) 4x2 + 3y2 = 48
x + 2y – z = 12
x2 y 2
x2 y 2
(c)
(d)

1

1
x+y+z=8
16 4
16 20
3x + 4y + z = 20
31. A rectangular beam is to be cut from a log with
has
circular cross section of diameter d. If the strength of
HCU-2009
the beam is proportional to its width w and the
(a) Infinite solutions
square of its depth h, find the w and h which give the
(b) Finite set but more than one solution
strongest beam
(c) Unique solution
d
2
(d) Empty solution set
,h 
d
(a) w 
6x  6
3
3
40. Let f  x   x  1 and g(x)  2
be real valued
x 1
2
3
d,h 
d
(b) w 
functions. Then, what is the largest domain on which
3
2
the composition function of f with g, f 9 g is defined?
(c) w  3d , h  2d
HCU-2009
(a)
x

1
(b)
x
>
5
w

2
d
,
h

3
d
(d)
(c) – 5 < x < 1
(d) x > 1
1
32. Consider the graphs y1 = logex and y2  log e   41. What is the relationship between a, b and c in the
 x
following figure?
plotted in the xy-plane. The point-wise distance
HCU-2009
between y1(x) and y2(x)
(a) Initially increases upto a point and then decreases
(b) Initially decreases upto a point and than starts
increasing
(c) Monotonically
(d) Monotonically decreases.
4
dx
33. The value of the integral 
is
2
0
 x  2
(a) c  a2  b2  a2
(b) c2 = a2 + b2
(a) -1
(b) 1
(c) 0
(d) Does not exist
(c) c  a  c
(d) N.O.T
34. Given three vectors a, b and c, an ant started walking
+  ℤ+ where f(x) = greatest
42.
Let
a
relation
f
:
ℤ
from the initial point of the vector a. The vectors are
integer  x then f is
placed such that the initial point of b is at the
HCU-2009
terminal point of a and the initial point of c is at the
(a)
One-to-one
(b)
Onto
terminal point of b. If the ant is walking along the
(c) Bijection
(d) One-to-many
vectors, what is the condition such that the ant comes
43. Given A  (X  B) = A, then, which of the
back to the starting point?
following should necessarily hohld good?
(a) (a  b)  c = 0
(b) (a . b) . c = 0
HCU-2009
(c) (a + b) + c = 0
(d) (a + b) – c = 0
(a) X is contained in A
35. What is the area bounded by the function f(x) = x +
(b) B is contained in A
sin x and its inverse function when 0  x  
(c) Intersection of X and B is a subset of A
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(d) Both X and B are contained in A
(a) 0
(b) 2
(c) 4
(d) 6
44.
Inverse matrix of
36. In an equilateral PQR, the coordinates of P and Q
are (4, 2) and (6, 4) respectively. What are the
1 1

coordinates of point R?
1

2 3
HCU-2009


1 1 1
(a) 5  3,3  3
(b) 5  3,3  3
A
2 3 4
(c) 3  3,5  3
(d) 3  3,5  3


1 1 1
37. Let f : R  R is a continuous function such that
x
 3 4 5 
f  x    f  t  dt then, what is the value of f(ln
0
is
2009)
36
30 
36
30 
 9
 9
HCU-2009



(a)  36 140 160  (b)  36 192 180 
(a) 2009
(b) 0
 30 160 180 
 30 180 180 
(c) 1
(d) N.O.T
38. An integer is represented as a 4-bytes value where
each byte is 8 bits long. If the leftmost bit is 1, then
the integer is considered as a negative number.
Given the hexadecimal number 8000ABCF, what is
the value stored?
HCU-2009
3
INFOMATHS/MCA/MATHS/
INFOMATHS
1 1 
 1
 5 4 3 
5 4 3


1 1
1
 
(c) 60  4 3 2
(d)  


 4 3
2
 3 2 1 


1
1


1 
2
 3

45. Consider a 4 × 5 matrix A then the solution set of
system of equations AX = 0
HCU-2009
(a) consists of only trivial solution 0
(b) is a finite set
(c) is a vector space with dimension ≥ 1
(d) none of the above can be concluded without
knowing A
46. Consider a matrix A, of order m × n with m ≤ n and
if AT is its transpose then
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(a) rank (A) > rank (AT) (b) rank (A) = rank (AT)
(c) rank (A) < rank (AT) (d) none of the above can
be confirmed without knowing A
47. Eigen values of
 0 1 i 0 
A  1  i 0 1  i 
 0 1  i 0 
are
(a) 0,1  3,1  3
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(b) 1  i 3,1  i 3,1
(c) 1 + i, 1 – i, 0
(d) 1  i 3,1  i 3, 0
48. If f(x) and g(x) are polynomials over ℝ with all roots
in ℝ, then, which of the following is always true?
(a) f (g(x)) is a polynomial with all its roots in ℝ
(b) f(g(x)) is a polynomial with all its roots in R and
contains roots of g as its subset
(c) f(g(x)) is a polynomial with all its roots in ℝ and
contains roots of f as its subset
(d) N.O.T
49. Number of solutions of the equation tan x + sec x = 2
cos x lying in the interval [0, 2] is
(a) 0
(b) 1
(c) 2
(d) 3
50. Euler’s function (n) for n positive integers is
defined as the number of positive integers that are
co-prime to n and smaller than n. For example (15)
= 8. Now, (143) = ? (Note that 143 = 13 x 11)
HCU-2009
(a) 98
(b) 130 (c) 122 (d) 120
51. What is the cardinality of P(P(P())) where P
denotes power set
(a) 1
(b) 2
(c) 4
(d) 8
The questions 52-54 are based on the flow chart given
here.
52. The flow chart will find a statistical parameter for a
series of n integer numbers. What is that statistical
parameter?
(a) mean
(b) median
(c) mode
(d) N.O.T
53 What will be the output if the series of input data are
given as [3 2 3 4 5 4 2 5 3 5 4 5 3 5 3]
(a) 5 5
(b) 3 5
(c) 5 4
(d) 4 2
54. What will be the output, if the inequality in the
condition MAX < TABLE [VAL] is changed to
MAX > TABLE [VAL], for the series [3 2 3 4 5 4 2
5 3 5 4 5 3 5 3]
(a) 2 2
(b) 5 5
(c) 0 0
(d) – 1 0
55. The differential equation whose solutions are ellipses
centered at the origin is
(a) y2 + xy’2 – yy' = 0
(b) xyy” + xy’2 – yy’ = 0
(c) yy” + xy’2 – xy’ = 0
(d) N.O.T
56. If the sum to n terms of an arithmetic progression is
(Cn(n – 1), where C  0, the sum of the squares of
these terms is
(a) C2n2 (n + 1)2
2
(b) C 2 n  n  1 2n  1
3
2 2
(c) C n  n  1 2n  1
3
(d) 2C (n – 1)
57. If ABC is an acute angled triangle, then, which of the
following is true?
4
INFOMATHS/MCA/MATHS/
INFOMATHS
(a) sin A + sin B + sin C > cos A + cos B + cos C
67. In ABC, a = 1, perimeter is six times the arithmetic
(b) sin A + sin B + sin C < cos A + cos B + cos C
mean of sine of angles then the A is
(c) sin A + sin B + sin C = cos A + cos B + cos C



(a)
(b)
(c)
(d) N.O.T
(d) sin2A + sin2B + sin2C = cos2A + cos2B + cos2C
6
3
4
58. Which one of the following matrices denotes an anti68. Harmonic mean of the roots of the polynomial x2 –
reflexive relation on A = {1, 2, 3}
7x + 14 is
0 1 0
0 0 0
(a) 1
(b) 2
(c) 3
(d) 4
(a) 0 0 0
(b) 1 0 1 
69. What is the curve whose parametric representation




r(t) = (cosh t, sinh t, 0)
1 0 1 
0 1 0
(a) circle
(b) parabola
1 0 1 
0 0 0
(c) hyperbola
(d) ellipse
(c) 0 0 0
(d) 0 1 0
70.
What
is
the
approximate
area
of the shaded region in




the diagram below if the side of the big square is 10
0 1 0
1 0 1 
cm?
59. What will be the equation of the circle (x2 + y2 – 6x
– 6y) = 0 if the origin is shifted to (3, 3)?
(a) x2 + y2 = 0
(b) x2 + y2 – 6x – 6y = 18
(c) x2 + y2 – 6x – 6y – 36 = 0
(d) x2 + y2 = 18
60. The mean of a Poisson random variant X is 6. Then
Pr (X = 7) / Pr(X = 5) is
(a) 13 sq. cm
(b) 16 sq. cm
HCU-2009
(c) 8 sq. cm
(d) 10 sq. cm
(a) 7/6
(b) 7/5
(c) 5/7
(d) 6/7
71. What does the following equation represent?
61. The linear regression equation, y on x, fitted to the
(x, y, z) = (1, 2, 5) + t1 (2, 0, 0) + t2(0, 1, -2)
data set {(x1, y1), (x2, y2)}
(a) A plane passing through the point (1, 2, 5) and
(a) pass through (x1, y1) only
parallel to the vectors (1, 2, 5) and (0, 1, -2)
(b) Pass through (x2, y2) only
(b) A pair of lines passing through the points (2, 0, 0)
(c) Pass through (x1, y1) and (x2, y2)
and (0, 1, -2); and, (1, 2, 5) and (2, 0, 0)
(d) Will not pass through (x1, y1) and (x2, y2)
(c) A triangular region bounded by (1, 2, 5), (1, 2, 5)
62. The correlation coefficient between
and (0, 1, -2)
x = [1 3 1 4 5 6] and y = [4 4 4 4 4 4] is
(d) A plane passing through the point (1, 2, 5) and
(a) 0
perpendicular to the vectors (1, 2, 5) and (0, 1, -2)
(b) 1
72. When doing matrix row operations on a set of linear
(c) – 1
equations, you happen to get a row that looks like
(d) Not possible to compute
[0 0 0 … 0 |x ],
63. The distribution of Y = a × ebx, where X follows
where x is any non-zero number. Then, the system of
normal distribution is
equations you are working with it
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(a) Inconsistent
(a) Normal
(b) Exponential
(b) Consistent and has a unique solution
(c) Lognormal
(d) Gamma
(c) Consistent and has an infinite number of
64. Give that Pr(A  B) = 0.5, Pr(A) = 0.4 and Pr(B) =
solutions
0.3 which of the statement is false
(d) Consistent and has exactly two solutions with
HCU-2009
one as inverse of the other
(a) Event A is more likely
73. What is the acute angle between the planes
(b) A  B is non-trivial event
2x – y + z = 6
(c) A and B are independent events
x + y + 2z = 3
(d) Pr (A – B) = 0.2
(a) 60
(b) 45
(c) 30
(d) N.O.T
65. A ten feet pole is dropped into a milling saw and 74. What is the volume of tetrahedron whose edges are
randomly cut into three shorter poles. What is the
represented by the vectors 2i + 3k, 6j + 2k 3i + 3j?
probability that these three pieces will form a
(a) 66
(b) 33
(c) 22
(d) 11
triangle?
75. If A B = {1, 3, d, z} and A = {1, 2, a, d} then, B is
(a) 0.5
(b) 0.25 (c) 0.75 (d) 0.10
(a) {1, d, 3, 2}
(b) {2, 3, a, z}
7 
(c)
{2,
a,
d,
3}
(d) cannot be determined
1 
66. The value of cos   sin
 is
6 



5
7
(a)
(b)
(c)
(d)
3
6
3
6
MY PERFORMANCE ANALYSIS
No. of Questions
Attempted (=A)
No. of Right
Responses (=R)
No. of Wrong
Responses (=W)
5
Net Score
(NS = R – 0.25W)
Percentage Accuracy
(= PA= 100R/A)
INFOMATHS/MCA/MATHS/
INFOMATHS
6
INFOMATHS/MCA/MATHS/