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INFOMATHS
HYDERABAD - 2008
INSTRUCTIONS
1. (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.
2. All the answers should be marked clearly in the
OMR answer sheet only.
3. 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.
4. Every correct answer carries 1 (one) mark and
1th
for every wrong answer
mark will be
4
deducted.
5. 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.
6. During the examination, anyone found
indulging in copying or have any discussions
will be asked to leave the examination hall.
7. Use of non-programmable calculator and logtables in allowed.
8. use of mobile phone is not allowed inside the
hall.
9. Submit both the question paper and the OMR
sheet to the invigilator before leaving the
examination hall.
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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
lemons cost?
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(a) Rs. B (b) Rs. 16 (c) Rs. 1 (d) Rs. 24
6. 10 cards numbered 0 to 9 are arranged in a stack in
such a way that: while saying out loud Z,E,R, we
move the cards from the top to the bottom of the
stack and when saying 'O' we turn the card face up
and we get 0. We then remove this card from the
stack. We now repeat the above procedure with
O,N,E and get '1' and so on... What is 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
1
BEST OF LUCK
balls (each with
the diameter of the large ball).
6
Which of the following statement is TRUE?
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PART A
(a) The two boxes are of equal weight
1. A teacher when giving an assignment, instructed the
(b) The second box is heavier
students that a student can exchange notes but only
(c) The first fox is heavier
with those who are taller than him/her. In a class of
(d) Depends on the exact amounts of space left in the
40 students, how many exchanges are possible?
box.
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9. Given a 5  5 grid, in how many ways can the cells
(a) 780 (b) 40
(c) 39
(d) 0
be filled with the numbers 1, 2, 3, 4 and 5 in such a
2. Seven digits from 0, 1, 2, 3, 4, 5, 6, 7, 8 & 9 are
way that no number is repeated in any row or
represented by a different letter in the figure below.
column?
The products A  B  C, B  G  E and D  E  F
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are equal. What digit does G represent?
(a) 120 (b) 153 (c) 25
(d) 62
A
D
10. Find the total number of ways a child can be given at
B
G E
least one rupee from four 25 paise coins, three 50
C
F
paise coins and two one-rupee coins
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(a) 4
(b) 2
(c) 8
(d) 1
(a) 53
(b) 51
(c) 54
(d) 55
3. Two objects are weighed using a faulty balance that
either over- or under-weighs every object by a 11. A sensitive instrument can measure lengths upto 10 10
metre. A square. A square sheet of paper of side 1
constant amount. The first object weighed 50kg and
metre is repeatedly folded into halves. What is the
the second weighed 25kg on such a balance. When
maximum number of folds that can be made such
they both are weighed together they weighed 77kg.
that the instrument can still successfully measure it?
What is the true weight of the first object?
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(a) 10
(b) 20
(c) 30
(d) 40
(a) 52kg (b) 27kg (c) 51kg (d) 49kg
4. Big Baazar is celebrating its 10th anniversary by 12. If (a1, a2, a3) = (100, 0, 1) and (b1, b2, b3) = (1, 100,
00) then find a sequence s1, s2, …., sk of numbers
offering a 20% discount for the whole 1st week of
from 1, 2, 3 such that as1 as2 …. ask = bs1 bs2 … bsk.
April. On April 5, which is the date of inauguration,
(For example 13 is not a solution as a1a3 = 1001 and
they offer an additional discount of 15% (on
b1b3 = 100)
discounted price). What is the overall discount?
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1
INFOMATHS/MCA/HCU-2008
INFOMATHS
(a) 1322132
(b) 1322322
(a) 155 (b) 77
(c) 50
(d) 110
(c) 1311322
(d) 1312312
23. A 3-inch cube is colored red on all sides. The cube is
13. What is the value of the ten’s digits in the sum 1! +
cut into small 1 inch cubes. The number of cubes
2! + 3! + …… + 2008!
which have atleast two sides colored red is
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(a) 0
(b) 1
(c) 9
(d) 40
(a) 19
(b) 21
(c) 22
(d) 20
14. A four digit number a3a2a1a0 is formed from digits 1
24. Whenever Anoop sings, Bobby gets a headache and
… 9 such that
Rohit groans. If Rohit is not groaning, which of the
following statements must be TRUE?
ai  1

if ai+1 is even
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
2

i = 0, 1, 2
(a) Anoop is singing and Bobby has a headache.
ai  
  ai  1 or  ai  1
(b) Bobby has a headache but Anoop is not
otherwise
  2   2 
necessarily singing.

(c) Anoop is singing, but Bobby does not necessarily
 a  is the smallest integer larger than a and b  is
have a headache.
the largest integer smaller than a. The smallest value
(d) Anoop is not singing.
that a3 can have is
25. Find the probability that a leap year will contain
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either 53 Tuesdays or 53 Wednesday.
(a) 5
(b) 7
(c) 9
(d) 1
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15. How many 5-digit prime numbers can be formed
1
2
2
3
using the digits 3, 5, 7, 2 and 1 once each?
(a)
(b)
(c)
(d)
5
5
3
7
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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 Part B.
place and riding back. He would gained 2 hrs by 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
riding both ways. The time he would take to walk
then R is
both ways is
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(a) Reflexive only
(a) 3 hrs 45 min
(b) 7 hrs 45 min
(b) Reflexive and symmetric but not transitive
(c) 7 hrs 30 min
(d) 11 hrs 45 min
(c) Reflexive and transitive but not symmetric
17. A number when divided by 783, gives a remainder
(d) An Equivalence relation.
48. What remainder would be obtained by dividing
27.
If f(x) = a loge|x| + bx2 + x has the extrema at x = 1
the same number by 29?
and x = 3 then
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(a) 29
(b) 27
(c) 19
(d) None of these
3
3
1
1
18. Four students have to be chosen – 2 girls as captain
(a) a  , b  
(b) a   , b 
and vice – captain and 2 boys as captain and vice –
8
8
4
4
captain. There are 15 eligible girls and 12 eligible
3
1
(c) a   , b  
(d) None of these
boy. In how many ways can they be chosen if
8
4
Sunitha is sure to be captain?
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(a) 114 (b) 1020 (c) 360 (d) 1848
(a) 24
(b) 22
(c) 23
(d) 25
19. If there are 20 possible lines connecting non-adjacent
1
 2
points of a polygon, how many sides does it have?
29. If f  x   e x , x  0 and f(0) = 0 then f ' (0) is
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(a) 12
(b) 10
(c) 8
(d) 9
(a) 0
(b) 1
(c) e
(d) None of these
20. From 5 different green balls, four different blue balls
and three different red balls, how many combinations 30. It is given that square matrix A is orthogonal and
also that det A is not equal to 1. Then,
of balls can be chosen taking atleast one green and
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one blue ball?
(a) |A| is zero
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(b) |A| > 1
(a) 60
(b) 3720 (c) 4096 (d) None of these
(c) |A| cannot be determined
21. From city A to B, there are 3 different roads. From B
(d) None of the above
to C there are 5 and from C to D there are 2 different
31.
Which of the following numbers has the largest
roads. Laxman has to go from A to D attending to
number of ‘1’s when represented in binary
some work in B and C on the way and has to come
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back in the reverse order. In how many ways can he
(a) 8192 (b) 4099 (c) 1031 (d) 63
complete his journey if he does not take the exact
32. Suppose x and y are sides of a right angled triangle
same path while coming back?
and x is increased by dx, y is decreased by dy, then
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the hypotenuse h of the triangle is changed by dh =
(a) 250 (b) 870 (c) 90
(d) 100
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22. If the sum of the least and greatest of 55 consecutive
integers is 154, then the average of the 55
xdx  ydy
xdx  ydy
(a)
(b)
consecutive integers is
x2  y2
x2  y2
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2
INFOMATHS/MCA/HCU-2008
INFOMATHS
(c)
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
xdx  ydy
(d)
xdx  ydy
2 x y
2 x y
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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3
n
(a) 3n
(b)
(c) 3n/3
(d) 3n-1
3
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
1 1 1
1
If s  lim n  2  2  2  ....  2 the
1 2 3
n
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3
(a) unbounded
(b) lies between 1 and
2
3
7
(c) 0
(d) lies between
and
2
4
The sum of two positive real numbers is 2a. The
probability that product of these two numbers is not
3
less than
times the greatest possible product is
4
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1
1
1
9
(a)
(b)
(c)
(d)
3
16
2
4
If f(0) = f '(0) = 0 and f " (x) = tan2 x then f(x) is
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1
1
(a) log sec  x   x 2
(b) log sec  x   x 2
2
2
1 2
(c) log cos  x   x
(d) None of the above
2
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
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
The set having only one subset is
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(a) {}
(b) {0} (c) {{}} (d) None of these
A cubic f(x) vanishes at x = - 2 and has relative
minimum / maximum at x = - 1 and x = 1/3. If
1
14
1 f  x  dx  3 , 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
 x  y  f  x  f  y
Let f 
for all real x and y. If

2
 2 
f ' (0) exists and equals – 1 and f(0) = 1, then, f(2) is
2
2
2
2
3
43.
44.
45.
46.
47.
48.
49.
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(a) -1
(b) 2
(c) 0
(d) 1
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) 2, 2 (b) 4, 2 2 (c) 2 2, 2 (d) 4 2, 4
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
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
If f(x) = sin(log x), then, the value of
x
f  xy   f    2 f  x  cos log  y  is
 y
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(a) 0
(b) – 1
(c) 1
(d) – 2


Consider the function f  x   sin  2 x   on ℝ.
3

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) 2n  : n  ℤ
(d) n  : n  ℤ
3
3
n
n
 
n i
Value of     sin i A 1  sin A  (for n, a
i
i 0
 
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
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)


3  1 100
(b)


3  1 100
(c) 3 100
(d) 100 / 3
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
INFOMATHS/MCA/HCU-2008
INFOMATHS
52. The equation of the circle having the chord x – y = 1
25
of the circle x2 + y2 – x – 3y –
= 0 as a diameter
2
is
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21
(a) x2 + y2 – 3x – y +
=0
2
25
(b) x2 + y2 + 3x + y +
=0
2
25
(c) x2 + y2 – x – 3y +
=0
2
21
(d) x2 + y2 – 3x –y –
=0
2
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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10


(a) 245
(b) 255
(c)   (d) None of these
2
 i i 
 1 1
8
54. If A  
 and B   1 1  then A equals

i
i




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
59. If the sequence of numbers read is 1, 5, 7, 9, 17, 23,
the value of |(A – I)| =
45, 56, 63, 99, 101, 109, 121, 130, 142, 146, 150,
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(a) 1
(b) – 1
(c) 0
(d) None of these
how many times is the comparison I  J done before
56. If a, b, c are the roots of x3 + px2 + q = 0, then
the key 130 is found.
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a b c
(a) 3
(b) 4
(c) 2
(d) 5
b c a 
60. For the same sequence of numbers as above, if the
c b a
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
(a) p
(b) p2
(c) p3
(d) q

 
 
 
61. If 8192 numbers are read and the key is a number
57. If d    a b   u  b c   v  c a  ,
that is not present in the sequence read, how many

 
 

times is the comparison I  J done before it prints

     1
  
KEY NOT FOUND?
v  c a  , a .  b c   and d .  a  b  c  = 3 then

 
 3


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(a) 4096 (b) 8192 (c) 13
(d) 8191
 + u + v is
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10) with a radius of 5 is
(a) 6
(b) 9
(c) 1
(d) 0
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58. The eigen vectors of a real symmetric matrix
(a) x2 + y2 + 4yx – 55y – 39 = 0
corresponding to different eigen values are
(b) x2 + y2 = 44x – 54y – 37 = 0
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(c) x2 + y2 – 12x – 12y + 47 = 0
(a) Singular
(b) Orthogonal
(d) x2 + y2 + 12x + 12y + 47 = 0
(c) Non-Singular
(d) None of the above
63. The value of x for which the volume of
The questions 59 – 61 are based on the flow chart
parallelepiped formed by the vectors i + xj + k, j +
given here.
xk and xi + k is minimum is
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1
1
(a) – 3
(b)
(c) 3
(d)
3
3
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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4
INFOMATHS/MCA/HCU-2008
INFOMATHS
(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,
Let a , b and c are three non-zero vectors, no two
9, 10.5, 12, what is the value of the sum of the



deviations taken from the mean?
of which are collinear. If a  2 b is collinear with c
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





and b  3 c is collinear a , then a  2 b  6 c is
(a) 16.5 (b) 6.5
(c) 7.5
(d) None of these
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

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(a) 0
(b) parallel to a
(a) 2311 (b) 2300 (c) 3200 (d) 2003


(c) parallel to b
(d) parallel to c
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
Which of the following functions cannot define a
probability distribution:
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1
(a) f  x   for x = 3, 4, 5, 6
4
x2
(b) f  x  
for x = 0, 1, 2, 3, 4
25
x
(c) f  x  
for x = 0, 1, 2, 3, 4, 5
15
75. What does the above flowchart do?
5  x2
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(d) f  x  
for x = 0, 2
6
(a) Computes Least Common divisors



(b) computes Least Common Multiple
If a  i  2 j  3k , b  2i  j  k and c is a vector
(c) Computes Greatest Common Divisor

 
 
 
(d) None of these
satisfying a  c  a  b and a . c  0 then 3 c 
x y
 1
8 6
x y
1
(c) 
7 16
(a)
66.
67.
68.
69.
x2

16
x2
(d)

16
(b)
y2
1
9
y2
1
7
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30
3
3 10
(c)
(d)
4
4
2
a
b


70. Let A  

c
d


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.
HCU-2008
(a) 0
(b)
5
1
A
11
A
21
B
31
D
41
D
51
C
61
C
71
D
2
B
12
C
22
B
32
A
42
A
52
D
62
C
72
B
3
A
13
B
23
D
33
D
43
B
53
D
63
B
73
D
4
B
14
D
24
D
34
C
44
A
54
B
64
A
74
B
HCU-2008
5
6
A
A
15 16
C
B
25 26
D
D
35 36
D
A
45 46
B
A
55 56
C
C
65 66
D
A
75
B
7
B
17
C
27
C
37
A
47
A
57
B
67
D
8
A
18
D
28
C
38
B
48
C
58
B
68
B
9
A
19
A
29
A
39
C
49
A
59
B
69
D
10
C
20
B
30
D
40
A
50
B
60
C
70
A
INFOMATHS/MCA/HCU-2008