1. Let A and B be two solid spheres such that the surface area of B is 300%
higher than the surface area of A. The volume of A is found to be k% lower than
the volume of B. The value of k must be
A. 85.5
B. 92.5
C. 90.5
D. 87.5
2. A test has 50 questions. A student scores 1 mark for a correct answer, 1/3
for a wrong answer, and –1/6 for not attempting a question. If the net score of
a student is 32, the number of questions answered wrongly by that student cannot
be less than
A. 6
B. 12
C. 3
D. 9
3. The sum of 3rd and 15th elements of an arithmetic progression is equal to the
sum of 6th, 11th and 13th elements of the same progression. Then which element
of the series should necessarily be equal to zero
A. 1^{st}
B. 9^{th}
C. 12^{th}
D. None of these
4. When the curves y = log10 x and y = x1 are drawn in the xy plane, how many
times do they intersect for values
A. Never
B. Once
C. Twice
D. More than twice
5. At the end of year 1998, Shepard bought nine dozen goats. Henceforth, every
year he added p% of the goats at the beginning of the year and sold q% of the
goats at the end of the year where p>0 and q>0. If Shepard had nine dozen goats
at the end of year 2002, after making the sales for that year, which of the
following is true?
A. p = q
B. p<q
C. p>q
D. p = q/2
6. A leather factory produces two kinds of bags, standard and deluxe. The profit
margin is Rs.20 on a standard bag and Rs.30 on a deluxe bag. Every bag must be
processed on machine A and on machine B. The processing times per bag on the two
machines are as follows:
The total time available on machine A is 700 hours and on machine B is 1250
hours. Among the following production plans, which one meets the machine
availability constraints and maximizes the profit?
A. Standard 75 bags, Deluxe 80 bags
B. Standard 100 bags, Deluxe 60 bags
C. Standard 50 bags, Deluxe 100 bags
D. Standard 60 bags, Deluxe 90 bags
7. The function f(x) = x – 2 + 2.5 – x + 3.6 – x, where x is a real number,
attains a minimum at
A. x = 2.3
B. x = 2.5
C. x = 2.7
D. None of these
8. In a 4000 meter race around a circular stadium having a circumference of 1000
meters, the fastest runner and the slowest runner reach the same point at the
end of the 5th minute, for the first time after the start of the race. All the
runners have the same starting point and each runner maintains a uniform speed
throughout the race. If the fastest runner runs at twice the speed of the
slowest runner, what is the time taken by the fastest runner to finish the race?
A. 20 min
B. 15 min
C. 10 min
D. 5 min
9. 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 1, while in exactly two out of the three cases the leading digit
is 1. Then M equals
A. 31
B. 63
C. 75
D. 91
10. Which one of the following conditions must p, q and r satisfy so that the
following system of linear simultaneous equations has at least one solution,
such that p + q + r <0?
x + 2y – 3z = p
2x + 6y – 11z = q
x – 2y + 7z = r
A. 5p – 2q – r = 0
B. 5p + 2q + r = 0
C. 5p + 2q – r = 0
D. 5p – 2q + r = 0
11. How many even integers n, where ,
are divisible neither by seven nor by nine?
A. 40
B. 37
C. 39
D. 38
12. Twentyseven persons attend a party. Which one of the following statements
can never be true?
A. There is a person in the party who is acquainted with all the twentysix
others.
B. Each person in the party has a different number of acquaintances.
C. There is a person in the party who has an odd number of acquaintances.
D. In the party, the is no set of three mutual acquaintances.
13. Let g(x) = max(5 – x, x + 2). The smallest possible value of g(x) is
A. 4.0
B. 4.5
C. 1.5
D. None of these
DIRECTIONS for Questions 14 and 15: Answer the
questions on the basis of the information given below.
New Age Consultants have three consultants Gyani, Medha and Buddhi. The sum of
the number of projects handled by Gyani and Buddhi individually is equal to the
number of projects in which Medha is involved. All three consultants are
involved together in 6 projects. Gyani works with Medha in 14 projects. Buddhi
has 2 projects with Medha but without Gyani, and 3 projects with Gyani but
without Medha. The total number of projects for New Age Consultants is one less
than twice the number of projects in which more than one consultant is involved.
14. What is the number of projects in which Medha alone is involved?
A. Uniquely equal to zero
B. Uniquely equal to 1
C. Uniquely equal to 4
D. Cannot be determined uniquely
15. What is the number of projects in which Gyani alone is involved?
A. Uniquely equal to zero
B. Uniquely equal to 1
C. Uniquely equal to 4
D. Cannot be determined uniquely
DIRECTIONS for Questions 16 to 33: Answer the
questions independently of each other.
16. Given that and w = vz/u, then which
of the following is necessarily true?
A.
B.
C.
D.
17. If the product of n positive real numbers is unity, then their sum is
necessarily
A. a multiple of n
B. equal to n+(1/n)
C. never less than n
D. a positive integer
18. There are 8436 steel balls, each with a radius of 1 centimeter, stacked in a
pile, with 1 ball on top, 3 balls in the second layer, 6 in the third layer, 10
in the fourth, and so on. The number of horizontal layers in the pile is
A. 34
B. 28
C. 36
D. 32
19. In the figure below, the rectangle at the corner measures 10 cm 20 cm. The
corner A of the rectangle is also a point on the circumference of the circle.
What is the radius of the circle in cm?
A. 10 cm
B. 40 cm
C. 50 cm
D. None of these
20. A vertical tower OP stands at the center O of a square ABCD. Let h and b
denote the length OP and AB respectively. Suppose angle APB = 60^{o}
then the relationship between h and b can be expressed as
A. 2b^{2} = h^{2}
B. 2h^{2} = b^{2}
C. 3b^{2} = 2h^{2}
D. 3h^{2} = 2b^{2}
21. How many three digit positive integers, with digits x, y and z in the
hundred’s, ten’s and unit’s place respectively, exist such that x < y, z < y and
x is not 0?
A. 245
B. 285
C. 240
D. 320
22. In the figure given below, AB is the chord of a circle with center O. AB is
extended to C such that BC = OB. The straight line CO is produced to meet the
circle at D. If angle ACD = y degrees and angle AOD = x degrees such that x =
ky, then the value of k is
A. 3
B. 2
C. 1
D. None of these
23. If log3^{2}, log3(2^{x} – 5), log3(2^{x} – 7/2) are
in arithmetic progression, then the value of x is equal to
A. 5
B. 4
C. 2
D. 3
24. In the diagram given below, angle ABD = angle CDB = angle PQD = 90^{o}.
If AB : CD = 3 : 1, the ratio of CD : PQ is
A. 1 : 0.69
B. 1 : 0.72
C. 1 : 0.75
D. None of these
25. In a triangle ABC, AB = 6, BC = 8 and AC = 10. A perpendicular dropped from
B, meets the side AC at D. A circle of radius BD (with center B) is drawn. If
the circle cuts AB and BC at P and Q respectively, then AP : QC is equal to
A. 1 : 1
B. 3 : 2
C. 4 : 1
D. 3 : 8
26. Each side of a given polygon is parallel to either the X or the Y axis. A
corner of such a polygon is said to be convex if the internal angle is 90^{o}
or concave if the internal angle is 270o. If the number of convex corners in
such a polygon is 25, the number of concave corners must be
A. 20
B. 0
C. 21
D. 22
27. Let p and q be the roots of the quadratic equation x^{2} – ( p  2)
x  q  1 = 0. What is the minimum possible value of p^{2} + q^{2}?
A. 0
B. 3
C. 4
D. 5
28. The 288^{th} term of the series a, b, b, c, c, c, d, d, d, d, e, e,
e, e, e, f, f, f, f, f, f…. is
A. u
B. v
C. w
D. x
29. There are two concentric circles such that the area of the outer circle is
four times the area of the inner circle. Let A, B and C be three distinct points
on the perimeter of the outer circle such that AB and AC are tangents to the
inner circle. If the area of the outer circle is 12 square centimeters then the
area (in square centimeters) of the triangle ABC would be
A.
B.
C.
D.
30. Let a, b, c, d be four integers such that a + b + c + d = 4m + 1 where m is a
positive integer. Given m, which one of the following is necessarily true?
A. The minimum possible value of a^{2} + b^{2} + c^{2}
+ d^{2} is 4m^{2} – 2m + 1
B. The minimum possible value of a^{2} + b^{2} + c^{2}
+ d^{2} is 4m^{2} + 2m + 1
C. The maximum possible value of a^{2} + b^{2} + c^{2}
+ d^{2} is 4m^{2}  2m + 1
D. The maximum possible value of a^{2} + b^{2} + c^{2}
+ d^{2} is 4m^{2} + 2m + 1
31. In the figure below, ABCDEF is a regular hexagon and angle AOF = 90^{o}.
FO is parallel to ED. What is the ratio of the area of the triangle AOF to that
of the hexagon ABCDEF?
A. 1/12
B. 1/24
C. 1/6
D. 1/18
32. The number of nonnegative real roots of 2^{x} – x – 1 = 0 equals
A. 0
B. 1
C. 2
D. 3
33. Three horses are grazing within a semicircular field. In the diagram given
below, AB is the diameter of the semicircular field with centre at O. Horses
are tied up at P, R and S such that PO and RO are the radii of semicircles with
centers at P and R respectively, and S is the centre of the circle touching the
two semicircles with diameters AO and OB. The horses tied at P and R can graze
within the respective semi circles and the horse tied at S can graze within the
circle centred at S. The percentage of the area of the semicircle with diameter
AB that cannot be grazed by the horses is nearest to
A. 20
B. 28
C. 36
D. 40
DIRECTIONS for Questions 34 and 35: Answer the
questions on the basis of the information given below.
A certain perfume is available at a dutyfree shop at the Bangkok international
airport. It is priced in the Thai currency Baht but other currencies are also
acceptable. In particular, the shop accepts Euro and US Dollar at the following
rates of exchange:
US Dollar 1 = 41 Bahts
Euro 1 = 46 Bahts
The perfume is priced at 520 Bahts per bottle. After one bottle is purchased,
subsequent bottles are available at a discount of 30%. Three friends S, R and M
together purchase three bottles of the perfume, agreeing to share the cost
equally. R pays 2 Euros. M pays 4 Euros and 27 Thai Bahts and S pays the
remaining amount in US Dollars.
34. How much does M owe to S in US Dollars?
A. 3
B. 4
C. 5
D> 6
35. How much does R owe to S in Thai Baht?
A. 428
B. 414
C. 334
D. 324
DIRECTIONS for Questions 36 to 39: Each question is
followed by two statements, A and B. Answer each question using the following
instructions.
Choose [A] if the question can be answered by one of the statements alone but not
by the other.
Choose [B] if the question can be answered by using either statement alone.
Choose [C] if the question can be answered by using both the statements together,
but cannot be answered by using either statement alone.
Choose [D] if the question cannot be answered even by using both the statements
together.
36. Is a^{44} < b^{11}, given that a = 2 and b is an integer?
A. b is even
B. b is greater than 16
37. What are the unique values of b and c in the equation 4x^{2} + bx + c
= 0 if one of the roots of the equation is (1/2)?
A. The second root is 1/2
B. The ratio of c and b is 1
38. AB is a chord of a circle. AB = 5 cm. A tangent parallel to AB touches the
minor arc AB at E. What is the radius of the circle?
A. AB is not a diameter of the circle
B. The distance between AB and the tangent at E is 5 cm.
39. D, E, F are the mid points of the sides AB, BC and CA of triangle ABC
respectively. What is the area of DEF in square centimeters?
A. AD = 1 cm, DF = 1 cm and perimeter of DEF = 3cm
B. Perimeter of ABC = 6 cm, AB = 2 cm, and AC = 2 cm
