26. The inhabitants of Planet Rahu measure time in hours and minutes which are different from the hours and minutesof our earth. Their day consists of 36 hours with each hour having 120 minutes. The dials of their clocks show 36 hours. What is the angle (in Rahuian degrees) between the hour and minute hands of a Rahuian clock when it shows a time of 9:48? Rahuians measure angles in degrees (°) the way we do on earth. But for them, the angle around a point is 720 Rahuian degrees [instead of 360° that we have on earth].
(1) 112° (2) 100° (3) 24° (4) None of these
27. A ladder is placed against a wall at an angle. Let the area enclosed by the ladder be A1. The ladder slides on the floor by a few feet and makes a new angle and let the area enclosed be A2. Which of the following is true?
(1) A2 > A1 (2) A2 < A1 (3) A2 = A1 (4) Data insufficient
28. The set Y consists of the following numbers. Y = {1, 31/2, 3, 33/2, ……, 39, 319/2, 310}. In how many ways can a pair of distinct numbers be selected from the set Y such that their product is greater than or equal to 310? Assume that a x b is the same as b x a.
(1) 110 (2) 210 (3) 105 (4) 100
29. A stone weighing 121 kg fell from a height of 10 m and broke into exactly 5 pieces - all of different weights. Find the sum (in kg) of the weights of the smallest piece and the largest piece, if it is known that it is possible to weigh any weight (using a common balance) in kg from 1 to 121 kg using the 5 pieces?
(1) 118 (2) 82 (3) 65 (4) Cannot be determined
30. Six friends share a circular pizza equally by cutting it into six equal sectors. If three of them cut out and eat only the largest possible circle from their respective slices and leave the rest while the others eat their whole slice, then the approximate
percentage of pizza wasted is
(1) 11% (2) 15% (3) 17% (4) 22%
32. In a regular hexagon of side 4 cm, the midpoints of three alternate sides are joined in order to form a triangle. What is the area of this triangle?
(1) 8 3 sq.cm. (2) 12 3 sq.cm. (3) 9 3 sq.cm. (4) 18 3 sq.cm.
33. In a number system to the base 20, letters A, B, C, …. to K of the English alphabet are sequentially used to digitallyrepresent the values 10, 11, 12, …. to 20 (to the base 10). Calculate the decimal equivalent of the value (in base 10)
of [CAKE](20)- [BAKE](20).
(1) 1483 (2) 1488 (3) 1000 (4) 8000
34. R and S are the centres of two unequal circles touching externally at the point T. P and Q are the points of contact ofa direct common tangent with the larger and smaller circles respectively and the common tangent at T intersects PQ at U. What is the measure of the angle RUS?
(1) 45° (2) 90° (3) 135° (4) None of these
35. How many small squares are crossed by the diagonal in a rectangular table formed by 16 x 17 small squares?
(1) 32 (2) 33 (3) 34 (4) None of these
36. Let S = 141414 …. Upto 202 digits. What is the remainder when S is divided by 909?
(1) 115 (2) 216 (3) 418 (4) 721
38. In the following figure, find the ratio of the areas of the triangles ABE and DCE given that TA
: TD : TF = 5 : 4 : 10.
(1) 16 : 25 (2) 25 : 36 (3) 36 : 49 (4) 25 : 49
39. How many three-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7 and 8 without any repetition of thedigits and wherein the tens digit is greater than the hundreds digit but less than the units digit?
(1) 48 (2) 56 (3) 64 (4) 72
40. The set of all positive integers is divided into two subsets {a1, a2, a3, …an, …} and
{b1, b2, b3, …bn, …} where ai < ai + 1, bi < bi + 1 and ai = bj for any i, j. Also, bi =2ai−1 + ai
for all i except i = 1. What is the value of b1?
(1) 1 (2) 2 (3) 4 (4) Cannot be determined
41. If three playing squares are chosen at random from the 64 playing squares of a 8 x 8 chessboard, then find theprobability that exactly two of them are of the same colour?
(1) 9/21 (2) 16/21 (3) 14/21 (4) 18/21
42. In the above figure, ABCD is a parallelogram. P and Q are the points of trisection of AB and R is
the midpoint of DC. What is the ratio of the area of the parallelogram ABCD to that of the
quadrilateral PBCR?
(1) 16 : 7 (2) 15 : 7 (3) 2 : 1 (4) 12 : 7
43. Four people need to cross a stream. At a time only two people can cross the stream using a certain boat which isavailable. The times taken by the four people to cross the stream individually are 3, 7, 11, 17 minutes respectively.If the faster person on the boat drives it and no person drives the boat more than two trips in total, what is the least time required for all the four to cross the stream? (Reaching from one bank to the other bank is one trip).
(1) 23 minutes (2) 59 minutes (3) 31 minutes (4) 37 minutes
DIRECTIONS for questions 44 and 45: These questions are based on the following data.
There are 100 players numbered 1 to 100 and 100 baskets numbered 1 to 100. The first players puts one ball each in every basket starting from the first basket (i.e., in the baskets numbered 1, 2, 3, …and so on upto 100), the second player then puts two balls each in every second basket starting from the second (i.e., in the baskets numbered 2, 4, 6, … and so on upto 100), the third player puts three balls each in every third basket starting from the third (i.e., in the baskets numbered 3, 6, 9, ... and so on upto 100), and this is comtinued so on till the hundredth player puts 100 balls in the 100th basket.
44. Which basket will finally have the maximum number of balls?
(1) 96 (2) 98 (3) 100 (4) None of these
45. How many baskets will finally have exactly twice the number of balls as the number on the basket itself?
(1) 8 (2) 6 (3) 4 (4) 2
DIRECTIONS for questions 46 to 50: Select the correct alternative from the given choices.
46. A cylindrical vessel has its radius and height in the ratio 1 : 12 and it can hold the same quantity of water as another conical vessel whose height is one-third of its height. What is the ratio of the lateral surface area of the cylinder and that of thecone? (Ignore the thickness of the vessel in both cases)
(1) 3 : 2 (2) 8 : 5 (3) 1 : 1 (4) None of these
47. If (21)n x (36)n = (776)n and (12)n x (63)n = (x)n then find x.
(1) 510 (2) 540 (3) 756 (4) 776
48. What is the area enclosed by x = 0, x = 3, y = 0 and y = | x - 1 | + | x - 2 | ?
(1) 4 sq.units (2) 4.5 sq.units (3) 5 sq.units (4) 6 sq.units
49. There are two parallel lines and a circle in a plane dividing the plane into distinct non-overlapping regions. What is the maximum number of regions into which the plane can be divided?
(1) 8 (2) 5 (3) 6 (4) 7
50. The area of a triangle which is inside a semicircle is equal to the area outside the triangle but within the semicircle. What is the ratio of the area of the complete circle to that of a parallelogram formed with its base as the diameter of the circle and height equal to the height of the triangle, if the base of the triangle is the diameter of the circle and the third vertex of the triangle lies on the circle?
(1) 1 : 2 (2) 4 : 1 (3) 2 : 1 (4) 1 : 4
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