CAT2003L Related Question Answers
51. A game consists of tossing a coin successively. There is an entry fee of Rs. 10 and an additional fee of Re. 1 for each toss of coin. The game is considered to have ended normally when the coin turns heads on two consecutive throws. In this case the player is paid Rs. 100. Alternatively, the player can choose to terminate the game prematurely after any of the tosses. Ram has incurred a loss of Rs. 50 by playing this game. How many times did he toss the coin?A. The game ended normally.B. The total number of tails obtained in the game was 138.
52. Each packet of SOAP costs Rs. 10. Inside each packet is a gift coupon labelled with one of the letters S, O, A and P. If a customer submits four such coupons that make up the word SOAP, the customer gets a free SOAP packets. Ms. X kept buying packet after packet of SOAP till she could get one set of coupons that formed the word SOAP. How many coupons with label P did she get in the above process?A. The last label obtained by her was S and the total amount spent was Rs. 210.B. The total number of vowels obtained was 18.
53. If A and B run a race, then A wins by 60 seconds. If B and C run the same race, then B wins by 30 seconds. Assuming that C maintains a uniform speed what is the time taken by C to finish the race?A. A and C run the same race and A wins by 375 metres.B. The length of the race is 1 km.
55. When the curves $$y = log_{10}x$$ and $$y = x^{-1}$$ are drawn in the x-y plane, how many times do they intersect for values $$x \geq 1$$ ?
56. 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[CAT 2003 leaked]
57. 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 $$\neq$$ 0?x+ 2y - 3z = p2x + 6y - 11z = qx - 2y + 7z = r
58. 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?
59. 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?
60. 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
63. The function f(x) = |x - 2| + |2.5 - x| + |3.6 - x|, where x is a real number, attains a minimum at
64. How many even integers n, where $$100 \leq n \leq 200$$ , are divisible neither by seven nor by nine?
65. 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
66. 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?
67. Is $$a^{44} < b^{11}$$, given that a = 2 and b is an integer?A. b is evenB. b is greater than 16
68. 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.
69. 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.
70. Is $$(1/a^2 + 1/a^4 + 1/a^6 +...) > (1/a + 1/a^3 + 1/a^5 +...)$$?A. $$0< a \leq 1$$B. One of the roots of the equation $$4x^2-4x+1 = 0$$ is a
71. 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 = 3 cmB. Perimeter of ABC = 6 cm, AB = 2 cm, and AC = 2 cm.
72. 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?[CAT 2003 leaked]
73. 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° or concave if the internal angle is 270°. If the number of convex corners in such a polygon is 25, the number of concave corners must be
75. Let p and q be the roots of the quadratic equation $$x^2 - (\alpha - 2) x - \alpha -1= 0$$ . What is the minimum possible value of $$p^2 + q^2$$?
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