CAT2004 Related Question Answers
2.
Directions for the following three questions: Answer the questions on the basis of the information given below
In the adjoining figure I and II are circles with centres P and Q respectively, The two circles touch each other and have common tangent that touches them at points R and S respectively. This common tangent meets the line joining P and Q at O. The diameters of I and II are in the ratio 4: 3. It is also known that the length of PO is 28 cm.What is the ratio of the length of PQ to that of QO?[CAT 2004]
5.
Directions for the following two questions:Answer the questions on the basis of the information given below.$$f_1(x) = x$$ if $$0 \leq x \leq 1$$ $$f_1(x) = 1$$ if x >= 1 $$f_1(x) = 0$$ otherwise$$f_2(x) = f_1(-x)$$ for all x$$f_3(x) = -f_2(x)$$ for all x$$f_4(x) = f_3(-x)$$ for all xHow many of the following products are necessarily zero for every x:$$f_1(x)f_2(x), f_2(x)f_3(x), f_2(x)f_4(x)$$
7.
Directions for the following two questions: Answer the questions on the basis of the information given below.In an examination, there are 100 questions divided into three groups A, B and C such that each group contains at least one question. Each question in group A carries 1 mark, each question in group B carries 2 marks and each question in group C carries 3 marks. It is known that the questions in group A together carry at least 60% of the total marks.If group B contains 23 questions, then how many questions are there in group C?
8. If group C contains 8 questions and group B carries at least 20% of the total marks, which of the following best describes the number of questions in group B?
9. Two boats, traveling at 5 and 10 kms per hour, head directly towards each other. They begin at a distance of 20 kms from each other. How far apart are they (in kms) one minute before they collide.
10. A rectangular sheet of paper, when halved by folding it at the mid point of its longer side, results in a rectangle, whose longer and shorter sides are in the same proportion as the longer and shorter sides of the original rectangle. If the shorter side of the original rectangle is 2, what is the area of the smaller rectangle?[CAT 2004]
11. If the sum of the first 11 terms of an arithmetic progression equals that of the first 19 terms, then what is the sum of the first 30 terms?
12. If a man cycles at 10 km/hr, then he arrives at a certain place at 1 p.m. If he cycles at 15 km/hr, he will arrive at the same place at 11 a.m. At what sped must he cycle to get there at noon?
13. On January 1, 2004 two new societies S1 and S2 are formed, each n numbers. On the first day of each subsequent month, S1 adds b members while S2 multiples its current numbers by a constant factor r. Both the societies have the same number of members on July 2, 2004. If b = 10.5n, what is the value of r?
14. If $$f(x)=x^3-4x+p$$ , and f(0) and f(1) are of opposite signs, then which of the following is necessarily true[CAT 2004]
15. Suppose n is an integer such that the sum of digits on n is 2, and $$10^{10} < n < 10^{11}$$. The number of different values of n is
16. A milkman mixes 20 litres of water with 80 litres of milk. After selling one-fourth of this mixture, he adds water to replenish the quantity that he had sold. What is the current proportion of water to milk?[CAT 2004]
18. N persons stand on the circumference of a circle at distinct points. Each possible pair of persons, not standing next to each other, sings a two-minute song one pair after the other. If the total time taken for singing is 28 minutes, what is N?[CAT 2004]
19. A father and his son are waiting at a bus stop in the evening. There is a lamp post behind them. The lamp post, the father and his son stand on the same straight line. The father observes that the shadows of his head and his son's head are incident at the same point on the ground. If the heights of the lamp post, the father and his son are 6 metres, 1.8 metres and 0.9 metres respectively, and the father is standing 2.1 metres away from the post then how far (in metres) is son standing form his father?
21. Each family in a locality has at most two adults, and no family has fewer than 3 children.Considering all the families together, there are adults than boys, more boys than girls, and more girls than families.Then the minimum possible number of families in the locality is
22. Let $$C$$ be a circle with centre $$P_0$$ and $$AB$$ be a diameter of $$C$$. Suppose $$P_1$$ is the mid point of the line segment $$P_0B$$,$$P_2$$ is the mid point of the line segment $$P_1B$$ and so on. Let $$C_1,C_2,C_3,...$$ be circles with diameters $$P_0P_1, P_1P_2, P_2P_3...$$ respectively. Suppose the circles $$C_1, C_2, C_3,...$$ are all shaded. The ratio of the area of the unshaded portion of $$C$$ to that of the original circle is
23. Consider the sequence of numbers $$a_1, a_2, a_3$$....... to infinity where $$a_1 = 81.33$$ and $$a_2 = -19$$ and $$a_j = a_{j-1} - a_{j-2}$$ for $$j > 3$$. What is the sum of the first 6002 terms of this sequence?
24. A sprinter starts running on a circular path of radius r metres. Her average speed (in metres/minute) is $$\pi$$ r during the first 30 seconds, $$\pi$$ r/2 during next one minute, $$\pi$$ r/4 during next 2 minutes, $$\pi$$ r/8 during next 4 minutes, and so on. What is the ratio of the time taken for the nth round to that for the previous round?
25. Let $$u = ({\log_2 x})^2 - 6 {\log_2 x} + 12$$ where x is a real number. Then the equation $$x^u = 256$$, has
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