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1 Hundred lines are drawn on a plane. These lines consist of n sets, where n is a natural number, and the lines in each set are parallel to each other. Given that the number of intersection points is 3200 , which of the following is true?a. n = 1b. n = 2c. n = 3d. None of these

2 swer Question Number 2 to 4 on the basis of the information given below: The seven basic symbols in a certain number system and their respective vales are as follows : I =1 , V = 5, X =10 , L=50 , C=100 , D= 500 and M = 1000 In general, the symbols in the number system are read from left to right, starting with the symbol representing the largest value; the same symbol cannot occur continuously more than three times; the value of the numeral is the sum of the values of the symbols. For example, XXVII = 10+10+5+1+1 = 27 . An exception to the left-to-right reading occurs when a symbol is followed immediately by a symbol of greater value; then the smaller value is subtracted from the larger. For example, XLVI = (50-10) + 5 + 1 = 46. 2.The value of the numeral MDCCLXXXVII isa. 1687b. 1787c. 1887d. 1987

3 The value of the numeral MCMXCX isa. 1999b. 1899c. 1989d. 1889

4 Which of the following represent the numeral for 1995? I. MCMLXXV ? ? II. MCMXCV ? ? III. MVD ? ? IV. MVM ? ?a.Only I and IIb.Only III and IVc.Only II and IVd. Only IV

5 A series of 8 equilateral triangles is formed such that the ratio of sides of two consecutive triangles is constant. The ratio of sides of the smallest and largest triangles is 1: 128. The length of the side of the fifth largest triangles is one-fourth the common ratio. Find the area of the third largest triangle.a. v3b. 4v3c. v3/4d. 16v3

6 AConsider the set S = {1, 2, 3, . . ., 1000}. How many arithmetic progressions can be formed from the elements of S that start with 1 and end with 1000 and have at least 3 elements?a. 3b. 4c. 6d. 7

7 For a positive integer n. if 2n - 1 is prime, then n is:a.Evenb. Oddc.Primed.None of these

8 swer Question Number 8 and 9 on the basis of the information given below: A caterpillar was crawling on a huge stem 50 inches long. Initially, it was at the mid point of the stem. On the first morning, it would crawl 5 inches up and in the evening it would Fall 9 inches down. Next morning, it would crawl 13 inches up and in that evening it would fall 17 inches down. It would go on crawling in the described sequence until it reaches either of the end points of the stem. 8.On which day the caterpillar would reach the end of the stem?a. 4th dayb. 5th dayc. 6th dayd. 7th day

9 What would be the total distance traveled by the caterpillar?a. 25 inchesb. 275 inchesc. 324 inchesd. 413 inches

10 How many natural numbers less than 1000 can be expressed as the difference of two perfect squares in at least one way?a.750b.792c.810d.749

11 7 ballerinas dance for 8 hours and lose a total of 20 pounds. How many more ballerinas dancing would it take to lose a total of 20 pounds in only 4 hours, if the new dancers lost weight only half as fast as the original 7?a.7b. 21c. 27d. 14

12 How many triplets (a, b, c) satisfy the following system of equations: - a = 12b/(1+b) ; b = 12c/(1+c) ; c = 12a/(1+a) a, b , c are positive real numbersa. 2b. 1c. 3d. Infinite

13 Which is the minimum number of cubes with which one can construct a cuboid of dimensions 20 cm x 16 cm x 12 cm.a.60b.27c.20d. 9

14 There are 12 towns grouped into four zones with three towns per zone. It is intended to connect the towns with telephone lines such that every two towns are connected with three direct lines if they belong to the same zone, and with only one direct line otherwise. How many direct telephone lines are required?a. 72b. 90c. 96d. 144

15 The sum of the third and ninth term of an A.P. is 8. Find the sum of the first 11 terms of the progression.a. 22b. 44c. 66d. 88

16 The perimeter of an isosceles triangle is 80 cm and the altitude to its base is 20 cm. Find area of the triangle?a. 60cm2b. 30cm2c. 150cm2d. 300cm2

17 The sum of four consecutive two-digit odd numbers, when divided by 10, becomes a perfect square. Which of the following can possibly be one of these four numbers?a. 21b.25c.41d.67

18 There were 165 questions in CAT 2000. If 1 mark is awarded for every correct answer and 1/3rd mark is deducted for every wrong answer, how many different net scores are possible?a. 661b. 660c.659d. 658

19 A car is being driven, in a straight line and at a uniform speed, towards the base of a vertical tower. The top of the tower is observed from the car and, in the process, it takes 10 min for the angle of elevation to change from 45 degree to 60 degree. After how much more time will this car reach the base of the tower?a. 5 (v3+1)b. 6 (v3+v2)c. 7(v3 - 1 )d. 8(v3 - 2)

20 I have 10 coins of value 1 , 2 , 3 & 10. I divide the coins into two piles of 5 each. What is the probability that one of the piles has the product of values of the coins equal to a multiple of 162?a. 1/6b. 1/7c. 1/21d. 1/12

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