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Test Maths Paper-1
1. The test comprises of 30 questions.
a. n = 1 b. n = 2 c. n ≥ 3 d. None of these Ans: a Answer 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. 1687 b. 1787 c. 1887 d. 1987 Ans: b 3.The value of the numeral MCMXCX isa. 1999 b. 1899 c. 1989 d. 1889 Ans: a 4. Which of the following represent the numeral for 1995?I. MCMLXXV II. MCMXCV III. MVD IV. MVM a.Only I and II b.Only III and IV c.Only II and IV d. Only IV Ans: c 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. √3 b. 4√3 c. √3/4 d. 16√3 Ans: a 6. Consider 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. 3 b. 4 c. 6 d. 7 Ans: d 7. For a positive integer n. if 2n - 1 is prime, then n is:a.Even b. Odd c.Prime d.None of these Ans: c Answer 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 day b. 5th day c. 6th day d. 7th day Ans: c 9.What would be the total distance traveled by the caterpillar?a. 25 inches b. 275 inches c. 324 inches d. 413 inches Ans: b 10.How many natural numbers less than 1000 can be expressed as the difference of two perfect squares in at least one way?a.750 b.792 c.810 d.749 Ans: d 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.7 b. 21 c. 27 d. 14 Ans: d 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 numbers a. 2 b. 1 c. 3 d. Infinite Ans: a 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.60 b.27 c.20 d. 9 Ans: c 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. 72 b. 90 c. 96 d. 144 Ans: b 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. 22 b. 44 c. 66 d. 88 Ans: b
a. 60cm2 b. 30cm2 c. 150cm2 d. 300cm2 Ans: d 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. 21 b.25 c.41 d.67 Ans: c 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. 661 b. 660 c.659 d. 658 Ans: d 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 (√3+1) b. 6 (√3+√2) c. 7(√3 - 1 ) d. 8(√3 - 2) Ans: a 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. 1/6 b. 1/7 c. 1/21 d. 1/12 Ans: a Answer Question Number 21 and 22 on the basis of the information given below:Two runners Patrick and Quentin start jogging from the vertex A of a square track in the same direction. Patrick completes one round about the square track and meets Quentin at a point S, while Quentin is yet to complete his first round. Upon meeting at S. Patrick reverses his direction and both of them meet again, this time at point A. The other three vertices of the square track are B, C and D in that order.21.What is the ratio of the speeds of Patrick and Quentin ?a. √ 2 : 1 b. √ 2 + 1 : 1 c. 1 : √2 - 1 d. Either (a) or (c) Ans: b 22. Point S lies betweena. A and B b. B and C c. C and D d. Cannot be determined Ans: c 23. The number of solutions of the equation 2x + y = 40 where both x and y are positive integers and X ≤ Y is:a. 7 b. 13 c.14 d. 18 Ans: b 24. If both a and b belong to the set {1, 2, 3, 4}, then the number of equations of the form ax2 + bx + 1 = 0 having real roots isa. 10 b.7 c.6 d. 12 Ans: b 25. Find the number of two-digit numbers where the product of the digits is greater than the sum of the digits?a.61 b. 62 c. 63 d. None of these Ans: c 26. A red light flashes three times per minute and a green light flashes five times in 2 min at regular intervals. If both lights start flashing at the same time, how many times do they flash together in each hour?a. 30 b. 24 c. 20 d. 60 Ans: a 27. How many integral solutions (x, y , z) are there given that x + (-1)z y = 2z , and x , y, z ≤ 10 ?a. 3 b. 37 c. 38 d. 35 Ans: b 28. If log10X - log10radic;X = 2 log10X, the possible value of x is given bya.10 b. 1/100 c. 1/1000 d. None of these Ans: b 29. The number of employees in Obelix Menhir Co. is a prime number and is less than 300. The ratio of the number of employees who are graduates and above, to that of employees who are not, can possibly be:a.87 : 100 b. 110 : 111 c. 85 : 98 d. 97 : 84 Ans: d 30. What is the sum of all two-digit numbers that give a remainder of 3 when they are divided by 7?a.666 b.676 c.683 d. 777 Ans: b |

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