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1 wer 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. v 2 : 1b. v 2 + 1 : 1c. 1 : v2 - 1d. Either (a) or (c)

2 Point S lies betweena. A and Bb. B and Cc. C and Dd. Cannot be determined

3 The number of solutions of the equation 2x + y = 40 where both x and y are positive integers and X = Y is:a. 7b. 13c.14d. 18

4 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. 10b.7c.6d. 12

5 Find the number of two-digit numbers where the product of the digits is greater than the sum of the digits?a.61b. 62c. 63d. None of these

6 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. 30b. 24c. 20d. 60

7 How many integral solutions (x, y , z) are there given that x + (-1)z y = 2z , and x , y, z ? 10 ?a. 3b. 37c. 38d. 35

8 If log10X - log10radic;X = 2 log10X, the possible value of x is given bya.10b. 1/100c. 1/1000d. None of these

9 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 : 100b. 110 : 111c. 85 : 98d. 97 : 84

10 What is the sum of all two-digit numbers that give a remainder of 3 when they are divided by 7?a.666b.676c.683d. 777

11 Directions for Questions 1 and 2. "Directions for Questions 1 and 2. Two trains X and Y start simultaneously at 9 am form A and B towards B and A respectively. The ratio of speeds of X and Y is 2:1 respectively. On a normal day they meet at 2 p.m. One day, train X met with an accident and thereafter traveled at half of its normal speed. They met that day at 3 p.m. " 1. What is the scheduled arrival time of train X at B?a.12 mid-nightb.7.30 pmc.4.30p.md.none

12 On the day of accident, how many hours was train X late at B?a. 6 hrsb. 5 hrsc. 4.5 hrsd. 7 hrs

13 In how many ways can you express 840 as a product of two co prime natural numbers?a.8b.9c.16d.12

14 A circle is inscribed in an equilateral triangle and a square is inscribed in the circle. The ration of the area of the triangle to the area of the square isa.3:2b.3v3:2c. v3:v2d.none

15 For how many different values of n is n4 + 4 a prime number? (n is a natural number)a.Only 1b.Only 2c.Only 3d.infinitely many

16 Thre consecutive natural numbers to the first, second and third powers respectively, when added, make a perfect square, the square root of which is equal to the sum of the three consecutive integers. The middle one of these natural numbers would bea. 4b. 1c. 3d. Cannot be determined

17 rections for Questions 7 & 8. Gangs of 17 thieves steal a sack of platinum coins. When they try to divide it equally, there are three coins left over. They fight over these extra coins and one of them is killed. They try to divide the coins equally a second time, but now there are 10 left over. Again they fight and one more of them get killed. When they try to divide it (now for the third time) there are no coins left after dividing the coins equally among those surviving. 7. What is the smallest number of coins they could have stolen?a.3930b.7860c.1880d.11790

18 What was the share of each of the thieves in the second attempt distribution?a.245b.490c.735d.980

19 For what value of V will the sum of squares of the roots of x2 - vx =1 'll be minimum?a.3b.3c.1d.1 or 2

20 if (V+A)/2 = V.A ( i.e. a decimal point between V and A ). If V and A are both natural numbers, then which of the following is the value of V-A?a.1b.-1c.2d. cant be determined

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