1 There are two alloys A and B of copper and Zinc. The ratio of copper and zinc in alloy is 8 : 1 and that of alloy B is 2: 7 . it is found that if the alloy A and B are mixed in a certain ration , the weights of copper and zinc in the resultant alloy are also in the ration . What is that ratio?a. 4:3b.3:2c.5:3d.2:1

2 A king has 50 identical diamond rings, which he stores in five different coloured chests, In how many ways can be the king store rings among the chests such that every chest contains at least one ring?a.C(49,4)b.C(50,4)c.C(49,5)d.C(50,5)

3 [x] is deifned as the greatest integer less than x and {x} is defined as the least integer greater than x , for all real values of x . Consider the following four statementsa. [x] + [-x] = -1b. {x} + [-x ] =0c. {[x]} + [{-x}] = 1d. [2x]+{3x}<=5x

4 There are four friends A, B , C and D . Their ages, in completed years, satisfy the following conditions. A's age is twice that of C and B's age is 50% more than that of D . If the sum of the ages of A and B is 35 , and C is not younger than D, find the present age (in completed years ) of C.a.16b.13 < /li>c.10d.either (1) or (2) or (3)

5 What is the area of the land that is not ploughed in a rectangular field of side 30 m and 20m if 2 tracks of 2 m width are ploughed, along the length and the breadth?a.504b.100c.500d.450

6 In a factory , machines A , B and C manufactures 25% , 35% and 40% of the total production of bulbs . 6%, 4% and 7% of the bulbs manufactured by machines A, B and C respectively are defective. A bulb is drawn at random and is found to be defective. What is the probability that it was produced by machine A?a.6/11b.5/11c.4/19d.5/19

7 The sum of all the ages of a cuboid is 76 cm. If all the edges (in cm) are integers, what is minimum possible length of its longest diagonal?a.11 cmb.12 cmc.13 cmd.14 cm

8 Find the length of the altitude to the hypotenuse of a right-angled triangle having an inradius of 1cm and circumradius of 2.5cm.a.2cmb.2.4cmc.2.8cmd.3cm

9 In the upper-class lounge at the city railway station there are thirty chairs in a row, all of them initially unoccupied. From time to time, a passenger enters the lounge and sits in one of the free chairs. If either of the neighboring chairs is occupied, one of the neighbors gets up immediately and leaves. What is the maxium number of chairs that can be occupied at any given time?a.15b.16c.21d.29

10 A solid cube of side 3 cm, painted red on the outside is cut into 27 equal cubes. When all the 27 cubes are considered, what is the difference between the area that is not red and the area that is red?a.54 cmb.72 cmc.81cmd.108cm

11 A , B and C have a total of 40 marbles among them . A triples the number of marbles with the others. Next, B triples the number of marbles with others. if B now has 10 marbles , find the number of marbles he had at the beginning.a.11b.10c.9d.12

12 The ten digit number 9793a6160b is divisible by 11. if 0 < a < b, find the sum of remainders when the number is divided by a+b and a suceesively.a. 6b. 3c. 2d. 9

13 The equation x4 - px3+qx2+rx+1=0 , has four integral roots . which of the following could be the value of the expression pq+qr+rpa.-32b.16c.32d.0

14 A=minimum [24-8x-x2, x2+9x-6] . For what value/s of x does A assume its maximum value?a.-10b.3/2c. a or bd.39/4

15 The hands of a strange clock move such that they would meet twice as frequently if they run in opposite than if they run in same direction. How many times would the faster hand meet the slower hand in the time that the slower hand completes 20 rotations, given that the hands run in opposite directions?a.80b.60c.40d.120

16 A planned to save his earnings in the following manner . On 1st January 2005, he saved Re.1 On every day starting from jan 2nd 2005, he saved Re 1 more than the previous day. Find the first date after jan 1st 2005 on which his total savings will be a perfect square.a.17th janb.19th febc.26th jand.none

17 rections for Questions 7 to 9. a1 , a2 ,a3, a4 and a5 are five positive integers in ascending order. Any number from 1 to 121 , both included , can be obtained by using a linear combination of these integers with coefficients 1, 0 or -1. 7. Find the value of a1+2a2+3a3+4a4+5a5a.547b.537c.527d.517

18 Find the index of the largest power of 3 contained in the product a1 a2 a3 a4 a5a.10b.11c.12d.13

19 If the sum of the 5 coefficients is 1, find the largest number that can be obtained.a.107b.113c.81d.121

20 ections for Questions 10 to 12. A class has certain number of students , each having 1 to 6 books. The total number of students having 2 to 5 books each is 10. A total of 7 students have 4 to 6 books each . The total number of students having 2 or 3 books each is 4. 10. how many students have 6 books each ?a.2b.1c.3d.0

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