1 A rope of length P cm is cut into a number of equal pieces of D cm length and a piece of 13 cm is left. Another rope of length 12 p cm is cut into a number of equal pieces of D cm length and a piece of 2 cm is left over. If P and D are whole numbers greater than 13, how many values can D take ?a. 1b. 4c. 7d. 8

2 Of 128 boxes of oranges, each box contains at least 120 and at most 144 oranges . The number of boxes containg the same number of oranges is at leasta. 5b. 103c. 6d. Cannot be determined

3 What is the units place of 251 ?a.2b. 8c. 1d. 4

4 IF F(n) = { x/x is a prime factor of n}; answer the following question. F(110) ? F(165)a. {5 ,11}b. {1, 5,11}c. {1, 2 , 3 , 5 , 11}d. {2 , 3 , 5, 11}

5 There are a certain number of apples in a big box. A boy takes half apple more, than half of them. Another boy takes half apple more than half of the remaining . Like this after the 7th boy takes his share the number of apples in the big box is 635 less than the original number of apples. If no apple is cut in the entire process, how many apples are left after the fifth boy takes apples from the box?a. 9b. 19c. 39d. 59

6 A number is formed writing first 54 natural numbers in front of each other as 12345678910111213...Find the remainder when this number is divided by 8.a. 1b. 7c. 2d. 0

7 If (a +b ) : (b+c) : (c+a) = 6 : 7 :8 and a+b+c= 14 , compute the value of ca. 2b. 4c. 6d. 8

8 In a certain competition six contestants together earned a total of 2100 points. The minimum points required to qualify for the next round are 360. Which of the following statements is necessarily true?a. At least one person qualified for the next round.b. At least one person failed to qualify for the next round.c. At most one person failed to qualify for the next round.d. More than one of the above

9 Chris has a number of blocks of size 1 x 2 x 6. the smallest number of blocks he needs in order to build a solid cube isa. 6b. 12c. 24d. 18

10 In putting up a fence around a square field, a man saves 2 poles on each side of the field if he uses five evenly spaced poles instead of n poles spaced at intervals of 5 m each. The poles placed on each side are considered including are the corner poles. If the distance between the five poles is ‘n’ meters, find the area of the field.a. 441 sq.mb. 784 sq.mc. 841 sq.md. 900 sq.m

11 Number of students who have opted for subjects A , B and C are 60 , 84 and 108 respectively. The examination is to be coducted for these students such that only the students of the same subject are allowed in one room. Also the number of students in each room must be same. What is the minimum number of rooms that should be arranged to meet all these conditions ?a. 28b. 60c. 12d. 21

12 x and y are real numbers satisfying the conditions 2 < x < 3 and -8 < y < -7. which of the following expressions will have the least value ?a. xyb. 2xyc. 5xyd. None

13 The area of the triangle whose vertices are (a ,a) , ( a+1 , a+1) and (a+2 , a) isa. a3b. 1c. 2ad. 2

14 The remainder when 72002 is divided by 10 isa. 1b. 3c. 7d. 9

15 Mahinder had a rectangular piece of cardboard out of which he clipped away the largest possible square and was left with a piece exactly similar in shape to the original piece . The area of the piece remaining with Mahinder forms approximately , what percent of the area of the original piece ?a. 22%b. 33%c. 38%d. Cannot be determined

16 what is the sum of the areas of regions enclosed by x + y = k , x = k -1 , and the x- axis where 1 ? k ? 5 and k is an integera. 0.5 sq. unitsb. 5 sq.unitsc. 2.5 sq.unitsd. 5?2 sq. units

17 ection for question 27 & 28 Amar , Akabar and Anthony are three friends. Only three colours are available for their shirts , viz. red , gree and blue. Amar does not wear red shirt. Akbar does not wear green shirt. Anthony does not wear blue shirt. 27. If Akbar and Anthony wear the same colour of shirts, then which of the following is not true ?a. Amar wears blue and Akbar wears greenb. Amar wears green and Akbar does not wear bluec. Amar wears blue and Akbar does not wear blued. Anthony wears red

18 If two of them wear the same colour , then how many of the following must be false? i. Amar wears blue and Akbar does not wear green. ii. Amar does not wear blue and Akabar wears blue. iii. Amar does not wear blue and Akbar does not wear blue. iv. Amar wears green, Akbar does not wear red , Anthony does not wear green.a. Noneb. Onec. Twod. Three

19 (13)6 – 1 is not exactly divisible bya.8b.9c. 11d. 18

20 If x > 5 and y < -1 , then which of the following statements is true ?a.(x + 4y) > 1b. x > -4yc. -4x<5yd. None

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