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1 Side AB of a triangle ABC is 80 cm long, whose perimeter is 170 cm . If ?(ABC) = 60 degree , the shortest side of triangle ABC measuresa.40 cmb.36 cmc.17 cmd.14 cm

2 Beginning with what number do the terms of the sequence Xn = n2 - 5n + 6 , n ? N , satisfy the inequality X n+1 > X n ? ii. 2021 > 2120a. n = 5b. n = 3c. n = 7d. n = 8

3 Three runners A, B and C run a race with runner A finishing 12m ahead of runners B and 18m ahead of ruuner C, while runner B finishes 8m ahead of runner C. each runner travels the entire distance at a constant speed. What was the length of the race?a.36mb.48mc.60md.72m

4 A change-making machine contains one-rupee , two-rupee and five-rupee coins. The total number of coins is 300. The amount is Rs. 960. If the numbers of one-rupee coins and two-rupee coins are interchanged , the value comes down by Rs.40. The total number of five-rupee isa. 100b. 140c. 60d. 150

5 In a watch, the minute hand crosses the hour hand for the third time exactly after every 3 hrs, 18 min, 15 sec of watch time. What is the time gained or lost by this watch in one day ?a. 14 min 10 seconds lostb. 13 min 50 seconds lostc. 13 min 20 seconds gainedd. 14 min 40 seconds gained

6 The 2000th letter in the sequence ABCDEDCBAABCDEDCBAABCDEDCBA . . . Isa. Ab. Cc. Dd. B

7 Harinder had five regular solids of different shapes and all of equal volume. They were, a Tetrahedron, a Cube, a Sphere, a Septahedron and an Octahedron . If he has to paint all these solids at a cost Rs. 2.50 per unit area then which of the above mentioned solids will prove to be the costliest to paint ?a. Cubeb. Tetrahedronc. Octahedrond. Septahedron

8 If m is a positive integer, for how many values of m 72/(m2 -? 3) or 72/(m3 - 3) is an integer ?a.2b.3c.4d.More than 4

9 A man invest Rs. 3000 at a rate of 5% per annum. How much more should he invest at a rate of 8%, so that he can earn a total of 6% per annum?a.Rs. 1200b.Rs. 1300c.Rs. 1500d.Rs. 2000

10 A is set of positive integers such that when divided by 2, 3, 4, 5 , 6 leaves the remainders 1, 2 , 3, 4 ,5 respectively . How many intgers between 0 and 100 belong to set A ?a. 0b. 1c. 2d. None

11 (BE)2 = MPB , where B , E , M and P are distinct integers . then M =a. 2b. 3c. 9d. None

12 Find the area bounded by the lines y = |x - 1| and y = 4.a. 16 sq. unitsb. 12 sq.unitsc. 4 sq.unitsd. cannot be determined

13 We define a relative prime due to a day for which the number of the month and the number of the day have no common factors other than 1. For example 22/5 (22 May) is such a day because 22 and 5 have no common factors other than 1 . The month with the smallest number of relatively prime day isa. Februaryb. Marchc. Decemberd. June

14 ABCD is a rectangle. X and Y are two points on the sides AB and BC respectively. If areas of triangle DAX, triangle YCD and triangle XBY are 5, 4 and 3 respectively ; what is the area of quadrilateral ABCD ?a. 20b. 4c. 8d. either (a) or (b)

15 How many ways are there to place a 5 by 5 square on an 8 by 8 chessboard so that each vertex is at the center of some field ?( solutions obtained from each other by reflection or rotations are not considered different )a. 8b. 10c. 12d. cant be determined

16 n3 is odd. Which of the following statement(s) is (are) true ?i. n is odd ii. n2 is odd iii. n2 is evena. I onlyb. II onlyc. I and IId. I and III

17 Let f be a function such that for all integers x and y applies f(x +y) = f(x) + f(y) + 6xy +1 and f(x) = f(-x) . then , f(3) equalsa.26b.27c.52d. 53

18 From a circular sheet of paper with a radius of 20 cm, four circles of radius 5 cm each are cut out. What is the ratio of the uncut to the cut portion ?a.1 : 3b. 4 : 1c. 3 : 1d. 4 : 3

19 A person starts counting from the thumb , then the fore finger , then middle finger, and then the ring finger followed by the little finger. Then again the ring finger followed by the middle finger and so on. Which finger would he finish at when he counts 6449 ?a. Thumbb. Forefingerc. Middle fingerd. Ring finger

20 The fee charged by TIME for the students of MBA is 25% less than that charged for the students of MCA. If the total amount received from MBA os 50% more than that from MCA , the number of students in MCA course is what percent of that in MBA?a.80%b.75%c.50%d.None

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