1 Find the equation of the line where y-intercept shapes and the gradient have the same numerical value and the line passes through the point (-3 , -5).a. 2y – 5x = 5b. y = 1.25x + 2.5c. 3y = 4x +4d. 4y – 5x = 5

2 Which of the following equation best describes the data provided in the table ?a. V = -1.5t – 0.5b. v = 1.5t + 0.5c. v = -2.5t – 2.5d. v = 3.5t + 9.5

3 If S1 = {1} , S2 = { 2 , 3} , S3 = { 4 , 5 ,6 } , S4 = { 7, 8 , 9 , 10 } and so on , then what is the sum of all the elements or S15 ?a. 1695b. 1235c. 2056d. 3751

4 A number when divided by N leaves a remainder of 4. When one-third of the number is divided by N, it leaves a remainder 29. what is the least such number greater than 1000?a. 1089b. 1152c. 1083d. 1079

5 ection for questions 25 to 27. Both Sir Able and Sir Gallant have small volunteer armies at their disposal. Some of the soldiers are foot soldiers , some are mounted troops. Together, the two armies total fifty men. The number of mounted troops in Gallant’s force equals the number of foot soldiers in Able’s force. Sir Able has two fewer troops in total than sir Gallant , and the number of mounted troops in Able’s army is four fewer than the number of mounted troops in Gallant’s army. 25. How many mounted soliders are there in Able’s army?a. 8b. 10c. 12d. 14

6 How many foot soldiers are there in Gallants’s army?a. 8b. 10c. 12d. 14

7 How many foot soldiers are there in Able’s army ?a.8b.10c.12d.14

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

9 If k and m are natural numbers, then the remainder when (3k + (-1)m)6 is divided by 9.a. is always 1b. is always 8c. is either 1 or 8d. depends upon the value of m

10 Three sides of a right triangle have their length as integers in arithmetic progression. The length of any side of such a triangle can never bea.33b. 64c.115d.314

11 If x , y and z are distinct positive integers , and x + y + z = 11 , then the maximum value of ( xyz + xy + yz + zx) isa.84b. 78c. 72d. 58

12 A and B working by themselves can build a wall respectively in 8 days and 18 days more than what they would take when working together. In how many days can A alone build the wall ?a. 20b. 24c. 30d. 18

13 Direction for questions 3 to 5 A deck of playing cards is placed on a table and repeatedly shuffled in the following manner. First the top most is drawn out and then replaced to occupy the 27th place from the bottom, and then the bottom most card is drawn out and replaced to occupy the 26th place from the top. Each time this set of operations is done , one round of shuffling is said to be completed. 3.At which position will the card which was initially at the top of the deck be immediately after the first 17 rounds of shuffling?a. 42nd from the topb. 10th from the bottomc. 42nd from the bottomd. 10th from the top

14 Which of the following statements is true regarding the deck of cards immediately after the first 26 rounds of shuffling?a.The card that was initially at the top of the deck will be immediately next to the card that was initially at the bottom of the deck.b.The top 26 cards will become the bottom 26 cards, in the same order.c.The bottom 26 cards will become the top 26 cards, in the reverse order.d.None of the above

15 What is the minimum number of rounds of shuffling required to bring the card which was initially the third card from the top, back to its original position?a. 26b. 29c. 52d. 55

16 Four horses are tethered at four corners of a square plot of side 14 m so that the adjacent horses can just reach one another. There is a small circular pond of area 20 m2 at the center. Find the ungrazed area.a. 22 m2b. 42 m2c. 84 m2d. 168 m2

17 On a staright road XY , 100m long , five heavy stones are placed 2 m apart beginning at the end X. A worker , starting at X , has to transport all the stones to Y, by carrying only one stone at a time. The minimum distance he has to travel isa. 472 mb. 422 mc. 744 md. 860 m

18 For the three equations x + 2y – z = 5 , 3x + 2y + z= 11 , (x +2y)2 - z2 = 15 , what is the value of y ?a. 0b. -1c. 2d. 4

19 Pavithra Kumar looked at the six-digit number on her CAT admit card and said “ if I multiply the first two digits with three, I get all one’s. If I multiply the next two digits with six, I get all two’s. If I multiply the last two digits by 9, I get all three’s “. What is the sum of the digits of the number on Pavithra Kumar’s admit card?a.30b.33c.90d.60

20 A tank contains 530 liters of water. An outlet emptying 14 ltrs. of water every minute is opened. 12 ˝ minutes later, a second tap is opened. What should be the rate at which water is emptied from the second tap if the entire tank is to be emptied in 30 mins?a.6.29 ltr/minb.14 ltr/minc.23.18 ltr/mind.28.3 ltr/min

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