1 A 65' long ladder is leaning against a straight wall . Its lower end is 25' from the bottom of the wall. If the upper end is moved down by 8' , how much further away will the lower end of the ladder be from the base of the wall?a. 8'b. 10'c. 14'd. 52'

2 The number of positive divisors of 15! Isa. 2304b. 2496c. 2688d. none

3 A positive integer is said to be prime if it is not divisible by any positive integer other than itself and one. Let P be a prime number strictly greater than 3. Then , when P2 + 17 is divided by 12 , the remainder isa. 6b. 1c. 0d. 8

4 Given odd positive integers x , y and z , which of the following is not necessarily true?a. x2y2z2 is oddb. 3(x2 + y2)z2 is evenc. 5x2 + y + z4 is oddd. z2(x4 + y4)/2 is even

5 Two oranges three bananas and four apples cost Rs.15 . Three oranges , two bananas and one apple cost Rs. 10 . I bought 3 oranges , 3 bananas and 3 apples. How much did I pay?a.10b.8c.15d.Cannot be determined

6 If a right circular cone , a right circular cylinder and a hemisphere , all have the same radius , and the heights of cone and cylinder equal their diameters , then their volumes are proportional respectively toa. 1:3:2b. 2:1:3c. 3:2:1d. 1:2:3

7 If a right circular cone of height h is cut by a plane parallel to the base and at a distance h/3 from the vertex ; then the volumes of the resulting cone and frustrum are in the ratioa. 1:3b. 1:26c. 1:4d. 1:7

8 if a+b+c=0 , where a ? b ? c then [(a2)/(2a2+bc)] +[(b2)/(2b2+ac)] + [(c2)/(2c2+ab)] is equal toa. 4b. 5c. 6d. 7

9 The maximum possible value of y = min(1/2 - 3x2/4 , 5x2/4) for the range 0 < x < 1 isa. 1/3b. 1/2c. 5/27d. 5/16

10 IF one root of x2+px+12=0 is 4 , while the equation x2+px+q=0 has equal roots , then the value of q isa.49/4b.4/49c.4d.1/4

11 What is the value of n for which (n17 - n)(42n - 1) is divisible by 289?a.7b.51c.17d.34

12 A number is picked from the odd numbers formed by the products of numbers shown up when 5 dice are rolled. What is the probability that it ends with 5?a.1- (2/3)5b.1 - (1/3)5c. 1- (1/6)5d. 0

13 if f(x)= (x2 + 12x + 12)/(x2 + 3x + 3) , then find max f(x)a.2b.4c.8d.cannot be determined

14 The sides of a right-angle triangle have lengths which are integers in AP. In which of the following smallest side of a triangle does there exist such a triangle ?a.2000cmb.2001cmc.2002cmd.none

15 rections for Questions 5 & 6. A , B , C , D are four item who are being weighed one after the other in the same order . Each time whena item is weighed the average weights till then is recalculated . It is found that the average weights so calculated were in A.P. with common difference of 2 kg. 5.The minimum weight of D if the weights of A, B , C and D are natural numbers isa. 7kgb. 9kgc. 13kgd. 28kg

16 What is the average weight of A , B , C, D if the weight of A is 4 kg?a. 7kgb. 10kgc. 28kgd. none

17 A man enters a shop which sells bottled water . There are full one liter bottles which cost Rs.22 half liter bottles which cost Rs. 11 and empty bottles which cost Rs.1 . He wants to buy at least 2 liters water and 3 bottles . How many of each will he have to buy to ensure that he spends the least amount of money ?a.2 full , 0 half , 1 emptyb.1 full , 2 half , o emptyc.1 full 1 half 1 emptyd.there can be more than one way

18 There is an alloy (A) of silver and copper . A certain weight of this alloy is mixed with 15kg of pure silver and melted . The new alloy (B) contains 90% of silver . If the alloy ( A) is mixed with 10kg of a 90% silver alloy, the new alloy (C) is found to contain 84% silver . Find the percentage of silver in (A)a.80%b.90%c.75%d.84%

19 A big cube is cut into 64 equal cubes . If 6 liters of paint was used to paint the big cube , how many more litres will you need for the smaller cubes to be painted on all sides?a.24 litersb.23 litersc.30 litersd.18liters

20 If n> 1 and x ? 0 , then (1+x)n - nx - 1 is divisible by :a.x3b.x2c.x4d. All of these

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