1. The test comprises of 30 questions.
2. The total time allocated is 45 minutes.
3. There is only one correct answer to each question.
4. All questions carry four marks each.
5. Each wrong answer will attract a penalty of one mark.
6. Do not use calculators.
7. Directions for answering the questions are given before each group of questions to which they apply. Read these directions carefully.
8. For marking the answers, click on the oval corresponding to the answer selected by you.
1. What is the value of n for which (n17 - n)(42n - 1) is divisible by 289?
2. 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?
b.1 - (1/3)5
c. 1- (1/6)5
3. if f(x)= (x2 + 12x + 12)/(x2 + 3x + 3) , then find max f(x)
d.cannot be determined
4.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 ?
Directions 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 is
6. What is the average weight of A , B , C, D if the weight of A is 4 kg?
7. 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 empty
b.1 full , 2 half , o empty
c.1 full 1 half 1 empty
d.there can be more than one way
8.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)
9. 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?
10. If n> 1 and x ≠ 0 , then (1+x)n - nx - 1 is divisible by :
d. All of these
11. How many factors of 1296 will have total number of factors exactly equal to 3?
12. If (52a)b = (169)11 and a and b differ by two , find (a + b).
13. Find the number of integral solution to |x| + |y| + |z| = 15.
14. A circle is inscribed in a right angled triangle . The point of tangency with the circle divides one of the sides into two segments 6 cm and 10cm in length . The area of the triangle is ?(in cm2)
15.Two friends A and B leave at 8 A.M everyday to meet each other at point P after two hours. On one day A walks at 5/6 th of the usual speed while B starts one hour late , so he increases his speed by 25% . Now A takes 1/2 hour more than usual to meet B and they meet half kilometer away from point P. Find out the speeds of A and B and total distance traveled by them. ?
a.5 kmph 5 kmph 20km
b.6kmph 4kmph 22km
c.6kmph 4kmph 20km
d.4kmph 6kmph 20km
16. 11 22 36 412 520 . . . . . . 25 terms . Find the highest power of 75 that can divide the given series?
d.cant be determined
17. A man had three daughters , who celebrated their birthday on the same day , but were born in 1955 , 1978 and 1979 respectively . On one such birthday , if the product of their ages was divided by their respective ages in turn , the sum of quotients , would have been 74 . The age of the oldest daughter is
18. Find the remainder when (((1112)13)14) is divided by 9 ?
19. There are 3 clubs X , Y and Z in a town with 40 , 50 and 60 members respectively . While 10 people are members of all the 3 clubs , 70 are members in only one club. How many belong to exactly two clubs?
20.In a six node network , two nodes are connected to all the other nodes. Of the remaining four , each is connected to four other nodes . What is the total number of links in the network ?
d. none of the above
21. If s(n) is the set of all factors of n , then what is the probability that a randomly chosen element of s(1050) is a multiple of 5 ?
22.In a circular pond, a fish starts from a point on the edge , swims 600 feet due east to reach another point on the edge , turns south and swims 800 feet to reaxh yet another point on the edge. The diameter of the pond is
23. Let A , B and C be distinct positive integers satisfying A < B < C and A+B+C=k . What is the smallest value of k that does not determine A , B , C uniquely ?
24. A box contains 6 black and 5 white balls. Each ball is of a different size. The probability that the black ball selected is the smallest black ball , is
25.If log 7 log5 √(x + 5) + √x ) = 0 , find the value of x .
Directions for Questions 26 to 28.
Two people P and Q moved between two points A and B. Q started to move from point B towards point A exactly an hour after P started from A in the opposite direction. Q's speed was twice that of P. when P had covered oneâ€“sixth of the distance between the points A and B. Q had also covered the same distance.
26. The point where P and Q would meet is
a. closer to A
b. Exactly between A and B
c. Close to B
d. P and Q will not meet at all
27. How many hours would P take to reach B?
28.How many more hours would P (compared to Q) take to complete his journey?
29. If the HM between two positive numbers is to their GM as 12:13 , then the numbers could be in the ratio
30. Let Un+1 =2Un + 1 ; (n =0 ,1 ,2 . . . .) and U0 = 0 . Then U10 is nearest to