Test Maths Paper-13
1. The test comprises of 30 questions.
There are 100 players numbered 1 to 100 and 100 baskets numbered 1 to 100. The first player puts one ball in every basket starting from the first basket (i.e. in baskets numbered 1, 2 , 3) . The second player puts 2 balls each in every second basket starting from the second ( i.e. in baskets numbered 2,4,6. . .) The third player puts three balls each in every third basket starting from the third , and so on till the hundredth player.
1. The test comprises of 30 questions.
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
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