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. The sequence of numbers t1 , t2 , t3 , t4 ... is defined by t1 = 2 , tn+1 = (tn - 1)/ (tn + 1 ) , for every positive integer n. what is the value of t999 ?
Direction for questions 2 to 4
During the batting analysis of Mr. Saddam , it was found that he faced 64 balls from Mr. Bush . he scored 32 singles, 3 two's , 7 three's , 7 boundaries & 2 msaaive sixes which went straight out of the stadium nad landed in the river Tigris.. the rest were dot balls. It was found that he ran for "3", five times on the ON side . His runs combining singles & doubles are equal on both sides He scored both sixes on one side of the ground. HE hit 1 boundry more on the OFF side. He scored 7 runs more on the OFF side. Based on the above data answer the following questions :
2. How many singles did he take on OFF side ?
d. cant be determined
3.How many over boundaries did he hit on the OFF side ?
d. cant be determined
4. What percentage of runs did he score less on the ON side than on the OFF side ?
Direction for questions 5 & 6
Mr. and Mrs. Smith celebrated the wedding of their youngest daughter in 1994. At that time the ages of all 3 of them could be expressed in the form p3q , where p and q are prime numbers. The ages of both Mr. and Mrs. Smith are between 45 and 80 and Mr. Smith is elder than Mrs. Smith.
5.What is the age of Mr. Smith?
d. either a or b
6. In which year was their daughter born?
7.In a four-digit number , the sum of the first 2 digits is equal to that of the last 2 digits. The sum of the first and last digits is equal to the third digit. Finally, the sum of the second and fourth digits is twice the sum of the other2 digits. What is the third digit of the number?
8. A rhombus ABCD has sides of length 10. A circle with center A touches the point C. Likewise, another circle with center B touches the point D. If the two circles touch each other at one point only, what is the area of the rhombus?
a. 65 sq.units
b. 75 sq.units
c. 80 sq.units
d. 90 sq.units
9. Anita had to do a multiplication. In stead of taking 35 as one of the multipliers, she took 53. As a result, the product went up by 540. What is the new product?
10. Ashish is given Rs. 158 in one-rupee denominations. He has been asked to allocate them into a number of bags such that any amount required between Rs. 1 and Rs. 158 can be given by handing out a certain number of bags without opening them. What is the minimum number of bags required ?
11. Lets express the date in the format DDMMYYYY, where DD represents the day of the month, MM - month and YYYY - the year. If the last possible date in the 20th century with all the eight digits (in the date as expressed in the above format) being odd is a Sunday, then what day of the week will the first date of the 21st century with all the eight digits even be?
12. In some code letters a, b, c, d and e represent numbers 2 , 4, 5 , 6 and 10. We just do not know which letter represents which number, consider the following relationships:
I. a + c= e
II. b - d = d
and III. e + a = b.
Which of the following is true?
a.b=4 , d =2
b. a=4 , e=6
c. b=6 , e=2
d. 1=4 , c=6
13. Ujakar and Keshab attempted to solve a quadratic equation. Ujakar made a mistake in writing down the constant term. He ended up with the roots ( 4, 3). Keshab made a mistake in writing down the coefficient of x. He got the roots as (3 ,2 ). What will be the exact roots of the original quadratic equation
b. (-3 , -4)
c. (4, 3)
d. (-4 , -3)
14. A leader leans against a vertical wall. The top of the ladder is 8m above the ground. When the bottom of the ladder is moved 2 m farther away from the wall, the top of the ladder rests against the foot of the wall. What is the length of the ladder ?
15.The number of digits in the smallest number considering of only ones and zeros and divisible by 225 is
16. If a, b , c and d are four positive real numbers such that abcd = 1 , what is the minimum value of ( 1 +a) (1 +b)(1 +c)(1 +d)
17. shopkeeper gives a discount equal to the profit he gets on an article. If he gets a profit equal to 25% of selling price, what is the percentage of discount he gives on the article?
Direction for questions 18 to 20
Let En= 2 - 4 + 6 - 8 +10 -------- (-1)n+1 (2n) and E1n = 4 +1 - 2 + 12 + 3 - 6 + 36 + 9 - 18 ---------- n terms
18.What is the value of E110 ?
19. If En = 452 then what is the value of n ?
20. If 2 E1n = 816 then what is the value of n?
21.How many right-angled triangles of integer sides are possible given that one of the sides is 15 cm long?
22.Let n be the number of different five-digit numbers, divisible by 4 with the digits 1, 2 , 3 , 4 , 5 and 6 . no digit being repeated in the numbers. What is the value of n?
23. At his usual rowing rate , Rahul can tarevel 12 miles downstream in a certain river in 6hr less than it takes him to travel the same distance upstaream. But if he colud his usual rowing rate for this 24 miles round trip, the downstreams 12 miles would then take only 1 hr less than the upstream 12 miles. What is the speed of the current in miles per hour ?
24.The ratio of the common difference of two series in arithmetic progression is 4 : 9 . If the ratio of their sum of the first 25 terms of the series 4 : 9. what is the ratio of their 75th terms of the series ?
25. At a certain fast food restaurant, Brian can buy 3 burgers , 7 shakes and one order of fries for Rs, 120 exactly . At the same place it would cost Rs. 164.5 for 4 burgers, 10 shakes, and one order of fries. How much would it cost for an ordinary meal of one burger, one shake, and one order of fries
a. Rs. 31
b. Rs. 41
c. Rs. 21
d. Cannot be determined
26. What is the remainder when 25 x (1331)2196 is divisible by 13?
Direction for question 27 & 28
A mason employed a certain number of workers to finish constructing a wall in a certain scheduled time. Some time later he realized that the work would get delayed a by a fourth of the scheduled time, so he immediately increases the number of workers by a third and thus manages to finish the wall on schedule. Some time the work force was increased, all of the newly added workers left due to an issue regarding wages while at the same time the remaining workers reduced their efficiency by half as a mark of protest against low wages. If the work finally got completed with a delay of 50% of the scheduled time then
27.What fraction of the total work was still incomplete by the end of the scheduled time?
28. Find the percent of the work that was finished by the time the work force was increased??
Direction for question 29 & 30
Several runners, numbered 1, 2, 3.. And so on, start simultaneously at the same point on a circular track and run continuously, in the same direction, around the track. They run such that the speed of the runner numbered n (n>1) is n times that of the runner numbered
29. If there are exactly six runners, then at how many distinct points on the track is the runner numbered 1 overtaken by any of the other five runners?
30. If there are exactly for runners, then at how many distinct points on the track do two or more runners meet?