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.
Direction for questions 1 to 3.
Five different currencies are considered, and their exchange rates on a particular day are as follows: The numbers in cells in every horizontal row represent the number of units of currency of the column in consideration that are the equivalent of 1 unit of currency in the row in consideration. For example, in row 1, column 2, 1.55 denotes that 1.55 units of currency B are the equivalent of 1 unit of Currency A
1. A1 = ?
2. A2 = ? is :
d. can’t be determined
3.A12 = ?
4. The remainder when 12345678 is divided by 10 is
5.Consider the five points comprising the vertices of a square and the intersection point of its diagonals. How many triangles can be formed using these points?
6. If m and n are integers and 2m – n = 3, then m – 2n must be
a. equal to -3
b. equal to 0
c. a multiple of 3
d. an odd integer
7.A set of consecutive positive integers beginning with a is written on the blackboard. A student came along and erased one number. The average of the remaining numbers is 35 7/17 . what was the number erased ?
Direction for questions 8 to 10.
A, B, C and D collected one – rupee coins following the given pattern
Together they collected 100 coins.
Each of them collected even number of coins.
Each one of them collected at least 100 coins.
No two of them collected the same number of coins.
8.The maximum number of coins by any one of them cannot exceed
9. If A collected 54 coins , then the difference in the number of coins between the one who collected maximum number of coins and the one who collected the second highest number of coins must be at least
10. If A collected 54 coins and B collected two more coins than twice the number of coins collected by C, then the number of coins collected by B could be
11. Find the sum to 20 terms of the series 1 x 22 + 3 x 42 + 5 x 62 . . .
a. 12, 832
12. The minimum value of the expression 4x2 + 2y2 + 6x + 5y + 5 , given x , y ? R.
a. – 33/8
13. For a Fibonacci sequence , from the third term onwards, each term in the sequence is the sum of the previous two terms in that sequence. If the difference in sequence in squares of 7th and 6th terms of this sequence is 517, what is the 10th term of this sequence?
d. Cannot be determined
14. Fresh grapes contain 90% water by weight while dried grapes contain 20% water by weight. What is the weight of dry grapes available from 20 kg of fresh grapes?
a. 2 kg
b. 2.4 kg
c. 2.5 kg
15.A yearly payment to the servant is Rs. 90 plus one turban. The servant leaves the job after 9 months and recives Rs. 65 and a turban. Then find the price of the turban.
d. cannot be determined
16. Four identical coins are placed in a square. For each coin the ratio of area to circumference is same as the ratio of circumference to area. Then find the area of the square that is not covered by the coins.
a. 16(p -1 )
b. 16(8 - p)
c. 16(4 - p)
d. 16(4 - p/2)
17. Let f be a function satisfying f(xy) = f(x)/y for all positive real numbers x and y . If f(30) = 20 , then the value of f(40) is
Direction for questions 18 & 19.
Production pattern for number of units (in cubic feet) per day
|No. of Units
For a truck that can carry 2,000 cubic ft, hiring cost per day is Rs. 1,000. Storing cost per cubic feet is Rs. 5 per day.
18.If all the units should be sent to the market, then on ehich days should the trucks be hired to minimize the cost?
a. 2nd , 4th, 6th, 7th
c. 2nd , 4th, 5th, 7th
19. If the storage cost is reduced to Re. 0.80 per cubic feet per day, then on which day(s), should truck be hired?
c. 4th and 7th
20. Ravi invested a certain amount in a 15 years fixed deposit scheme. An interest of Rs. 1,250 was accrued for the 5th year whereas Rs. 2,450 was accrued for the 11th year. If the interest is compounded annually , what is the maturity value of Rs. 1, 00,000 invested today, at the end of the 15 years of the fixed deposit scheme ?
a. Rs. 5,37,824
b. Rs. 5,87,624
21.Richard wrote all the possible two-digit numbers such that whenever one of the two digits is prime, the other is even ,and whenever one of the two digits is even, the other is prime. How many two-digit numbers did he write in all?
22.If there are 10 positive real numbers n1 < n2 < n3 . . . . < n10. how many triplets of these numbers (n1 ,n2 ,n3 ) , ( n2, n3, n4). . . can be generated such that in each triplet the first number is always less than the second number , and the second number is always less than the third number ?
23. A rectangular pool of 20m wide and 60m long is surrounded by a walkway of uniform width. If the total area of the walkway is 516m2, how wide, in meters, is the walkway?
24.AA unit circle is divided into 10 sectors such that the area of the second sector is twice that of the first sector, the area of the third sector is twice that of the second and so on. Find in radians, the angle made by the first sector.
25.TOne bacterium splits into eight bacteria of the next generation. But due to environmental condition only 50% survives and remaining 50% dies after producing next generation. If the seventh generation number is 4,096 million , what is the number in first generation ?
a. 1 million
b. 2 million
c. 4 million
d. 8 million
Direction for questions 26 & 27
A company purchases components A and B from Germany and USA respectively. A and B form 30% and 50% of the total production cost. Current gain is 20%. Due to change in the international scenario, cost of the German mark increased by 30% and that of USA dollar increased by 22%. Due to market conditions, the selling price cannot be increased beyond 10%.
26.What is the maximum current gain possible ?
27. If the USA dollar becomes cheap by 12% over its original cost and the cost of German mark increased by 20% , what will be the gain ?( the selling price is not altered ?)
Direction for questions 28 & 29
Consider the following 2 equations for answering the below questions
(k + 1)X + 8Y = 4K
kX + (k+3)Y = 3K -1
28. For what value of K will these equations have no solution ?
29. For what value of K will these equations have more than one solution?
30. Four positive integers are such that any two of thefour have the same common factors and no two have any other factor in common.If the LCM ( Least Common Multiple ) of two of the four numbers is 2585 and theLCM of the other two numbers is 4277 , find the highest common factor of thefour numbers?