2016 Admn Test Aceg

Vidyamandir/ADMTEST/ACEG/JEE-2016 1

19/01/2014 ADMISSION TEST IITJEE - 2016

11.00 A.M. - 02.00 P.M. PAPER CODE - A C E G M.M. : 200

Read the following Instructions very carefully before you proceed.

The paper contains 20 pages and a total of 50 Objective Type Questions divided into three sections: Section - I, Section - II and Section - III.

Section - I, Section - II contain 20 questions each and Section - III contains 10 questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE CHOICE is correct.

For each question in Section - I, you will be given 3 marks if you have darkened only the bubble corresponding to the correct answer and zero marks if no bubble is darkened. In all other cases, minus one (–1) marks (NEGATIVE MARKING) will be given.

For each question in Section - II, you will be given 4 marks if you have darkened only the bubble corresponding to the correct answer and zero marks if no bubble is darkened. In all other cases, minus one (–1) marks (NEGATIVE MARKING) will be given.

For each question in Section - III, you will be given 6 marks if you have darkened only the bubble corresponding to the correct answer and zero marks if no bubble is darkened. In all other cases, minus two (–2) marks (NEGATIVE MARKING) will be given.

For answering a question, an ANSWER SHEET (OMR SHEET) is provided separately. Please fill your Name, Roll Number, Seat ID, Date of Birth and the PAPER CODE properly in the space provided in the ANSWER SHEET.

IT IS YOUR OWN RESPONSIBILITY TO FILL THE OMR SHEET CORRECTLY. A blank space has been provided on each page for rough work. You will not be provided with any

supplement or rough sheet. However some blank pages for rough work are given at the end of this paper. The use of log tables, calculator and any other electronic device is strictly prohibited.

There are no errors in the paper. Please do not disturb the invigilator or any other student for any corrections/suggestions in the paper. Violating the examination room discipline will immediately lead to the cancellation of your paper and no excuses will be entertained.

FILL THE FOLLOWING INFORMATION PROPERLY BEFORE YOU PROCEED.

ROLL NUMBER SEAT ID

NAME DATE OF BIRTH

Invigilator’s Signature ROOM NO.

Vidyamandir Classes : Innovating for your success

2 JEE-2016/ACEG/ADMTEST/Vidyamandir

SUGGESTIONS: Before starting the paper, spend 2-3 minutes to check whether all the pages are

in order and report any issues to the invigilator immediately. Try to attempt the Sections in their respective order. Do not get stuck on a particular question for more than 6-8 minutes. Move on to

a new question as there are 50 questions to solve.

SECTION - I

1. If p2 – 13p + 40 = q, and p is a positive integer between 1 and 10, inclusive, then the probability that q < 0 is:

(A) (B) (C) (D)

2. If are the roots of , then :

(A) (B) (C) (D)

3. The value of is :

(A) (B) 3 (C) (D)

SPACE FOR ROUGH WORK



4. If , then the ratio of x to y is :

(A) (B) 2 (C) 3 (D) 9

5. If , then is equal to :

(A) 0 (B) 2ab (C) (D)

6. If where a and b are constants, and , then the value of #7# is :

(A) 5 (B) 0 (C) (D)




7. A spherical ball of diameter 9 cm fits exactly into a cubical box. The approximate volume of the unoccupied space is (in cm3) :(A) 342 (B) 348 (C) 376 (D) 334

8. If and abc = 16, then the value of is :

(A) only 1 (B) only (C) only (D) 1 or

9. The arithmetic mean of two numbers is and one of them is . The square root of the other number is :

(A) (B) (C) (D)




10. The value of is :

(A) (B) (C) 1 (D) 2

11. Area of rectangular region formed by is (in square units) : (A) 9 (B) 12 (C) 15 (D) 20

12. If is divisible by , then it is also divisible by :

(A) (B) (C) (D)




13. If , then the value of x is :

(A) 1 (B) 2 (C) (D)

14. The value that must be subtracted from p and added to q so that the ratio of the resultant becomes 1 : 3 is :

(A) (B) (C) (D)

15. In the adjacent figure, if AC is the diameter of the circle where and O is the centre of the circle, then is :

(A)(B)(C)(D)




Paragraph for Questions 16 - 17

means Z is multiplied by the sum of X and Y.

means product of X and Y is divided by Z.

means X is subtracted from the sum of Y and Z.

16. If 8 @ 4% 16 = a, then the value of is :(A) 150 (B) 200 (C) 190 (D) 110

17. If , then the value of 60 @ 2% x is :(A) 7 (B) 10 (C) 5 (D) 15

18. A ladder is lying against a wall which is 5 meters high. If the ladder slips 2 meters away from the wall, the top of the ladder touches the foot of the wall. The length of the ladder is (in meters) : (A) 5 (B) 5.25 (C) 7.25 (D) 4




19. The arithmetic mean of the series is x. The arithmetic mean of the series

is y. The arithmetic mean of the series is :

(A) (B) (C) (D)

20. The probability that a number selected from (–10, –6, –5, –4, –2.5, –1, 0, 2.5, 4, 6, 7, 10) can fulfill (x + 5) (x + 10) (2x – 5) = 0 is :(A) 1/12 (B) 1/6 (C) 1/4 (D) 1/3




SECTION - II

21. While reading a certain newspaper, you notice that four pages of one section are missing. One of the missing pages is 13. The last page number printed in the newspaper is 40. The three missing pages in the section are : (Note: Any section of a typical newspaper has 4 pages)(A) 15, 29, 30 (B) 14, 26, 27 (C) 14, 27, 28 (D) 16, 29, 30

22. Raman receives an increment in his salary. His salary presently forms 30% of the total income of his family. Before the increment his salary used to form 20% of the total income of his family. Then, the percentage increase in Raman’s salary to his initial family income is :

(A) % (B) % (C) 10 % (D) 8 %

23. In the adjacent figure, circle with centre O has two equal chords PQ and QR. OA and OB bisect the chords PQ and QR respectively. If , then is :(A) (B)(C) (D)




24. If and , then the simplified form of is :

(A) (B) 2 (C) (D)

25. In the adjacent figure, AD is median from A to BC, AE is median from A to BD, AF is median from A to DC. DG is median from D to AB and DH is median from D to AC. The area of quadrilateral AGDH (in cm2) if

the area of :

(A) 8 (B) 16(C) 24 (D) 32

26. If where , then the value of is:

(A) (B) (C) (D)




27. An object attached to a parachute is dropped from a plane flying at a height of 2075 meters. The distance the object falls through in t seconds is 3t2 meters. The distance it falls through in t seconds, with parachute

open is meters. The height at which the parachute should be opened so that the object reaches

the ground in exactly 50 seconds is (in meters) :(A) 625 (B) 750 (C) 2000 (D) 1200

28. In the adjacent figure, PQR is an equilateral triangle and ABCD is a rectangle. If length of the base of triangle is y units and PB :PR = x : 1, then area of rectangle ABCD is (in square units):

(A) (B)

(C) (D)

29. If k is a positive integer that satisfies then the sum of first k natural

numbers is :(A) 28 (B) 21 (C) 55 (D) 45




30. In the adjacent figure, circle has center O, diameter AB and a radius of 5. Line CD is parallel to the diameter. The perimeter of the shaded region is :

(A) (B)

(C) (D)

31. At the centroid G of an equilateral triangular field ABC, a pole GP is situated in such a way that the side AB is subtending an angle of at P. If the side of the triangle ABC is 16 meters, then the height of the pole (in meters) is :

(A) (B) (C) (D)

32. A trader mixes two varieties of rice, the cost prices of which differ by Rs. 7 per kg., in a certain ratio and the effective cost price of the resultant mixture is Rs. 11 per kg. If he mixes the varieties in the inverse ratio, the effective cost price will be Rs. 14 per kg. The cost price (in Rs. per kg) of the less expensive variety of rice is : (A) 16 (B) 15 (C) 14 (D) 9




33. If , then the possible value of x is :

(A) 2 (B) 1 (C) 4 (D) 3

Paragraph for Questions 34 - 35

ABC is an equilateral triangle. Three circles of equal radius with centres

D, E, F are drawn inside the triangle such that they touch each other

externally as shown in the figure. Circle with centre C1 touches 3 circles

externally. Circle with centre C3 touches circles with centres E and F

externally and line BC is tangent to it whereas circle with centre C2

touches the lines AB, BC and the circle with centre E externally.

34. If the radii of the circles with centres D, E and F are all equal to r, then the area of circle with centre C1 in terms of r is:

(A) (B) (C) (D)

35. The ratio of areas of circles with centres C2 and C3 is :(A) 16 : 9 (B) 9 : 4 (C) 25 : 16 (D) 49 : 16




36. Mr. Singh is paid according to the number of hours he puts in per month. The rate of pay was increased by per hour, but the number of hours put in by him went down by . The percentage increase

(or decrease) in his income is :(A) decrease (B) increase (C) decrease (D) increase

37. If a : b = 3 : 4 and c : d = 2 : 3, then the value of is :

(A) (B) (C) (D)

38. A test had 200 questions. Each correct answer carried 2 marks, unanswered questions carried no marks but each wrong answer carried mark. Arun attempted all the questions in the test and scored 360 marks. The marks that he would have got in the paper if for each correct answer he got only 1/2 mark and for each wrong answer he lost 2 marks are :(A) 80 (B) 60 (C) 40 (D) 100




Paragraph for Questions 39 – 40

The following line-graph shows the monthly expenditures of different persons A, B, C, D, E and F and another graph (pie chart) shows the breakup of expenditure of person D on different items. Study these graphs carefully and answer the questions given below it.

39. If the expenditure of D on food was 20% more than the average expenditure of all the six persons on food, then the average monthly expenditure on food for the given persons is (in Rs.) :(A) 5,133 (B) 5,000 (C) 5,250 (D) 5,400

40. The total expenditure of D on Rent, Education and Telephone and Electricity bills is (in Rs.) :(A) 12,300 (B) 15,600 (C) 16,500 (D) 18,200




SECTION - III

41. In the diagram, points A, B, and C are on the diameter of the circle with centre B. Additionally, all arcs pictured are semicircles. Suppose angle YXA = 105 degrees. The ratio of the area of the shaded region above the line YB to the area of the shaded region below the line YB is (Note: Diagram is not drawn to scale and angles drawn are not accurate but arcs AB and BC are semicircles with their respective centres) :(A) 3/4 (B) 5/6 (C) 1 (D) 7/5

42. The telephone bill consists of a fixed monthly rent and a variable part that varies with the number of units of calls made per month. The monthly rents charged for a telephone connection in Mumbai and Delhi are in the ratio of 5 : 3. The bill amounts corresponding to 100 calls made from a phone in Delhi and 300 calls made from a phone in Mumbai are respectively Rs.500 and Rs.1100. The difference in the fixed monthly rent of a telephone connection in Mumbai and one in Delhi, if call rate per unit is same in both cities is (in Rs.) :(A) 200 (B) 100 (C) 500 (D) 300




43. Rohan and Sohan play a game in which Rohan has to give Sohan as many coins as Sohan has when hours and minutes hand in a clock are apart. At 3’O clock and at 9’O clock, Sohan has to give Rohan half the coins that Sohan has at that point of time. They start playing at 12’O clock and decide to play for 12 hours. Initially, if Sohan has x coins, then the number of coins he will have after 12 hours is :(A) (B) (C) (D)

44. The number of integral values of a for which the quadratic equation (x + a) (x + 1991) + 1 = 0 has integral roots are :(A) 3 (B) 0 (C) 1 (D) 2




45. Two buses go down a hill, normally at the same speed. One bus stops at a certain point on the way down. The second bus goes completely down the hill. On the uphill trip, the speeds of both the buses are less than the corresponding speeds in the down the hill trip. But, as the number of passengers in the first bus is more than that in the second bus, the speed of first bus on the uphill trip reduces by 75% of its normal speed and that of the second bus reduces to 2/3rd of its normal speed. Both return to the starting point, taking the same time for the round trip. The percentage of the distance the second bus travelled more than the first bus is :(A) 40% (B) 100% (C) 50% (D) 25%

46. Some chocolates are divided among four boys A, B, C and D. The ratio of number of chocolates given to B to the total number of chocolates given to A and D is 1 : 2. The ratio of the number of chocolates given to C to that given to others is 2 : 5. D gets 2 chocolates more than B. A gets half the number of chocolates than that C gets in the process. The total number of chocolates distributed are :(A) 21 (B) 18 (C) 19 (D) 24




47. A, B, C participate in a bike race where they have to pass through three different terrains – Highway, Rocky and Sandy – in that order. They can drive at their normal speeds on the Highway. A’s speed decreases to half on the Rocky terrain and 1/4th on the Sandy terrain. B’s speed becomes 1/4th on Rocky terrain and 1/8th on Sandy terrain. C’s speed reduces to 1/3rd on Rocky terrain and 1/4th on Sandy terrain. The length of Rocky terrain is twice the length of Highway and the length of the Sandy terrain is thrice the length of the Highway. Speeds of B and C on the Highway are 60% and 20% more than the speed of A on the Highway respectively. The first person to complete the race is : (A) A (B) B (C) C (D) Both A and C

48. If and , the number of possible (a, b) pairs is :

(A) 1 (B) 2 (C) 3 (D) 4




49. On his Birthday, Arun went to the bakery to buy donuts for his office mates. He chose a quantity of similar donuts, for which he was charged a total of Rs.150. As the donuts were being boxed, Arun noticed that a few of them were slightly ragged-looking so he complained to the clerk. The clerk immediately apologized and then gave Arun 3 extra donuts for free to make up for the damaged goods. As Arun left the shop, he realized that due to the addition of the 3 free donuts, the effective price of the donuts was reduced by Rs.20 per dozen. The number of donuts that Arun received in the end are :(A) 18 (B) 21 (C) 24 (D) 28

50. If then the value of is :

(A) 1 (B) (C) 3 (D)





End of 2Year Admission Test/JEE-2016


2016 Admn Test Aceg

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