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SUBJECT CODE BOOKLET CODE

2012 (Il) rî" v ENGINEERING SCIENCES TEST BOOKLET Time : 3:00 Hours y Maximum'À/'Iarks.` 200

INSTRUCTIONS

1. This Test Booklet contains one hundred and fifteen (20 Part‘A’+25 Part ‘B’ +70 Part Multiple Choice Questions (MCQs). You are required to answer a maximum of 15, 20 and 2Q questions from part ‘A’ ‘B’ and ‘C’ respectively. If more than required number of questions are answered, only first 15, 20 and 20 questions in Parts ‘A’ ‘B’ and ‘C’ respectively, will be taken up for evaluation.

2. Answer sheet has been provided separately. Before you start filling up your particulars, please ensure that the booklet contains requisite number of pages and that these are not torn or_ mutilated. If it is so, you may request the Invigilator to change the booklet. Likewise, check the answer sheet also. Sheets for rough work have been appended to the test booklet.

3. _Write your Roll No., Name, Your address and Serial Number of this Test Booklet on the Answer sheet in the space provided on the side l of Answer sheet. Also put your signatures in the space identified.

4. You must darken the aggrogriate circles with a pencil related to Roll Number

Subject Code, Booklet Clode'andCentre Code on sheet. It is

. I .Y l . vllwvll :l l“ the sole resmnslblllg of the candidate to meticulously follow the Instructions

iven on the Answer failing which, the comgŕilteçgílállvnot be able t0

decipher thev correct details which may ultimereiy- result in loss= includin reiection of the OMR answer sheet. , s n . I . . A A

5. Each question in Pan ‘Á’ canties'Z marks, Part ‘B’ 3.5 marks and Part ‘C’ 5 marks

respectively. There will be negative marking 25% for each wrong answer. i . _ . _ . .__ Y

I v l I Y o V . .. Twill vlellô .

6. Below each question in Part ‘A’, ‘B’ and ‘C’ four alternatives or responses are given. Only one of these alternatives is the “conect” option to the question. You have to ñnd, for each question, the correct or the best answer.

7. Candidates found copying or resorting to any unfair means are liable to be

disgualifled from this and future ekaminations.

8. _ Candidate should not write anything anywhere except on answer sheet or

sheets for rough work.

9. After the test is over, MUST hand over the kTest Booklet and the answer sheet

(OMR) to the invigilator.

Use of scientiñc calculator without data connectivitv is nermitted.

I have verified all the information ñlled in by the candidate.

What is the number of distinct arràngements of the letters of the Word UGCCSIR so that U and I cannot come together?

l. 2520 2. 720 >3. 1520 4. 1800

Suppose the sum of the seven positive numbers is 21. What is the minimum possible value of the average of the sqaures of these numbers?

Which of the following is true?

Which ofthe following nufnbers is the largest? 234 243 324 342 423 _ 432

1

. 234

2.

342

3.

432

4.

423

The cube ABCDEFGH in the ñgure has each edge equal to a. The area of the triangle with vertices at A, C and F is

6.

If the sum ofthe next two terms of the éeries below is x, what is the value of logzx ?

1.128 2. 3. 256 4. s

A conical vessel with semi-vertical angle 30° and height 10.5 cm has a thin lid. A sphere kept inside it touches the lid. The radius of the sphere in cm is v '

l. 3.5 2. 5 3. 6.5 4. 7

Acircle of radius 5 units in the XY plane has its centre in the ñrst quadrant, touches the x-axis and has a chord of length 6 unitsy on the y-axis.` The coordinatés of its centre are

A wire of length is used to make a tetrahedron of each edge 1m, using only one strand of wire for eaeh'edge. The minimum number of times the wire has to be cut is

10. What does this diagram demonstrate? '

13.

Suppose there are socks of N different colors in a box.- If you take out one sock ata time, what is the maximum number of socks that you have to take out before a matching pair is found? Assume that N is an even number.

At what time after 4 O’ clock, the hour and the minute hands will lie opposite to each

other?

Which ofthe following curves just toúches the x axis?

14..

15.

16.

17.

18.

Suppose we make N identical smaller spheres from a big sphere. The total surface area of the smaller spheres is X times the total surface area of the big sphere, where X is

Four lines are drawn on a plane with no two parallel and no three concurrent. Lines

are drawn joining the points of intersection of the previous four lines. The number of '

new lines obtained this way is

. If AB is paralled to CD andÍ AO=ZOD, then the area of triangle OAB is bigger than the

area of trianglç OCD by a factor of

`1.2 2.3 3.4 4.8

Amar, Akbar and Anthony are three friends, one of Whom is a doctor, another is an engineer and the third is a professor. Amar is not an engineer. Akbar is the shortest. The tallest person is a doctor. The engineer’s height is the geometric mean of the heights of the other two. Then which of the following is true?

Amar is a doctor and he is the tallest Akbar is a professor and he is the tallestY Anthony is an engineer and he is shortest Anthony is a doctor and he is the tallest

19. If 100 cats catch 100 mice in 100 minutes, then how long will it take for 7 cats to catch

mice?

1. 100/ 7 minutes 2. 100 minutes

3. 49/100 /minutes 4. 7 minutes

20.

A semi-circular arch of radius R has a vertical pole put on the ground together with one of its legs. An ant on the top of the arch finds the angular height of the tip of the pole to be 45°. The height of the pole is

MATHEMATICS

21.

23.

24.

25.

The number of distinct real roots ofthe equation 13x13 - 1 = 0 is

(1)0 (2)1 (3) 2 (4) 1.3

¿_ The minimum value of the function f: 11R-»IR deñned by f (x) = ff, 2x etetzdt is

(l) an converges and bn diverges

(2)` Zoff-_.1 bn converges and 22:1 an diverges

(3) 222:1 an and bn converge

(4) 22121 an and 2:1():1 bn diverge

; Let S be the sphere x2 y2 l. The value~ the surface integral

26.

27.

28.

29.

30.

Let A be a 2 2 matrix. Suppose and are eigen Vectors cdì'responding to

the eigen values l and 2 of A respectiçely. Theh A is

(l) l l (2) 5 (3) 14 (4) 21

Let D = xl 0 or 1 fori = 1,2,3,4}. A vector is chosén at random from the set D. The probability that the product of the first and third coordinate is 0, is '

(l) l (2) È (3) i (4) â

The differential equation for which and x2 are linearly independent solutions is

ENGINEERING APTITUDE 1

Which of the following statements is true regarding the effect of earth on >’che capacitance of single-phase and three-phase transmission lines?

(l) Ideally the presence of the earth does not affect the capacitance.

(2) Ideally the earth increases the capacitance but for practical-‘values of heights of

n .I 1 . . .

conductors above the ground, this enhancement can be neglected.

. (3) f Ideally, the earth reduces` the capacitance but for practviîzevlvgfvah-xes of heights of

conductors above the ground, reduction can be lneglected.

_ _ „v_ __', _ v „n annun., »um »all UC lngwULCU.

4 Ideall ,the resence of earth enhances the ca acitance si niñcantl and for y P . P g y practical value of heights of conductors above the ground, this enhancement

eannot be neglected.

33.

34.

35.

36.

37.

Consider a uniformly charged sphere of radius, R. The charge per unit volume is p. The magnitude of the electric field at a distance of r from the centre ofthe spheŕe (r

R), is givven by: (so is the permittivity free space)

A long current carrying conductor having radius R, is carrying a uniformly distributed current through its cross-section. The magnetic field intensity inside the conductor is Hi while the magnetic ñeld intensity outside the conductor is H0. Which of the following statements is true?

(l) Both Hi and H0 are inversely proportional to the distance from the centre of the i

conductor. (2) Both Hi are proportional to the distance from the centre of the conductor (3) Hi is proportional to the distance from the centre of the conductor and H0 varies

i inversely with the distance from the centre ofthe conductor (4) Hi varies inversely with the distance from the centre of the conductor and H0 is

proportional to the distancç from the centre of the conductor.

The properties of Monoclinic crystal system are

lll all uuuuvnv.. Y in nickel crystalv appears at 62.13o when x-rays of Wave length of 0.1542 nm was used. What are the indices of the plane ifthe lattice parameter of nickel is 0.352 nm?

The number average molecular weight of polyvinyl chloride (PVC), when its degree ofapolymerization is 340, is . t (atomic weights of C, H and Cl are 12.01, 1.01 and 35.45 g/mol, respectively)

(1) 20563 (2) 21250 (3) 32959 (4) non@ Ofthese

For a flow lo be incompressible

(l) density must be constant.

¿23 veloci-ty field must be divergence free.

(3) vorticity vector must be a null vector.

l v " (4) streamline, streakline and pathline are identical.