Elite2011 Pet1 Qns p1

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BRILLIANTS

MOCK ALL-INDIA TESTS (B.MAT)

NATIONAL SIT-DOWN

PROGRESSIVE EVALUATION TEST 1FOR STUDENTS OF

OUR TWO-YEAR ELITE POSTAL COURSE

TOWARDS

IIT-JOINT ENTRANCE EXAMINATION, 2011

QUESTION PAPER CODE

Time: 3 Hours Maximum Marks: 240

Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.

INSTRUCTIONS:

Name: . Enrollment No.:

Brilliant Tutorials Pvt. Ltd. EELP/I PET/CMP/P(I)- 1

1

A. General

1. This booklet is your Question Paper containing 60 questions. The booklet has 28 pages.

2. This question paper CODE is printed on the right hand top corner of this sheet and on the back page

(page no. 28) of this booklet.3. This question paper contains 7 blank pages for your rough work. No additional sheets will be provided

for rough work.

4. Blank papers, clipboards, log tables, slide rules, calculators, cellular phones, pagers, and electronicgadgets in any form are not allowed to be carried inside the examination hall.

5. Fill in the boxes provided below on this page and also write your Name and Enrollment No. in thespace provided on the back page (page no. 28) of this booklet.

6. The answer sheet, a machine-readable Objective Response Sheet (ORS), is provided separately.

7. DO NOT TAMPER WITH/MUTILATE THE ORS OR THE BOOKLET.

8. Do not break the seals of the question-paper booklet before being instructed to do so by the invigilators.

B. Filling the ORS

9. On the lower part of the ORS, write in ink, your name in box L1, your Enrollment No. in box L2 and

Name of the Centre in box L3. Do not write these anywhere else.

10. The ORS has a CODE printed on its lower and upper parts.11. Make sure the CODE on the ORS is the same as that on this booklet and put your signature in ink in

box L4 on the ORS affirming that you have verified this.

12. IF THE CODES DO NOT MATCH, ASK FOR A CHANGE OF THE BOOKLET

C. Question paper format: Read the instructions printed on the back page (page no. 28) of this booklet.

D. Marking scheme: Read the instructions on the back page (page no. 28) of this booklet.

SEAL

SEAL

DON

OTBREAKTHESEALSONTHISBOOKLET,AWAITINSTRUCTIONSFROMT

HEINVIGILATOR

ELITE 2011

I PET/CMP/P(I)/QNS

02.08.2009

CHEMISTRY MATHEMATICS PHYSICS

PAPER I

I have read all the instructionsand shall abide by them.

...............................................

Signature of the Candidate

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PART A : CHEMISTRY

SECTION I

Single Correct Choice Type

This section contains 8 multiple choice questions. Each question has 4 choices (A), (B),(C) and (D) for its answer, out of which ONLY ONE is correct.

1. The nucleus of an atom can be assumed to be spherical. The radius of the nucleus

of mass number A is given by 1.25 1013

A1/3

cm. Radius of atom is 1 . If the mass number is 64 then the fraction of the atomic volume that is occupied bythe nucleus is

(A) 1.0 103

(B) 5.0 105

(C) 2.5 102

(D) 1.25 1013

2. Wave number of first line in Lyman series of Hydrogen spectrum (RH

= 109678 cm1

)

is

(A) 82259 cm1

(B) 82200 cm1

(C) 97492 cm1

(D) 102823 cm1

3. In OF2, oxygen has the hybridisation of

(A) sp (B) sp2 (C) sp

3 (D) sp

3d

4. The d-orbital involved in the sp3

d hybridisation is

(A)dx

2 y

2 (B) dxy (C)dz2 (D) dxz

5. Two glass bulbs A and B are connected by a very small tube having a stop cock.

Bulb A has a volume of 100 cm3

and contained the gas while the bulb B wasempty. On opening the stop-cock, the pressure fell down to 40%. The volume ofthe bulb B will be

(A) 250 cm3 (B) 40 cm

3 (C) 140 cm

3 (D) 150 cm

3


SPACE FOR ROUGH WORK

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6.At certain temperature, the r.m.s velocity for CH4 gas molecules is 100 m/sec.

The r.m.s velocity for SO2 gas molecules at the same temperature will be

(A) 400 m/sec (B) 200 m/sec (C) 25 m/sec (D) 50 m/sec

7.A metal oxide has the formula Z2O3. It can be reduced by hydrogen to give free

metal and water. 0.1596 g of the metal oxide required 6 mg of hydrogen forcomplete reduction. The atomic weight of metal is

(A) 27.9 (B) 159.6 (C) 79.8 (D) 55.8

8.A solution containing Na2CO

3and NaOH requires 300 mL of 0.1 N HCl for

neutralisation using phenolphthalein as indicator. Methyl orange is then addedto the above titrated solution, when a further 25 mL of 0.2 N HCl is required.

The amount of NaOH present in the solution is [NaOH = 40, Na2CO3 = 106]

(A) 0.8 g (B) 1.0 g (C) 1.5 g (D) 2.0 g

SECTION II

Multiple Correct Choice Type

This section contains 4 multiple choice questions. Each question has 4 choices (A), (B),(C) and (D) for its answer, out of which ONE OR MORE is/are correct.

9. Which of the following give a straight line plot for ideal gas?(A) P versus V at constant Temperature

(B) V versus T at constant Pressure

(C) P versus T at constant Volume

(D) P versus1

Vat constant Temperature



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10. Which of the following have sp3

hybridisation for the central atom?

(A) PH3 (B)SO32 (C)SO

4

2 (D) XeF4

11. Isotones of32

76Ge are

(A)32

77Ge (B)

33

77As (C)

34

77Se (D)

34

78Se

12. Which of the following have the same mass?

(A) 0.1 mole of O2 gas

(B) 0.1 mole of SO2 gas

(C) 6.02 1022

molecules of SO2

gas

(D) 1.204 1023 molecules of O2 gas

SECTION III

Comprehension Type

This section contains 2 groups of questions. Each group has 3 multiple choicequestions based on a paragraph. Each question has 4 choices (A), (B), (C) and (D), forits answer, out of which ONLY ONE is correct.

Paragraph for Question Nos. 13 to 15

Diffusion refers to the spreading of a gas throughout the space or into a second gasor substance. Effusion refers to the escape of a gas through an orifice. Grahams law ofdiffusion states that under similar conditions of temperature and pressure, the ratesof diffusion of different gases are inversely proportional to square root of theirdensities.



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13. The ratio of the rate of diffusion of a given gas to that of helium is 1 : 4. Themolecular weight of the gas is

(A) 20 (B) 64 (C) 8 (D) 16

14. The time taken for a certain volume of gas x to diffuse through a small hole is 2minutes. It takes 5.65 minutes for oxygen to diffuse under similar conditions.The molecular weight of x is

(A) 64 (B) 32 (C) 8 (D) 4

15. 50 mL of H2 diffuses out through a small hole from a vessel in 20 minutes. The

time needed for 40 mL of oxygen to diffuse out under similar conditions is

(A) 12 minutes (B) 64 minutes

(C) 48 minutes (D) 36 minutes


A chemical bond is a force which holds the atoms of a molecule together. Atomsform bonds since it leads to decrease in energy. The important types of chemical bondsare ionic, covalent, coordinate and metallic. In addition, attractive interactionsbetween atoms of different molecules develop weak bonds between the molecules suchas Hydrogen bond and van der Waals interactions. The covalent bond is not always100% covalent. Polarity is developed in the bond due to the electronegativitydifference between the bonded atoms.

16. The correct order of the strengths of the bonds is

(A) H ... F > H .... O > H .... N

(B) H ... O > H ... N > H .... F

(C) H .... F > H .... N > H .... O

(D) H .... O > H .... F > H .... N



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17. Out of the following arrangements, the incorrect order of decreasing boilingpoints is

(A) HF > HI > HBr > HCl (B) H2O > H

2Te > H

2Se > H

2S

(C) CH4 > GeH4 > SiH4 (D) Br2 > Cl2 > F2

18. The polarity of a covalent bond in the molecule develops dipole moment. Dipolemoment is a vector quantity. H2O has a net dipole moment while BeF2 has zero

dipole moment, because

(A) H2O molecule is linear while BeF2 is bent.

(B) BeF2 molecule is linear but H2O is bent.

(C) Fluorine is more electronegative than oxygen

(D) Be has more electronegativity than oxygen

SECTION IV

Matrix-Match Type

This section contains 2 questions. Each question contains statements given in twocolumns, which have to be matched. The statements in Column I are labelled A, B, Cand D, while the statements in Column II are labelled p, q, r, s and t. Any givenstatement in Column I can have correct matching with ONE OR MOREstatement(s) in Column II. The appropriate bubbles corresponding to the answers to

these questions have to be darkened as illustrated in the following example:If the correct matches are A p, s and t; B q and r; C p and q; and D s and t; thenthe correct darkening of bubbles will look like the following.



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PART B : MATHEMATICS

SECTION I

Single Correct Choice TypeThis section contains 8 multiple choice questions. Each question has 4 choices (A), (B),(C) and (D) for its answer, out of which ONLY ONE is correct.

21. If a, b, c are in G.P., and if log2a

3b, log

3b

5c, log

5c

2aare in A.P., then a, b, c are the

lengths of the sides of a triangle which is

(A) right angled (B) acute angled

(C) equilateral (D) obtuse angled

22. If x, y, z are different positive numbers in H.P., then the minimum value ofx 4y

2x y

z 4y

2z yexceeds

(A) 11 (B) 12 (C) 13 (D) 10

23. Sum to infinity of the series1

13

2

135

3

1357

4

13579+ .... is

(A) 32(B) 12

(C) 1 (D) None of these

24. If1, 2, 3, 4 are the smallest positive angles in ascending order of magnitude

which have their sines equal to the positive number , then the value of

4 sin

1

2+ 3 sin

2

2+ 2 sin

3

2+ sin

4

2is equal to

(A)2 (B)2 1 (C)2 1 (D) None of these



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25. The value of k for which the equation

2 + kx2

+ sin1

(x2 2x + 2) + cos

1(x

2 2x + 2) = 0 has a real solution is

(A)

2

2

(B)

2

2

(C)

2 2 (D)

2 2

26. The sum of the infinite series sin1

1

2 sin

1 2 1

6 sin

1 3 2

12+ .... is

(A)

4

(B)

3

(C)

2

(D)

27. In ABC, D and E are the points of trisection of BC and , , are the opposite

angles, thensin sin

sin sin is

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

28. The general solution of cosx

4 2 sin x sin x 1 sin x

4 2 cos x cos x = 0 is

(A) 8n + 2 (B) 2n + 2

(C) 4n + 2, where n N (D) None of these

SECTION II





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29. The value ofa for which the equation sin x + cos (a + x) + cos (a x) = 2 has realsolution satisfy

(A) sin2

a 1

2

(B) sin2

a 1

4

(C) cos2

a 1

4

(D) cos2

a 3

430. In ABC if the median through A is inclined at an angle 45 with the side BC

and C = 30, then B is

(A) 75 (B) 15 (C) 105 (D) 135

31. If x y =1

3and sin

2x sin

2y = 3

2then the ordered pair (x, y) is

(A) 512 , 112(B) 1712, 1312

(C) 712 , 1112

(D) 1112 , 712

32. In a G.P., the product of the first 4 terms is 9 and the 2nd term is reciprocal ofthe 4th term, then the sum to infinity of the G.P. is

(A)27

2(B)

27

2(C)

1

8(D)

1

8

SECTION III

Comprehension TypeThis section contains 2 groups of questions. Each group has 3 multiple choicequestions based on a paragraph. Each question has 4 choices (A), (B), (C) and (D), forits answer, out of which ONLY ONE is correct.


For any progression

rth term = Sum to n terms Sum to (n 1) terms.



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36.Value ofsin C

1

sin B1

sin C2

sin B2

is

(A) 2 cos A (B) 4 cos A (C) cos A (D) 3 cos A37. The sum of the areas of the possible triangles is

(A)1

2b

2cos 2A (B)

1

2b

2sin 2A

(C)1

2b

2sin A (D) None of these

38. If a = 3.5, b = 4 and A = 60 the difference between the two possible values of c is

(A) 2 (B) 3 (C) 1 (D) 2SECTION IV

Matrix-Match Type

This section contains 2 questions. Each question contains statements given in twocolumns, which have to be matched. The statements in Column I are labelled A, B, Cand D, while the statements in Column II are labelled p, q, r, s and t. Any givenstatement in Column I can have correct matching with ONE OR MOREstatement(s) in Column II. The appropriate bubbles corresponding to the answers tothese questions have to be darkened as illustrated in the following example:

If the correct matches are A p, s and t; B q and r; C p and q; and D s and t; thenthe correct darkening of bubbles will look like the following.



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39. Column I Column II

(A) The value of Ltn

k = 1

n

tan1 2k

k

4

k

2

2

is (p)

12

(B) In (0, ) the sum of a pair of solutions of

81cos

2x 81

sin2

x= 30 is

(q)

4

(C) If in ABC 1 a

c

b

c 1

c

b

a

b= 3, then Ais (r)

2

(D) Maximum value of sin x

6 cos x

6in 0,

2

is attained at x =

(s)

3

(t)

640. Column I Column II

(A) If k = 1

n

j = 1

k

i = 1

j

2 = An3

+ Bn2

+ Cn, then 3 (A + C) + B is (p) 2

(B) If 64, 27, 36 are the pth, qth, rth terms of a GP, then

3r p

q is (q) 4

(C) If in ABC, b2

+ c2

= 3a2, then

cot B cot C

cot A is (r) 0

(D) The number of solutions of 1 + sin x sin2x

2= 0 in ( , ) is (s) 1

(t) 5



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PART C : PHYSICS

SECTION I

Single Correct Choice TypeThis section contains 8 multiple choice questions. Each question has 4 choices (A), (B),(C) and (D) for its answer, out of which ONLY ONE is correct.

41. The radius vector of a point depends on time t, as r = c t bt2

2where c and b

are constant and collinear vectors. Then the modulus of velocity of the point is

(A) (c + bt) (B) (c bt) (C) c2

+ b2t (D) c

2+ b

2t2

42. The velocity-displacement equation of a particle moving along a straight line isgiven byv = 2s. Then the ratio of acceleration a to displacement s is equalto

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

43. The potential energy of a particle varies with distance x from a fixed origin as

U = A x

x2 B

2 where A and B are dimensional constants. Then dimensional

formula for AB is

(A) M1

L7/2

T2

(B) M2

L5/2

T2

(C) M1

L11/2

T2

(D) M1

L9/2

T2

44. Suppose the diameter of a wire is measured to be 2.40 cm. What is itscircumference? (Given = 3.14159)

(A) 7.540 cm (B) 7.54 cm (C) 7.541 cm (D) 7.542 cm



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45.Velocity-time graph of a particle moving in a straight line is as shown in Figure.At t = 0, displacement s = 0. Then thedisplacement-time graph

(A) between 0 and 2s is a parabola withnon-zero slope at t = 0

(B) between 4 and 6s is an invertedparabola

(C) between 2 and 4s is not a straight line

(D) has zero slope at t = 8 sec

46. Two particles separated by a distance of 1 m are projected simultaneously at t = 0,one vertically up and the other at an angle , from the same horizontal level. Thevelocity of the particle projected vertically is 10 m/s. If the two particles move inthe same vertical plane and collide at t = 1 sec, the angle of projection for the

other particle is (g = 10 m/s2)

(A) tan1

(10) (B) tan1

(5) (C) tan1

(15) (D) tan1

(20)

47. Two particles A and B start at the origin O and travel in opposite directionsalong a circular path of radius 5 m at constant speeds vA= 0.7 m/s and vB = 1.5 m/s

respectively. Determine the time when they collide.

(A) 8.5 s (B) 11.2 s (C) 14.3 s (D) 17.2 s



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48. Two blocks of masses 7 kg and 3 kg are connected by a spring of stiffness1000 N/m and placed on a smooth horizontal surface. They are acted upon byhorizontal forces F

1= 7 2 N a n d F

2= 32 N in opposite directions as shown in the

Figure. When accelerations of the blocks are equal and constant, the extension

in cm of the spring is

(A) 4 cm (B) 5 cm (C) 6 cm (D) 8 cm

SECTION II



49. To a man walking at the rate of x km/hr the rain appears to fall vertically. When

he doubles his speed, it appears to fall with a velocity of3 2 kmhr making anangle of 45 with the vertical. Then

(A) The value of x is 3 km/hr

(B)Vertical speed of rain is 2 km/hr

(C) The rain would appear to fall behind the back of the man(D) The rain would appear to fall in front of the man

50.A mass m kg is subjected to a constant force F kgf under which it moves adistance of x metre in t seconds and acquires a velocity of v m/s. Distance x inmetre is

(A)gt2

mF (B)v

2m

gF(C) Fgt

2

2m(D)v

2m

2gF



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51. In the arrangement shown, pulleys are massless and frictionless andthreads are inextensible. The block of mass m1 remains at rest. Then

(A) m1 =

4m2

m3

m2 m

3

(B) m1

= m2

+ m3

(C) Tension T1

in the string connected to mass m1

is4m

1m

3

m2 m

3

g

(D) Tension T2

in the string connected to mass m2

is2m

2m

3

m2 m3

g

52.A particle starts from a point O along a straight line OX with a velocity of

40 cms1

and an acceleration of 8 cms2

. At the same instant, another particlestarts from a point O behind O, (OO = 36 cm) in the same direction with a

velocity of 70 cms1

and a retardation of 4 cms2

. Then

(A) the two particles meet twice

(B) the timings of their meetings are 2 sec and 3 sec

(C) the timings of their meetings are 1 sec and 4 sec

(D) the distances from the point O at which they meet are 96 cm and 156 cmrespectively

SECTION III

Comprehension Type

This section contains 2 groups of questions. Each group has 3 multiple choicequestions based on a paragraph. Each question has 4 choices (A), (B), (C) and (D), forits answer, out of which ONLY ONE is correct.



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A particle of mass 102

kg is moving along the positive x-axis under the influence

of a force F(x) = K

2x2 where K = 10

2

N/m

2

. At time t = 0, the particle is at x = 1.0 m

and its velocity is v = 0.

53.Velocity of the particle when it reaches x = 0.50 m is

(A) 1 m/s (B) 1 m/s (C) 2 m/s (D) 1.5 m/s

54. The time at which it reaches x = 0.25 m is

(A) t = 53 34

(B) t = 2 54

(C) t =

3

3

4(D) t =

1

3

3

4

55.Average acceleration during the time the particle takes to go from x = 1.0 m tox = 0.5 m is

(A)3

2 m s

2

(B)4

2 ms

2

(C)4

2m s

2(D)

1

2ms

2


A smooth ring A of mass m can slide on a fixed horizontal rod. A string tied to thering passes over a fixed pulley B and carries a block C of mass M (= 2m) as shown in



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Figure. At an instant the string between the ring and the pulley makes an angle with the rod.

56. If the ring slides with a speed v, the block descends with speed

(A)v

cos

(B) v cos (C) v sin (D)v

tan 57. If the system is released from rest with = 30, the ring will start with

acceleration

(A) 6.8 m/s2 (B) 8.6 m/s

2 (C) 9.2 m/s

2 (D) 10.2 m/s

2

58. Tension in the string if m = 1 kg is

(A) 5.5 N (B) 4.4 N (C) 6.9 N (D) 7.8 N

SECTION IV

Matrix-Match Type

This section contains 2 questions. Each question contains statements given in twocolumns, which have to be matched. The statements in Column I are labelled A, B, Cand D, while the statements in Column II are labelled p, q, r, s and t. Any givenstatement in Column I can have correct matching with ONE OR MOREstatement(s) in Column II. The appropriate bubbles corresponding to the answers tothese questions have to be darkened as illustrated in the following example:



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If the correct matches are A p, s and t; B q and r; C p and q; and D s and t; thenthe correct darkening of bubbles will look like the following.

59. Match the items in columns I with those in column II

Column I Column II

(A) Weight (p) Depends on place

(B) Force (q) Depends on frame of reference

(C) Vector (r) Independent of frame of reference

(D) Unit vector (s) No unit

60. Match the items in column I with those in column II

Column I Column II

(A) Change in velocity is constant (p) Uniform motionin magnitude and direction withrespect to time

(B) Change in velocity is constant in (q) A body falling under gravity

direction but not in magnitude from a height comparable towith respect to time the earths surface

(C) Position vector r is (r) A body falling under gravity

such that r constant near the earths surface

(D) Position vector r is such thatdr

dt(s) Velocity is not constant

is constant

(t) Uniform circular motion



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Name: . Enrollment No.:

Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.

C. Question paper format:

13. The question paper consists of 3 parts (Part A: Chemistry, Part B: Mathematics and Part C: Physics).

Each part has 4 sections.

14. Section I contains 8 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its

answer, out of which only one is correct.

15. Section II contains 4 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its

answer, out of which one or more is/are correct.

16. Section III of each part contains 2 sets of Comprehension (paragraph) type questions. Each setconsists of a paragraph followed by 3 questions. Each question has 4 choices (A), (B), (C) and (D), out of

which only one Choice is correct.

17. Section IVcontains 2 questions. Each question has four statements (A, B, C and D) given in column I

and five statements (p, q, r, s and t) in Column II. Any given statement in Column I can have correct

matching with one or more statement(s) given in column II. For example, if for a given question,

statement B matches with the statements given in q and r, then for that particular question, against

statement B, darken the bubbles corresponding to q and r in the ORS.

D. Marking scheme:

18. For each question in Section I, you will be awarded 3 marks if you darken the bubble corresponding

to the correct answer and zero mark if no bubble is darkened. In case of bubbling of incorrect answer,

minus one (1) mark will be awarded.

19. For each question in Section II, you will be awarded 4 marks if you darken the bubble(s)

corresponding to the correct choice(s) for the answer, and zero mark if no bubble is darkened. In all

other cases, minus one (1) mark will be awarded.

20. For each question in Section III, you will be awarded 4 marks if you darken the bubble corresponding

to the correct answer and zero mark if no bubble is darkened. In all other cases, minus one (1)

mark will be awarded.

21. For each question in Section IV, you will be awarded 2 marks for each row in which you have

darkened the bubble(s) corresponding to the correct answer. Thus, each question in this section carries a

maximum of8 marks. There is no negative markingfor incorrect answer(s) for this section.

Elite2011 Pet1 Qns p1

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