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Brilliant Tutorials Pvt. Ltd. IIT/PT 6/CPM/P(II) - 1

DONOTBREAKTHESEA

LSONTHISBOOKLET,AWAITINSTRUCTIONSFROMTHEINVIGILATOR

B.MAT PART TEST 6FOR OUR STUDENTS

TOWARDS

IIT-JOINT ENTRANCE EXAMINATION, 2012

QUESTION PAPER CODE

Time: 3 Hours Maximum Marks: 240

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

INSTRUCTIONS:

A. General

1. This booklet is your Question Paper containing 60 questions. The booklet has 23 pages.

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

(page no. 23) of this booklet.

3. This question paper contains 3 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 the

space provided on the back page (page no. 23) of this booklet.

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

appropriate bubble for each question must be darkened with HB pencil.

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. Question paper format: Read the instructions printed on the back page (page no. 23) of this booklet.

C. Marking scheme: Read the instructions on the back page (page no. 23) of this booklet.

Name: . Enrollment No.:

CHEMISTRY PHYSICS MATHEMATICS

6

I have read all the instructions andshall abide by them.

Signature of the Candidate

I have verified all the informationsfilled in by the Candidate.

Signature of the Invigilator

SEAL

SEAL

PAPER II

IIT-JEE 2012

PT6/CPM/P(II)/Qns

13.11.2011

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SECTION I

Single Correct Answer TypeThis section contains

8 multiple choice questions. Each question has four choices

(A), (B), (C) and (D) out of which ONLY ONE is correct.

1. The formula of the complex tetraisothiocyanatozincate (II) ion is

(A) [Zn(NCS)4]2

(B) [Zn(NCS)4]

(C) [Zn(CNS)4]2

(D)2

4[Zn(NCS)]

2. Calcium crystallizes in a FCC unit cell with a = 0.556 nm. Calculate the density if

it contains 0.1% Schottky defects?

(A) 2.0 g/cm3 (B) 1.54 g/cm

3

(C) 1.54 g/dm

3

(D) 2.0 g/dm

3

3. Which of the following compounds does not give Lassaignes test for nitrogen?

(A) Hydrazine hydrochloride (B) Hydroxylamine

(C) Hydrazoic acid (D) All of them

4. Which of the following is not characteristic of chemisorption?

(A) Adsorption is irreversible

(B) H is in the order of 900 kJ

(C)Adsorption is specific

(D)Adsorption increases with increase of surface area.

5.A colorless inorganic compound imparts a green colour to the flame. Its aqueoussolution does not give a precipitate with H

2S but gives a white precipitate with

H2SO4. When the solid is heated with solid K2Cr2O7 and Conc. H2SO4, a red gas

is evolved. This gas when passed through aqueous NaOH solution turns it yellow.

The original compound is

(A) Ba(NO3)2 (B) Pb(NO3)2 (C) BaCl2 (D) NaCl

SPACE FOR ROUGH WORK

PART A: CHEMISTRY

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6. The electrolytic reduction of MnSO4 in H2SO4(aq) will give MnO2. If a current of

51.0 ampere is used with a current efficiency of 85%, the time taken to produce

1 kg of MnO2 will be (Molar mass of MnO2 = 87)

(A) 14.22 hr (B) 28.44 hr (C) 10.0 hr (D) 50.0 hr

7. If 2.58 g of phenol is dissolved in 100 g of the solvent (phenol undergoing partial

dimerization) the freezing point of solvent (Kf= 14.1 K mol 1

kg) is depressed by

2.37 K. The amount of phenol dimerized is about

(A) 1.0 g (B) 1.5 g (C) 2.0 g (D) 0.5 g

8. For a first order reaction +2 5(g) 2(g) 2(g)2N O 4NO O . The total pressure is

284.5 mm after 30 min and 584.5 mm after almost complete reaction. The rate

constant of the reaction is (in min 1

)

(A) 1.2 10 3

(B) 2.4 10 3

(C) 5.2 10 3

(D) 8.2 10 3

SECTION II

Multiple Correct Answer(s) Type

This section contains 4 multiple choice questions. Each question has four choices

(A), (B), (C) and (D) out of which ONE or MORE may be correct.

9. Which of the following do not form an azeotrope?

(A) Cyclohexane + Cycloheptane (B) Chloroform + acetone

(C) Ethanol + water (D) Benzene + Toluene

10. Which of the following are concentration cells?

(A)1 2

2 2

C CZn Zn Zn Zn+ + (B)

1 1

2 2

C CZn Zn Cu Cu+ +

(C)

11 1 2

2 2p pC C

Pt H , H H , H Pt+ + (D)

21 1 1

2 2p pC C

Pt H , H H , H Pt+ +


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11. Which of the following statements are true regarding interhalogen compounds?

(A) Interhalogen compounds are of AB, AB3 , AB5 and AB7 types

(B) The halogen atom having less electronegativity shows positive oxidation

state.

(C) ClF is called fluorine monochloride

(D) The central atom can never be fluorine.

12. Which of the following pairs of ions can be separated by H2S in dilute HCl?

(A) Bi3+

, Sn4+

(B) Al3+

, Hg2+

(C) Zn2+

, Cu2+

(D) Ni2+

, Cu2+

SECTION III

Integer Answer Type

This section contains 6 questions. The answer to each of the questions is a single-digitinteger, ranging from 0 to 9. The appropriate bubbles below the respective question

numbers in the ORS have to be darkened. For example, if the correct answers to

question numbers X, Y, Z and W (say) are 6, 0, 9 and 2, respectively, then the correct

darkening of bubbles will look like the following:

X Y Z W0 0 00

11 1 1

2 222

3 3 3 3

4444

5 5 5 5

6666

7 7 7 7

8 888

9 9 99

13. The number of pseudohalogens of the following is _______________.

SCN

, SeCN

, CH3COO

, OCN

,

3N , HN3, OCl

, HSCN


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14. Under the same reaction conditions, initial concentration of 1.386 mol dm 3

of a

substance becomes half in 40 sec and 20 sec through first order and zero order

kinetics respectively. Then the ratio 1

0

k

kis about x 10

1, where x is ___________.

15. If NaCl is doped with 10

3 mol % BaCl2, the concentration of cation vacancies is

x 1018

where x is about ________________.

16. For the coagulation of 105 mL of a sulphide sol 20 mL of 0.5 M NaCl is required.

The flocculation value of NaCl in m mol L 1

is x 101

where x is ______________.

17. The oxidation state of chromium in ( )

3

2 4 3Cr C O is _____________.

18. The current strength required in amperes to liberate 10 g of bromine from KBr

solution in half an hour is about ________________. (F = 98450 coulombs)

SECTION IV

Matrix-Match Type

This section contains 2 questions. Each question contains statements given in two

columns, which have to be matched. The statements in Column I are labelled A, B, C

and D, while the statements in Column II are labelled p, q, r, s and t. Any given

statement in Column I can have correct matching with ONE OR MORE statement(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; then

the correct darkening of bubbles will look like the following.

A p q r s

p q r s

p q r s

p q r s

B

C

D

p q r s

t

t

t

t

t


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19. Column I Column II

(A) NaCl type structure (p) FCC lattice of cations

(B) ZnS type structure (q) FCC lattice of anions

(C) CsCl type structure (r) Coordination number is 4

(D) Na2O type structure (s) density

=

3

1 M

a N

(t) density

=

3

4 M

a N


(A) +2 2(g) 2(g) 2(g)SO Cl SO Cl (p)aE /RTk Ae

=

(B)11

3 2 5CC

CH COOC H OH+ (q) = t

1 [A]k nt [A]

+3 2 5CH COO C H OH

(C)+

+ H

12 22 11 2C H O H O (r) Polarimeter

6 12 6 6 12 6G F

C H O C H O+

(D)2 2

2 248S O 2I 2SO I

+ + (s)t

1vs

[A]t plot is a straight line

(t) t99.9% = 10 t50%


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SECTION I



(A), (B), (C) and (D) for its answer, out of which ONLY ONE is correct.

21.A ray of light is incident on a plane mirror along a vector ( )i j k+ + . The normal

to the mirror at the point of incidence is along the vector ( )i j+ . The unit vectoralong the reflected ray is

(A) ( )1

i j k3

+ + (B) ( )1

i j k3

+

(C)

( )

1i j k

3 + (D)

( )

1i j k

3

22.A linear shaped object AB of length 10 2 cm is

placed before a concave mirror as shown in Figure.

What is the size of the image if the radius of

curvature of the mirror is 40 cm?

(A)15 2 cm (B) 20 2 cm

(C) 20 cm (D) 18 cm

23.Figure aside shows a system consisting of a massless

pulley, a spring of force constant 5 N/m and a block ofmass m = 100 gm. The mean position of the body is

20 cm. If the focal length of the convex mirror is 10 cm,

find the amplitude of vibration of the image. [g = 10 m/s2

]

(A) 0.27 cm (B) 0.47 cm

(C) 0.67 cm (D) 0.87 cm

A

30 cm

45

B

m20 cm


PART B: PHYSICS

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24. For a given prism, the angle of minimum deviation is 38 when the angle of

emergence is 49. For the same prism when the angle of maximum deviation is

58, what is the angle of emergence?

(A) 20 (B) 42 (C) 36 (D) 28

25. 0.1 % of the photons emitted by a light source contributes towards ejection ofphotoelectrons in a photocell. If the current in the photocell is 0.96 A and the

wavelength of the photon is 400 nm, what is the power of the light source?

[e = 1.6 10 19

C ; h = 6.64 10 34

Js]

(A) 3 mW (B) 5 mW (C) 8 mW (D) 10 mW

26.A radioactive sample emits n -particles in 2 seconds, then it emits (0.75 n) -particles

in the next two seconds. What is the mean life of the sample?2

log 0.06243

=

(A) 14 sec (B) 7 sec (C) 3.5 s (D) 1.75 s

27.A tank is filled with two immiscible liquids of refractive

indices4

3and

3

2respectively as shown in Figure. An object

is suspended from the surface to a depth h < d, from the free

surface of the liquid. The bottom of the tank is fitted with a

plane mirror. When a man swims with his face towards the

mirror, at what distance is the image from him when he

views normally (d = 12 cm, h = 4 cm)?

(A) 15 cm (B) 24 cm (C) 18 cm (D) 28 cm

28. In the case of a thin lens of focal length f, a linear object of length is placed with

its near end at a distance a1

from the first focus. What is the magnification of the

image in units of f2? [a2 is the distance from the second focus]

(A) a1

a2 (B) (a

1b

1)

1

(C) (a1 + a2) 2

(D) (a2 + a1 )2


d

dh

4/3

3/2

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SECTION II



(A), (B), (C) and (D) for its answer, out of which ONE OR MORE may be correct.

29.A thin hollow equiconvex lens, silvered at the back converges a parallel beam oflight at a distance of 0.2 m in front of it. Then the lens is filled with water having

4

3 = . Now pick out the correct statements from the following:

(A) Radius of curvature of the silvered surface is 0.4 m

(B) Power of the lens when it is hollow is zero

(C) Power of the lens when it is filled with water is 8.33

(D) Image will be formed at a distance of 12 cm in front of the lens

30. Two coherent sources A and B emitting light of wavelength are placed at

positions (0, D) and (3, D) respectively (D >> ). Then,y

x

(x, 0)

A B

O P

(A) the number of minima on +x-axis is 3

(B) coordinates of the 3rd minimum on +x-axis is5D

, 011

+

(C) the number of maxima on y-axis is 3

(D) the number of maxima on y-axis is 5


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31. The Figure below shows the apparatus used by a student to measure the

acceleration of free fall g. Pressing switch S1 simultaneously starts the timer and

releases the ball. The counter is stopped when the ball closes the switch S2. The

acceleration of free fall is calculated from the expression d = 0.5 gt2

where d is the

distance the ball falls and t the time it takes. A student conducted the

experiment and measured the distance d with a metre rule. Now pick out the

correct choices from the following:

Timer

1S

2S

ball

d

(A) The experiment introduces into the measurement random error mainly due to

parallax

(B) When the student recorded the distance as d = (90.4 0.1 cm) and the time t

as t = (0.43 0.01 s), the absolute uncertainty in the value of g turns out to be

0.5 (correct to one significant figure)

(C) The calculation of g with the aid of a graph reduces random error in the

measurement of d and t

(D) The calculation of g with the aid of a graph reduces systematic error in the

measurement of d and t

32.An X-ray tube works at a potential difference of 105

V. Only 0.1% of the energy of

cathode rays is converted into X-ray radiation and heat is generated in the target

at the rate of 120 calories per second, then [neglecting relativity correction and

with e = 1.6 10 19

C, m = 9.1 10 31

kg and 32 5.66= ]

(A) velocity of the electron reaching the target is 1.88 108

ms 1

(B) the number of electrons reaching the target per second is 3.15 1016

(C) current in the tube is approximately 5 mA

(D) all the above


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SECTION III

Integer Answer Type

This section contains 6 questions. The answer to each of the questions is a single-digit

integer, ranging from 0 to 9. The appropriate bubbles below the respective question




X Y Z W0 0 00

11 1 1

2 222

3 3 3 3

4444

5 5 5 5

6666

7 7 7 7

8 888

9 9 99

33. The mass equivalent of the energy emitted when a H. atom makes a transition

from n = 3 to n = 1 state is given approximately by n 10 35

kg. What is n?

34. An electron is released far away from a proton towards which it moves. If r is the

distance of the electron from the proton, the de Broglie wavelength of the electron

is found to be proportional to

1

nr . What is n?

35. For the nuclear reaction4226 222

88 86 2Ra Rn He + , the radium nucleus is initially

at rest and the -particle carries the energy 5.3 MeV. The energy released in the

reaction is found to be 0.54 10n in electron volt. What is n?

36. The smallest value of index of refraction of the material of a prism that allows

the passage of light through it, when the refracting angle of the prism is A is

given by

1

nn A1 cotn

= +

. What is n?


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37.A beam of neutrons of kinetic energy 0.0327 eV, while covering a distance of 10 m

suffer a fractional decay of 3.96 10 6

. If the mass of neutron is 1.675 10 27

kg,

the mean life of neutrons is found to be approximately 1 10n

sec. What is n?

38.A parallel beam of microwaves of wavelength

= 0.2 mm falls on a Youngs double slit apparatus.The separation between the slits is 1.0 mm. The

intensity of microwaves is measured on a screen

placed parallel to the plane of the slits at a distance

of 1.0 m from it as shown in Figure. If the incident

beam makes an angle of 30 with the x-axis, the

coordinates of the first maximum above the central

maximum is given bynD

y7n 2

=+

. What is n?

SECTION IV

Matrix-Match Type



and D, while the statements in Column II are labelled p, q, r, s and t. Any given

statement in Column I can have correct matching with ONE OR MORE statement(s)



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.

A p q r s p q r s p q r sp q r s

BCD

p q r s t

t

tt

t

1S

d

y

D

x

2S

screen


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39. With regard to convex mirror match the entries in Column I with those in Column II.

Given: u is object distance, v-image distance, f-focal length, R-radius of curvature

and m-magnification.

Column I Column II

(A) Real object (p) virtual image

(B) Virtual object with u < f (q) real image

(C) Virtual object with u > f (r) m = 1

(D) R (s) m > 1

(t) m < 1

40. With respect to photoelectric effect, match the entries in column I with those in

column II [Given frequency, I intensity and work function]

Column I Column II

(A) If is increased keeping I and constant (p) Stopping potential increases

(B) If I is increased keeping and

constant

(q) Saturation photoelectric current

increases

(C) If is decreased keeping and

I constant

(r) Maximum K.E. of photoelectronsincreases

(D) If the distance between anode

and cathode is changed, other

things remaining the same (, I

and constant)

(s) Stopping potential remains the

same

(t) Maximum K.E. of photoelectronsdoes not change


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SECTION I



(A), (B), (C) and (D) for its answer, out of which ONLY ONE is correct.

41. If the vectors a i j k, b 4i 3j 4k= + + = + + and c i j k= + + are linearly dependent,

then

(A) = 1, = 1 (B) = 1, = 1

(C) = 1, = 1 (D) = 1, = 1

42. For any vector a , the value of ( ) ( ) ( )2 2 2

a i a j a k + + =

(A)2

a (B)2

3 a (C)2

4 a (D)2

2 a

43. A unit vector perpendicular to i j k+ + and coplanar with ( )i j 2k+ + and ( )i 2j k+ + is

(A)j k

2

+(B)

i k

2

(C)

i j

2

(D) k j

44. If the angle between the line+

= =x 1 y 1 z 2

1 2 2and the plane + + =2x y z 4 0

is

1 1sin3

, then =

(A) 3

5(B)

5

3 (C)

4

3(D)

3

4

45. If the distance between the points P and Q is d and the projections of PQ on the

coordinate planes are d1, d2, d3, then + + =22 221 3d d d

(A) d2 (B) 2d

2 (C) 3d

2 (D) 4d

2


PART C: MATHEMATICS

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46. The shortest distance between the lines = + 1L : r (1, 1, 1) (0, 1, 1) and

= + 2L : r (1, 1, 0) ( 1, 1, 0) is

(A)1

2(B)

1

3 (C)

1

2(D)

1

5

47. Four digit numbers are formed by using the digits 0, 2, 3, 4, 5 without repeating

any digit. The probability that a number chosen at random is an odd number is

(A)1

2(B)

3

8 (C)

3

4(D)

1

5

48. Fifteen persons among whom are A and B, sit down at random at a round table.

The probability that there are exactly 4 persons between A and B is

(A)1

168(B)

1

14 (C)

1

7(D)

1

84

SECTION II



(A), (B), (C) and (D) for its answer, out of which ONE OR MORE may be correct.

49. In a college, 25% of the boys and 10% of the girls offer Mathematics. The girls

constitute 60% of the total number of students. A student is selected at random

and found to be studying Mathematics. Then

(A) the probability that the student is a girl5

6=

(B) the probability that the student is a girl 38

=

(C) the probability that the student is a boy =5

8

(D) the probability that the student is a boy1

6=


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50. E1 and E2 are independent events such that 0 < P(E1) < 1 and 0 < P(E2) < 1. Then

(A) ( ) ( )1 2 21P E /E P E /E 1+ = (B) ( ) ( ) ( )1 2 1 2P E E 1 P E P E =

(C) ( ) ( ) ( )1 21P E P E P E+ = (D) ( ) ( ) ( )2 12P E P E P E+ =

51. Let a 5i 12j= + and b be two vectors perpendicular to each other in the xy-plane.

The vector c in the same plane having projections of magnitude 4 and 7 along a

and b is

(A)8i j+ (B) 8i j (C) 8i j (D) 8i j +

52. Let , , be unit vectors such that and are mutually perpendicular and is

equally inclined to and at an angle . If ( )x y z = + +

, then

(A) z2

= 1 2x2 (B) z

2= 1 2y

2

(C) z

2

= 1 x

2

y

2

(D) z

2

= x

2

+ y

2

SECTION III

Integer Answer Type

This section contains 6 questions. The answer to each of the questions is a single-digit

integer, ranging from 0 to 9. The appropriate bubbles below the respective question




X Y Z W0 0 00

11 1 1

2 222

3 3 3 3

4444

5 5 5 5

6666

7 7 7 7

8 888

9 9 99


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53. The position vectors of the vertices A, B, C of a ABC are i j 2k, i 2j k + + and

2i j 3k + respectively. If the length of the altitude AD is , then [] where [x]

is the greatest integer x is

54. If

( ) ( ) ( )

2a b c b c 2a c a 3b p a b c + =

then p =

55. If the lines x = b ay, z = d cy and x = ay + b, z = cy + d are perpendicular

then aa + cc =

56. The equation of the plane through the points, (1, 0, 0) and (0, 2, 0) and at a

distance6

7units from the origin is 6x + 3y 2z = k. If is the angle that the

normal to the plane from the origin makes with the z-axis then |2 sec | =

57. Consider 5 independent Bernoullis trials each with probability of success p. If the

probability of at least one failure is equal to

31

32 then 8p =

58.An experiment has 12 equally likely outcomes. Let A and B be two non-empty

events of the experiment. If A consists of 4 outcomes then the least number of

outcomes that B must have so that A and B are independent is

SECTION IV

Matrix-Match Type



and 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 MORE statement(s)



If the correct matches are A p, s and t; B q and r; C p and q; and D s and t; then

the correct darkening of bubbles will look like the following.


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A p q r s p q r s p q r sp q r s

BCD

p q r s t

t

tt

t


(A) If a and b are unit vectors such (p)4

that 1

a b a b4

=

, then the angle

between a and b is

(B) If a, b, c are non-coplanar unit (q) 0

vectors such that

( )

b ca b c 2

+ =

,

then the angle between a and b is

(C) If a b c 0,+ + = a 3, b 5, c 7,= = = (r)3

then the angle between a and b is

(D) Let the vectors a, b, c, d be such (s)6

that ( ) ( )a b c d 0 = . Let P1and P2 be two planes determined by

a, b and c, d respectively. Then

the angle between the planes P1

and P2 is

(t)3

4


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(A) The equation of the plane which is (p) x y + z = 1

perpendicular to the vector

3i 4 j 7k+ + and which passes

through the point with positionvector 2i 3j k+ is

(B) The equation of the plane through (q) x 2y + z = 0

A (1, 2, 3) and parallel to the plane

3x + 4y + 7z = 2 is

(C) The equation of the plane through (r) 3x + 4y + 7z = 32

(3, 2, 0) and containing the linex 3 y 6 z 4

1 5 4

= = is

(D) The equation of the plane containing (s) 3x + 4y + 7z = 11the lines

x 1 y 2 z 3

2 3 4

= = and

x 2 y 3 z 4

3 4 5

= = is

(t) x y + z + 1 = 0


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Name: . QUESTION PAPER CODE:

Enrollment No.:

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

B. Question paper format

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

part has 4 sections.

10. 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.

11. 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.

12. Section III contains 6 questions. The answer to each of the questions is a single-digit integer, ranging

from 0 to 9. The answer will have to be appropriately bubbled in the ORS as per the instructions given at the

beginning of the section.

13. Section IVcontains 2 questions. Each question has four statements (A, B, C and D) given in Column I andfive statements (p, q, r, s and t) in Column II. Any given statement in Column I can have correct matchingwith one or more statement(s) given in Column II. For example, if for a given question, statement Bmatches with the statements given in q and r, then for that particular question, against statement B, darkenthe bubbles corresponding to q and r in the ORS.

C. Marking scheme

14. 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.

15. 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. No negative marks will be

awarded for incorrect answers in this section.

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

to the correct answer and zero mark if no bubble is darkened. There are no negative marks in this

section.

17. For each question in Section IV, you will be awarded 2 marksfor each row in which you have darkened

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

8marks. There is no negative markingfor incorrect answer(s) for this section.

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