fst 4 revision adv 22-05-2013 p 2 c 0 english

PAPER - 2INSTRUCTIONSA. General :

1. This Question Paper contains 45 questions.

2. The question paper CODE is printed on the right hand top corner on this sheet of this booklet.

3. No additional sheets will be provided for rough work.

4. Blank paper, clipboard, log tables, slide rules, calculators, cellular phones, pagers and electronic gadgetsin any form are not allowed.

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

6. Do not Tamper / mutilate the ORS or this booklet.

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

8. Write your Name, Roll No. and Sign in the space provide on the back page of this booklet.

B. Filling the Top-half of the ORS :

Use only Black ball point pen only for filling the ORS. Do not use Gel / Ink / Felt pen as it might smudge theORS.

9. Write your Roll no. in the boxes given at the top left corner of your ORS with black ball point pen. Also, darkenthe corresponding bubbles with Black ball point pen only. Also fill your roll no on the back side of your ORSin the space provided (if the ORS is both side printed).

10. Fill your Paper Code as mentioned on the Test Paper and darken the corresponding bubble with Black ballpoint pen.

11. If student does not fill his/her roll no. and paper code correctly and properly, then his/her marks will not bedisplayed and 5 marks will be deducted (paper wise) from the total.

12. Since it is not possible to erase and correct pen filled bubble, you are advised to be extremely careful whiledarken the bubble corresponding to your answer.

13. Neither try to erase / rub / scratch the option nor make the Cross (X) mark on the option once filled. Do notscribble, smudge, cut, tear, or wrinkle the ORS. Do not put any stray marks or whitener anywhere on theORS.

14. If there is any discrepancy between the written data and the bubbled data in your ORS, the bubbled data willbe taken as final.

C. Question paper format and Marking scheme :

15. The question paper consists of 3 parts (Physics, Chemistry & Mathematics). Each part consists of ThreeSections.

16. For each question in Section�I, you will be awarded 4 marks if you darken the bubble corresponding to thecorrect choice for the answer and zero mark if no bubbled is darkened. There is no negative marking forincorrect answer(s) in this section.

17. For each question in Section�II, you will be awarded 2 marks for each row in which you have darkened thebubble corresponding to the correct answer. Thus, each question in this section carries a maximum of8 marks. There is no negative marking for incorrect answer(s) in this section.

18. For each question in Section�III, you will be awarded 4 marks if you darken the bubble(s) correspondingto the correct choice for the answer and zero mark if no bubbled is darkened. In case of bubbling ofincorrect answer, minus one (�1) mark will be awarded.

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

Date : 22-05-2013 Duration : 3 Hours Max. Marks : 204

TARGET : JEE (ADVANCED)-2013 COURSE : REVISION CLASSES

CODE

0FULL SYLLABUS TEST-4 (FST-4)-JEE (ADVANCED)

PHYSICS

Space for Rough Work

RESONANCE P2FST4220513C0-1

PART I : PHYSICS

SECTION - IMultiple Correct Answers Type

This section contains 5 multiple correct answer(s) type questions. Each question has 4 choices(A), (B), (C) and (D), out of which ONE OR MORE is/are correct.

1. Two solid isotropic blocks A and B are placed as a shown in the figure. Ifblock 'B' falls into the liquid, the level of liquid may :

A(A) decrease

(B) remains same

(C) increase

(D) can't say

2. In a Young's Double Slit experiment, films of thickness tA and tB and refractive indices A and B are

placed in front of slits A and B respectively. If A A B Bt t , then the central maxima may

(A) not shift (B) shift torwards A (C) shift towards B (D) None of these

3. Choose the correct statements from the following :(A) Good reflectors are good emitters of thermal raidations(B) Burns caused by water at 100ºC are more severe than those caused by steam at 100ºC.

(C) All bodies emit thermal radiations at all temperatures greater than 0 K.(D) It is impossible to construct a heat engine of 100% efficiency.

PHYSICS



4. A particle of mass m and charge q is fastened to one end of a light stringof length . The other end of the string is fixed to the point O. The wholesystem lies on a frictionless horizontal plane. Initially, the mass is at restat A. A uniform electric field in the direction shown is switched on. Then : A

B O

60°

E

l (A) the speed of the particle when it reaches B is mqEl2

(B) the speed of the particle when it reaches B is m

qE l

(C) the tension in the string when particles reaches at B is 2qE(D) the tension in the string when the particle reaches at B is zero

5. Regarding a nucleus, choose the correct options :(A) Density of a nucleus is directly proportional to mass number A.(B) Nucleus radius 3 A

(C) Nuclear forces are dependent on the nature of nucleons.(D) Nuclear forces are short range forces.

SECTION - IIMatrix - Match Type

This section contains 2 questions. Each question contains statements given intwo columns, which have to be matched. The statements in Column-I are labelledA, B, C and D, while the statements in Column-II are labelled p, q, r, s and t. Anygiven statement in Column-I can have correct matching with ONE OR MOREstatement(s) in Column-II. The appropriate bubbles corresponding to the answersto 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 ofbubbles will look like the following :

PHYSICS



6. A source of sound stationary with respect to medium emits sound of frequency f and wavelength . Thespeed of sound with respect to medium is C, speed of medium is V

m. The observer O

1 receives waves of

frequency f1 and wavelength

1. The observer O

2 receives waves of frequency f

2 and wavelength

2. Match

the column given below if Vs is speed of source with respect to ground.

Column�I Column�II

(A) Medium at rest, source at rest, O1 and O

2 moves (p)

1 < <

2

(B) medium at rest, O1, O

2 at rest, source moves (q) f

1 > f > f

2

(C) medium moves, source at rest, O1,O

2 at rest (r)

1 =

2 =

(D) medium moves source moves, O1 , O

2 at rest (s) f

1 < f < f

2

(t) 1 > >

2

PHYSICS



7. In a hydrogen atom, a0 = 0.529 Å, E

1 = �13.6 eV. Some modified situations are given compare the energy

of levels and radius of allowed orbits.

Column�I Column�II

(A) An atom consists of positive charge 2e and (p) 2

E1 or 2E1

mass m and an electron of mass m revolving aroundthe centre of mass of the system

(B) An atom consists of positron and an electron (q) 2a0 or

2

a0

revolving around the centre of mass of system

(C) An atom consists of a particle of mass double that (r) 92

E1 or

29

E1

of electron and charge same as that of electron revolvingaround a heavy nucleus of charge 4e

(D) An atom consists of a nucleus of infinite mass and an (s) a0 or 8a

0

electron revolving around the nucleus of charge 2e

(t) 4E1

PHYSICS



SECTION - IIIInteger Answer Type

This section contains 8 questions. The answer to each of the questions isa single digit integer, ranging from 0 to 9. The appropriate bubble belowthe respective question number in the ORS have to be darkened.

8. The figure shows a trolley with a light piston(area = 10 cm2 )fitted on one end placed on a smooth horizontalsurface .Two moles of a diatomic gas is filled in the trolley. The piston is placed in contact with an idealspring which is undeformed.The walls of the trolley and the piston are adiabatic.There is no friction between

the trolley and the piston.Initially the value of is 10 cm. Now the gas is given 20 cal of heat.After some

time it was found that the temperature of the gas was increased by 1.8 K and the piston was at rest with

respect to the trolley and which was then not in contact with the spring .Also the value of is now 14.2 cm.

Neglect the heat capacity of the piston and the cylinder. If the kinectic energy of the trolley (with the pistonand the gas) at this instant is 4.2 p joule, find the value of p. (Take R(gas constant) = 2 cal/moleK and1 cal = 4.2 J. and P

atm = 105 N/m2)

PHYSICS



9. A converging lens (focal length f) is broken in two equal pieces and placed at 60 cm as shown alongwith the object. It is found that real images are formed at the same place and ratio of image heights

is 9 : 1, if the value of f is

x1

22 cm then value of x is :

10. If work done by an ideal diatomic gas in a process from A to B as shown in P�V graph is 20 J :

If increase in internal energy of the gas is 50 x, (in joule) then x is :

11. When an object is moved along the principal axis of a thin converging lens of focal length 12 cm, twoimages three times the size of object are obtained when object is at x

1 and x

2 distance from the lens. The

ratio of 1

2

xx

is :

12. The pressure inside the two soap bubbles is 1.01 and 1.02 atmosphere. when they are in air The ratio oftheir volumes is : (both have same surface tension)

PHYSICS



13. An ice cube of edge length 20 cm is floating in a tank of base area 2500 cm2 partially filled with water. Thedisplacement of centre of mass of hole system is (in cm), when ice cube melts completely will be:(

ice = 900 kg/m3,

= 1000 kg/m3, g = 10 m/s2)

14. The probability of a radioactive nucleus to survive one mean life is xe

1

, then x is :

15. A particle is moving in a circle of radius 1 cm and with constant speed of 8 cm/s. Centre of the circlelies on principal axis of a converging lens of focal length 50 cm and at a distance of 75 cm from thelens. Plane of the circle is perpendicular to principal axis, if speed of image is 2x cm/s then x is :

CHEMISTRY


PART- II - CHEMISTRY

Atomic masses : [H = 1, D = 2, Li = 7, C = 12, N = 14, O = 16, F = 19, Na = 23, Mg = 24, Al = 27, Si = 28,P = 31, S = 32, Cl = 35.5, K = 39, Ca = 40, Cr = 52, Mn = 55, Fe = 56, Cu = 63.5, Zn = 65, As = 75,Br = 80, Ag = 108, I = 127, Ba = 137, Hg = 200, Pb = 207]

SECTION - IMultiple Correct Answers Type

This section contains 5 multiple correct answer(s) type questions. Each question has 4 choices (A),(B), (C) and (D), out of which ONE OR MORE is/are correct.

16. Assume ideal gas behaviour for all the gases considered & neglect vibrational degrees of freedom. Separateequimolar sample of Ne, O

2, CO

2 & SO

2 were subjected to a two step process as mentioned. Initially all are

at same state of temperature & pressure.Step- I All undergo reversible adiabatic expansion to attain same final volume, which is double the originalvolume thereby causing the decreases in their temperature.Step- II After step-I all are given appropriate amount of heat isochorically to restore the original tempera-ture.Mark the correct option (s) :(A) Due to step-I only, the decrease in temperature will maximum for Ne.(B) During step-II, heat given will be minimum for SO

2.

(C) There will be no change in internal energy for any of the gas after both the steps of process are com-pleted.(D) The P�V graph of O

2 & CO

2 will be same.

17. The equilibrium constant Kp for the reaction,

SO2Cl

2(g) SO

2(g) + Cl

2(g)

is 1.125 atm at temperature T. Select the correct statements for dissociation of pure SO2Cl

2 (g) at equilibrium

state at 2 atm equilibrium pressure and temperature T :(A) degree of dissociation of SO

2Cl

2 is 0.5

(B) degree of dissociation of SO2Cl

2 is 0.6

(C) average molar mass of final equilibrium mixture will be 84.375(D) average molar mass of final equilibrium mixture will be 75


CHEMISTRY



18. The standard reduction -potential for the half-cell

NO3�(aq) + 2H+ + e� NO

2 (g) + H

2O is 0.78 V [Take

FRT303.2

= 0.06, log 2 = 0.3]

Select correct options :(A) Reduction potential of half cell in 8 M H+ (considering other species to be at unit concentation) is 0.888

volt.(B) Reduction potential of half cell in 8 M H+ (considering other species to be at unit concentation) is 0.672

volt.(C) Reduction potential of half cell in a neutral solution (considering other species to be at unit concentation)

is 1.62 volt.(D) Reduction potential of half cell in a neutral solution (considering other species to be at unit concentation)

is �0.06 volt.

19. The correct statements about the following reaction are

CH CH=C3

CH3

H

CH CH2 3 (P) + (Q) Product/s (R)

Br / CCl2 4

Br / h2

(X)

CH3

monobromination

H / Ni2

(S)

(A) P and Q have same value of optical rotation with opposite sign

(B) P and Q have different boiling points

(C) R contains two racemic mixture.

(D) S contains a mixture of two diastereomers.

CHEMISTRY



20. Which of the following are true about the following reaction sequence.

HBr

(PhCOO)2

HBr

KOH(DMSO)

H O/AgNO2 3

P1

P2

(A) P2 gives instant turbidity with Lucas reagent

(B) P1 , P

2 are stereoisomers

(C) P1 is converted to P

2 on keeping in H

3O+

(D) P1 is more readily oxidised by CrO

3/H+ while P

2 is unreactive towards oxidising agents under normal

conditions.


This section contains 2 questions. Each question contains statements given in twocolumns, which have to be matched. The statements in Column-I are labelledA, B, C and D, while the statements in Column-II are labelled p, q, r, s and t. Anygiven statement in Column-I can have correct matching with ONE OR MOREstatement(s) in Column-II. The appropriate bubbles corresponding to the answersto 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 ofbubbles will look like the following :

21. Column-I Column-II(A) Number of lone pairs > 2 (p) XeF

5

�

(B) Planar species (q) XeO4

(C) All bond angles are equal (r) ClF3

(D) Non-Polar in nature (s) NH3

(t) NO3

�

CHEMISTRY



22. Column � I Column � II

(A) OHNH/AgNO 43 (p)

(B)

CH3

C�CH=O

O

)excess(NaOH(q)

(C) /OH/KMnO4 (r)

(D) 2I/NaOH (s)

(t)


This section contains 8 questions. The answer to each of the questions isa single digit integer, ranging from 0 to 9. The appropriate bubble below therespective question number in the ORS have to be darkened.

CHEMISTRY



23. 6.2 g of a sample containing Na2CO

3, NaHCO

3 & non-valatile inert impurity on heating loses 5% of its weight

due to formation of H2O and CO

2 as in reaction

2NaHCO3 Na

2CO

3 + H

2O + CO

2.

Residue is dissolved in water and formed 100 ml solution and its 10 ml portion requires 4.5 ml of 0.2 Maqueous solution of BaCl

2 for complete precipitation of carbonates.If number of moles of Na

2CO

3 in the origi-

nal sample were 'q' then the value of '100 q' is :

24. A mixture of 32 gm of O2 gas and 16 gm D

2 gas is allowed to effuse through an orifice. If the relative rate of

effusion

2

2

O

D

r

r at the start of effusion is expressed as p × 2 , then the value of p is :

25. If certain decomposition reaction found to obey equation in term of partial pressure (P) of reactant :

2

2

p

pa = b kt, what is order of reaction if a, b and k are constant (t represents time) ?

26. A crystal of formula AB3 has A ions at the cube corners and B ions at the edge centres. The coordination

numbers of A and B respectively are x and y then sum of x and y is :

27. How many total isomers are possible for square planar complex [Pd(Cl)2(SCN)2]?

28. How many position isomers of dibromonaphthalene is possible if each ring of naphthalene has one halogen?

29. CH3�CH=O + CH

3CH

2�CH=O

,HO mixture of aldols(z) total number of aldols including stereoisomers.

Report your answer as (z � 5).

30. The total number of isomeric Bromo-chloro-fluoro-iodopropadienes is ............ .


MATHEMATICS

PART- III - MATHEMATICS

SECTION - IMultiple Correct Answer Type

This section contains 5 questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out ofwhich ONE OR MORE is/are correct.

31. Which of the following statment(s) is/are True for the functionf(x) = (x � 1)2(x � 2) + 1 defined on [0, 2] ?

(A) Range of f is

1,

2723

.

(B) The coordinates of the turning point of the graph of y = f(x) occurs at (1, 1) and

2723

,35

.

(C) The value of p for which the equation f(x) = p has 3 distinct solutions lies in interval

1,

2723

.

(D) The area enclosed by y = f(x), the lines x = 0 and y = 1 as x varies from 0 to 1 is 127

.

32. Let j��i�a

, k��j�b

, i��k�c . If d

is a unit vector such that 0d.a

= ]d,c,b[

, then d

(A) )k�2�j�i�(6

1 (B) )k��j�i�(

3

1 (C) � )k�2�j�i�(

6

1 (D) � )k��j�i�(

3

1

33. Given f(x) =

3x

3x3�

if

if

e�2

x�103�x

2

. The graph of f(x) is

(A) continuous and differentiable at x = 3 (B) continuous but not differentiable at x = 3(C) differentiable but not continuous at x = 3 (D) niether differentiable nor continuous at x = 3



MATHEMATICS


34. Consider the sequence an given by a

1 =

21

, an+1

= an

2 + an , Let S

n =

1a1

1 +

1a1

2 +....+

1a1

n then

find the value of [S2012

], where [.] denotes greatest integer function.

(A) 1 (B) [e/2] (C) [e] (D) [ � 1]

35. Two sides of a triangle are parallel to the coordinate axes. If the slopes of the medians through the acuteangles of the triangle are 2 and m, then m can be equal to

(A) 21

(B) 2 (C) 4 (D) 8


This section contains 2 questions. Each question contains statements given in twocolumns, which have to be matched. The statements in Column-I are labelledA, B, C and D, while the statements in Column-II are labelled p, q, r, s and t. Anygiven statement in Column-I can have correct matching with ONE OR MOREstatement(s) in Column-II. The appropriate bubbles corresponding to the answersto these questions have to be drakened 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 ofbubbles will look like the following :

36. Column-I Column-II

(A) If k�m�j�ni�17a 22

, k�j�ni�17b 2

, then number of (p) 1

integral values of m such that a

and b

are perpendicular

(B) If the distance from the orthocentre to the vertex of the (q) 2triangle, is k times the distance from the circumcentre tothe middle point of the opposite side, then k equals

(C) The remainder when 337 is divided by 80 is equal to (r) 3

(D) Number of values of k for which the equations x3 + x2 � kx � k = 0, (s) 4x3 � x2 � 3x + k = 0 have a common root, is

(t) 5


MATHEMATICS


37. A variable plane cuts the x-axis, y-axis and z-axis at the points A,B and C respectively such that the volumeof the tetrahedron OABC remains constant equal to 32 cubic unit and O is the origin of the coordinatesystemColumn-I Column-II

(A) The locus of the centroid of the tetrahedron is (p) xyz = 24

(B) The locus of the point equidistant from O, A, B and C is (q) (x2 + y2 + z2)3 = 192xyz

(C) The length of the foot of perpendicular from origin to the (r) xyz = 3plane is

(D) If PA, PB and PC are mutually perpendicular then the locus (s) (x2 + y2 + z2)3 = 1536xyzof P is

(t) xyz = 1


This section contains 8 questions. The answer to each of the questions isa single digit integer, ranging from 0 to 9. The appropriate bubble below therespective question number in the ORS have to be darkened.

38. Suppose f(n) = log2(3). log

3(4). log

4(5)..........log

n �1 (n) then the sum

100

2k

k )2(f = , then 1683

is equal to

39. If (/4, /2) and

1nntan

1= sin + cos then the value of tan2 is


MATHEMATICS


40. If the value of

100

0

1�1� ]x[tan]x[cot dx is 100 + p cotp, then the value of p is

(where [.] denotes greatest integer function)

41. Let , , , (0, ) be such that 2cos + 6 cos + 7 cos + 9 cos = 0 and2 sin � 6 sin + 7 sin � 9sin = 0 then the value of for which cos (+ ) = 7 cos ( + ) is

42. Two functions f(x) and g(x) are defined as f(x) = 24x10x

2xlog

210

and g(x) =

153]x[2

sin 1

where [.] denotes greatest integer function, then the number of even integers for which f(x) + g(x) is definedis

43. The positive value of 'c' that makes the area bounded by the graph of y = c(1 � x2) and the x-axis equal to 1,can be expressed in the form p/q where p,q N and in their lowest form, then (p + q) equals

44. Suppose a,b,c are such that the curve y = ax2 + bx + c is tangent to y = 3x � 3 at (1, 0) and is also tangentto y = x + 1 at (3, 4) then the value of (2a � b � 4c) equals

45. Let S(x) = 1 + x � x2 � x3 + x4 + x5 � x6 � x7 +...., where 0 < x < 1. If S(x) = 2

12 then the value of [x] equals

where [.] denotes greatest integer function.

Name of the Candidate Roll Number

I have read all the instructions andshall abide by them.

-------------------------------- Signature of the Invigilator

I have verified all the informationfilled in by the Candidate.

-------------------------------- Signature of the Candidate

(Space for rough work)

fst 4 revision adv 22-05-2013 p 2 c 0 english

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