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GRAND TEST-8

Sri Chaitanya IIT Academy, India A.P, TELANGANA, KARNATAKA, TAMILNADU, MAHARASHTRA, DELHI, RANCHI

A right Choice for the Real Aspirant ICON CENTRAL OFFICE, MADHAPUR-HYD

Sec: Sr.IPLCO_IC_ISB_LIIT Date: 30-04-16 Time:2.00 pm to 5.00 pm Max. Marks: 198

Name of the Student: ___________________ H.T. NO:

PAPER-2 30-04-16_ Sr.IPLCO_IC_ISB_LIIT _GTA-8(P2)_Weekend Syllabus

Mathematics : Total Syllabus

Physics : Total Syllabus

Chemistry : Total Syllabus

Sri Chaitanya IIT Academy 30-04-16_Sr.IPLCO_IC_ISB_LIIT _JEE-ADV_(2012_P2)_GTA-8_Q.P

Sr.IPLCO_IC_ISB_LIIT _Adv_Q.P space for rough work Page 3

JEE-ADVANCED-2012-P2-Model Time: 2:00 P.M to 5:00 P.M IMPORTANT INSTRUCTIONS Max Marks: 198

PHYSICS:

Section Question Type +Ve

Marks - Ve

Marks No.of Qs Total marks

Sec – I(Q.N : 1 – 8) Questions with Single Correct

Choice 3 -1 8 24

Sec – II(Q.N : 9– 14) Questions with Comprehension Type (3 Comprehensions : 2+2+2 = 6Q)

3 -1 6 18

Sec – III(Q.N : 15 – 20) Questions with Multiple Correct

Choice 4 0 6 24

Total 20 66

CHEMISTRY:


Marks - Ve


Sec – I(Q.N : 21 – 28) Questions with Single Correct Choice 3 -1 8 24

Sec – II(Q.N : 29 – 34) Questions with Comprehension Type (3 Comprehensions : 2+2+2 = 6Q)

3 -1 6 18


Choice 4 0 6 24

Total 20 66

MATHEMATICS:


Marks - Ve


Sec – I(Q.N : 41 – 48) Questions with Single Correct

Choice 3 -1 8 24

Sec – II(Q.N : 49 – 54) Questions with Comprehension Type (3 Comprehensions : 2+2+2 = 6Q)

3 -1 6 18


Choice 4 0 6 24

Total 20 66


Sr.IPLCO_IC_ISB_LIIT _Adv_Q.P space for rough work

PHYSICS: Max.Marks : 66

SECTION I

Single Correct Answer Type

This section contains 8 multiple choice questions. Each question has four choices A), B), C) and D) out of

which ONLY ONE is correct. 1. Figure shows an isolated system of two smooth spheres ‘A’ and ‘B’ at rest. mA= mB =

m ; 2RA=RB=R. Now an impulse is imparted to sphere A. Find the maximum value of impulse such that spheres ‘A’ does not looses contact with ‘B’.

I

A B

A) 3

3Gm

R B)

323Gm

R C)

343Gm

R D) Zero

2. Consider a hypothetical hydrogen like atom in which electrostatic potential between

electron and nucleus is given by 3

kVr

where k is a constant. If n be the principle

quantum number of the orbit, v = speed of the electron, r = radius of the orbit of electron. Assuming Bohr’s theory valid for this atom

A) 1r n B) 3r n C) 2r n D) 0r n 3. A parallel plate capacitor has plate area A and separation d between the plates. The

space between plates is filled with a dielectric of dielectric constant k and resistivity .

The capacitor is initially charged to Q0 using a battery. After removing battery at t = 0,

current density in the dielectric at any time t is

A) 00

0

tkQ e

k A

B) 00

0

tkQ e

k

C) 00

02

tkQ e

k A

D) 00

0

2t

kQ ek



4. A rod of mass m and length is held vertically on a smooth horizontally floor. When it

is released from this position, find the speed of its centre of mass when it makes angle

53º with the vertical

A) 96365

g B) 48365

g C) 26027

g D) None of these

5. In the figure shown a uniform ring of mass m is placed on a rough horizontal platform.

The coefficient of friction between left half of ring and table is 1 whereas between

right half and table is 2 . The ring has angular velocity in clockwise sense. Find the

magnitude of instantaneous acceleration of centre C of ring. Given2

1 20.6 , 0.2 10 /and g m s .

A) 24 /m s B) 22 /m s C) 21 /m s D) Zero

6. Figure shows a cylindrical space with a cylindrical cavity. Distance between their axis

is d. In this space (except cavity) uniform time varying magnetic field ( ,dB cdt

constant)

parallel to z-axis is present. In cylindrical cavity a small uniform rod (mass = m, length = l, charge = Q) is held at rest in x-y plane. Now rod in released. Instantaneous acceleration of rod is.

Z X

A) zero B) 2

Qcdm

C) Qcdm

D) 2Qcdm



7. Figure shows two thin rectangular slabs of glass, cross section of one is rectangular and the other is triangular wedge shaped. A monochromatic light incident nearly normally on the slabs as shown in figure.

A) Fringes are obtain only in case (X)

B) Fringes are obtain only in case (Y)

C) In case (X) fringe pattern is uniform but in case (Y) fringe pattern is non uniform

D) In case (X) fringe pattern is non uniform but in case (Y) fringe pattern is uniform

8. An empty glass jar is submerged in tank of water with open mouth of the jar

downwards, so that air inside the jar is trapped and cannot get out. As the jar is pushed

down slowly, the buoyant force on the jar.

A) increases

B) decreases

C) remains same

D) Information is insufficient to draw any conclusion



SECTION II Paragraph Type

This section contains 6 multiple choice questions relating to three paragraphs with two questions on each paragraph. Each question has four choices A), B), C) and D) out of which ONLY ONE is correct.11. Passage-1

In many nuclear probes a neutron or a proton is projected from a large distance towards the fixed target nucleus. The projectile need not be aimed directly towards the centre of the nucleus. Even if it is off by a certain distance called impact parameter b), the projectile may be captured by the nucleus. Crudely, we can say that it is captured if it reaches the edge of the nucleus. For this, maximum impact parameter b) for neutron is equal to the radius of the nucleus, for proton which is repelled by the nucleus, maximum impact parameter is less than the radius. But for a proton, the kinetic energy

of incident proton should be greater than 2

04Ze

R , (Z is atomic number and R is radius

of nucleus), otherwise proton (at a large distance from nucleus) will not reach the nucleus. If neutron or proton are used as a projectile, nuclear reaction may be triggered off.

R

b

9. In a certain situation, we have protons (at a large distance from nucleus) of energy2

0

0 06Z e

R . Here R0 is the radius of nucleus, being used and Z0 is its atomic number. It

will not be captured by this nucleus. We decide to choose a different nucleus as a target nuclei so that the proton with the same energy is captured by the nucleus?

A) nucleus with higher atomic number and same mass number B) nucleus with low atomic number and same mass number

C) nucleus with higher atomic number and low mass number



D) nucleus with same atomic number and low mass number.

10. The impact parameter for protons with kinetic energy K (K is the KE when it is at a

large distance form nucleus) just to be captured

A) 2

0

14

zeRRK

B) 2

0

18

zeRRK

c) 2

0

14

zeRRK

D) 2

0

18

zeR

RK

Passage-2

A thin superconducting (zero resistance) ring is held above a, vertical long solenoid, The cylindrically symmetric magnetic field around the ring can be described approximately in terms of the vertical and radial component of the magnetic field vector as 0 1zB B z and 0rB B r , where 0 ,B and are constants, and z & r are vertical and radial position coordinates, respectively,

Initially, plane of the ring is horizontal, has no current flowing in it. When released, it starts to move downwards with its axis still vertical

Initial coordinates of the centre of the ring is z=0 and r=0. In the given diagram point O is on the axis and above the solenoid having vertical and

radial position coordinates as (0, 0). Ring has mass m radius 0r and self inductance L. Acceleration due to gravity is g.



11. As ring moves some current will get induced in it. Find the magnitude of current in the ring at a vertical position z.

A) 20 0

1 B r ZL

B) 20 0

1 B r ZL

C) 20 0

12

B r ZL

D) 20 0

12

B r ZL

12. Due to current Lorentz force acting on ring at vertical position Z

A)2 2 4

0 0B r ZL

B)2 2 4

0 02 B r ZL

C)2 2 3

0 0B r ZrL

D)2 2 3

0 02 B r ZrL

Passage-3

A thin non conducting spherical shell of radius R has charge Q distributed uniformly on

its surface.

R

+Z

13. The sphere is set in rotation with constant angular velocity about z-axis. What is line integral of the magnetic field .B dl

along z-axis from to

A) 04Q

B) 02Q

C) 0

4Q

D) 0

2Q

14. Let sphere’s angular velocity increases linearly with time 0 kt Consider a very small circular coil placed at the centre of the sphere in xy-plane, assume that

coil spherer R and the normal to the plane containing the coil is along +z-axis. What is line

integral of electric field .E dl

along the closed coil.

A)2

0

6kr QR

B) 2

0

3kr QR

C) 2

03 kr QR

D) 2

06 kr QR



SECTION III

Multiple Correct Answer(s) Type This section contains 6 multiple choice questions. Each question has four choices A), B), C) and D) out of

which ONE or MORE are correct.

15. Consider a travelling simple harmonic wave sin( )y A t kx on a string of mass per

unit length and tension T. Kinetic energy per unit length is given by 21

2kyut

and potential energy per .unit length is given by 21

2pyu Tx

Mark the correct options:

A) for a very small element ku and pu will change periodically with angular frequency

B)uk and up simultaneously attain their maximum and minimum values. C)total energy per unit length of a string is constant when a harmonic wave travels on it.

D)a very small element of string has zero potential energy when it is at its equilibrium position.

16. A series RLC circuit is activated by a ac source of variable frequency. ac source of

voltage VS volt as shown in the circuit. VRL and VC are the potential drops across RL

and C respectively. Select the incorrect statement(s)

A) At low frequency limit, both VRL and VC are proportional to VS

B) At high frequency limit VRL approaches VS.

C) At high frequency limit, both VRL and VC are proportional to VS

D) At low frequency limit VC approaches VS



17. The angle of deviation vs angle of incidence (i) is plotted for a prism. Pick up the

correct statements.

A) The angle of prism is 60

0

B) The refractive index of the prism is 3n

C) For deviation to be 650 the angle of incidence 1 55i

D) The curve of ' ' vs ‘i’ is parabolic

18. X rays from a tube with a target A of atomic number Z shows strong K lines for target

A and weak K lines for impurities. The wavelength of K lines is z for target A and

1 and 2 for two impurities. 1

4z

and 2

14

z

. Screening constant of K lines to be

unity. Select the correct statement(s)

A) the atomic number of first impurity is 2z – 1 B) the atomic number of first impurity is 2z + 1

C) the atomic number of second impurity is 12

z

D) the atomic number of second impurity is 12z



19. In one dimensional elastic collision between a given incoming body A of mass 1m and

another body B of mass 2m initially at rest

A) B will recoil with greatest speed if 2 1m m

B) B will recoil with greatest momentum if 2 1m m

C) B will recoil with greatest kinetic energy if 1 2m m

D) B will recoil with greatest kinetic energy if 2 12m m

20. A wave travels on a string. The equation of the wave in this string is

0sin 30Y A kx wt . At x=0 this string is connected to another uniform string which

is present for x>0. mass density of strings is different after that. Wave is reflected from

a joint. If 64 % of the incident energy is getting reflected. The equation of transmitted

wave (Yt) and reflected wave (Yr) may be. (K`=wave propagation constant for

transmitted wave, )

A) 00.6 sin ' 30tY A k x wt B) 1.8 sin ' 30tY A k x wt

C) 0.8 sin 150rY A kx wt D) 00.8 sin 30rY A kx wt



CHEMISTRY: Max.Marks : 66

SECTION I



which ONLY ONE is correct. 21. If 2

2 HO HS S H O 0.86 H k Cal . Find H for ionization process of HS

A) +12.74 k Cal B) -12.74 k Cal C) -14.46 k Cal D) +14.46 k Cal

22. Which of the following statements is/are TRUE ?

20

|0.44 ; Fe Fe

E V 20

|0.25 ; Ni Ni

E V 30

|0.74 ; Cr Cr

E V 20

|2.37 ; Mg Mg

E V

P) Blocks of Mg are often strapped to the steel hulls of ships, since Mg prevents

corrosion by cathodic protection.

Q) Chrome plating on steel prevents corrosion by cathodic protection.

R) Nickel plating is suitable protective agent for corrosion of steel as long as no

scratch develops

A) P B) Q C) R D) PQR

23. Maximum KE of photo electrons is directly proportional to ____ of incident

radiations.

A) Intensity

B) wave length

C) wave number

D) number of photo electrons emitted per square cm.



24. One of the products formed when 2 2 7K Cr O reacts with concentrated 2 4H SO in cold is.

A) 2 4 3Cr SO B) 2 3Cr O C) 3CrO D) 2 2CrO Cl

25. Reactivity of borazole is greater than benzene because.

A)Borazole is non-polar compound B)B-N bonds in borazole are polar

C)Bolazole is electron difficient compound D)Complete aromatic character.

26.

OOH

OH OH

OH

and

OOH

OH OH

OH

are

A)Epimers B)Enantiomers C)Diastereomers D)Homomers

27. o-Aminobenzoic acid is treated with NaNO2 and dil. H2SO4 in cold condition and the

resulting solution is then reacted with N, N-dimethylaniline to give a red coloured dye

called methyl red. The structure of methyl red is,

A) N N

COOH NMe2

B) N N

COOH Me2N

C) N N NMe2

COOH

D) N NHOOC NMe2

28. 25 mL of household bleach solution was mixed with 30 mL of 0.50 M KI and

10 mL of 4N acetic acid. In the titration of the liberated iodine, 48 mL of 0.25 N

2 2 3Na S O was used to reach the end point. The molarity of the household bleach

solution is

A) 0.48 M B) 0.96 M C) 0.25 M D) 0.24 M



SECTION II Paragraph Type

This section contains 6 multiple choice questions relating to three paragraphs with two questions on each paragraph. Each question has four choices A), B), C) and D) out of which ONLY ONE is correct.11. Passage-1

Lead acid storage battery may be recharged after its usage. It consists of Pb anode

with coating of spongy lead, Pb with a coating of 2PbO , serves as cathode. 2 4H SO is

used as an electrolytic solution. 24 4 2 Pb SO PbSO e 0 0.31E V

22 4 4 24 2 2 PbO H SO e PbSO H O 0 1.70E V

29. During discharge of battery, which of the following statements are TRUE?

P) At anode and cathode respectively 2,Pb PbO are involved in the redox reaction

Q) Density and concentration of 2 4H SO decreases during discharging process

R) It needs no salt bridge since the oxidizing and reducing agents in both discharge

and recharge processes are solids.

S) Equivalent weight of 2 4H SO is 49 and that of 2H O is 18.

A) PQ B) PS C) PQR D) PQS

30. Find approximate energy obtained from lead storage battery in which 0.1 mole of lead

is consumed. Assume constant concentration of 2 4H SO to be 10m.

2.303 0.06; log 4 0.6 RT

F

A) 300 kJ B) 35 kJ C) 500 kJ D) 0.35 kJ



Passage-2

A yellow ppt of the compound ‘A’ is formed on passing 2H S through neutral solution

of the salt ‘B’. The compound ‘A’ is soluble in hot dil. 3HNO but in soluble in yellow

ammonium sulphide. The solution ‘B’ on treatment with small quantity of 3NH gives

white precipitate soluble in excess of the reagent forming. Compound ‘C’ . The

solution of ‘B’ gives white precipitate with small amount of KCN solution. The

precipitate is soluble in excess of reagent forming compound ‘D’, which on passing

2H S gives ‘A’. The solution of B in dil. HCl gives a white precipitate ‘E’ with 2BaCl

which is insoluble in conc. 3HNO .

31. Which of the following cation is present in ‘B’ ?

A) 3As B) 3Sb C) 2Zn D) 2Cd

32. The anion present in ‘B’ is

A) 24SO B) 2

3CO C) 23SO D) 2S

Passage-3

CH3CH3

3

2 2

1.2. /

OMe S H O 11 12 2C H O

3

1.2.NaOHH O

11 14 3C H O 3

3

1. ( )2.

CH Li excessH O 13 20 2C H O

HBr

13 19C H OBrO

CH3 CH3CH3

CH3

Compound Q Compound R

Compound P

Compound S

Compound T

Compound U

NaH



33. Which reaction is not found in the above scheme ?

A) Electrophilic addition B) Electrophilic substitution

C) Nucleophilic addition D) Nucleophilic substitution

34. Compound R is:

A)

O

OH

CH3

OHCH3

B)

OH

CH3

CH3

O

OH

C)

O

OH

OH

CH3

CH3

D)

OH

CH3

CH3

O

OH

SECTION III

Multiple Correct Answer(s) Type This section contains 6 multiple choice questions. Each question has four choices A), B), C) and D) out of

which ONE or MORE are correct.

35. Which of the following is/are TRUE ?

A) In NaCl crystal, each Na ion is touching 6 Cl ions but these Cl ions do not

touch each other.

B) In crystal lattices radius of tetrahedral void is smaller than octahedral void.

C) In NaCl crystal, / Na Clr r is greater than 0.414 required for exact fitting

D) No compound has both Schottky and Frankel defect



36. Which of the following is/are TRUE ? A) When a sample of 2 4H SO is treated with an equal number of moles of strong base

such as NaOH , the sample of acid is half neutralized. B) When a sample of 2

Ba OH is treated with an equal number of moles of strong acid such as ,HCl half of the sample of base is completely neutralized.

C) n n ionisation of WBSA SB SA WBH H H

D) n nNaOH HF NaOH strong acid

H H

37. 2XeF on reaction with 2H gives

A) Xe B) HF C) 2XeH D) 4XeF

38. Which charge /s on the 2N molecule would give a bond order of 2.5.

A)+1 B)+2 C)-1 D)-2

39. Quinine is the most important alkaloid obtained from cinchona bark which is used to treat Malaria. The molecular formula of the compound is C20H24N2O2. It may contain

A) 5 double bonds and 3 rings B) 6 double bonds and 4 rings C) 6 double bonds and 2 rings D) 7 double bonds and 3 rings 40. How many of the following compound(s) doesn’t exhibit tautomerism ?

A)

O

CH3 CH3

B)

CH3 CH3

NO

C)

O

O

D)

NO

NO



MATHS: Max.Marks : 66

SECTION I



which ONLY ONE is correct. 41. For r = 0, 1, ....., 10, let Ar, Br and Cr denote, respectively, the coefficient of xr in the

expansion of (1 + x)10, (1 + x)20 and (1 + x)30, then 10

rr 1

A (B10 Br – C10 Ar) is equal to

A) C10 – B10 B) 0 C) A10 (B102 – C10 A10) D) B10 – C10

42. M is the mid point of side AB of an equilateral triangle ABC. P is a point on BC such

that AP + PM is minimum. If AB = 20 then AP + PM is

A) 10 7 B) 10 3 C) 10 5 D) 10

43. If 9x + 1 + (a2 – 4a – 2)3x + 1 > 0 x R, then

A) a R B) a R+ C) a [1, ) D) a R {2}

44. sin2

__________2 20

2 52 3 4cos

dx IIf and I thenx

A)0 B)1 C)4 D)5

45. If the lengths of two perpendicular tangents from a point to a parabola are of 3 and 4

units and the length of latusrectum is K units, then [K]=---------

([.] represent greatest integer function)

A)2 B)4 C)8 D)10



46. a , b, c are three real and distinct numbers and ‘a ’ is H.M of b and c. then one of the

solutions of 2 2 2 2ax bxy cy bx cxy ay d is

A)

2 2 2 2

,2 2

dc b c db b cx y

b b bc c c b bc c

B)

2 2 2 2

,2 2

da b c dc a cx y

c b bc c a b bc c

C)

2 2 2 2

,2 2

db b c db a cx y

c b bc c a b bc c

D)

2 2 2 2

,2 2

db b c dc a cx y

c b bc c a b bc c

47. If 1Cos SinCos Sin

then

3 3Cos SinCos Sin

_______

A) 1 B) 0 C) 4 D) ½

48. A person wishes to lay a straight fence across a triangular field ABC, with A B C

so as to divide it into two equal areas. The length of the fence with minimum expense,

is (where ‘ ’ represents, area of triangle ABC)

A) B2 cot2

B) C2 tan3

C) A B Ctan tan tan2 2 2

D) A2 tan2



SECTION II

Paragraph Type This section contains 6 multiple choice questions relating to three paragraphs with two questions on each

paragraph. Each question has four choices A), B), C) and D) out of which ONLY ONE is correct.11. Passage-1

Consider a hyperbola 4xy and a line 2 4y x . O is centre of hyperbola. Tangent at

any point P of hyperbola intersect the co-ordinate axis at A and B.

49. Locus of circum centre of OAB is

A)an ellipse with eccentricity 12

B)an ellipse with eccentricity 13

C)a hyperbola with eccentricity 2 D) a circle

50. Let the given line intersect the x-axis at R. If a line through R intersect the hyperbola

at S and T, then the minimum value of RS RT is

A)2 B)4 C)6 D)8

Passage-2

The real valued functions 1 2 3, ,f x f x f x and 4f x are defined as

22 1

1 3 2

4 3

, 0 11 , 10 ,

x x f x f xf x x and f x f x

other wise f x f x

Answer the following questions

51. How many of the following products are necessarily zero for all x?

1 2 2 3 3 4. , . , .f x f x f x f x f x f x A)0 B)1 C)2 D)3



52. The value of 10

1 2 3 40

f x f x f x f x dx is

A) 543

B) 553

C) 563

D) 573

Passage-3 All the 52 cards of a well shuffled pack of playing cards are distributed equally or

unequally among 4 players named P1, P2, P3 & P4 .

For i = 1, 2, 3, 4, let

i = number of ace(s) given to Pi

i = number of black card(s) given to Pi

i = number of red card(s) given to Pi

i = number of diamond(s) given to Pi

53. The probability that i 1 i = 1, 2, 3, 4, is

A) 13C4 × 13

4!4

B) [224 + 3 × 212 – 313 – 1]/224

C) [134 – 4C1 124 + 4C2 114 – 4C3 104 + 4C4 94]/134

D) 1 – 4(3/4)13 – 6 (1/2)13 – (1/4)12

54. If i + i = 13 i = 1, 2, 3, 4 then the probability that i = 1 i = 1, 2, 3, 4, is

A) 54 72 /134 B) 3

2 2

1317 7 5

C) 34 132 /174 27 D) 3 2

4

7 313



SECTION III Multiple Correct Answer(s) Type

This section contains 6 multiple choice questions. Each question has four choices A), B), C) and D) out of which ONE or MORE are correct.

55. Let f(x).g(x) be differentiable at x = a and g(x) is also differentiable at x = a then

A) f(x) must be diff. at x = a

B) if f(x) is non diff. then g(a) = 0

C) if g(a) 0 then f(x) must be differentiable

D) if f(x) is discontinuous then g(a) = 0

56. 2 2

1 tA t ,t 1 t 1

. If A (a), A (b) and A(c) are the vertices of equilateral triangle then

(where a,b,c > 0)

A) minimum value of a2 + b2 + c2 is 3.

B) area of the triangle is 2 2 2

a b b c c a12 a 1 b 1 c 1

C) area of the triangle is 3 316

D) centroid of the triangle lies on a line parallel to y-axis

57. The value of the determinant cos( ) sin( ) cos 2

sin cos sincos sin cos

is

A) independent of for all R B) independent of and when = 1 C) independent of and when = 1 D) independent of for all



58. In a triangle ABC, perpendiculars drawn from vertices A, B, C meet the opposite sides

BC, CA, AB at D, E, F respectively, triangle DEF is completed. The perimeter of

triangle DEF is greater than or equal to 3 3 r, where r is in-radius of triangle ABC.

Also r 3 and perimeter of triangle ABC is 18. Then

(A) triangle ABC is right angled

B) triangle ABC is equilateral

C) area of triangle ABC is 9 3

D) ratio of area of triangle ABC to triangle DEF is 4 : 1 59. Let z1 and z2 be two distinct complex numbers and let w = (1 – t)z1 + tz2 for some real

numbers t with 0 < t < 1. If Arg (z) denotes the principal argument of a non–zero complex number z, then

A) |w – z1| + |w – z2| = |z1 – z2| B) Arg (w – z1) = Arg (w – z2)

C) 1 1

2 1 2 1

w z w z0

z z z z

D) Arg (w – z1) = Arg (z2 – z1)

60. Let :f R R such that '2 2 4 , 0 0.f x y f x f y xy x y R and f If

1 0 2

1 2 30 1 1/2

, ,I f x dx I f x dx and I f x dx then

A) 1 2 3I I I B) 1 2 3I I I C) 1 2 3I I I D) 1 2 3I I I

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