11-jee-adv grand test 11 question paper (p 1) - 18-05-2014

IIT Section

Subject Topic Grand Test – Paper I Date

C + M + P Grand Test – 11 IIT – GT – 11

18th May 2014 I20140504

Max. Marks: 180 Duration: 3 Hrs

This paper consists of 60 questions with 3 parts of Chemistry, Mathematics and Physics

Each Part consist of 3 sections

Section – I : 10 Multiple Choice Questions with one correct answer (with negative marks). A

correct answer carries 3 Marks. A wrong answer carries a penalty of 1 mark

Section – II : 5 Multiple Choice Questions with one or more correct answers (No negative

marks). A correct answer carries 3 Marks.

Section – III : 5 Integer Type question with one correct answer. A correct answer carries 3

Marks. A wrong answer carries a penalty of 1 mark

2. Darken the appropriate bubble using a pen in the OMR sheet provided to you. Once entered,

the answer cannot be changed. Any corrections or modifications will automatically draw a

penalty of 1 mark.

3. Use of calculators and log tables is prohibited.

4. No clarification will be entertained during the examination. Doubts in the paper can be

reported to the coordinator after the exam.

All the best !!

Useful Data

At. Wt.:

N = 14; O = 16; H = 1; S = 32; Cl = 35.5; Mn = 55; Na = 23; C = 12; Ag = 108; K = 39; Fe = 56; Pb = 207

Physical constants:

346.626 10 J.sech , 23 -1

aN 6.022 10 mol , 8 -1C 2.998 10 ms , 31

em 9.1 10 kg

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Ace Insignia Rough Work

Chemistry

Section I

Multiple Choice Questions with one correct answer. A correct answer carries 3 marks. A wrong

answer carries a penalty of 1 mark 10 x 3 = 30

1. 2

4 ( )aqCoCl

is blue in colour while

2

2 6 aqCo H O

is pink. The colour of reaction mixture

2 2

2 4 264 6

aq laqaqCo H O Cl CoCl H O

is blue at room temperature while it is pink

when cooled hence

(a) reaction is exothermic

(b) reaction is endothermic

(c) Equilibrium will shift in forward direction on adding water to reaction mixture

(d) Equilibrium will not shift in backward direction on adding water to equilibrium mixture

2. The solubility products of 3

Al OH and 2

Zn OH are 238.5 10 and 141.8 10 respectively.

If 4NH OH is added to a solution containing 3 2Al and Zn ions, then substance precipitated first is

(a) 3

Al OH (b) 2

Zn OH (c) both together (d) none of these

3. An organic compound P on keeping in slightly acidic aqueous solution gives yellow precipitate

with 2,4-dintirophenylhydrazine. It also decolourizes 2 4/Br CCl solution and gives coloured

solution/precipitate with neutral 3FeCl solution. The structure of P can be

(a) 3 2OHC C CH CHO (b)

(c) (d)

(CH3)3 C C H

O

(CH3)3 C C CH

O

CHO

CH3 O O

CH3 CH3

CH3

CH3

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4. In which of the following reaction allyl alcohol will be formed with fastest rate, on reaction with

aqueous NaOH solution?

(a)

(b)

(c)

(d)

5. The percentage of copper in a copper (II) salt can be determined by using a thiosulphate titration.

0.305g of a copper (II) salt was dissolved in water and added to an excess of potassium iodide

solution liberating iodine according to the following equation.

2

2( )2 4 2 aqsCu aq I aq CuI I

The iodine liberated required 24.5 3cm of a 0.100 mole 3dm solution of sodium thiosulphate.

2 2

2 3 2 4 62 2aq aq aq aqS O I I S O . The percentage of copper, by mass in the copper (II) salt is

[Atomic mass of copper = 63.5]

(a) 64.2 (b) 51.0 (c) 48.4 (d) 25.5

CH2 CH CH2 O C2H5

CH2 CH CH2 O C CH3

O

CH2 CH CH2 O S

O

O

NO2

CH2 CH CH2 O C

O

NO2

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6. A complex cation is formed by Pt with ligands (in proper number so that coordination number of

Pt becomes six). Which of the following can be its correct IUPAC name?

(a) diamminethlyenediamminedithiocyanato –S- platinate (II) ion

(b) diamminethlyenediamminedithiocyanato –S- palatinate (IV) ion

(c) diamminethlyenediamminedithiocyanato –S- platinum (IV) ion

(d) diamminebis (ethylenediammine) dithiocyanate – S – platinum (IV) ion

7. The number of chiral centres present in the following

compound is

(a) 7 (b) 8

(c) 9 (d) 10

8. The standard reduction potentials of 2 2/ and /Cu Cu Cu Cu are 0.337 V and 0.153 V respectively.

The standard electrode potential of /Cu Cu half-cell is

(a) 0.184V (b) 0.827V (c) 0.521V (d) 0.490V

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9. 2, 3X Dihydroxy Butane dioic acid. The stereochemical formula of diastermer ' 'Y of optically

active compound ' 'X is

(a)

(b)

(c) (d)

10. In which of the following molecules all the effects namely inductive, mesomeric and

hyperconjugation operate?

(a) (b)

(c) (d)

COOH

H OH

HOOC H

OH

OH

H COOH

HOOC H

OH

OH

H COOH

HO COOH

H

COOH

HO H

H OH

COOH

Cl CH3

CH3

COCH 3

CH3

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Section II

Multiple Choice Questions with one or more correct answer. A correct answer carries 3 marks.

No negative mark 5 x 3 = 15

11. Which observation/s will be correct about the major products X and Y of the following reaction?

12. Which of the following statements are correct?

(a) Average velocity of molecules of a gas in a container is zero

(b) All molecules in a gas are moving with the same speed

(c) If an open container is heated from 300K to 400K , the fraction of air which goes out with

respect to originally present is 1/4

(d) If compressibility factor of a gas at STP is less than unity then its molar volume is less than

22.4L at STP

ClD

D D

DD

D D

Cl

D D

D

DD

D D

(a) X is (b) X is

(c) Y is (d) Y is

DD

D D

YSO2Cl2

peroxide

alc.KOH/ X

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13. Titration curves for 0.1M solutions of three weak acids

1 2 3,HA HA and HA with ionization constants 1 2 3, andK K K respectively

are plotted as shown in the figure. Which of the following is/are true?

(a) 2 1 3 / 2K K K (b) 1 3K K

(c) 1 2K K (d)

2 3K K

14. In which of the following pairs hybridization of the central atom is same?

(a) 3 3,ClF ClF O (b)

3 3 2,ClF O ClF O (c) 2 4,ClF O ClF O

(d) 4 4,ClF O XeOF

15. Which statement is/are correct about the following reaction?

2

hR H X R X HX

(a) The selectivity of free radical for C – H bonds of different types follows the order

Br Cl F

(b) The reactivity of halogens towards a given C H bond follows the order2 2 2 2I F Br Cl

(c) The reactivity of alkanes follows the order isobutene > propane > ethane > methane

(d) One mole of product is formed by absorption of one photon of light of appropriate wave

length

Section III

Integer answers type questions. Each carries 3 marks. A wrong answer carries a penalty of 1

mark 5 x 3 = 15

16. A compound (P) is formed by heating xenon and fluorine in the molecular ratio of 1:20 under

pressure in a nickel tube. (P) Undergoes stepwise hydrolysis to yield final product (Q). (Q) is also

formed when (P) is stored in glass vessels. The no. of lone pairs around central atom in (Q) is/are

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17. A sample of wustite, ,x yFe O contains one Fe (III) for every three Fe (II). Calculate the value of x.

18. An optically active compound (A), 3 7 2C H O N

forms a hydrochloride but dissolves in water to give a

neutral solution. On heating with sodalime, (A) yields 2 7C H N B . Both (A) and (B) react with

2NaNO and HCl , the former yielding a compound (C) 3 6 3 ,C H O which on heating is converted to (D),

6 8 4C H O while the latter yields (E), 2 6 .C H O The types of carbon to which N is attached to (A) is

19. A weak field octahedral complex of 2Ni has magnetic moment value of 2.82 B.M. The number of

electrons in the 2gt level 2Ni will be

20. The number of carbon atoms in the ring in compound C is

CH3

CH3

4 4.dil KMnO HIO OHA B C

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Mathematics

Section I



21. Suppose ABCDEFGH I J is a ten digit number, where the digits are distinct. It is given that :

A B C and 9A B C ,

D E F are consecutive even digits,

and G H I J are consecutive odd digits.

The value of A is

(a) 8 (b) 7 (c) 6 (d) 5

22. If the ends of a quadrant of a circle have the coordinates 1, 3 and 3, 1 then the centre of such a

circle is

(a) 2, 2 (b) 3, 3 (c) 4, 4 (d ) 2, 6

23. Let , , a b x and y satisfy 4ax by , 2 2 2ax by and 3 3 3.ax by Then the value of

(2 1)(2 1)x y is

(a) 4 (b) 3

(c) 5 (d) cannot be determined

24. Let ( )f x be a real-valued function satisfying 2( ) ( )af x bf x px qx r , where ,a b are distinct

real numbers and ,p q and r are non-zero real numbers. Then ( ) 0f x will have a real solution, if

(a) 2 2

4

a b r

a b pq

(b)

2 2

4

a b r

a b pq

(c)

2

2

4a b pr

a b q

(d)

2

2

4a b pr

a b q

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25. An event x can take place in conjunction with any one of the mutually exclusive events , ,A B C . If

, ,A B C are equally likely and the probability of x is 5

12 and the probability of x taking place

when A has happened is 3

8 while it is

1

4 when B has taken place then the probability of x taking

place in conjunction with C is

(a) 5

24 (b)

3

8 (c)

1

3 (d)

5

8

26. The solution of the differential equation 2 2 2 22 tan( ) 2dy

x y x y xydx

, given (1)2

y

, is

(a) 2 2 1sin( ) xx y e (b) 2 2sin( )x y x (c) 2 2cos( ) 0x y x (d) 2 2sin( ) xx y e e

27. If ( , )h k is a point on the axis of the parabola 2 2 22( 1) 2( 1) ( 2)x y x y from where three

distinct normals may be drawn, then

(a) 2h (b) 4h (c) 8h (d) 8h

28. 3

4 2 1

sin

(cos 3cos 1)[tan (sec cos )]

xdx

x x x x

(a) 1tan (sec cos )x x C (b) 1log tan (sec cos )x x C

(c) 2

1

(sec cos )C

x x

(d) none of these

29. Let f x be a continuous function on 0, 1 . If 1 1

0 01, 2f x dx x f x dx and

1 2

03x f x dx , then the number of roots of the equation 0f x in 0, 1 is

(a) exactly one (b) atleast one (c) atmost one (d) zero

30. The value of 1 1

2 3n n

r srs

r s

, where 0, if

1, if rs

r s

r s

, is

(a) 6

(6 1)5

n (b) 6 1n (c) 1

(6 1)5

n (d) none of these

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Section II



31. The th4 term in the expansion of 10

32

8

x

has the maximum numerical value. Then the values of

x can be in the interval

(a) 64

, 221

(b)64

2, 21

(c)64

, 21

(d)64

, 21

32. Three vectors p 0p , q and r are such that 3p q p r . Also 1p q and 1

3r . If the

angle between q and r is 60 , then

(a) 3q r p (b) 3q r p (c) 3 2q r p (d) 3 2q r p

33. Let , , , a b c d be in A.P. with common difference D . If ( ) 1

t a t b t a c

f t t b t c t

t c t d t b d

and

4

0

( ) 32f t dt , then D

(a) 0 (b) 2 (c) 2 (d) 1

34. Given that the complex numbers which satisfy the equation 3 3 350zz zz form a rectangle in the

Argand plane with the length of its diagonal having an integral number of units, then

(a) area of the rectangle is 48 square units

(b) If 1 2 3 4, , ,z z z z are the vertices of the rectangle, then 1 2 3 4 0z z z z

(c) the rectangle is symmetrical about the real axis

(d) arg 1 2( )4

z z

or 3

4

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35. The number of ways of choosing a triplet ( , , )x y z such that max , z x y and

, , 1, 2, 3, , , 1x y z n n is

(a) 1 23 3

n nC C (b) ( 1)(2 1)

6

n n n (c) 2 2 21 2 n (d) 2 1

3 22( )n nC C

Section III


mark 5 x 3 = 15

36. Let a function ( )f x satisfy ( ) ( ) ,xf x f x e (0) 0f and (0) 1.f Then 5 (5)e f

37. The number of positive integral solutions of the equation 1 2 3 4 5 1 2 3 4 5x x x x x x x x x x is .k

Then 10

k=

38. If 2 2 2 2 1x y z xyz , then 2 2 2

3

1 1 1

dx dy dz

x y z

39. 3 2

2 2

( 1)

xdx

x x x x

1 1

tanP x Q C P Qx

40. A light ray 1L emerges from the point ( 5, 6) making an angle 1tan ( 2) with x axis. It is

reflected on x axis along the line 2L and then reflected on y axis along the line

3 : 0.L ax by c If g.c.d of , ,a b c is 1 , then a b c

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Physics

Section I



41. A man watches a steamboat starting from a point directly in front of him on the opposite bank of

river flowing at a speed of 18 km/hr. The boat has a velocity vo with respect to river at an angle o

with the bank. If the steamboat blows a whistle of frequency fo , then for which of the following

combinations of vo and o the frequency registered by the man will be highest?

(a) 0 010 / , 30m s (b)

0 010 / , 30m s

(c) 0 010 / , 60m s (d) same for all the above

42. The ratio of specific heats at constant pressure & volume of a gas is 9 / 7 , then the

number of degrees of freedom of the gas molecules is:

(a) 3 (b) 5 (c) 6 (d) 7

43. A uniform bar of mass M and length L collides with a horizontal

surface. Before collision velocity of C.O.M. of bar was V0 and angular

velocity was zero. Just after Collision, velocity of centre of mass of bar

becomes V in upward direction (as shown in the figure). Angular

velocity of bar just after impact is

(a) 06 cosV V

L

(b)

06 cosV V

L

(c)

0 cos

6

V V

L

(d)

0 cos

6

V V

L

44. A particle of charge q and mass m starts moving from the origin under the action of an electric field

0ˆE E i and magnetic field 0

ˆB B k . Its velocity at ,3,0x is ˆ ˆ4 3i j . The value of x is

(a) 0 036E B

qm (b)

0

25

2

m

qE (c)

0

10m

qE (d) 0 025E B

m

M,L

V

v 0

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45. The de Broglie wavelength of the electron in the first Bohr orbit of the hydrogen atom is

(a) equal to the diameter of the first orbit

(b) equal to the circumference of the first orbit

(c) equal to half the circumference of the first orbit

(d) independent of the size of the first orbit

46. In the arrangement shown in the figure when the switch S2 is open, the

galvanometer shows no deflection for / 2l L . When the switch 2S is

closed, the galvanometer shows no deflection for 5

12l L . The internal

resistance (r) of 6V cell, and the emf E of the other battery are

respectively

(a) 3 , 8 V (b) 2 , 12V

(c) 2 , 4V (d) 3 , 12V

47. A bird in air looks at a fish directly below it inside in a transparent liquid in a tank. If the distance of

the fish as estimated by the bird is 1h and that of the bird as estimated by the fish is

2h , then the

refractive index of liquid is

(a) 2

1

h

h (b) 1

2

h

h (c) 1 2

1 2–

h h

h h

(d) 1 2

1 2

–h h

h h

48. A thin horizontal disc of radius R is located within a

cylindrical cavity filled with oil whose viscosity is ' ' .

The distance between the disc and horizontal planes

of cavity is ' 'h . The power developed by the viscous

forces acting on the disc when it rotates with angular

velocity is (The end effects are to be neglected)

(a) 2 44 R

h

(b)

2 4

4

R

h

(c)

2 4

2

R

h

(d)

2 4R

h

A

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49. A cyclic process ABCA is performed on an ideal gas in which gas

expanded isobarically from A to B , then it is cooled isochorically

from B to C and finally it is compressed isothermally from C to

A . The net heat +20 joule is absorbed in this cyclic process.

Similarly in process BCDB heat absorbed is +5 joule. For a cyclic

process ADCA performed on the same ideal gas,

(a) +15 joule net heat is absorbed (b) +15 joule net heat is rejected

(c) +25 joule net heat is absorbed (d) +25 joule net heat is rejected

50. The sensitivity of a potentiometer can be increased by

(a) decreasing the length of potentiometer wire

(b) increasing the length of potentiometer wire

(c) increasing the emf of the cell in primary circuit

(d) decreasing the external resistance connected in primary circuit

Section II



51. A balloon having a ladder connecting its top and bottom is floating fully

submerged inside water in a large container. A person of mass m standing

at the bottom most rung of the ladder climbs slowly to the top whose

height is H . Mass of the balloon is M . Neglect friction everywhere. Then,

(a) the work done by the person is mgH

(b) the centre of mass of the balloon and person system does not change

(c) the centre of mass of the ( balloon + person + water ) system does not change

(d) during climbing up the ladder the pressure at the bottom of the container becomes more

than the pressure when the man is not climbing

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52. Electric field E acts horizontally in a region of space. The gravitational field g acts vertically down.

Then

(a) the magnitude of the resultant field 2 2E g

(b) the direction of the resultant field is 1tang

E with horizontal

(c) the direction of the resultant field is 1tanE

g with horizontal

(d) the resultant field is not defined

53. Two identical capacitors 1C and

2C are kept connected to two identical batteries. Two identical

dielectric blocks are inserted in the gaps of the two capacitors. The

dielectric in 1C is introduced very slowly, while that in

2C is

introduced very fast. Heat loss in both the circuits due to dielectric

insertion are 1H and

2H respectively. The mechanical work done by

the capacitors in pulling the dielectric are 1W and

2W respectively,

Then

(a) 1 2 1 2 andW W H H (b) 1 2 1 2 andW W H H

(c) 1 2 1 2 andW W H H (d)

1 2 1 2 andW W H H

54. 40

19 K converts to 40

18 Ar by positive decay as well as electron capture. Let Q values for the decay

and electron capture be 1Q and

2Q respectively in the above reaction.

(a) 1 2Q Q

(b) 1 2Q Q

(c) Neutrino emitted in positive decay is monoenergetic

(d) Neutrino emitted in electron capture is monoenergetic

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55. A solid uniform hemisphere is placed vertically 1 as shown and

released on a rough horizontal surface. It rolls without slipping to

a position 2 where its flat surface becomes horizontal. At this

position 2

(a) Friction force on the hemisphere is zero

(b) Normal reaction force Mg

(c) Friction force 0 and acts to left

(d) Normal reaction force Mg

Section III


mark 5 x 3 = 15

56. A liquid of density given by 0 1 y is stored in a container, where y is the distance from the

top of the liquid surface. 12.

3m

0 is the density of the liquid at the top level. A very small hole

is made at the bottom of the container. Find the velocity of efflux (in m/s) when the liquid height is

1m (assume streamline flow)

57. Heat is generated uniformly per unit volume inside a spherical volume of radius 1m at rate of

320 /W m . The thermal conductivity of the spherical volume is1

/6

W mK . If the outer surface

temperature of the sphere is 20 C . If the temperature of the centre of the sphere is 10x (in degree

centigrade), find the value of x .

58. In a nuclear reactor an element X decays to a radioactive element Y at a constant rate of 1510 atoms

per second and releases 100MeV energy per each decay. Half-life of Y equals to X and decays to a

stable product Z . The decay of each nucleus of Y releases 50MeV . All energy released inside the

reactor is used to produce electricity at an efficiency of 25% . Calculate the electrical power in KW

generated in the reactor in steady state.

R

(1)

M

(2)

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59. The radius of curvature of each surface of an equi-convex lens is 42R cm . Refractive index of the

glass 1.25 . If the final image forms after four internal reflections inside the lens (for paraxial

incident beam) calculate the distance (in cm) of the image from the lens.

60. A parallel beam of light falls normally on the first face of a prism of small angle. At the second face

it is partly refracted and partly reflected, the reflected beam striking the first face again and

emerging from it in a direction making and angle 0 16 30 with the reversed direction of the incident

beam. The refracted beam is found to have undergone a deviation of 0 11 15 from the original

direction. Find the angle of prism in degrees.

11-jee-adv grand test 11 question paper (p 1) - 18-05-2014

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