jee-adv grand test question paper (p 2) - 10-05-2014

IIT Section

Subject Topic Grand Test – Paper II Date

C + M + P Grand Test – 07 IIT – GT – 07

10th May 2014 I20140510

Max. Marks : 237 Duration : 3 Hrs

1. This paper consists of 57 questions with 3 parts of Chemistry, Mathematics and Physics

Each Part consist of 4 Sections

Section – I : 6 Multiple Choice Questions with one correct answer (with negative marks). A

correct answer carries 5 Marks. A wrong answer carries a penalty of 2 mark

Section – II : 5 Integer type questions. A correct answer carries 3 Marks. No negative marks.

Section – III : 6 Comprehension Type questions. A correct answer carries 3 Marks. A wrong

answer carries a penalty of 1 mark

Section – IV : 2 Matrix Match type questions. A correct answer carries 8 Marks. No

negative 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.

5. 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

IIT Section



10th May 2014 I20140510

Ace Insignia Rough Work

Chemistry

Section I

Multiple Choice Questions with one correct answer. A correct answer carries 5 marks. A wrong

answer carries a penalty of 2 marks 6 x 5 = 30

1. The shape and hybridisation of some xenon oxyfluorides are given choose the wrong set

(a) 32 ShapeXeOF T sp d (b) 3 2

4 Square pyramidalXeOF sp d

(c) 32 2 Distorted trigonalbipyramidalXeO F sp d (d) 3

3 2 OctahedralXeO F sp d

2. The standard half-cell reduction potential for |Ag Ag is 0.7991V at 25 c . Given the

experimental value spK = 101.56 10 for AgCl , calculate the standard half-cell reduction

potential for the |Ag AgCl electrode

(a) 0.2192V (b) 0.2192V (c) 1.2192V (d) 1.2192V

3. Give the structure of the compound X formed in the following reaction.

(a )

O

O

(b )

OCH3

OH

O

(c ) O O CH3

H5C2

(d)

O O

OCH3

O

O

X

2 5(i) C H MgI

3(ii) H OÅ

IIT Section



10th May 2014 I20140510


4. Which is optically inactive?

5. Which of the following acids will not evolve 2H gas on reaction with alkali metals?

(a) hydrazoic acid only (b) perxenic acid only

(c) boric acid only (d) all of these

6. Stomach acids, a dilute solution of HCl in water, can be neturalized by reaction with sodium

hydrogen carbonate. 3( ) ( ) ( ) 2 2( )aq aq aq glNaHCO HCl NaCl H O CO . How many millilitres

of 0.125 M 3NaHCO solution are needed to neutralize 18.0mL of 0.100M HCl ?

(a) 14.4 mL (b) 12.0 mL (c) 14.0 mL (d) 13.2mL

Section II

Integer answers type questions. Each carries 3 marks. No negative marks. 5 x 3 = 15

7. In a certain polluted atmosphere containing 3O at steady state concentration of 82.0 10 ,M

the hourly production of 3O by all sources was estimated as 157.2 10 .M if the only mechanism

for destruction of 3O is the second order reaction, 3 22 3 .O O The rate constant for the

destruction reaction defined by the rate law for 3 3 1 110

d Ois x Lmol s

dt

. Value of x is

C CC C

a

b

C

a

b

(a) (b)

(c) (d) CC C

a

b

a

b

CC C

a

b

C

a

b

a

N

d

e

b

IIT Section



10th May 2014 I20140510


8. The density of phosphorous vapour at 310 C and 775 torr is 32.64 /g dm . Number of

phosphorous atoms in a molecule is

9. When a compound, on reaction with 2 3Na CO gives compound B with which sulphur gives

compound C . The compound C is used in photography. The number of bonds in a

molecule of C is

10. 3

6Fe CN has

1.41BM and 3

2 6Fe H O

has 5.92 .BM The sum of unpaired

3d electrons in Fe in both the compounds is

11. An organic compound A fumes in moist air and reacts with cold water to give an acid B .

Acid B reacts with 3NH to give amide C . C on heating with 2 5P O gives propane nitrile.

The number of functional isomers of A is

Section III

Comprehension type questions. A correct answer carries 3 marks. A wrong answer carries a

penalty of 1 mark 6 x 3 = 18

Comprehension – I

In presence of metal catalyst , ,Ni Pt Pd hydrogen adds to

When nickel is used as a catalyst, the reaction is carried out at 200 300 C and in presence of Pt or

Pd , the hydrogenation can occur even at room temperature. Hydrogenation reactions are

exothermic in nature. Hydrogenation follows free radical mechanism. The metal catalysts are used

in finely divided state in solvent like ethanol. These are classified as heterogenous catalysts. Both

C C

C C and bonds

IIT Section



10th May 2014 I20140510


2H and alkene get adsorbed at the surface of metal. The less crowded alkene adsorbs with faster

rate. Both breaking of bond of alkene and bond of 2H take place at metal surface. If palladium

is precipitate at the surface of calcium carbonate and is treated with quinolone it becomes deactivated

for adsorption of alkenes. But it can effectively catalyse hydrogenation of C C . The alkene can

adsorb at the surface of poisoned metal catalyst and syn addition of hydrogen atoms take place.

If sodium or lithium metals dissolved in liquid ammonia are used with alkynes then the metal

transfers its electrons to framework of C C bond and an anion radical is formed. Liquid

ammonia provides H atom and a vinylic radical is formed

12. Which of the following involves homogeneous reduction?

(a) 2 /2 2 3 3

H NiCH CH CH CH

(b) 3( )/3 3 3 3 2

lNa NHCH C C CH CH CH CH CH NaNH

(c) 2 3/ / /3 3

H Pd CaCO QuinolineCH COCl CH CHO

(d) 2 4/ / /3 3 2

H Pd BaSO quinolineCH C CH CH CH CH

13. The relative rate of catalytic hydrogenation of following alkenes is

(a) I>IV>III>II (b) II>III>IV>I (c) III>IV>I>II (d) II>IV>I>III

(I) (II) (III) (IV)

IIT Section



10th May 2014 I20140510


14. In which case the reaction is most exothermic with 2 / ?H Ni

Comprehension – II

On adding copper sulphate to an aqueous solution of a compound A a brown precipitate is

obtained which turns white on addition of excess of sodium thiosulphate solution. When Ag ion

solution is added to the aqueous solution of A . A yellow curdy precipitate is obtained which is

insoluble in ammonium hydroxide

15. The yellow curdy ppt. which is insoluble in 4NH OH is of

(a) AgBr (b) AgCl (c) AgI (d) none of these

16. The compound (A) is

(a) KI (b) KCl (c) NaCl (d) NaBr

17. The brown ppt. which turns white on addition of excess of 2 2 3Na S O solution is of

(a) 2CuI (b) 2 2Cu I (c) 2CuCl (d) 2 2Cu Cl

(a) (b)

(c) (d)

IIT Section



10th May 2014 I20140510


Section IV

Matrix Match type questions (4 rows per matrix type, 2 marks per row) 2 x 8 = 16

18. Matrix Match –I

Column I (Complex)

Column II (Magnetic Moment in B. M)

(A)

4

6Fe CN

(p)

1.73

(B) 3

2 6Ti H O

(q) 5.91

(C) 2

2 6Ni H O

(r) 0.00

(D) 3

6FeF

(s) 2.83

19. Matrix Match –II

Column I

Column II

(A)

zero

(p)

1 1mol lit s

(B) first

(q) 1 1mol lit s

(C) second

(r) 1s

(D) third

(s) 2 2 1mol lit s

IIT Section



10th May 2014 I20140510


Mathematics

Section I



20. Two cards are selected randomly from a pack of 52 cards. The probability that the first is a club

and the second is not a queen is

(a) 82

221 (b)

51

221 (c)

1

221 (d)

4

17

21. Let 0x . If the angle between the vectors 2ˆˆ ˆlog 6 3a c x i j k and

2 2ˆˆ ˆlog 2 2 logb x i j c x k is obtuse, then c belongs to

(a) 0, (b) , 0 (c) 4

, 03

(d) 2

1, 0 0,3

22. If 2 2 2 2 0a b c ab , then the point of concurrency of the family of straight lines

0ax by c lies on the line

(a) y x (b) 1y x (c) y x (d) 1x y

23. Let , , ,x y z n be positive integers and let 6n . If 2 3x y z n , then the number of ordered

triplets , ,x y z satisfying the above equation is

(a) 6n

nC (b) 3n

nC (c) 23

n C (d) none of these

24. The quadratic equation

1

x b x c x c x a x a x b

b a c a c b a b a c b c

has

(a) two real and distinct roots (b) two equal roots

(c) complex roots (d) infinite roots

IIT Section



10th May 2014 I20140510


25. Let ,z w be complex numbers such that 0z iw and arg zw . Then arg z equals

(a) 4

(b)

2

(c)

3

4

(d)

5

4

Section II


26. Suppose a matrix A satisfies the equation 2 5 7 0A A I . If 5 ,A aA bI then the value of

2 3 1450a b is

27. Let [ ]x denote the greatest integer x . If the period of the function

sin cos tan

12 4 3

x xx

is , then the value of 201 4820 is

28. If

2 3 97

1

97lim

1x

x x x xl

x

, then 4760 l is equal to

29. A balloon is in the form of a right circular cylinder of radius 1.5 m and length 4 m and is

surmounted by hemispherical ends. If the radius is increased by 0.01 m and the length by

0.055 m, the percentage change in the volume of the balloon is %abcd . If abcd is equal to

2380 k , then k

30. A special dice is so constructed that the probabilities of throwing 1, 2, 3, 4, 5 and 6 are

1 1 2 1 1 1 2, , , ,

6 6 6 6 6

k k k k k

and

1

6

k respectively. If two such dice are thrown and the

probability of getting a sum equal to 9 lies between 1

9and

2

9, then the number of integral

solutions of k is

IIT Section



10th May 2014 I20140510


Section III



Comprehension – I

Euler’s substitution

Integrals of the form 2( , )R x ax bx c dx are calculated with the aid of one of three Euler

substitutions

1. 2ax bx c t x a if 0a

2. 2ax bx c tx c if 0c

3. 2ax bx c x t if 2ax bx c a x x , , if is a real root of

2 0ax bx c

31. Which of the following functions does not appear in the primitive of 2

1

1 2 2x x

if t is a function of x ?

(a) log 1e t (b) log 2e t (c) 1

2t (d) none of these

32. Which of the following functions does not appear in the primitive of 2 1

dx

x x x

if t is a

function of ?x

(a) loge t (b) log 2e t (c) log 1e t (d) log 1t

IIT Section



10th May 2014 I20140510


33. Which of the following substitutions can be used for evaluating 27 10

xdx

x x ?

(a) 2

2

5 2

1

tx

t

(b)

2

2

5

2

tx

t

(c)

2

2

2 5

3 1

tx

t

(d) none of these


Consider the relation 2 24 5 6 1 0,l m l where ,l mR and let the line 1 0lx my touch a

fixed circle C

34. The centre and radius of C are

(a) 2, 0 , 3 (b) 3, 0 , 3 (c) 3, 0 , 5 (d) none of these

35. Tangents PA and PB are drawn to C from the points P on the line 1 0x y . Then the

chord of contact AB passes though the fixed point

(a) 1 5

,2 2

(b)

1 4,

3 3

(c) 1 3

, 2 2

(d) none of these

36. The number of tangents which can be drawn from the point 2, 3 to the circle C is

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

IIT Section



10th May 2014 I20140510


Section IV



Column I Column II

(A) Let 2 7 .z i z i k The values of k for which the

locus of z is an ellipse are

(p) 7

(B) For any complex number ,z the minimum value of

2z z i is

(q) 8

(C) Let 3 4z z i k . The values of k for which the

locus of z is a hyperbola, are

(r) 2

(D) Let 3 4 ,

50

kz i az az b where 3 4 .a i Then

the locus of z is a hyperbola if k

(s) 4

(t) 5


Let A and B are two independent events such that 1 1

, .3 4

P A P B

Column I

Column II

(A)

P A B

(p)

1

12

(B) P A A B

(q) 1

2

(C) P B A B

(r) 2

3

(D) P A B

(s) 0

IIT Section



10th May 2014 I20140510


Physics

Section I



39. A projectile of mass 3 m explodes at highest point of its path. It breaks into three equal parts.

One part retraces its path; the second one comes to rest. The range of the projectile was 100 m. If

no explosion would have taken place, the distance of the third part from the point of projection

when it finally lands on the ground is

(a) 100 m (b) 150 m (c) 250 m (d) 300 m

40. Three capillary tubes of same radius 1 cm but of lengths 1m, 2m and 3m are fitted horizontally to

the bottom of a long cylinder containing a liquid at constant pressure flowing through these

tubes. What is the length of a single tube which can replace the three capillaries

(a) 6

11m (b) 6m (c) 5 m (d)

13

4m

41. 5.6 litre of helium gas at STP is adiabatically compressed to 0.7 litres. Taking the initial

temperature to be 1T the work done in this process is

(a) 19

8RT (b) 1

3

2RT (c) 1

15

8RT (d) 1

9

2RT

42. The wavelength of the first spectral line in the Balmer series of hydrogen atom is 6561 oA . The

wave length of second spectral line in the Balmer series of singly-ionized helium atom is

(a) 1215 oA (b) 1640 oA (c) 2430 oA (d) 4687 oA

IIT Section



10th May 2014 I20140510


43. A 2 F capacitor is charged as shown in figure. The

percentage of it’s stored energy dissipated after the switch S

is turned to position 2 is

(a) 6%

(b) 20%

(c) 75%

(d) 80%

44. A particle of charge q and mass m moves in a circular orbit of radius r with angular speed .

The ratio of the magnitude of its magnetic moment to that of its angular momentum depends on

(a) and q (b) , q and m (c) q and m (d) and m

Section II


45. A car leaves station X for station Y every 10 min. The distance between X and Y is 60 km. The

car travels at speed 60 km/h. A man drives a car from Y towards X at speed 60 km/h. If he

starts the moment when first car leaves station X , how many cars would he meet on route?

46. Power supplied to a particle of mass 2 kg varies with time as 23

2

tP W . Here t is in second. If

velocity of particle at 0t is 0v . The velocity of particle at time 2t s in m/s will be

47. In Young’s double slit experiment 410d

D

( d = distance between slits, D = distance of screen

from the slits). At a point P on the screen resulting intensity is equal to the intensity due to

individual slit oI . Then the distance of point P from the central maximum in mm is (Wave

length of source is 6000Ao

)

2

s

1

2 F

8 F

V

IIT Section



10th May 2014 I20140510


48. Mean free path ( ) in a fission reaction is the average distance covered by a neutron between two

fissions. Generation of nearly 200 neutrons are needed to fission all the nuclei in 10kg of U 23592 .

If cm 4 and the fastest moving neutrons generated in a fission reaction have an energy of

2MeV, then the time for 200 neutron generation is found to be p 710 seconds. Find ' 'p .

49. Some magnetic flux is changed from a coil of resistance 10 . As a

result an induced current is developed in it, which varies with time

as shown in figure. the magnitude of change in flux through the coil

in webers is

Section III



Comprehension – I

Two rods 1 and 2 are released from rest as shown in figure. Given :

1 4l l , 1 2m m , 2 2l l and 2m m . There is no friction between the

two rods. If be the angular acceleration of rod 1 just after the rods

are released. Then

50. What is the normal reaction between the two rods at this instant?

(a) 16 3ml (b) 4

3

ml (c)

32

3 3

ml (d)12 3ml

( )t s

4

0.1

( )i amp

B

l

A

2

1

IIT Section



10th May 2014 I20140510


51. What is the horizontal force on rod 1 by hinge A at this instant?

(a) 32 12 3

3 3ml

(b) 16 2 3

3ml

(c) (14 2 3)ml (d) 3ml

52. What is initial angular acceleration of rod 2 in terms of the given parameters in the question?

(a) 2 3

2 32

g

l

(b)

3 33

g

l

(c)

6 35 3

8

g

l

(d)

3 3 8

8 3

g

l


(i) When a conducting rod of length l is moved in a magnetic field B , a potential difference V Bvl

is developed across its two ends. Here v is the velocity of the rod. Condition is that, the three vectors

,B v and I should be mutually perpendicular to each other.

(ii) ,R Cq

V iR VC

and Ldi

V Ldt

(iii) Magnetic force on a current carrying conductor in a magnetic field is given by ( )mF i l B .

In the figure shown a conducting wire PQ of length 1 ,l m is moved

in a uniform magnetic field 4B T with constant velocity 2 /v m s

towards right. Given : 2 , 1R C F and 4L H .

Current through resistance, capacitor and inductor at any time t are

1 2,I I and 3I respectively. Current through wire PQ is I .

53. At 2t s , the value of 3I is

(a) 0 (b) 2A (c) 4 A (d) 6 A

54. Find the force required to move the wire with the given constant velocity of 2m/s at 2t s

(a) 8 N (b) 16 N (c) 24 N (d) 32 N

R C L V

B

P

Q

IIT Section



10th May 2014 I20140510


55. At 2t s , suppose P is the total power generated by the applied force, 1P the power stored in

magnetic field of inductor and 2P the power dissipated in resistance, Then

(a) 72 /P J s (b) 1 40 /P J s (c) 2 32 /P J s (d) 2 80 /P J s

Section IV



A charged particle with some initial velocity is projected in a region, where non-zero electric

and / or magnetic fields are present. In column I, information about the existence of electric

and / or magnetic field and direction of initial velocity of charged particle are given, while in

column II the probable path of the charged particle is mentioned. Match the entries of Column I

with the entries of Column II.

Column I Column II

(A) 0, 0,E B and initial velocity of the

particle is at any angle with B

(p) Straight line

(B) 0, 0,E B and initial velocity of the

particle is at any angle with E

(q) Parabola

(C) 0, 0,E B E B and initial

velocity of the particle is perpendicular

to both

(r) Circular

(D) 0, 0,E B E perpendicular to B and

initial velocity of the particle is

perpendicular to both E and B

(s) Helical path with non-uniform pitch

IIT Section



10th May 2014 I20140510


F

Ring

F

Disc

F

Solid Cylinder

R/2


Assume sufficient friction to prevent slipping.

Column I Column II

(A)

(p) Body accelerates forward

(B)

(q) Rotation about the centre of mass is

clockwise

(C)

(r) Friction force acts backward

(D)

(s) No friction acts

F

Solid Cylinder

R/2

jee-adv grand test question paper (p 2) - 10-05-2014

Documents