ai iitjee modeltest 05

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Model Test - 05

Take This test comprising 3 sections with a duration of 2 hours eachsection.Each section contains 50 questions. Observe the given weightage toeach question. 1/3 rd negative marking do exist for the wrong answers.Maintaining the time limit of 2 hours for each section is of atmost im-portance, while taking the test.

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Questions 1 - 5 are based on the following passage

X-ray diffraction can be used to determine the inner structure of crystals, as the wavelengths of X-rays are roughtlyequal to the interatomic spacing in crystalline matter, on the order of 10-10 m. X-rays, upon entering the highly orderedlattice structure of a crystal, will diffract off of the different atoms. Analysis of the wave interference effects of the X-rays as they leave the crystal alows for precise calculation of the distance between layers of atoms. This type ofwave phenomena is called Bragg diffraction.

Students can study the effects of Bragg diffraction without being exposed to potentially harmful X-rays. By scalingthe wavelength of the incoming radiation up from 1-10 m to 10-2 m, relatively harmless microwaves can be beamed intoperiodic layers of steel balls, each separated by a small number of centimeters.

Figure 1 is a schematic showing two microwaves bouncing off of consecutive layers of the lattice. The angle ofincidence (and reflection), θ , is varied as the experiment is carried out. Because the space between layrs is d, thedifference in path length between the two rays is 2d, sin θ . The experimenter can use a microwave detector to locatethe angles at which constructive interference occurs. As the difference in path length between two waves undergoingconstructive interference is a interger multiple of the wavelength, the following equation can be used to determine dfor the lattice.

...3 ,2 ,1n,sind2n −θ=λ

1. What is the spacing between the planes of steel balls if 3-cm microwaves generate constructive interference 190?(sin 190 = 0.33)

a) 1.5 cm b) 2.0 cm c) 3.0 cm d) 4.5 cm

2. The detector is moved to a fixed angle, θ , where an maxima of reflected microwave intensity occurs. How does theintensity of the reflected signal change if the consecutive layers of steel balls are moved apart?

a) The intensity falls b) The intensity risesc) The intensity rises, then falls d) The intensity falls, and then rises.

3. A decrease in the intensity of the incoming microwaves would?

a) increase the values of the angles at which constructive interference occurs.b) decrease the values of the angles at which constructive interference occurs.c) have no effect on the results of the experiment.d) decrease the distance between the layers of steel balls.

4. Which of the following is the equation that describes the angles at which microwaves reflecting off of consecutivelayers of steel ball undergo destructive interference?

a) θ=λ sin dn b) θ=λ 2sin d2n c) θ=λ+ sin d)1n( d) θ=λ+ sin d)2/1n(

5. Which of the following is an example of the frequency of oscillation of microwaves?

a) 3.3 x 10-12 Hz b) 1.0 x 10-2 Hz c) 3.0 x 106 Hz d) 3.0 x 1010 Hz

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Paper - I : Physics - 1 to 50


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Questions 6 to 45 are independent Question

6. The number of possible overtones of air column in a closed pipe of length 83.2cm and of a diameter 6cm whosefrequencies lie below 1000 Hz will be — (velocity of sound = 340m/s)

a) 5 b) 2 c) 6 d) 3

7. A bar of mass M=5 kg is held between four disks, each of mass, m=2 kg and radius r. If the normal forces exerted onthe disks are sufficient to prevent slipping, then the acceleration of the bar immediately after it has been released fromrest is —

M

a)37g

b)49g

c)511g

d)59g

8. A uniform circular disc of mass m and radius ‘a’ rotates freely is a vertical plane about its centre. Initially the disc isrotating with angular velocity W0 and is reduced to rest in a time T by a constant force ‘F’ applied tangentially at rim.The F will be equal to —

a) 0

4maW

Tb) 0

2maW

Tc) 02maW

Td) 03

4maW

T

9. A sound wave is represented by sin(1000 3 )y a t x= π − . The distance between two points having a phase

difference of 3π

is —

a)29π

b) 18π

c) 9π

d)518

π

10. A hollow cone floats with its axis vertical upto13 of its height in a liquid of density d1 with its apex submerged. When

a liquid of density d2 is filled in it, it floats with12 of its height submerged. The ratio

2

1

dd

=—

h

a) 57 : 147 b) 47 : 349 c) 57 : 648 d) 2 : 3

11. A thermally insulated vessel containing a diatonic gas whose molar mass is M moves with a velocity v. Thetemperature rise in the gas resulting from the sudden stoppage of vessel would appropriately be :

a)22

5mvR

b)2

5mv R

c)22

5mv R

d)2

5mv

R

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12. Three moles of an ideal gas (monoatomic) perform a cycle as shown. The temperatures in different states are,

1 400T K= , 2 800T K= , 3 2400T K= and 4 1200T K= . The work done during the cycle is nearly ———K.Joules

P

T

1

2 3

4

a) 310 b) 21.5 10× c) 20 d) 10

13. A cyclic process ABCA is shown in V – T diagram as shown. The same process on the P – V diagram is —

V

TA

BC

I)

P

V

AB

C

II)

P

V

A

B

C

III)

P

V

A B

C

IV)

P

V

A

BC

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

14. A parallel plate an capacitor is charged to a certain potential difference. A dielectric bar is put into the capacitor. Thecharge on the plates is needed to be increased three times to restore the former potential difference. The relativepermittivity of the bar is —

a) 0.333 b) 3 c) 0.166 d) 6

15. A parallel plate air capacitor is charged by a battery so that the plates of the capacitor acquire a potential differenceequal to the emf of the battery. The ratio of the work done by the battery and the energy stored in the capacitor —

a) 1 : 1 b) 1 : 2 c) 2 : 1 d) 1 : 4

16. The potential difference between A and B is 23V. The potential difference across 3 Fµ capacitor is —— volts.

++ +2ì F 3ì F 4ì F

A B8V 5V

a) 7 b) 8 c) 23 d) 4

17. The flux through a loop varies with time according to the relation 20.1( 6 )t tφ = − . Tesla – m2 where t is in seconds.The induced emf in the loop varies in the time according to the graph —

a)

E

t

b)

E

t

c)

E

t

d)

E

t

18. Two coils are wound on the common core. The inductance of the first coil is 0.2H, and that of the second is 0.8H. The

resistance of second coil is 600 Ω . The current that will flow through the second coil if the current of 0.3A in the firstcoil is switched off during 0.001 sec ——.a) 1A b) 0.4A c) 0.2A d) 0.1A

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19. A coil of inductance 0.25 µ and negligible resistance is connected to a source of supply whose voltage is given by22 3V t t= + . If the voltage is applied, when t = 0 and switched off at t = 2 sec., the energy stored in the inductor

will be ——

a) 125 J b) 250 J c) 288 J d) 144 J

20. A current of 2 Amp flows in a pure inductance of 4 µ . The coil is suddenly disconnected from the source and almost

simultaneously connected across a 10 Ω resistance. The initial rate of change of current is ——— Amp/sec

a) 0.25 b) 0.50 c) 0.75 d) 1.0

21. A current of 2 Amp flows through a square frame ‘x’ of wire 2m long. The same amount of current also flows througha circular coil ‘y’ of perimeter 2m. The ratio of the magnetic fields at the centres of y and x is ——

a)2

16π

b) 16π

c)2

8π

d) 8π

22. Two cells, each of emg ‘E’ and internal resistance ‘r’ are connected in parallel across a resistance R. The powerdelivered to the resistance will be maximum, if R = ——

a) 4r b) 2r c) r d) 2r

23. Sixteen thin convex lenses of focal lengths , 2 , 4 ,8 ,..........f f f f are placed in contact with each other. Thecombination will behave as a convex lens of focal length (approximately) ——

a) 136 f b) 39 f c) 2 f d) 2f

24. A U–tube of uniform cross sectional area containing a liquid is mounted on a horizontal turn table notating with anangular speed ω about the axis shown. Then h = ?

h

L

a)2

2Lg

ωb)

2 2

2L

gω +

c)2 2

2Lg

ωd)

2 2

2L

gω −

25. In the arrangement shown in figure, mass of block B and A is 2m and m respectively. Surface between B and floor issmooth. The block B is connected to the block C by means of a pulley system. If the whole system is released. Findthe minimum value of mass of the block C so that the block A remains stationary with respect to the block B.Coefficient of friction between A and B is µ .

C

B

A

a)mµ b)

21

mµ + c)

31

mµ − d)

62 1

mµ −

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26. A prism of refractive index µ and angle A is placed in the minimum deviation position. If the angle of minimumdeviation is equal to A, then the value of A is ——

a)1Sin

2− µ

b) 12Sin ( 1) / 2− µ − c)12cos

2− µ

d)12sin

2− µ

27. A quarter cylinder of radius R and refracture index µ is placed on a table at a distance mR from a point P. The valueof m for which a ray from P will converge at a point Q distant R from curved surface is —

P Q

RmR R

a)2

( 2)µ µ − b)1

( 2)µ µ − c) 1µ

µ + d)2

2

13

µ −µ +

28. In Youngs expermient the wavelength of red light is 7800 Aº and that of blue light is 5200Aº. The value of n for whichthe (n+1)th blue bright band coincides with the nth red band is ——

a) 2 b) 3 c) 4 d) 5

29. The plot of the number (N) of left over atoms versus activity (A) of a radio active substance is —

I)

N

A

II)N

A

III)

N

A

IV)

N

A

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

30. An electron, in a hydrogen like atom, has total energy –3.4eV. Its kinetic energy is ——

a) –3.4 eV b) +3.4 eV c) –1.7 eV d) +1.7 eV

31. Use the diagram below to answer the question. 40 spheres of equal mass make two rings of 20 spheres each. Thering on the right has a radius twice as large as the ring on the left.

A BD

C

0

r 2r

1 2 3 4If the position of the spheres approximates two uniformly dense rings, which of the following is true concerning amass placed at position D?

a) The net gravitational force due to the spheres of the larger ring would be zero.

b) The net gravitational force due to the spheres of the smaller ring would be zero.

c) The net gravitational force due to the spheres of both rings would be zero.

d) If the smaller ring were removed, the mass would move toward the center of the larger ring.

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32. The bottoms of two vertical cylinders of different cross sections are connected by a thin pipe. Each cylinder containsgas at constant temperature and is covered by a movable piston. The mass of one piston is m1=1.0kg. the otherm2=2.0kg. Initially, the pistons are at the same height h=0.40m. What would be the difference in the heights of thepistons (H) if an extra load of m=1.0kg is placed on the lighter piston? Assume the entire arrangement is placed invaccum.

a) 1.5 m b) .90 m c) .60 m d) No difference

33. Consider a cone, with a light bulb at the vertex, cut by a plane making an angle of 30º with base. The area of the planeinside the cone has an image of area s on the base. If the area of the base is A and the average light intensity at thebase is I, what is the average light intensity on the inclined plane?

A S

a) 2IA

s b)2I

Asc)

32

IAs

d)IAs

34. Which of the following is NOT true for a converging lens in optics?

a) A ray parallel to the optic axis passes through the focus.

b) A ray originating at the focus is bent parallel to the optic axis.

c) A ray through the center of the lens is bent parallel to the optic axis.

d) An object placed at the focus has image at infinity.

35. A photon strikes a free electron at rest and is scattered straight backward. If the speed of electron after collision iscα , where 1α<< then,

a) electron’s kinetic energy is a fraction α of photon’s initial energy.

b) electron’s kinetic energy is a fraction 1α of photon’s initial energy.

c) electron’s kinetic energy is a fraction 2α of photon’s initial energy.

d) electron’s kinetic energy is a fraction 21

α of photon’s initial energy.

36. When a monochromatic point source of light is at a distance of 0.2m from a photoelectric cell, the cut-off voltage andthe saturation current are respectively 0.6V and 18.0 mA. If the same source is placed 0.6m away from thephotoelectric cell, then

1) the stoping potential will be 0.2V 2) the stopping potential will be 0.6V

3) the saturation current will be 6.0 mA 4) the saturation will be –1 mA

Which of the given statement(s) match with the main statement.

a) 2, 4 b) 1, 4 c) 3, 4 d) 2, 3

37. A stationary 10 kg box is lifted and placed at rest on top of a 10 m shelf. The move takes 2 s. A student argues thatthe minimum average power is greater than 500W. The student is :a) right because the box must have a change in kinetic energy in addition to the change in potential energy.b) right because the box had to be accelerated which requires a force greater than mg.c) wrong because the box can be moved at an infinitely slow constant velocity, and thus the work done is equal to

the weight times the distance.d) wrong because the force on the box could be twice the weight for the first half of the trip, and zero for the second

half of the trip.

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38. Direction : Refer to the below diagram an ideal fluid with a specific gravity of 1.0 flows through the pipe in thedirection from c to a. The pipe has the same diameter at a and c. The vertical pipes are vacuum sealed at the top. Theheight of the fluid at h1, h2 and h3 are measured from the center of the pipe, and are not drawn to scale.

floorHeights h , h and h not drawn to scale1 2 3

a b

c

h1

h2

h3

If a second ideal fluid with a specific gravity of 2.0 were passed through the pipe at the same volume flow rate, theheight h1 would;

a) decrease by a factor of 2.

b) remain the same.

c) increase by a factor of 2.

d) more information is required to predict the change in h1.

39. Direction : Refer to the diagram below a sphere with mass m is placed at the surface of a very shallow pool (depth h)of a fluid with density ρ and oscillated a distance y every t seconds. Waves with a frequency f and amplitude A aregenerated on the fluid surface and propagate away from the sphere with a velocity v. The distance between the wavecrests is given by x.

h

y

mx

If the wave generating apparatus were placed on the moon, and y remained the same, which of the following wouldoccur?

a) ρ would decrease b) f would increase c) x would increase d) v would decrease

40. A metallic chain of length L and mass M is vertically hung above a surface with one end in contact withit. The chainis then released to fall freely. If x is the distance covered by the end of the chain, how much force (exerted by thebottom surface) will the chain experience at any instance during the process?

X

X

L

a) ''N Mg Mx= − b) 3N Mg= c) 2 ''N Mg Mx= − d) (3 / )N M L gx=

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41. A movable heavy piston is supported by a spring inside a vertical cylindrical container as shown. When all air ispumped out of the container, the piston is in equilibrium as shown in Diagram1, with only a tiny gap between thepistorn and the bottom of the container. When a portion of gas at temperature T is introduced under the piston, thelatter rises to a height h as shown in Diagram 2.

What would be the height of the piston above the bottom of the container if the gas is then heated to temperature 2T?Assume that the piston moves without friction and that the spring obeys Hooke’s law.

h

Diagram 1 Diagram 2

a)12

h b) h c) 2 h d) 2h

42. Direction : Refere the digram below E is the electric field created by q1. V is the voltage at a given point in the fieldE. Assume that the electric field created by q2 is negligible compared to E. k is Coulomb’s Law constant, m1 is themass of q1and m2 is the mass of q2.

d

q2

q1

2r

r

If q1 is positive, then when q2 is mvoed from its present location to a distance r from q1, the magnitude of the voltageexperienced by q2 due to E:

a) decreases by a factor of 4. b) remains the same

c) increases by a factor of 2. d) increases by a factor of 4.

43. Two cylinders are rapidly spinning in the opposite directions as shown. The axes of the cylinders are a distance dapart. A uniform board of mass M is placed horizontally on the cylinders as shown. The coefficient of kinetic frictionbetween the board and the cylinders is sµ . Which of the following statements correctly describe the subsequentmotion of the board.

I) The center of the board will oscillate with period 22 kg

dT = πµ , so the board will begin the oscillation moving

to the left.

II) The center of the board will oscillate with period 22 kg

dT = πµ , so the board will begin the oscillation moving

to the right.a) only I is correctb) only II is correctc) both are wrongd) cannot describe the motion with the given information

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44. Recall the equation for a series RLC circuit. Compare this to the parallel resonant circuit shown and find Rp if a seriesRLC circuit and the parallel RLC circuit are to have the same equations for the potential of capacitor while they bothhave the same L, C and Q.

C L

I1 I2

Rp

a) pR R= b) pR L= c) 1/pR C= d) /pR L RC=

45. Direction : Refer to the diagram below. A conducting bar is slid at a constant velocity v along two conducting rods.The rods are separted by a distance l and connected across a resistor R. The entire apparatus is placed in an externalmagnetic field B directed into the page.

R vB in l

How will the current in the apparatus shown above be generated?

a) sinusoidally

b) clockwise

c) counterclockwise

d) There is not enough information to determine the direction of the current

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Magnetic resonabce, first discovered in 1946, has found its way into many scientific arenas as a diagnostic tool. Itsusefulness lies in its ability to create images of the interior of structures without the use of ionizing radiation like x-rays. The two main drawbacks of using x-rays are their high-energy bound breaking potential, as well as their relianceon the presence of contrast enhancing material.

Modern day MRI machines used in clinical imaging create a standing magnetic field aligned with the patient fromhead to toe. These machines use the proton of a hydrogen atom as their target, due to its abundance in the humanbody. When the field is applied, the magnetic moment of the protons exposed to the field will dynamically align withor against the field, according to the equation.

N-N+ = -E/kT (Equation 1)

Where N+ is the number of protons in the lower energy level, N- is the number of protons in the higher energy level,E is the energy difference between the two states, k is Boltzmann’s constant (1.38 x10-23 j/K), and T is the temperaturein Kelvins.

In the presence of such a large magnetic field, a proton will precess, or wobble, about the axis through its magneticmoment, at a specific frequency called the Larmor frequency.

'00 Bf γ= (Equation - 2)

Where B0 is the strength of the magnetic field in Tesla, and γ is the gyromagnetic ratio, a constant unique to everyatom ( γ for 1 H is 42.56 MHz/Tesla)

Once aligned, an electromagnetic radio frequency (RF) pulse is applied at the specific Larmor frequency for the targetproton, causing the protons to become excited to the higher energy state Various measurements can then taken asthe RF pulse is removed and the protons release the absorbed energy. (Note : planck’s constant h =6.6 x10-34 j.s.)

46. How much power is required to excite a single proton exposed in a 1.5-T field by a 2 second RF pulse?

a) 4. 22 x 10-26 W b) 1. 44 x 10-24 Wc) 6.36 x10-38 W d) 2.11 x 10-26 W

47. All ofr the following will affect the ratio of protons given in Equation 1 EXCEPT:

a) Increasing the magnetic fieldb) Decreasing the temperature.c) Targeting other elemental protons other than 1Hd) Increasing the wavelength of the RF pulse.

48. If the magnetic field strength were doubled, how would the energy required to excite a proton from the lower energyto the higher energy spin change?

a) It would double b) There would be no changec) It would decrease by one-half d) It would increase by one-half.

49. A uniform magnetic field, B, runs at a height h parallel to the ground. A free electron (mass me) is placed in the field,initially moving at speed v in the opposite direction to the field. Neglecting air resistance, what is the magnitude ofthe net force on the electron?

a) meg + evB b) meg - evB c) meg d) 22e )evB()gm( +

50. How many times greater is the energy of a 1019 Hz X-ray photon than the energy of the RF photon used in the MRIdescribed in the passage, when the applied field is 1.5T?

a) 6. 39 x 106 b) 1.57 x 1017 c) 2.35 x 1011 d) 3.52 x 1011

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Consider a series of the form

11 131 2

1 2 3

( )( ) ( ).............

( ) ( ) ( )f xf x f x

f x f x f x+ + + the sum of such a series can be obtained in the following way;

Step1: Obtain the product 1 2( ) ( )......... ( ) ( )nf x f x f x g x= (say)

Step2: Take log of both the sides, then

1 2log ( ) log ( ) ............. log ( ) log ( )nf x f x f x g x+ + + =

Step3: Differentiate bothe sides w.r to x,

11 1 11 2

1 2

( )( ) ( ) ( ).............( ) ( ) ( ) ( )

n

n

f xf x f x g xf x f x f x g x

+ + + =

The above method can be extended for the sum of infinite returns of the series provided the series is convergent.

51. The sum of n terms of the series 3 7

2 4 81 2 4 8 .....

1 1 1 1x x x

x x x x+ + + +

+ + + + is

a)12

2

1 21 1

n

n

n xx x

−

−− −

b)12

2

1 21 1

n

n

n xx x

−

+− +

c)12

2

1 21 1

n

n

n xx x

−

− −− −

d)12

2 2

1 121 1

n

n nn x

x x

− − +

− +

52. If 1x < then the sum to infinite terms of the series given in above question is

a)1

1 x− b)1

1 x+ c)1

1x − d) 1

53. If 1 2 3sin sin sin ...........sin ( )n fθ θ θ θ = θ then 1 2 3cot cot cot ..........cot nθ + θ + θ + θ =

a) 1( )( )

ff

θθ b)

1( )( )

ff

− θθ c) 1

log ( )( )f

fθ

θd)

1( )( )

ff

θθ

54. The value of the product 12 4 8 2(1 ) (1 ) (1 ) (1 ) ....... (1 )n

x x x x x−

+ + + + + is

a)21

1

nxx

−−

b)21

1

nxx

+−

c) 2(1 ) (1 )n

x x− − d)2

2

1

1

n

n

x

x

−

+

Questions 55 - 95 are independent questions

55. f(x) = ax2 + bx + C, where 0a ≠ . If f(-1) < + 1, f(1) > -1 and f(3) < - 4, the

a) b + 1 > 0 b) 8a + 1 < 0 c) a is negative d) b is positive

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Paper - I I : Mathematics - 51 to 100


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56. In a class tournament, where the participants have to play each one game with another, two players fell ill afterplaying three games each. If the total number of games played is 84, the number of players at the beginning was

a) 12 b) 10 c) 15 d) 18

57. If the tangents at Z1 and Z2 on the circle 3 Z r meet at P(Z ),= then Z3 is

a)21

21ZZ

ZZ+ b) 1 2

1 2

Z ZZ Z

+

c)21

21ZZ

Z2Z+ d)

21

21 Z2ZZ Z +

58. If A = cor 84o cot 48o and B = tan 24o tan 12o, then

a) A = B b) 2A = B c) 2B = A d) A = -B

59. The line y = m1x, y = m2x and y = m3x meet the line x + y = 1 at A, B, C respectively. If AB = BC, then 1 + m1, 1+ m2, 1+m3 are

a) in A.P. b) in G.P.c) in H.P. d) not the terms of a progression

60. In ∆ABC, a co-ordinates of A are (4, 6), πBAC=3 and AB= 12. The middle point of AC is (4, 12). Then the radius

of the incircle of the ABC∆ is

a) 3 3 b) 2 3 c) 4 3 d) 3

61. A point of contact of a tangent of slope 1 to the ellipse 2 2

1576 49x y+ = is

a)576 49,25 25

− b)

576 7,25 25

− c)

576 7,25 25

− − d)

24 7,25 25

−

62. The points with position vectors , , and ,a b a b a k b+ − + are collinear

a) for a finite number of real values of k b) for no real value of kc) for all real values of k d) for infinite number of real values of k

63. If the position vectors of A, B, C, D on a plane are , , , da b c and if ( 2d). ( )b c b c+ − −

( 2d) . ( ) 0c a c a= + − − = then D is

a) circumcentre of ∆ABC b) incentre of ∆ABC

c) orthocentre of ∆ABC d) centroid of ∆ABC

64. The position vectors of P, Q, R with respect to O are 3i - 2 j + k, i + 3 j+ 4 k and 2i + j - 2 k respectively.Then the distance of P from the plane OQR is

a) 2 b)113

c) 1 d) 4

65. An ordinary die is rolled n times. The probability of getting an odd number 2 times is equal to the probability ofgetting an even number 3 times. Then the probability of getting an odd number, odd number of times is equal to

a)1

16b)

132

c)3

16d)

12

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66. The domain of definition of y given by 2 1x cos y π−− = is

a) - 2π,- π π , 2π ∪ b) [ 2 , ] [ , 2 ]π π π π− − ∪

c)2 2, ,2 2 2 2π π π π

− − ∪

d) 4 , , 44 4π ππ π − − ∪

67. If f(x) = Max 1, cos x + sin x, sin x - cos x 50 ,4

x π≤ ≤ then

a) f(x) is not differentiable at x = 6π

b) f(x) is not differentiable at 5x =6π

c) f(x) is continuous for 5x 0,4π ∈

d) None of these

68. ( )2

2 2

cos tan 1sin 2cos

dθ θθ θ

−+∫ is equal to

a) 2 2log tan 1 tan 2 cθ θ − + + + b) 2 2log tan 1 tan 2 cθ θ − − + +

c) 1 2tan (tan 2)θ− + d) 1 2cot (tan 2)θ− +

69. The value of 21

(3 4 )

n

n

nLtr r n→∞ +∑

a)1

14 b) 2 c)12 d)

32

70.3

1cotπ

π

−

−∫ cot x dx is equal to

a) 22π b) 23π c) 29π d) 216π71. The differential equation of all those lines which are at a unit distance from the origin is

a)2 2

1dy dyy xdx dx

− = − b)

2

1dy dyy xdx dx

+ = +

c)2 2

1dy dyy xdx dx

− = + d)

2 2

1dy dyy xdx dx

− = −

72. If 2cos 2 1, 4 2 cos 23 6, 3θ θ− − are the first three terms of an A.P, then the common difference of A.P is

a) 2 b) 3 c) 1 d) 4

73. The number of ways in which 18 dice can be thrown so that each face is displayed exactly thrice is

a) 36 b) ( )63 c)( )63

18 d) ( )6183

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74. The number of terms with rational coefficients in the expansion of ( )632 3 x y z+ + is

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

75. The last two digits of the number 4003 are

a) 81 b) 43 c) 29 d) 01

76. If [.] denotes the greatest integer function and if 1 0,0 1,1 2,x y z− ≤ < ≤ < ≤ < then the

[ 1] [ ] [ ] [ ] ( 1] [ ]

[ ] [ ] [ 1]

x y zvolue of x y z

x y z

++

+ is

a) [ x ] b) [ y ] c) [ z ] d) 0

77. The number of points in the complex plane satisfying the conditions 2 2 (1 ) (1 ) 4Z and Z i Z i− = − + + =is

a) 1 b) 2 c) 0 d) more than 2

78. If x sec tan α = y sec tany y aα β β+ + = then sec secα β =

a)2 2

2 2

a yx y

++ b)

2 2

2 2

a yx y

+− c)

2 2

2 2

x ya y

++ d)

2 2

2 2

x ya y

−−

79. If the two circles 2 2 2 2 0x y gx fy+ + + = and 2 2 2 ' 2 ' 0x y g x f y+ + + = touch each other, then

a) ff' = gg' b) f'g = fg' c) 2 2 2 2f g = f' g d) fg' + f'g = 0

80. A B C is a triangle formed by the common tangents to the circles 2 2x 6 0y x+ − = and 2 2 2 0.x y x+ + = Then

a) the centroid of the ∆ABC is (-1, 0) b) circumradius of the ∆ABC is 43

c) area of the ∆ is 2 3 d) the angle BAC is 90o

81. If 2 2

2 2 1,x ya b

+ = (a > b) and 2 2 2x y c− = cut at right angles, then

a) 2 2 22a b c= = b) 2 2 22b a c− =

c) 2 2 22a b c− = d) 2 2 2 2a b c=

82. The period, if it exists, of f, defined by ( 2) ( 6)( )f x f x x R+ = − + ∀ ∈ is

a) 2 b) 8 c) 4 d) period does not exist

83. The set of values of ‘a’ for which ( ) sin cosx xf xa a

= + is maximum is (x denotes the fractional

part of x)

a) (0, )∞ b) , 4π ∞

c)10,π

d)40,π

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84. The chord joining the points where x = P and x = q on the curve 2y ax bx c= + + is parallel to the tangent at thepoint on the curve whose abscissa is

a)1 ( )2

p q+ b)1 ( )2

p q− c) 2pq

d)1 ( )2

q p−

85. The tangents at P and Q on the parabola x2 = 4y meet at T. If S is the focus, then

a) ST2 = SP . SQ b) ST2 = 2SP . SQ c) St = SP . SQ d) 2ST2 = SP . SQ

86. The function Rx, x cbaxf(x) ∈+−= (where (a, b, c > 0) assume its minimum value at x = 0, if

a) ba ≠ b) cb ≠ c) ac ≠ d) ac >

87. If / 2( 2) ( 3) ( 13) ,x x x+ = then the number of values of x is :

a) 2 b) 4 c) 1 d) none of these

88. Let ( ) , .x xf x e e x R−= + ∈ . Then

a) ( ) 2 .f x x R> ∀ ∈ b) ( )y f x= represents a hyperbola

c) 2( ) 4y f x= + represents a parabola d) none of these

89. The area of the region bounded by the curve 4 2 5(2 ) a y a x x= − is to that of the circle whose radius is a, isgiven by the ratioa) 4 : 5 b) 5 : 8 c) 2 : 3 d) 3 : 2

90.2 2sin sin

0

1 a at t

xy x y

Lt e dt e dt isx→

+

− ∫ ∫ (Here, a is a constant)

a) 0 b) 2sin ye c) 2sinsin 2 yy e d) none of these

91. If f is a continuous function such that (0) (1) 0,f f= = '(1) 2f = and ( )( ) ( )x f xy x f e e= then '(0)y is

a) 0 b) 1 c) 2 d) None of these

92. There are three piles of identical red, blue and green balls and each pile contains at least 10 balls. The number ofways of selecting 10 balls if twice as many red balls as green balls are to selected is

a) 2 b) 3 c) 4 d) 5

93. The straight line 3 2 1

3 1 0x y z− − −= = is

a) parallel to x-axis b) parallel to y-axisc) parallel to z-axis d) perpendicular to Z-axis

94. The equation of the sphere inscribed in a tetrahedron whose faces are x = 0, y = 0 and 2x - y + 2z = 4 is

a) 2 2 2 4 4 4 8 0x y z x y z+ + − + − + = b) 2 2 2 4 4 4 8 0x y z x y z+ + − − − + =

c) 2 2 2 4 4 4 8 0x y z x y z+ + + − + + = d) 2 2 2 4 4 4 8 0x y z x y z+ + − − + + =

95. If 12 ++ xx is a factor of ,23 dcxbxax +++ then the real root of 023 =+++ dcxbxax is

a) ad− b) a

cc) a

bd) none of these

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The graph of derivative of a function ( )f x is given (i.e. 1( )y f x= ) Analyse the graph in the given domain and

answer the following questions if it is given that (0) 0f = .

y

-a a x0

96. The function 1( )f x is

a) even b) odd c) indefinite d) neithr even nor odd

97. The graph of ( )y f x= has

a) no inflexion point b) one point of inflexionc) one extreme point d) two extreme points

98. The value of the integral ( )a

a

f x dx−∫ is

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

2 ( )a

f x dx∫99. The function ( )f x for a x a− ≤ ≤ is

a) always decreasing

b) always increasing

c) increasing for ( ,0)a− & decreasing for (0, )a

d) increasing for (0, )a & decreasing for ( ,0)a−

100. The function ( )f x is

a) even b) oddc) neither even nor odd d) indefinite

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Questions 101 to 105 are based on the following passageJust prior to World War I,the German chemist Fritz Haber developed a method for the large-scale production ofammonia from atmospheric nitrogen and hydrogen. Reaction 1 shows the equilibrium that is established betweennitrogen, hydrogen, and ammonia gases.

)g(2NH)g(H3)g(N 322 + (Reaction 1)

At 298 K, the quilibrium constant for this reaction is about 510 6 ∞ . The reaction however proceeds very slowly.From the kinetic aspect, the solution to this problem was to raise the temperature at which the reaction is carried out.However, raising the temperature favours the formation of the reactants. the van’t Hoff equation provides a way ofestimating the dependence of the equilibrium constant on the temperature.

−∆−=

12

0

1

2T1

T1

RH

KKIn (Equation 1)

Where K1 and K2 are the equilibrium constants at T1 and T2 respectively, 0H∆ is the standard change in enthalpyof the reaction, presumed to be temperature-independent, and R is the universal gas constant. Using this equationwith T1=298 K, the ratio of the equilibrium constant at 800 K to that 298 K is

11

298

800 107KK −×= (Equation 2)

The Haber process makes use of a catalyst composed of partially oxidized iron with a small amount of aluminumadded. As gaseous nitrogen and oxygen are circulated over (and adsorb onto) the catalytic surface, ammonia iscondensed out of the misture. Because the iron oxide catalyst is in a different phase than the reactant species, thisprocess is an example of heterogeneous catalysis.

101. Which of the following is the most likely role of the catalytic iron oxide surface in the Haber process?a) It facilitates the desorption of gaseous ammonia from the surfaceb) It interacts with the adsorbed N2 molecules and facilitates their dissociationc) It interacts with the ammonia molecules and weakens the N-H bonds.d) It stabilizes the ammonia, making the reaction more thermodynamically favorable.

102. Which of the following statements about the decomposition reaction of ammonia into nitrogen hydrogen is FALSE?a) Its equilibrium constant at 298 K is less than 1.b) Its equilibrium constant at 800 K is less than 1c) It is endothermicd) It leads to an increase in entropy

103. A scientist tries to synthesize ammonia in the laboratory?. If she wants to force the reaction to completion, which ofthe following methods should she NOT use?a) Cool the reaction bulb in an ice bath and increase the overall pressure.b) Remove some of the ammonia as it is formed.c) Transfer the gases to a larger bulb that is being heated on a hot plate.d) Transfer the gases to a smaller bulb at room temperature

104. What is the approximate equilibrium constant of Reaction 1 at 800 K?

a) 1 x 10-16 b) 4 x 10-7 c) 1 x 10-6 d) 4 x 10-5

105. Which of the following molecules will react with H2O4 and have the highest Keq for the reaction?

a) CH3CONH2 b) CH3CH2NH2 c) (CH3CH2)2 NH d) C6H5NH2

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106. Which of the following factors does not contribute to the energy )ε( α of a system that has a large number ofmolecules (N) ?

a) Electronic b) Nuclear c) Vibrational d) Thermal

107. Eugenol is a dental anesthetic that is isolated from oil of cloves . The structure is shown below . What functionalgroup are present in this toothache remedy ?

CCCH2 −= OH

3OCH

H 2H

a) aromatic ring ,alkene , alcohol ,and ether b) cycloalkyl ring , alkene , alcohol , and esterc) aromatic ring , alkyne , ether and ester d) aromatic ring ,alkene , alcohol and ester

108. The following values of a sample of gas were measured in the lab : P = 1.5 atm ; V = 10.3 L ; T = 298.0 K . Based onthese measurements ,a student calculated the number of moles using the equation PV = nRT. Which calculated value

has the correct number of significant figures ? (Note : the value of R is 0.08206 L atm )molK 1-1 −

a) 0.63 mol b) 0.632 mol c) 0.6318 mol d) 0.63180 mol

109. The Joule-Thompson experiment is a constant-enthalpy process measuring HP

T

∂∂

as real gases undergo :

a) an isothermal compression b) an isentropic expansion

c) a throttled adiabattic expansion d) an adiabatic compression

110. What is the length of the bond between C1 and C2 in the structure shown below ?

1

2

34

5

6

a) the length of a carbon-carbon bond in an alkane

b) the length of a carbon-carbon double bond in an alkene

c) shorter than the length of a carbon-carbon double bond in an alkene

d) between the length of a carbon-carbon bond in an alkane and the length of a carbon-carbon dould bond in analkene.

Questions 111 to 112 are based on the following passage Refer to the structures of D-aldoses below that are syntheized from D-glyceraldhyde to answer question 6 - 7

OHCH2

CHO

H

OH

OH

OH

H

HHO

H

OHCH2

CHO

H

OH

OH

H

HHO

HO H

OHCH2

CHO

OH

OH

H

H

HO HH OH

OHCH2

CHO

OHH

H OHHOHO H

H

Glucose-D Mannose-D Altrose-D Galactose-D

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111. what is the most specific relationship between D-glucose and D-altrose ?

a) diastereomers b) enantiomers c) epimers d) not stereoisomers

112. Of the four structures shown, which are diastereomers of D-glucose ?

a) D-mannose b) D-galactose and D-mannosec) D-mannose, D-altrose, and D-galactose d) D-altrose


113. Which of the following statements about chemical equilibrium is accurate ?

I) Equilibrium is reached when ∆G (free energy change) equals zero.

II) o∆G (standard free energy change) = -RT in eqK

(where T = temperature, R = gas constant, =eqK equilibrium constant.)

III) o∆G is Independent of pressure.

a) I only b) II and II c) I and II d) I, II, and III

114. Which of the following alcohols would undergo dehydration by an E1 mechanism the fastest ?

a)

OH

b)OH

c)

OH

d)

HO

115. Many chemists consider the electronegativity of helium to be undefined. Why ?

a) The small size of helium makes its electronegativity difficult to measure

b) Helium does not have inner-shell electrons

c) Helium atoms are electrically neutral

d) Helium does not form bonds with other elements

116. Use the van der Waals equation given below to answer question . The van der Waals equation is used to predict thebehavior of real gases. a and b are constants specific for a particular gas. Their values can be obtained byexperiment or from a reference book.

nRTnbVV

a =−

+ )(nP 2

2

vander Waals Equation

The constant a and b have positive values. What is the expected difference between using the ideal gas law,PV = nRT, to calculate the pressure from measured variables, and using van der Waals equation to calculatepressure from measured variables ?a) The pressure will always be lower when calculated with van der Waals equation.b) The pressure will always be greater when calculated with van der Waals equation.c) The pressure will always be the same when calculated with van der Waals equation.d) Whether the value for pressure is lower or greater when calculated with van der Waals equation will depend

upon the real volume and temperature.

117. Use Kohlrausch’s law to calculate the conductivity )(λo of OH.NH4 Use the fact that

248λ,150λ o(NaOH)Cl)o(NH4== and .127λo(NaCl) = The units of oλ are .molcmOhm 12-1 −

a) 525 b) 29 c) 271 d) 98

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Questions 118 to 119 are based on the following passage

Friedel-Crafts acylation is a reaction of an acid chloride with an activated aryl ring. Use the example reaction

OH

ClC

32CHCH

O

→ 3AlCl

OHOC =

32CHCHOC =

32CHCH

OH

118. The Friedel-Crafts acylation is a(n):

a) substitution reaction b) elimination reaction

c) addition reaction d) redox reaction

119. Which of the following aryl compounds would be most reactive with an acid chloride to form an aryl ketone ?

a) b) OCH c) 2NO d)

NC

CN


120. The following an unbalanced reaction :

O(g)H(g)CO(g)O(l)OHC 222112212 +→+

How many moles of oxygen gas are required to burn one mole of ?OHC 112212

a) 1 b) 6 c) 12 d) 24

121. An unknown compound is oxidized to a carboxylic acid, in the presence of potassium permanganate. The samecompound is oxidized to an aldehyde, losing an -α hydrogen in the pressence of pyridinium chloro-chromate

).ClCrONHH(C 355− The compound is also known to exhibit mild acidic properties since it reacts with active

metals (e.g. Na) liberating hydrogen gas, Based on these facts this compound is most likely :

a) a primary amine. b) a secondary ketonec) a primary alcohol d) a primary ketone

122. What is true about an 2SN reaction ?

I) A carbocation intermediate formed

II) The rate determing step is bimolecular

III) The mechanism has two steps

Which of the given statement(s) match with the main statement.

a) I only b) II onlyc) I and III only d) I, II, and III

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123. For question refer to Habeer process shown below :

Concentration

→Time

A

BC

2 2 2N (g)+3H (g) 2NH (g)

In 1912 Fritz Haber developed the Habber process for making ammonia from nitrogen and hydrogen. His develop-ment was crucial for the German war effort of World wat I, providing the Germans with ample fixed nitrogen for themanufacture of explosives.The Habber process takes plae at 500°C and 200 atm. It is an exothermic reaction. The graph below shows thechange in concentrations of reactants and products as the reaction processes.Instead of developing a catalyst, why don’t Haber increase the rate of the reaction by raising the temperature ?a) The Haber process is exothermic, so raising the temperature would have lowered the rate of the reaction.b) The Haber process is exothermic, so raising the temperature would have reduced the yield of the reaction.c) Higher temperatures would have caused an increase in pressure lowering the yield of the reaction.d) Higher temperatures might have decomposed the hydrogen.

124. Direction : Use the following information to answer question . Objects radiate heat at a given by the followingequation.

4ATP σε=

where P is the rate at which heat is radiated, σ is the Stefan-Boltzman constant ),KmW10(5.67 428 −−−× ε isthe emmissivity fo the object’s surface having a value between zero and one, A is the surface area, and T is thetemperature in Kelvin.

The rate at which objects absorb heat from their environment is given by the same equation except that T is thetemperature of the environment. The net rate of energy exchange due to radiative process is given by :

)(P 44n TTA env −=σε

where nP is the net rate of energy exchange and envT is the temperature of the environment.

An object 10 degrees warmer than the room in which it sits. In which of the following circumstance will the objectreach room temperature the fastest ?

a) The room is 0°C and the object is white. b) The room is 0°C and the object is black

c) The room is 10°C and the object is white d) The room is 10°C and the object is black

125. Which of the following statements concerning Michael addition is not true ?

a) The process involves nucleophilic addition

b) Carbanions are added to α, -β unsaturated carbonyl compounds forming carbon-carbon bonds.

c) A base is necessary to initiate the addition

d) Compounds such as ammonia, primary and secondary amines oftern tend to inhibit Michael addition

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126. Cyelohexanol is a solid in a cool room, while cyclohexane is a liquid, what is the explanation for the differentstates ?

a) Cyclohexanol has greater London Dispersion force than cyclohexane

b) Cyclohexanol has weaker London Dispersion forces than cyclohexane

c) Cyclohexanol has hydrogen bonding and cyclohexane does not

d) Cyclohexane has hydrogen bonding and cyclohexanol does not

127. A researcher wishes to have two 20.0 L chambers containing equal amounts (moles) of oxygen gas, one at 5 atm andthe other at 3 atm. Is this possible ?

a) Yes, if the oxygen samples in the contains have different densities

b) Yes, if the oxygen samples in the containers are at different temperatures

c) No, because once the volume and the number of moles of an ideal gas are known, all other parameters aredetermined

d) No, because volume and pressure are inversely proportional for an ideal gas

128. Direction : Use the diagram below to answer question . The isotherms of OH2 are shown as solid lines on pressurevs. molar volume phase diagram below

/atmP

218

85

15liquid

vaporliquid +

C400°C374°

C300°C200°

V

vapor

What is the name for OH2 at 219 atm and 375°C ?

a) liquid b) vapor c) supercritical fluid d) ice IX

129. 15.0 A were passed through a lead storate cell for 1.25 hours. During this time how much electricity (q) passedthrough the cell. (Note “q” = coulombs of electricity.)

a) q = (15. 0A) (1.25 hr) b) )hrsec01.25hr(36015.0A

1-

c) )hrsec(3600 1(1.25hr)(15.0A)q

−=

d)15.0A

)hrsec(3600(1.25hr)q1−

=

130. The rate of precipitate formation increases for the reaction of 1-bromobutane with Nal as the concentration of Nal isincreased. When the concentration of NaI is increased in the reaction of 2-chloro-2-methylpropane. no rate changeis observed. Why is there a change in rate in the first case and not in the second ?

a) −Cl is a better leaving group than .Br−

b) −Br is a better leaving group than −Cl

c) 1-bromobutane proceeds via a 2SN mechanism, while 2-chloro-2-methylpropane proceeds via a 1SNmechanism.

d) 1-bromobutane proceeds via a 1SN mechanism, while 2-chloro-2-methylpropane proceeds via a 2SNmechanism.

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131. An aromatic compound contains 69.4% carbon and 5.8% hydrogen. A sample of 0.303 g of this compound wasanalysed for nitrogen by Kjeldahl’s method. The ammonia evolved was absorbed in 50 ml. . of 0.05 M sulphuric acid.The excess of acid required 25 ml. of 0.1 M sodium hydroxide for neutralization. Determine the molecular formula ofthe compound if its molecular weight is for neutralization. Determine the molecular formula of the compound if itsmolecular weigh is 121.

a) NOHC 77 b) NOHC 56 c) NOCHHC 255 d) None of these

132. One emission line in the spectrum of the hydrogen atom occurs at a wavenumber of 23,032. Assuming the Rydbergconstant is 109, 678, the line represents a transition between which two quantum levels ?

a) 2 n 5 n =→= b) 1n 5 n =→= c) 1n 4n =→= d) 1n 3n =→=

133. Which of the following graphs below best represents the distribution of the blackbody radiation at severaltemperatures ?

a)

Energy

Wavelength

1000K

1500K

2000K

2500K

3000K

b)

Energy

Wavelength

1000K

1500K

2000K

2500K

3000K

c)

Energy

Wavelength

1500K

2000K

2500K

3000K

d)

Energy

Wavelength

1500K

2500K

2000K

3000K

1000K

134. Usae the table shown below to answer question

Acid apKCOOHCHCH 23

COOHCH3

COOHCHCHCH 223

COOHCHCHClCH 222

COOHClCH2

CCOOHCl3

4.874.74

4.824.522.86

0.64

Which of the following has the most acidic proton ?

a) COOHCHCH 23 b) COOHCH3

c) COOHClCH2 d) CCOOHCl3

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135. When 16.8 g of white solid X were heated, 4.4 g of acid gas A that turned lime water milky was driven off together with1.8 g of a gas B which condensed to a colourless liquid. The solid that remained, Y, dissolved in water to give analkaline solution, which with excess barium chloride solution gave a white precipitate Z. Thje precipitate effervescedwith acid giving off carbon dioxide.Which of the following statement(s) give the correct result of the identification

I) X is 3NaHCO II) A is 2CO and B is OH2

III) X is 3BaCO IV) Y is 32CONa

a) II & III

b) only III

c) I, II & IV

d) The given information is not sufficient for identification.

136. A metal complex having composition BrCl)Cr(NH 243 has been isolated in two forms (A) and (B). The form

(A) reacts with 3AgNO to give a white precipitate readily soluble in dilute aqueous ammonia, whereas (B) givesa pale yellow precipitate soluble in concentrated ammonia. Calculate their magnetic moments (spin - only value).

a) BM152 b) BM52

c) BM15 d) BM5

137. Several types of organics compounds undergo elimination to form alkenes when heated to relatively hightemperatures. Which of the compounds below does not exhibit this tendency ?

a) ester)an(CHROCH-CR '22−

O

b) xanthate)(aCHROCH-C-S-R '22

S

c)3OCSCH

H

S)(CH3 3C H

d)

CH2

OH

C

OH

CH2C

O

O

138. The polymerization reaction with adipic acid to form Nylon 6.6 is shown below, Nylon 6.6 is a(n)

COOH)nHOOC(CHNH)N(CHnH 422322 +

H OHC)NHC(CH)NH(CH 4262

O

O1)H(2n 2−

O

6.6Nylon

a) polyster b) polymidec) dicarboxylic acid d) diamine

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139. The Haber process can be represented by the following scheme :Identify A, B, C, D

3CaCO

2COCaO

OH2

ADNaHCO3 + NaCl

OHC 2+ EOHNH 23 ++

B

OH,NH 23

a) 2Ca(OH) 2CaCl 3CaCO 23)Ca(HCO

b) 34 OHCNH 323 OC)(NH ClNH4 3NH

c) 32CONa 3NaHCO NaOH NaCl

d) ClNH4 OHNH4 3NH 323 OC)(NH

140. Find the equilibrium constant for the reaction,

K298atCuInCuIn 322 +++ +→+

Given : V0.42E0.40V,E0.15V;E 0/InIn

0/InIn/CuCu 322 −=−== ++++++

a) 1010 b) 810 c) 610 d) none of these

141. The reactions below represents a possible mechanism for the chlorination of methane. Indicate which of thestatements below is (are) true.Mechanism

1) 2Cl.Cl lighuv2 → 2) 34 CHHClCHCl ⋅+→+⋅

3) ClCHClClCH 323 ⋅+→+⋅ 4) 2ClClCl →⋅+⋅

5) ClCHClCH 33 →⋅+⋅

I. Steps (2), (3) and (4) represents the chain propagating steps,.II. If we add oxygen to the reaction vessel, the series of reactions shown above would proceed more rapidly,

oxygen would catalyst the reaction.III. Step (4) is most likely the rate determinant step.IV. Step (5) represents a possible termination step for the reactiona) I only b) II only c) IV only d) II and IV only

142. The density of mercury is 13.6 g/ml. Calculate approximately the diameter of an atom of mercury assuming thateach atom is occupying a cube of edge length equal to the diameter of the mercury atom.

a) cmA91.2 b) cmA44.2 c) cmA36.1 d) cmA98.1

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143. The vaour pressure of the two miscible liquids (A) and (B) are 300 and 500 mm of Hg respectively. In a flask 10 molesof (A) is mixed with 12 moles of (B). However, as soon as (B) is added , (A) starts polymerizing into a completelyinsoluble solid. The polymerization follows first-order kinetics. After 100 minutes, 0.525 mole of a solute is dissolvedwhich arrests the polymerization completely. The final vapour pressure of the solution is 400 mm of Hg. Estimate therate of constant of the polymerization reaction. Assume negligible volume change on mixing and poilymerization andideal behaviour for the final solution.

a) 15 min10303.2 −−× b) 14 min10303.2 −−×

c) 14 min10005.1 −−× d) 14 min10905. −−×

144. Nitro benzene is formed as the major product along with a minor product in the reaction of benzene with a hot mixtureof nitric acid and sulphuric acid. The minor product consists of carbon : 42.86%. hydrogen : 2.40% nitroge : 16.67%,and oxygen : 38.07% (i) Calculate the empirical formula of the minor product. (II) when 5.5 g of the minor product isdissolved in 45g of benzene, the boiling point of the solution is 1.84 °C higher than that of pure benzene. The molarmass of the minor product and its molecular and structurral formula is.

a) The Molar mass is 184 g 1mol− and the product is m-dinitrobenzene

b) The molar mass is 184 g 1mol− and the product is 2 3 2 22(C H NO )

c) The molar mass is 168 g 1mol− and the product is 2246 )(NOHC

d) The molar mass is 253 g 1mol− and the product is 2246 )(NOHC

145. The standard molar enthalpies of formation of cyclohexane(l) and benzene (l) at 25°C are -156 and +49 kJ -1molrespectively. The standard enthalpy of hydrogenation of cyclohexene (l) at 25°Cis -119 kJ -1mol . Use these data toestimate the magnitude of the resosnance energy of benzene

a) -1Jmol357- b) -1Jmol205- c) -1Jmol152- d) -1Jmol562-

Questions 146 to 150 are based on the following passageOne technological application of thermodynamics in our society is in the form of heat packs and cold packs. Thesedevices contain chemicals, which react in an endothermic or exothermic chemical reaction. Commonly, cold packscontain ammonium nitrate and water in two separate compartments. When the contents of the separate compartmentsare mixed, a chemical reaction occurs due to the high solubility of ammonium nitrate in water. The associatedenthalpy change is referred to as enthalpy of solution or heat of solution. The process of dissolution (Reaction 1) ofammonium nitrate is highly endothermic and the cold pack absorbs heat from its surroundings, making it feel “cold”.the enthalpies of solution and solubility values for a number of ionic compounds are listed in Table 1.

mol/kJ69.25H Standard ),aq(NO)aq(NH )s(NONH rxn3434 +=∆+→ − Reaction 1

Compound H∆ Solution Solubility in water(kJ/mol) (g/100 mL)

Silver chloride 61 0.000089 (10 degrees C)

Sodium Chloride 26 35 . 7 (0 degrees C)

Lithium Fluoride 32 0.3 (18 degrees C)

Rubidium Fluoride -3 130 . 6 (18 degrees C)

Table 1

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The chemical processes which take place in hot packs are varied. One style of hot pack utilizes the energy changeswhich are associated with the crystallization of sodium acetate (NaCH3CO2) in the presence of water (Reaction 2)

)s(OH3.CONaCH O(1)3Haq)-COCH (aq)aN 223323 →+++

Standard mol/kJ6.387Hrxn −=∆ Reaction 2

Alternatively, the oxidation of transition metals, which is often exothermic, may be used to produce “heat” in a hotpack. When elemental Iron reacts with oxygen in the atmosphere, it oxidizes (Fig.3). One advantage of this reactionis the ability to package and store the iron in an environment void of oxygen unitl it is ready to use. If oxygen flowis somewhat restricted, hot packs of this type can maintain a temperature of 58 to 68 degrees Celsius for hours.

)s(OFe2)g(O3)s(Fe4 222 →+

kJ/mol 4.1648H tandardS rxn −=∆

146. From the information given in the passage, the molar solubility of solubility of sodium chloride in water at 0 degreesCelsius would be

a) 35.7 moles/L b) 0.611 moles/L c) 6.11 moles/L d) 1.64 moles/L

147. If 61.11 g of ammonium nitrate were dissolved in an excess of water, the amount of energy released would be

a) 61.1 kJ b) 0.764 kJ c) 19.62 kJ d) 25.69 kJ

148. The reason silver chloride would not be practical if used in a cold pack is

a) Silver chloride is not an ionic compound and is therefore not soluble in water.b) Silver chloride has an enthalpy of solution that is too highc) The solubility of silver chloride in water is too lowd) The dissolution of silver chloride in water is exothermic

149. What is the freezing point of a saturated aqueous solution of Lithium Fluoride (Kb=-1.86 K/m)?

a) -1.86 degrees Celsius b) -0.186 degrees Celsiusc) 0.186 degrees Celsius d) -0.1 degrees Celsius

150. The entropy change involved in the oxidation of iron (Reaction 3) would have which of the following thermodynamiceffects?

a) At very high temperatures, the oxidation of iron would be non-spontaneous.

b) At very low temperatures, the oxidation of iron would be non - spontaneous

c) At very high temperatures, the entropy change would be favorable.

d) The entropy change would have no effect on the oxidation of iron.

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ai iitjee modeltest 05

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