ai iitjee modeltest 04

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Model Test - 04

Take This test comprising 3 sections with a duration of 2 hourseach section.Each section contains 50 questions. Observe the given weightageto each question. 1/3 rd negative marking do exist for the wronganswers. Maintaining the time limit of 2 hours for each section isof atmost importance, while taking the test.

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Questions 1 - 5 are based on the following passageWhenever the human ear perceives music, or any other sound, it is always the result of a vibrating object. Thesevibrations, usually of a string or column of air in the case of an instrument, act to move the air around the viratingsource, creating a sound wave with the same frequency as the original vibration. The original waves are classifiedas either transverse or longitudinal, depending on whether a string or a coloumn of air is vibrating, respectivelyCertain frequencies of sound correspond to musical notes within an octave; for the same note one octave above,thefrequency is double its value in the lower octave. Therefore, in order to play a specific note of either a string orwind instrument, the string or column of air must vibrate at the appropriate frequency.In the case of string instruments, a series of strings is fixed at both ends, vibrating to produce a sinusoidal wave,figure - 1

Figure - 1The wavelength of any wave propagating in that string is dependent on the length of the string, which is assumedto remain constant during virbration. When the string vibrates at its lowest frequency, it is termed the first harmonic,vibrations at the second lowest frequency are termed the first overtone, or second harmonic, and so forth. When amusician presses on the strings, the effective length of the string shortens, increasing the frequency of the firstharmonic. However, even without pressing down on the strings, the musician can produce different sounds fromthem, since although the strings are of equal length, they do not have equal mass or equal tension. The dependenceof frequency on linear density, or mass per unit length, and tension is illustrated by equation 1.

λρ=

2/1)/T(f Equation - 1

Where f is the frequency, T is the tension on the string, p is the linear density of the string, and λ is the wavelength.In wind instruments, though the mechanism of sound production differes from that of the string instruments, thebasic principles of a vibrating medium are retained. These instruments use a column of air, open at one, both, orneither end, to propagate a sound wave. Nodes and antinodes are crreated along the length of the column of air. Anode exists when some value is maximally restricted from change; whereas an antinode exists where some valuecan maximally change. For example, a mode of vibration in terms of displacement of air would have a node at aclosed end, since air is not free to move there, resulting in no change in displacement, for example a mode in termsof air pressure. Analogously to the string instrument, the wind instrument may have its air column shortened orelongated by a skilled musician, producing specific notes, which are arranged in a specific way to produce music.

1. It is known that some note D# roughly corresponds to a frequency of 311 sec-1. A musician attempts to play thatsome note in an octave lower. If the wavelength of the vibrating string is 0.25 m, how fast must the wave be movingto achieve this note?

a) 77.8 m sec-1 b) 155.5 m sec-1 c) 332 m sec-1 d) 777.5 m sec-1

2. Which of the following is true regarding a vibrating string that is fixed at both ends?

a) Thefirst harmonic has 1 more displacement node than the third overtone has.b) The third overtone has 2 more displacement antipodes than the fifth harmonic has.c) the fifth harmonic has 3 fewer displacement nodes than eighth overtone has.d) The eighth overtone has 4 fewer displacement antipodes than the thirteenth harmonic has.

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Paper - I : Physics - 1 to 50




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3. What is the most likely explanation for using strings of different densities to achieve different sounds, ratherthanrelying solely on different string lengths?

a) Larger densities allow the strings to have less weight, leading to greater range of frequencies.b) There is only a finite number of wavelengths able to be produced by changing string length alone.c) The range of string lengths required for a variety of frequencies becomes impractical.d) The combination of altering string length and density allows for frequencies that are independent of velocity.

4. A student suspends a block vertically from a string, and when the string is plucked, it vibrates at some frequency.Which of the following can the student change in order double the frequency of vibration, assuming all othervariable remain unchanged?

a) have the mass of the stringb) double the wavelengthc) decrease the length of the string one -fourth isoriginal lengthd) quadruple the mass of the block

5. A spherical particle is travelling horizontally when it collides with a portion of a vibrating string with both endsfixed. Assuming the string was propagating a horizontal wave, and that this collision is completely inelastic, whichset of information allows for the determination of the particle’s velocity before the collision?

a) The final velocity of the particle.b) the density of the particle, length of the portion of string contributing to the collision, and volume of the

particle.c) the length of the portion of string contributing to the collision, the linear density of the string, the mass of

the particle, and the final velocity of the particle.d) the linear density of the string, the density of the particle, the volume of the particle, and the final velocity of

the particle.

Questions 6 to 45 are independent Question

6. A homogeneous copper disc of mass ‘m’ kg and radius ‘r’ mt is placed with its centre at ‘O’ in a magnetic field ofinduction B Tesla so that the disc is perpendicular to the magnetic field. When the circuit is closed the disc beginsto rotate in t sec acquiring a velocity of ‘n’ revolution per second. The current in the circuit is —

O

B+

a)2 n m

Btπ

b)n mBt

πc) 2

n mBt

πd) 2

n mBt

π

7. In a circular motion of a particle the tangential acceleration of the particle is given by 22tma ts

= . The radius of the

circle described is 4m. The particle was initially at rest. Time after which total acceleration of the particle makes45º with radial acceleration is —

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

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8. Three non-zero vectors will have zero resultant only when

a) the cross product of resultant of any 2 vectors with third vector is zero

b) the dot product of resultant of any two vectors with the third is zero

c) all the 3 vectors are collinear

d) none of these

9. 3 Cal of heat is given to one mole of a monoatomic gas contained in a closed vessel at 300k. The fractional changein the RMS speed of the molecules of the gas is nearly —

a)1

300 b)1

200 c)1

600 d)1

900

10. The two ends of a uniformly tapered nod are maintained at temperatures 100ºC and 0ºC respectively. Under steadystate, the temperature of the section AA’ is —

L

100ºC OºC

A1

AL2

a) 50ºC b) > 50ºC c) ∠ 50ºC d) none of these

11. Suppose the potential energy between electron and proton in hydrogen atom when they are at a distance ‘r’ is given

by 2 logU Ke r= , where K is a constant. Given e– the charge of electron/proton, m = mass of electron thenaccording to Bohr’s theory its velocity in nth orbit is —

a) 2hm rπ b) 22

n hm rπ c)

2Ken m d)

2Kem

12. A rope of mass M and length L hangs vertically. The time needed for a pulse to travel from the bottom to thesupport is —

a) 2 Lg

π b) Lgπ c) 2 L

g⋅ d) Lg

13. Sound waves of frequency 660 Hz fall normally on a perfectly reflcting wall. The shortest distance from the wallat which the air particles vibrate with maximum amplitude is ——— (Given velocity of sound in air = 330 m/s)

a) 2 m b) 1 m c) 0.25 m d) 0.125 m

14. Two waves 1 sin(3.14 50 )y a x t= − and 2 sin 3.14 503

y a x t π = + + superposed, then the first two nodes

(x > 0) for the standing wave is —

a) 0.833 m, 1.833 m b) 0.415m, 0.930 m c) 0.677 m, 1.677 m d) 0.1667 m, 1.667 m

15. A radio active isotope is being produced at a constant rate A. The isotope has a half-life T. After a time l >> T, themember of nuclei become constant. The value of this constant is —

a) 2ATl n b) 2AT l n⋅ c) 2A l n

T⋅ d) AT

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16. The daughter nucleus in a nuclear decay is itself radioactive. Let pλ and dλ be the decay constant of the parent

and the daughter nuclei. Also, let pN and dN be the number of parent and daughter nuclei at time ‘t’. Thencondition for which the number of daughter nuclei becomes constant is —

a) p p d dN Nλ > λ b) p p d dN Nλ < λ c) p p d dN Nλ = λ d)p d

p dN Nλ λ=

17. A cubical vesel with non transparent walls is so located that the eye of an observer does not see its bottom but see

all of the wall CD. The height of liquid ( 13 / 8)µ = should be poured into the vesel for the observer to see anobject ‘O’ located at a distance ‘b’ from the corner S is —

Q R

SbP

O

a) 2b

b) b c) 2b d) 3b

18. In Young’s double slit experiment (S1S2=d) given S1S – S2S = 2λ

, where λ = wavelength of light used. Then

central fringe of fring pattern forms at —

S

S1

S2

D

O

Screen

a) point O b) a distance 2Dd

λ above the point O

c) a distance 2Dd

λ below the point O d) none of these

19. A parallel sided slab has its refractive index variying linearly with the distance from one parallel side, from 1µ , at

the first side to 2µ , at the opposite side. The slab is placed in a medium of refractive index 0µ . If a parallel beam

mono-chromatic light is incident on the first surface from the outside medium at an angle of incidence α , the angleof emergence from the second face is —

a)1

2

µ ⋅αµ b)

1 1

2

sin sin− µ ⋅ α µ c)

1 1

2

sin sin− µ α µ d) α

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20. Two lenses A and B are placed at closer seperation as shown. The focal length of combination of these two lensesis f. An opaque screen ‘SS’ is introduced between them as shown, blocking half the space. The resulting focallength of combination in —

S

S

a) 2f

b) 2 f c) f d) cannot be determined

21. A beam of light consisting of two wavelengths 650nm and 520nm is used to obtain interference fringes in Young’sdouble slit experiment. The distance between slits is 2mm, and between the planes of slits and screen is 120cm.The least distance from the central maximum, where the bright fringes due to both waveleng coincide is —

a) 156 mm b) 1.56 cm c) 1.44 cm d) 144 mn

22. The time constant of the circuit shown is — (L–Inductance, R–Resistance) :

L L

R

R

a)LR b)

4LR c) 2

LR d)

34

LR

23. Magnetic flux linked with a stationary loop of resistance R varies with respect to time (t) during the time period Tas : ( )at T t= −φ , where a is a constant. Calculate the amount of heat generated in the loop during that time.Assume the inductance of the coil as negligible.

a)3

4aT

Rb)

2 3

4a T

Rc)

3 3

3a T

Rd)

2 3

3a T

R

24. In a certain polytropic process, the volume argon was increased by 4 times and pressure decreased by 8 timessimultaneously. The molar heat capacity of argon in this process is ——(Assume argon to be ideal)

a) 4.2Jk mol− b) 4.2J

k mol−

− c) 8.4Jk mol− d) 8.4J

k mol−

−

25. The initial velocity of a particle of mass 2kg is ( )4 4i j+ m/s. A constant force of 20 j N− is applied on the

particle. Initially the particle was at (0, 0). The x-coordinates of the point where its y-coordinate is again zero is —

a) 3.2m b) 6 m c) 4.8 m d) 1.2 m

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26. A small ball of mass ‘m’ is connected to a wire (AB) and a cord (BC) as shown. If the cord is cut then ratio oftension in supporting wire immediately after the cord is cut to that in the wire before the cord is cut is —

A

B Cm

a) 0 b) 1 c) 2cos θ d) 2sin θ

27. Orbital velocity is a certain orbit (1) is same as the escape velocity from some other orbit (2). The ratio for theamount of energy to be imparted to a satellite in order to transfer it from circular orbit (2) to (1), to gravitationalpotential energy is orbit (1) will be —

a)43 b)

34 c)

54 d)

45

28. A billiard ball rolls without slipping across a horizontal table and hits a vertical wall. During the impact both theball and the wall deform elastically. The coefficient of friction of the ball against the wall is µ . If both gravity androlling friction during impart neglected, the angle to the horizontal at which the ball will rebound from the wall is—

a) 1tan− µ b)1 1tan− µ

c)1tan

2− µ

d) 1tan (2 )− µ

29. A uniform circular disc which rolls without slipping with a velocity ‘v’ encounters an abrupt change in the directionof its motion as it rolls on to the incline ‘ θ ’. The new velocity v1 of the centre of the disc as it start up the

incline is —

V

a)(1 2cos )

3V + θ

b)(1 2cos )

3V − θ

c) (sin )V θ d) cosV θ

30. A particle executes SHM in a straight line. In the first second starting from rest it travels a distance ‘a’ and in thenext second a distance ‘b’ in same direction. The amptitude is —

a)22

3a

a b−b)

2

3aa b−

c) 2a b− d) a b−

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31. Calculate the natural frequency of the oscillation of spring (spring constant = K) loaded with a mass ‘m’ when it isset in motion. Both the springs are identical and are in tension all time.

mK

K

a)1

2Kmπ

b)1 2

2K

mπc)

12 2

Kmπ

d)1

2mKπ

32. Two point charges q1 and q2 are placed at A and B curve drawn represent the distribution of potential due to thecharges along the line connecting the charges. The curve indicates that

V V

Pq1q2

a) charges q1 and q2 are same in nature b) charges q1 and q2 are opposite in nature

c) electric field intensity at point P is zero d) none of the above

33. A metallic wire PQR in the shape of a radius ‘a’ slides with constant velocity ‘v’ is a uniform magnetic field ofinduction ‘B’ as shown resistance ‘R’ is —

VR

P

Q

a)BV aR

πb)

BV aR c)

2BV aR d) zero

34. A cylindrical container of height h and area A, is immersed in water to a depth ho. A small hole of area A2 appearsin the bottom of the container. The time in which the container sinks is ——(Neglect atmospheric pressure)

a)2

1

( )2

A h hoA gho

=b)

1

2 2A h

A gho c)1

2

( )2

A h hoA gho

−d)

1

2 2 ( )A h

A g h ho−

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35. A uniform elastic plank moves over a smooth horizontal plane due to a constant force F distributed uniformallyover the end face. The surface of the end face is equal to A and Young’s modulus of the material to Y. The strainof the plank in the direction of the acting force is —

a) 3FAY b) 2

FAY c)

FAY d)

32

FAY

36. A uniformly charged semi circular loop of radius R carries a uniformly distributed positive charge q as shown. Thenet electric field at the centre of loop is —

+ Y

X

++

+

++

+

+

a) zero b) 2 20

along Y axis4

qRπ ε

c) 2 20

2 along - axisq xRπ ε d) 2 2

0

along -axis2

q xRπ ε

37. Gas at pressure P0 is contained in a vessel of the masses of all the molecules are halved and their speed doubled, theresulting pressure P will be —

a) 4 P0 b) 2 P0 c) P0 d) P0/2

38. In the circuit shown, the final voltage drop (in steady state) across the capacitor ‘C’ is —

C

Vr3

r2

r1

a)1 2

1 2 3

( )V r rr r r

++ + b)

1 2

2

( )V r rr+

c)2

1 2

V rr r+ d)

1

1 2

V rr r+

39. Two wires A and B of the same material, having radii in the ratio 1 : 2 are carrying curents in the ratio 4:1. The ratioof the drift speed of electrons in A and B is —

a) 4 : 1 b) 1 : 4 c) 1 : 16 d) 16 : 1

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40. A cell of emf ε and internal resistance r is connected in series with a variable resistance. The potential difference(V) of the cell is measured for different values of current (I) external resistance. V and I is shown in figure. Internalresistance is —

Vo, q

p, oI

a) P b) q c)Pq d) q

P

41. Consider a circuit that consists of four ressitors (each with R = 1 MΩ ), a capacitor µΩ).1(C = and a battery (V= 10 MV) as shown. If the capacitor is fully charged and then the battery is removed, find the current at t = 0.5 s asthe capacitor discharges.

R

C

V

R

R

R

a) 40 A b) 20 A c) 24.3 A d) 5.4 A

42. The propagation of sound in a gas may be modeled as adiabatic in nature. For a three degree of freedeom ideal gas,by what factor does the sound speed change when the presure is doubled at constant density ?

a) increases by factor 2 b) decrease by factor 2

c) increases by factor 2 d) decrease by factor 2

43. Board A is placed on board B as shown. Both boards slide. Without moving with respect to each other, along africtionless horizontal surface at a speed v. Board B hits a resting board C “head-on.” After the collision, boards Band C move together, and board A slides on top of board C and stops ats motion relative to C in the position shownon the diagram. What is the length of each board ? All three boards have the same mass, size, and shape. It isknown there is no friction between boards A and B; the coefficient of kinetic friction between boards A and C is

.µk

AB

C

0v =B

AC

BEFORE AFTER

a) gk

2

6µv

b) gk

2

4µv

c) gk

2

2µv

d) gk

2

µv

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44. Refer to the diagram below. A very large, charged plate floats in deep space. Due to the charge on the plate, aconstant electric field E exists everywhere above the plate. An object with mass m and and charge q is shot upwardfrom the plate with a velocity v and at an angle θ . It follows the path shown reaching a height h and a range R.Assume the effects of gravity to be negligible.

E

hθ

R

Which of the following is true concerning the flight of the projectile shown ?

a) Increasing the mass m decreases the maximum height h.

b) Increasing the charge q increases the maximum height h

c) Increasing the mass m decreases the downward acceleration.

d) Increasing the charge q decreases the downward acceleration

45. Refer to the diagram below. inside a vacuum chamber, a point charge 1q is separated by a distance d from the

surface of a hollow sphere with a radius r and made from a conducting material. The sphere has a charge .q2(Note: k is the Coulomb’s law constant).

.q2

d1q

When 1q is removed, the force on the sphere charges. Which of the following represents the time between the

moment 1q is removed and the moment the sphere experiences any change in force ?

a) The sphere feels the change instantaneously

b) )103/( 8×d

c) d/)103( 8×

d) )103/()( 8×+ rd

Questions 46 - 50 are based on the following passage

A Vast majority of worldwide energy production comes from the combustion of fossil fuels or products derivedfrom fossil fuels. As energy demands constantly increase, there is a growing trend to supplant these less desirableforms of energy production with cleaner renewable alternatives such as wind, solar and hydroelectric power.solar power generation leverages the photovoltaic effect to convert sunlight into electricity. Initial efficienciesranged from 1-2% whereas curent technologies allow for the direct conversion of 7-17% of the solar energy reachingthe collection panels. these collection panels are commonly cmprised of two separate semiconductors. sandwichedtogether. The amount of energy that can be generated by these panels is inversely proportional to the ratio of thetransmission intensity, I, to light intensity, I0:

bx0II −= (Equation - 1)

Where I0 is the light intensity that reaches the surface of the panel, b is the absorption coefficient of the panel, andX is the thickness. One factor that contributes to decreasing the light intensity includes the conducting elementlining the surface of the panel.

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Unlike solar power, where solar energy is directly converted into electricity, both wind and hydroelectric powergeneration requires the conversion of kinetic energy into mechanical power, which is then used to create electricalpower. A wind turbine converts the kinetic energy of passing air molecules while a hydroelectric turbine convertsthe kinetic energy of passing water molecules. Both forms of energy production proceeds through the use of a largerotor connected to an induction generator. A siple induction generator is comprised of a flat rectangular coil rotatingin magnetic field, and the emf, ε , produced by such a generator can be calculated with the following formula.

ft)sin(2 max πε=ε (Equaton 2)

fNBA max =ε (Equation 3

Where maxε is the peak emf produced, N represents the number of turns in the coil, B is the constant magnetic field,A is the area covered by the coil, f represents the number of complete rotations the coils executes per second, andt is the duration of time that the generator is operating.

46. In the United States, the alternating emf produced power stations must oscillate at exactly 60 Hz. In order toincrease the potential voltage generated, manufacturers of generators may do all of the following EXCEPT.

a) Increase the magnetic field. b) Increase the number of turns in the coilc) Increase the rotational speed of the generator d) Increase the overal coil size

47. Current investigation into improving the efficiency of solar power conversion includes maximizing the amount ofphotons that are absorbed within the surface of collector panels. According to the passage, which of the followingwould NOT be useful for this purpose:

a) Increasing the number of conducting elements to maximize electrical transmission.b) Increase the thickness of the semiconductor plates.c) Using mirrors to combine and concentrate more sunlight onto the panel surface.d) Minimizing reflective loses from conducting elements.

48. Any photon striking an electron in a solar panel semiconductor must have sufficient energy to liberate that electronwithout causing heat because heat significantly decreases the conductivity and lifespan materials. Currently, thebest photovoltaic substances require light in the visible range. Which of the following the would best help tomaximize energy generation

a) Use semiconductive material whose electrons are liberated at the lowest possible frequencies.b) Coat the surface to remove infrared radiationc) Coat the surface to remove UV radiationd) Use a coolant to maintain a constant operating temperature.

49. A marooned physicist creates a crude hydroelectric generator hoping to use the kinetic energy of a small waterfallas a source of energy for his radio. Given a mechanical efficiency of 75%, power and AC cycling frequencyrequirement of 20 watts and 60 Hz respectively, along with a voltage requirement of 'rmsV120 how far below thetop of the waterfall should he place his generator ? (NOTE: Assume that 1kg of water strikes the surface of the rotorper second, and neglect air resistance)

a) 2 . 04 m b) 2 . 72 mc) 6 . 44 m d) 27 . 2 m

50. Wind turbines are giant fans mounted high above the ground. They are subject to shear forces from high winds ontheir rotor blades and mounting poles. To minimize the possible damage due to bending from extreme winds,engineers may employ all of the following EXCEPT.

a) Decrease the height of the mounting pole. Minimize the rotor blae profile tob) decrease the force exerted on the wind turbine.c) Increase the rotor blade size to maximize the conversion of the kinetic energy contained in high winds.d) Decrease the total number of rotor blades.

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Paper - I I : Mathematics - 51 to 100


Let ( )f x be a function and a be a point within or without the domain of ( )f x . Then we say that

1. ( )f x has an infinite discontinuity at x a= if ( )x aLt f x

−→ or ( )x aLt f x

+→ is infinite.

2. ( )f x has oscillating discontinuity at x a= if ( )x aLt f x

−→ and ( )x aLt f x

+→ lie in a certain range but do not

approach to a definite value at x a= .

3. ( )f x has jump ........ both exist finitely but their values are unequal. We define ( ) ( )x a x aLt f x Lt f x

− +→ →− =

jump function at x a= .

4. ( )f x has a removable discontinuity at x a= if ( ) & ( )x a x aLt f x Lt f x

− +→ → both exist finitely & their values

are equal but this value is ( )f a≠ . Such a function can be made continuous by redefining the function at

x a= so that ( ) ( ) ( )x a x aLt f x Lt f x f a

− +→ →= = .

51. The function defined by 1 ,

( ) 1,

x a

x a x af x e

O x a−

− ≠= +=

at x a= .

(a) is constant (b) has removable discontinuity

(c) has jump discontinuity (d) has infinite discontinuity

52. The function

1cos , 0( )

, 0

xf x x

O x

≠= =

at 0x = .


(c) has jump discontinuity (d) has oscillating discontinuity

53. The function ( )sin log , 0( )

, 0e x x

f xO x

≠= =

at 0x = .


(c) has jump discontinuity (d) has oscillating discontinuity

54. The function 1sin , 0

( ), 0

mx xf x x

O x

≠= =

is constant at 0x = if

(a) m O≥ (b) m O> (c) 1m ≥ (d) both (b) & (c)

Questions 55 - 95 are independent questions

55. If the square root of 2 2

2 2

1 31 is , then is2 16

x y x y x y i my x i y x y x m

+ + + + ± + −

a) 2 b) 3 c) 4 d) none of these

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56. The angle θ between the line az + az =0 and its reflection in real axis is given by

a) 2 2

Re(a) Im (a)tan θ =(Re( )) (Im( ))a a− b)

2 2

Re a Im (a)tan θ =

(Re( )) (Im( ))a a

⋅

+

c) 2 2

2Re (a) Im (a)tan θ =(Re( )) (Im( ))a a− d) none of these

57 Let I be the incenter of triangle ABC. Let the incircle of ABC touch the sides BC, CA and AB at K, L and Mrespectively. The line through B parallel to MK meets the lines LM and LK at at R and S, respectively.

Angle RIS is

a) acute b) obtuse c) right angle d) any of these

58. Two circles -1I and -

2I intersect at M and N.

Let l be the common tangent to -1I and -

2I so that M is closer to l than N is. Let l touch -1I at A and -

2I at B.

Let the line thorugh M parallel to l meet the circle -1I again at C and the circle -

2I again at D.Lines CA and DB meet at E; lines AN and CD meet at P; lines BN and CD meet at Q, thena) MP = MQ b) EP = EQ c) AP = CP d) both a & b

59. Show that 0

lim( 3)

nnk

kn k

Cn k→∞ =

=+∑

a) (2 - e) b) does not exist c) e - 2 d) e

60. The function 2 2( ) ( 1) [ 3 2 | cos(| |) is not differentiable at f x x x x x= − − + +

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

61. Find the points of discontinuity of 2

1 ,2

yu u

=+ − where

11

ux

=−

a) 1 , 1, 22 b) 1 , 1, 22 − c) 0, 1 d) 1, 2

62. The number of rectangels excluding squares from a rectangle of size 9 6× is


63. In a city no person have identical set of teeth and there is no human person without a tooth. Also no person hasmore than 32 teeth. If we disregard the shape and size of tooth and consider only the positioning of the teeth, thenthe maximum population of the city is

a) 322 b) 322 1− c) 322 1+ d) none of these

64. To avoid detection at customs, a smuggler has placed six narcotic tablets in a bottle containing nine vitamin pillsthat are similar in appearance. If the customs official selects three of the tablets at random for analysis, then theprobability that smuggler will be arrested for illegal possession of narcotics is

a)1265 b)

5365 c)

165 d) none of these

65. If ‘head’ means one and ‘tail’ means two, then coefficient of quadratic equation 2 0ax bx c+ + = are chosen bytossing three fair coins. The probability that roots of the equations are imaginary is

a) 5/8 b) 3/8 c) 7/8 d) 1/8

66. Let a, b, c be real. If 2 0ax bx c+ + = has two real roots α and β, where α < -1 and β > 1, then

a) 1 0c ba a

+ + < b) 1 0c ba a

+ + < c) 1 0c ba a

+ + < d) 0b ca+ <

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67. Find the value of : 1 1 -11cos(2 cos sin ) , where 0 cos π5

x x at x x− −+ = ≤ ≤ and -1π/2 sin π/2.x− ≤ ≤

a)2 6

5± b)

2 65

c)2 6

5− d) does not exist

68. Evaluate 8 / 7 6 / 7( ) ( )dx

x a x b+ −∫

a)1

77( )

x b ca b x a

− + + + b)

177

( )x a c

a b x b+ + + −

c)1

77( )

x a ca b x b

+ + − − d)

177

( )x b c

a b x a− + − +

69. Solve 4

4

sin

cos

( )(cos 2 ) ( )

t

t

f z dzI

f t z f z−

=− +∫

a) 21 1 sin 22 4

t− b) 21 1 sin 22 4

t− + c) 211 sin 22

t− + d) 21 1 sin 22 2

t− +

70. Determine the area of the figure bounded by two branches of the curve 2 3( )y x x− = and the straight line x = 1.

Y

O 1/2 1 2

x = 1

y = x - x x

xx

y

+=

a) 0 b)45 c)

25 d)

15

71. Find the equation of the curve such that the square of the intercept cut off by any tangent from the y-axis is equal tothe product of the coordinates of the point of tangency.

a) y = ce b) yxy 2log ±= c) x = ce

yx d) 2

x = ceyx

+

72. The sum of the torques about any point in the plane of the polygon of forces represented by the sides of the polygontaken in order is.a) twice the vector area b) vector area of closed planec) nothing can be said d) proportional to area of polygon

73. Given that vectors, A, B, C from a triangle such that A = B + C. Find a, b, c, d such that the area of the triangleis 5 6 where A = ai + bJ + cK. B = di + 3j + 4k, C = 3i + j - 2k.

a) -8, 4, 2, -11 b) 8, -4, -2, 11 c) 3, 4, 2, 5 d) 3, -4, 2, 5

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74. The curves 2 4y ax= and 2 34ay x= intersect each other at an angle of 1tan (1/ 2)− and also if 1PG and 2PG be the

normals to the two curves at common point of intersection (which is not orgin) meeting the axis of x in 1G and 2G ,

then 1 2G G ?=

a) 5a b) 4a c) 2a d) 10a

75. If cos (x - y), cos x and cos (x + y) are in H.P., then cos x. sec 2y

is equal to

a) 2 b) 2− c) 2± d) none of these

76. Given that (1 1 ) tan 1 1 ,x x x+ + = + − then value of sin 4x is equal to

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

77. A variable line thro’ P with co-ordinates (-2, 1) cuts the axis in A, B resp. Q is a point on AB such that PA, PQ andPB are in H.P. Then the locus of Q is a straight line.

a) x = 2y b) x = 2y + 1 c) x = 2y + 2 d) x = y + 2

78. If the line 3y x= cuts the curve 3 3 2 23 5 3 4 5 1 0x y xy x y x y+ + + + + + − = at the points A, B, C, then OA.OB.OCis

a)4 (3 3 1)

13− b) 3 3 1+ c)

2 73

+ d) none of these

79. The equation of four circles are 2 2 2( ) ( ) .x a y a c± + ± = The radius of a circle touching all the four circles is

a) ( 2 1) or ( 2 1)a a− + b) 2 2 a

c) (2 2)a− d) (2 2)a+

80. If from a point A, the two tangents drawn to the parabola 2 4y ax= are normals to the parabola 2 4 ,x by= then

a) 2 22a b> b) 2 24a b< c) 2 28a b> d) 2 27a b=

81. If the polar of 2 2

2 2 1x ya b

+ = is always touching the curve 2 2

2 2 1,x yb a

+ = then the locus of the pole is

a) parabola b) ellipse c) hyperbola d) circle

82. If the sum of the slopes of the normal from a point ‘P’ to the hyperbola 2xy c= is equal to +λ(λ R ),∈ then locus ofpoint ‘P’ is

a) 2 2x cλ= b) 2 2y cλ= c) 2xy cλ= d) none of these

83. Given lines are x + 2y + 3z + 4 = 0, 2x + 3y + 4z + 5 = 0

The axes being rectangular, find the equation of the perpendicular from the origin to the line

a)2 1 4x y z= = b)

2 1 4x y z= =

− −c)

2 1 4x y z= =

−d)

2 1 4x y z= =

−

84. Graph of the equation 2 2 0y z+ = in three dimensional space is

a) x-axis b) y - axis c) z-axis d) yz-plane

85. If sum of the first 2n terms of the A.P., 2, 5, 8,.......is equal to the sum of first n terms of the A.P. 57, 59, 61...., thenn equals

a) 10 b) 12 c) 11 d) 13

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86. If a, b, c d are four distinct positive numbers in H.P., then

a) 2 2 22a c b+ > b) 3 2 32b d c+ > c) 5 5 5a c b+ > d) all of these

87. The expression 2 24 4 | sin θ| - cos θx x+ attains the minimum value

a) -2 b) -1 c) -1/2 d) 0

88. If A = 840°, then 2 sin 2A

euqals

a) 1 sin 1 sinA A+ + − b) 1 sin 1 sinA A− + + −

c) 1+ sinA - 1 - sinA d) 1+ sinA - 1 - sinA−

89. Taking the function f(x) = (x - 3) log x,

There is at leat one value of x in (1, 3) which satisfies

a) x log x = 3 - x b) x log x = 3 + x c) x log x = x - 3 d) x log x = - 3 -x

90. Let 2 1( ) ,1 4. [.][ ]

xf x xx+= ≤ ≤ denotes the greatest integer function. Then

a) f(x) is monotonically decreasing [1, 3, 9] b) f(x) is monotonically increasing in [1, 3, 9]

c) The greatest value of f(x) is 172

d) The least value of f(x) is 2

91. Suppose, f(x) is a function satisfying the following conditions :

(i) f(0) = 2, f(1) = 1;

(ii) f has a minimum value at x = 5/2 and

iii) For all x baxbaxbax

bbbaxaxax

xf++++

−+++−

=2122)(2

1112122

)('

The constants a, b respectively will be

a)1 5,4 8 b)

1 5,4 4

c)1 5,4 4

− d)1 5,4 4

− −

92. Number of solutions of sin 2 22π x = x π 1 is2x + + +


93. In the expansion of (1 ) (1 ) (1 ) ,n n nx y z+ + + sum of the co-efficients of the terms of degree r’ is

a) 3nrC b) 3

nr

C c) 3nrC d) 23. n

rC

94. Solution set of the inequality x

x/1

2

2515

>+ is

a) (-2, 0) b) (-2, 2) c) (-5, 5) d) ),0( ∞

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95. If ,131

31372 >

xx

then

a) )1,0[∈x b) )16,0[∈x c) )64,0[∈x d) none of these


(IV) 3 2( ) , 0f x ax bx cx d a= + + + > then 1 2( ) 3 2f x ax bx c= + + .

Case:1 1( ) 0f x = has no real roots. Then ( )f x always increases as x increases & ( ) 0f x =

has one real root.

Case:2 1( ) 0f x = has two distinct roots &α β ( )α < β . If ( ) ( ) 0f fα β > then ( ) 0f x = has one real root.

Case:3 1( ) 0f x = has two distinct roots &α β ( )α < β . If ( ) ( ) 0f fα β < then the equation ( ) 0f x = has

three real roots.

Case:4 1( ) 0f x = has two distinct roots &α β ( )α < β , but ( ) 0f β = , also in this case ( ) 0f x = has

repeated root & one other root. (β, 0)

In general, the equation ( ) 0g x = has a repeated root ,x = α if 1( ) ( ) 0g gα = α = .

96. The equation 3 3 1 0x x− + = has

(a) three distinct real root (b) one repeated & one different root

(c) only one real root which is not repeated (d) only one repeated root

97. The no. of integral roots of the equation in previous question is

(a) 3 (b) 2 (c) 1 (d) 0

98. If the roots of 3 3 1 0x x− + = has roots , ,α β γ then the value of [ ] [ ] [ ]α + β + γ is

(a) 0 (b) 1

(c) –1 (d) not defined as all roots are not real

99. The equation 3 28 20 6 9 0x x x− + + = has

(a) one repeated root (b) all distinct real roots

(c) all roots repeated (d) only one real root which is not repeated

100. The solution set of the equation given in (1) is

a)1 1 3, ,

2 6 2−

b)

1 3,6 2

c)1 3,

2 2−

d)32

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Questions 101 to 105 are based on the following passage

A chemist is studying the boiling points of various silanes. Due to similarities in reactivity, many silanes exist asmistures with a variety of molecular formulas. In order to determine the boiling point of a pure silane, individualcompounds must be separated by distillation.

Experiment - 1 : A mixture of silanes is placed in a distillation apparatus at - 1150 C. The temperature is slowlyraised. Between - 1130 C and -1090C, a colorless vapor boils off the liquid mixture. This is collected and labeledFlask A. the chemist continues to raise the temperature, and another vapor is collected between -170C and -120C.This is labeled Flask B. Between 500C and 540C, a third sample is collected and labeled Flask C. Finally, theremainder of the mixture boils between 840C and 850C. This is collected in Flask D.

Experiment - 2 : The chemist injects 25 Lµ of the sample from Flask D into a gas chromatograph. Analysis of theresults shows that the sample is a mixture of straight-chain and branched-chain isomers. Expriment 3 Flasks A, B,C, and D are analyzed individually to give the boiling point data in Table - 1

Silane Normal Boiling Point (0C)

SiH4 -111.8

Si2H6 -14.5

Si3H8 52.9

Si4H10 84.3

Table -1

For comparison, the boiling points of several low-molecular weight hydrocarbons are shown in Table - 2

Hydrocarbon Normal Boiling Point (0C)

CH4 - 164

C2H6 - 88.6

C3H6 - 44

C4H10 - 05

Table - 2

101. Many low-molecular weight hydrocarbons are gases under standard conditions, making a determination of theboiling point difficult. What might a chemist do to determine the boiling point of a low - molecular weighthydrocarbon?a) Lower the temperature at which the determinations are madeb) Pressures, then extrapolate the curve to I atmc) Mix the hydrocrbons with suitably highermolecular weight compounds, then determine the boiling point of

the mixture.d) Determine the boiling point at lower pressures, then extrapolate the curve to 1 atm.

102. Compared with hydrocarbons of the same general moelcular formula, the boiling points of silanes are:a) Higher, because of the greater number of electrons and stronger intermolecular forces in silicon-based

compounds.b) Higher, because of the lower number of electrons and weaker intermolecular forces in silicon-based

compounds.c) Lower, because of the lower number of electrons and weaker intermolecular forces in siliconbased compounds.d) Lower, because of the greater number of electrons and stronger intermolecular forces in siliconbased

compounds.

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103. Which of the following quantum numbers correspond to the outermost valence electron of silicon?

a) n = 2; &ell; = 2 b) n=2; &ell; = 1c) n = 3; &ell; = 1 d) n = 3; &ell; = 2

104. Which of the Si4H10 isomers would be expected to have the higher boiling point?

a) The straight-chain isomer, because there are more sites for hydrogen bonding.b) The straight-chain isomer, because there is more opportunity for V an der Waals interactions.c) The branched-chain isomer, because V an der Waals interactions are more significant with substituted

structures.d) Neither, the structure does not affect the boiling point.

105. Why does the chemist observe a range of boiling temperatures for each silane compound?

I. minute differences in the structure of each compound cause differences in the boiling points.II. Each additional compound in the mixture acts a soluteIII. The substance that boils off is impurea) I only b) II onlyc) I and III only d) II and III only


106. Both 22OH and 3O acts as oxidising agents. The oxidising action in which they are similar

1) 4PbSOtoPbS 2) ++ 32 FetoFe

3) ])([Kto])([ 6364 CNFeCNFeK 4) decolourising of acidified 4KMnO

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

a) 1, 2, 3 b) 2, 3, 4 c) 1, 2, 4 d) none

107. 42SONa is water soluble but 4BaSO is insoluble because

1) The hydration energy of 42SONa is higher than that of its lattice energy

2) the hydration energy of 42SONa is less than that of its lattice energy

3) the hydration energy of 4BaSO is less than that of its lattice energy

4) the hydration energy of 4BaSO is higher than that of its lattice energy

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

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

108. 4C(OH) is unstable because a carbon atom cannot hold more than one -OH groups but 4Si(OH) is a stablecompound because

1) C-O bond energy is low 2) C-O bond energy is high3) Si-O bond energy is low 4) Si-O bond energy is highWhich of the given statement(s) match with the main statement.a) 1, 4 b) 1, 3 c) 1, 2 d) none

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109. Which of the following statements concern with transition metals ?1) Compounds containing ions of transition elements are usually coloured2) the most stable oxidation state is + 3.3) they show variable oxidation states, which differ by two units only4) they easily form complexes.a) 1, 2, 3 b) 2, 3, 4 c) 1, 2, 4 d) none

110. In electrorefining of metals, anode and cathode are made-up of impure metal and a strip, a pure-metal respectivelywhile the electrolyte is solution of a complex metal salt. This method cannot be applied for the refining ofa) Copper b) Sodium c) Aluminium d) Zink and Silver

111. A white sodium salt dissolves readily in water to give a solution, which is neutral to litmus. When silver nitratesolution is added to this solution, a white precipitate is formed which does not dissolve in dilute 3HNO . Theacidic would be

a) -23CO b) -Cl c) -2

3SO d) -Br

112. Amongst the following, choose the correct statement(s)

1) atomic hydrogen is obtained by passing hydrogen through an electric arc.

2) hydrogen gas will not reduce heated aluminium oxide.

3) finely divided paladium absorbs large amount of hydrogen gas

4) pure nascent hydrogen is the beast obtained by reacting Na with OHHC 52

a) 1, 2, 3 b) 2, 3, 4 c) 1, 2, 4 d) none

113. If one measures the gradient of the e.m.f of a cell with respect to temperature the end result will be a value for

a) ∆H of the cell reaction b) the heat of the cell reaction

c) ∆Sof the cell reaction d) ∆G of the cell reaction

114. The average osmotic pressure π ,of blood is 12.3 atm at 27°C . What concentration of glucose , 6 12 6C H O

will be isotonic with blood ?

a) 2.0M b) 0.025M c) 0.5M d) 1.5M

115. A balloon initially contains 20 grams of helium at a pressure of 1000 torr . After some helium is let out of theballoon ,the new pressure is 900torr ,and the volume is half of what is was .If the temperature has not changed ,howmuch helium is now in the balloon ?

a) 9 grams b) 10 grams c) 11 grams d) cannot

116. In a titration of 2 3Na CO with HCl,which of the relations shown below would yield the molarity of HCl to pH 4 end

point ? 2 3 2 32HCl+Na CO H CO +2NaCl

a) 2 3

2 3

(gNa CO ) (2)(mol.wt.Na CO ) (ml HCl/1000) b)

2 31( gNa CO ) 2

(mol HCl/1000)

c)2 3

1( moles Na CO ) 2

(ml HCl/1000)

d)

2 3moles Na CO(ml HCl/1000)

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117. Which of the following explains the pressure and volumes deviations in a real gas compared to an ideal gas ?I Ideal gas molecules don’t have volume and real gas molecules doII Ideal gas molecules don’t exert forces on one another and real gas molecules doIII Ideal gas molecules all move at the same speed for a given temperature , whereas the speed of real gas

molecules varies within a sample of gas at a given temperaturea) I only b) II only c) I and II only d) I , II and III

118. Reaction chambers A and B both contain equal amounts of pure 1-butene. A catalyst for the isomerization of1-butene to 2 - butene is added to chamber A . Assuming there are no other products ,and that both chamberseventually reach equilibrium:a) chamber A will always contain at least as much 2-butene as chamber B, with the difference increasing over

time.b) chamber A will always contain at least as much 2- butene as chamber B, with the difference first increasing, but

then decreasing over time. c) chamber A will always contain at least as much 2-butene as chamber B, with the difference first decreasing,

but then increasing over time.d) chamber B will always contain at least as much-2 -butene as chamber A, with the difference increasing over

time.119. Direction : Use the following information to answer the question Objects radiate heat at a rate given by the

following equation.4ATP σε=

where P is the rate at which heat is radiated, σ is the Stefan-Boltzman constant ),KmW10(5.67 428 −−−× ε isthe emissivity of 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 processes 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.

A black body radiator has an emissivity of :

a) 0 b) 0.5c) 1.0 d) The emissivity of a blackbody radiator may vary.

120. Hexane is infinitely soluble in octane Why ?a) Because hexane and octane have similar molecular weightsb) Because the hexane-octane intermolecular bond is much stronger than either the hexane-hexane or the

octane-octane intermolecular bondsc) Because hexane can hydrogen bond to octaned) Because the entropy increase upon mixing the two materials is the dominant factor in the free energy change

when the two are mixed.121. Suppose the amount of material undergoing an oxidation reduction reaction doubles, but all other conditions

remain the same. Which of the following also doubles ?I) Free energy changesII) Total change flowIII) Potentiala) I only b) II only c) I and II only d) II and III only

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122. Direction : Cocaine is stimulant that is isolated from coca leaves Refer to the structure of cocaine shown belowto answer question

3CHO

O

O

O

4

H5

N3CH9

8

76

1

1011

123

How much p character is in the hybridised orbital on the N8 nitrogen in the cocaine structure ?

a) 33.3% b) 50% c) 66.6% d) 75%

123. Direction : A lower heat of hydrogenation indicates a more stable alkene. Refer to the table below to answerquestion

AlkeneMolar heat

Of hydrogenation

ethylene

propene

1-butene

cis-2-butene

trans-2-butene

cis-2-pentene

2-methyl-2-butene

2, 3-dimethyl-2-butene

137 kJ

126 kJ

127 kJ120 kJ

116 kJ

120 kJ113 kJ

111 kJ

Which of the following alkenes is the Most stable ?

a) ethylene b) cis-2-butene c) 2-Methyl-2-butene d) 2, 3-dimethyl-2-butene

124. In the sturcture shown below, which carbon is most nucleophilic ?

O

4 2

3 1

O

a) The carbon atom labeled 1. b) The cabon atom labelled 2.c) The carbon atom labeled 3. d) The carbon atom labeled 4

125. The neurotransmitter shown below contains what functional groups ?

NO

O

a) a primary amine and a carboxylic acid b) a tetriary amine and a carboxylic acid

c) a tertiary amine and an ester d) a quaternary amine and an ester

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126. The stability of most cycloalkanes (which is indicated by their higher boiling and melting points) as welll as theirnon-planar structure is not dependent upon :

a) Baeyer strain b) Strecker strainc) Pitzer strain d) nonbonded interactions.

127. Catechol is treated with four reagents, as follows :

catechol Cl

OClCH-C 2

HCl- A 3POClB 23NHCH

DC 2HPdHCL−

What is the structure of D ?

a)

OHOH

322 CHCHCH −−

b)

OH

32 CHCH-C-H −

COOH

OH

c)

OH

32 CHNHCH-C-H −−

OH

OH

d)

OHCHO

3CH-NH-CO =

128. Calculate the number of carbon atoms in 27.3 g of trichloroacetic acid. (Atomic weights : C = 12.0, = 35.5,O = 16.0, H = 1.0)

a) 5.163/)1002.6()2(3.27 23× b) 5.163)2(3.27

c) )1002.6(2)3.27(5.163

23× d) )1002.6(5.1633.27 23×

129. A 0.56g sample of iron ore is dissolved in acid,the iron is oxidized to the +3 state and then precipitated as

O.xHOFe 232 ⋅ This precipitate is filtered, washed and ignited to .OFe 32 The 32OFe weighs 0.29 g. the

reaction is : 32 32Fe Fe O (s)+ → and the atomic weights of iron and oxygen are 55.9 and 16.0, respectively. The

percentage of iron in the sample would be equal to :

a)8.1592)9.55(

29.056.0100 ×× b)

56.0]8.159/)9.552[(29.0100 ××

c) 8.15956.0

)9.55(229.0100 ×× d)

56.0]29.0/)8.1592[(9.55100 ××

130. Which of the following statements is true of isotopes ?

a) They have different atomic numbers and the same atomic masses.

b) Their electronic configurations differ

c) slight differences in chemical behavior of isotopes (called isotope effects) influence rather the kind ofreaction than the rate of reaction itself.

d) The first ones discovered were those of neon.

131. Based on the Third Law of thermodynamics we know that all perfect crystals at absolute zero have :

a) the same enthalpy b) the same crystal lattices

c) differing A∆ values. d) two of the above, (a) and (c)

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132. For a homologous series (n-hexane, n-heptane, n-octane and n-octane), select the graph that appropriately repre-sents the relationship between the numbers of carbon atoms and the logarithm of the retention volume ( ).VR

a)

RV

log

#carbon atoms

b)

RV

log

#carbon atoms

c)

RV

log

#carbon atoms

d)

RV

log

#carbon atoms

133. A perpetual motion machine capable of generating increasing amounts of energy without interacting with itssurrounding cannot exist. This is best explained by the

a) First Law of Thermodynamics b) Third Law of thermodynamics

c) Energy conservation principle d) Gibbs-Helm holtz equation

134. An electron in a certain element can have energies of -2 . 3, -5 . 1, -5 . 3, -8 . 2, and -14 . 9 eV. is the ground state ofthe electron, and no other levels exists between -14.9and -2.3 eV. Which of the following represents a partial list ofphoton energies that could be absorbed by an electron in the ground state of this atom ? All energies are in electronvolts.

s) -2.3, -5.1, -5.3, -8.2, -14.9 b) 0.2, 2.8, 2.9, 6.7

c) 2.3, 5.1, 5.3, 8.2, 14.9 d) 6.7, 9.6, 9.8, 12.6, 15.0, 16.1

135. Direction : Use the following information to answer to the questionUsing calculus, the the rate law for a first order reaction can be transformed to :

0t g[A]303.2/log[A] lokt +−=

where t[A] is the concentration of A at time t, 0[A] is the initial concentration of A, and k is the rate constant ofthe reaction. Methyl isonitrile is converted to accetonitrile in a first order process as follows :

CN(g)CHNC(g)CH 33 →

The rate constant for the conversion of methyl isonitrile is .s105 15 −−× A scientist has a container containingmethyl isonitrile gas with a partial pressure of 100 torr. After 12.8 hours (approx. 46,000 seconds), what is thepartial pressure of methyl isonitrile gas inside the container ?

a) 1 torr b) 10 torr c) 25 torr d) 50 torr

136. The free energy of a gas depends on its partial pressure according to the expression ).(P/PInRTGG oo +=Which of the following plots below shows agreement with this relationship?

a)

P (atm)

(kj)

G en

erg y

,

Free

298

b)

P (atm)

(kj)

G en

erg y

,

Free

298

c)

P (atm)

(kj)

G en

erg y

,

Free

298

d)

1 n P (atm)

(kj)

G en

erg y

,

Free

298

137. Suppose a certain reaction has the rate law :

B][k[A] Rate 1/2=

Which of the following can be concluded about the reaction ?

a) Two molecules of B react for every molecule of Ab) Two molecules of A react for every molecule of Bc) B reacts at twice the rate of Ad) This reaction does not take place in a single step

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138. For question refer to Habeer process shown below :

Con

cent

ratio

n

→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 devel-opment was crucial for the German war effort of World wat I, providing the Germans with sample fixed nitrogenfor the manufacture of explosives.The Haber process takes place 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 progresses.Even at the high temperatures, the conversion of nitrogen and hydrogen to ammonia was slow. In order to make theprocess industrially efficient Fritz Haber used a metal oxide catalyst. Which of the following was accomplished byuse of the metal oxide catalust ?I) The rate of production ammonia increasedII) The energy of activation was raisedIII) The equilibrium shifted to the righta) I only b) II only c) I and II only d) I, II, and III

139. Given the fact that the standard free energies of formation of water vapor and liquid water are -229 kJ/mol and

-237 kJ/mol respectively, what is the free energy of the vaporization of water? Assume all measurements werepreformed at 25°C.

a) -466 kJ/mol b) -8 kJ/mol c) + 8kJ/mol d) +466 kJ/mol

140. When slat X is dissolved in water to form a 1 molar unsaturated solution, the temperature of the solution is seento drop. From this information, we can conclude that for dissolving this salt in water :

a) positive all areGand,,H oo ∆∆∆ oS b) negative all areGand,,H oo ∆∆∆ oS

c) negative isG positive; isH oo ∆∆

d) o oH is positive; no conlusion can be reached about G∆ ∆

141. Which of the following structures is an amide ?

a)OH

b)

NH2

O c)O

d) O

HO

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142. Refer to the structure of 3β - cholestanol to answer questions

lcholestano-3βHO

How many tertiary carbons are in 3β -cholestanol ?

a) 3 b) 5 c) 7 d) 9

143. The reaction of 1, 3-butadiene with HBr is shown below. At 40°C the major product is the 1,4-addition product;however, at -80°C the major product is the 1, 2-addition product. Use this information and the reaction below toanswer question

HBrBr

addition-21, addition-41,Br

Which product is more thermodynamically stable ?

a) 1, 2-addition product

b) 1, 4-addition product

c) The products have the same stability

d) The relative stability cannot be determined.

144. The iodoform test shown below is used to identify methyl ketones. A positive test gives the yellow crystalline

3CHI . Use the euqation shown below to answer question.

O3HCHIOCR4OH3ICH-C-R 2323 ++−−→++ −

OO

Why does the hydroxide substitute for the carbon group only after three iodine ions have added ?

a) The presence of the iodide atoms forms a much better leaving group

b) Iodide is a good leaving group.

c) HI is a strong acid.

d) Water is a good leaving group.

145. In the protein hemoglobin, the histidine residue is attached to the Fe of the heme group. The formation of thebond between the histidine and the Fe is a :

a) Lewis acid-base reaction

b) condensation reaction

c) dehydration reaction

d) hydrogenation reaction

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Water is often referred to as the “universal solvent”. Most compounds are at least partially soluble in water. Theefficiency of water as a solvent makes the purifying of water and the handling of water difficult for certain applications.Even in state of the art research facilities, sterile and deionized water is usually neither sterile nor devoid of solutes.The pH of this water, for example, is often as low as 5 instead of the expected 7 for pure water. Distillation of water9the process of evaporating and condensing water to remove impurities) is not a perfect method for purifyingwater, as distilled water will leach substances out of any container or tubing in which it is placed. Furthermore,water will dissolve gases from the air. While nitrogen gas (the main constituent in air) is inert for most purposes,oxygen in the water can lead to oxidation of any solutes. Carbon dioxide complexes with water to form carbonicacid, H2CO3H2CO3. Even though carbonic acid is a weak acid, the pH of a standing body of pure water will dropsteadily if left exposed to air.

Purification standards for drinking water are much less rigorous than those used in the laboratory. Techniques suchas distillation are much too energy inefficient to perform on the large scale needed for a public water supply.Instead, water purification for drinking water mainly involves slight chlorination to kill bacteria and the removal ofmost solids and particulates by sedimentation. As a result, drinking water is not pure by any real measure. Themajority of drinking water supplied to the public has a very hight mineral content consisting mostly of sodium andcalcium salts in additon to fluoride ions which are added for dental health. The presence of impurities can contributeto proplems such as corrosion, precipitation, and bad tasting water.

146. Which of the following salts would cause the most problems by precipitation in water pipes and fixtures?

a) NaCI b) Na2SO4

c) CaCI2 d) CaSO4

147. If the pH of carbonated water (water with dissolved carbon dioxide) is 5, what is the hydrogen ion concentration?

a) 1 x 10-5 M b) 5 Mc) 5 x 10-5 M d) 1 x 10-9 M

148. Water softeners replace calcium ions in “hard” water with sodium ions. By doing so, water softeners do all of thefollowing except?

a) Add more cations to the solutionb) Decrease the freezing point of the solutionc) Decrease the osmotic pressure of the solutiond) Increase the boiling point of the solution

149. Which of the following would affect the boiling point of and aqueous solution without alteringits electrical conductance?

a) Methanol b) Acetic acidc) Sodium chloride d) Sodium benzoate

150. Under what conditions will liquid water have absolutely no ions in solution?

a) In equilibrium with ice at 00 Cb) As a 90% sucrose solutionc) Perfectly buffered pH 7.00 solutiond) None

ai iitjee modeltest 04

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