ai iitjee modeltest 02

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Model Test - 02

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 atmostimportance, while taking the test.

How to answer ?

1. Download the test2. If possible take a print of the test3. Mark correct option on the test booklet or on a sheet of

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test.5. Enter all your answers and submit the answer sheet online

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Questions 1 - 5 are based on the following passage

A productor dsigener intends to build a vending machine that can recognize different types of coins in orderto dispense canned doda. The enegineer assembles an aparatus, which contains a 2.0 V battery, magnets,and speed sensors.

when the coin is inserted through the slot, it completes a circuit made by the battery and wires. For example,the current in the circuit is 0.5 A When an undamaged quarter is inserted. If the resistance of the coin - whichcomes from one of its surfaces - is within a certain, predetermined range, the coin continues down the track,if accepted, the metal coin then passes between two magnets. The magnets will induce circulating currents,called eddy currents, in the coin. These currents produce a magnetic force that always points in the oppositedirection to the coin’s motion. The magnetic force induced is directly proportional to the eddy current produced,which is itself related to the materials making up the coin. Once the coin has left the magnet, speed sensorsare used to determine its velocity. If the speed falls within a predetermined range, the sensors will trigger agate to accept the coin; otherwise, the coin will be rejected.

Once comlete, the apparatus is tested using three disks an undamaged quarter, a quarter with a hle of radius5.5 mm removed from its center, and a non-conducting plastic quarter. The friction in the experiments isnegligible. The engineer measures the resistance, the speed, and the magnetic force induced on each disk.Each disk has a diameter of 2.40 cm and a thickness of 2.5 x10-2 cm, but all have different masses. Theresults of the experiment are summarized in Table - 1.

Type of Quarter Undamaged With Hole Plastic

Resistance 1.0 1.2 Infinite

Speed 1.0 1.4 1.8

Magnetic Force 1.0 0.6 0

TABLE- 1

(Note : Values in table are given relative to the undamaged quarter)

1. What is the resistance per unit are of an undamaged quarter as it completes the circuit in the apparatus?

a) 2/cm 40.0 Ω

b) 2/cm 90.0 Ω

c) 2/cm 24 Ω

d) 2/cm 4.0 Ω

Paper - I : Physics - 1 to 50

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2. How would the results in Table 1 change if friction we no longer negligible?

a) the difference between resistance of the undamaged quarter and resistance of the quarter with a holewould increase

b) the difference between conductivity of the undamaged quarter and conductivity of the plastic quarterwould increase.

c) the magnetic force on the undamaged quarter would be double the magnetic force on the quarter with ahole.

d) the difference between speed of the undamaged quarter and speed of the quarter with a hole wouldincrease.

3. The 1.3 magnet used in the apparatus deflects a a+3.5 Cµ charge located on the very edge of a quarter. If theparticle, traveling in a direction perpendicular to the magnetic field, was deflected with a force of magnitude4.1 x 10-7N, what is the speed of the particle?

a) 0.09 m/s

b) 0.18 m/s

c) 181 m/s

d) 12.5 m/s

4. The speed of a coin passing through the apparatus would decrease if

a) the voltage of the battery was increased

b) the resistance of the coin was decreased

c) the thickness of the coin was increasedd) the diameter of the coin was decreased

5. Which statement best explains why, as it left the region containing the magnetic field, the quarter with the hole in it had agreater speed than the undamaged quarter?

a) the undamaged quarter has a larger mass than the quarter with a hole in it.b) The quarter with a hle in it has a lower resistance to current than the undamaged quarterc) The undamaged quarter has a larger magnetic dipole than the quarter with a hole init.d) The undamaged quarter has a larger area than the quarter with a hole in it.

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Questions 6 to 45 are independent Question

6. A helium-filled balloon (p = 0.5 kg/m3) is released into the air. The balloon is shperically - shaped with adiameter of 1 m. Neglecting air resistance, what will be the balloon’s initial upward acceleration when releasedfrom rest? (pair = 1.2 kg/m3)

a) 3.65 m/s

b) 5.34 m/s2

c) 13.73 m/s2

d) 19.45 m/s2

7. A certain element has a density of 10 g/cm3 and half-life 140 days. Over a period of 140 days the averagenumber of α emissions per day is found to tbe 12 x 1012 from a sample of initial mass 1 gµ . Estimate thenumber of atoms in 1 cm3 of element.

a) 2.66 x 1022

b) 3.36 x 1022

c) 12 x 1022

d) 10 x 1022

8. In a hydroelectric dam, water on one side of the dam is higher than the other. The energy is converted frompotential energy, to kinetic energy, electicity if the water in the dam were replaced with mercury, the energyproduced by ther dam would.

a) Increaseb) Decreasec) Remain the samed) Decrease then increase

9. Diving competitions usually have water spraying on the pool while divers dive because:

a) Reduces the surface tension through turbulent flow and reduces the amount of force absorbed by thediver.

b) Reduces the glare on the pool surface allowing divers to better see their target at the bottom of the poolc) Increases the surface tension through turbulent flow allowing for cleaner divesd) The turbulent flow provides allows pressure to equalize between the air and the water.

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10. A particle is projected with speed u so that it moves in a circle of radius r. The forces acting on it are such thatits acceleration is always inclined at 450 to the instantaneous inward radius. The speed of the particle aftertime t will be

a)ur

r - ut

b) u 2

c)u2

d)ur

2(r - ut)

11. In aeodynamic design, reducing the coefficient of friction is critical to reduced drag Most of the time thatmeans eliminating turbulent flow. Yet pure laminar flow is not ideal. Which of the folllowing is a NOT a reasonthat a golf ball flies better with asymmetric dimples laid in an isometric pattern?

a) A. It reduces the overall profile (corss-sectional area) of the ball

b) B. Turbulent flow from the dimples can actually lift the ball if it is spinning

c) C. Asymmetric dimples raise turbulent flow

d) D. Isometric patterns lower laminaor flow

12. The equations relating to circuits are the same equations in fluids and springs. If a spring is the same as acapacitor and a dashpot (the piston that slows a door) is the same as a resistor, which system stores moreenergy at equal tensions, two springs with constants 3 and 4 in series or in parallel? Both systems are equidistantand the length of stretch is the same.

a) Springs in series

b) Springs in parallel

c) Same

d) Depends on the temperature

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13. A pendulum bob of mass m is raised to a height h and released. After hitting a spring of non - linear force law2F kx bx= − − ,calculate compression distance x of the spring.

h

a) x = 2mgh/k

b) 1/4x = ( 4mgh /b )

c) x = 2k/b

d) 2 2 1/ 2x = [ 4mgh / b + k / / ]b k b−

14. A length 4a of uniform wire is bent in the form of a square and the opposite angular points are formed withstraight pieces of the same wire which are in contact at the intersection. A given current enters at the intersectionof diagonals and leaves at an angular point. Find the resistance of the whole network if ρ is the resistance perunit length.

a) ( 2 / 2 2+1) aρ

b) ( 2/2 2 - 1) aρ

c) (2 2+1 / 2 ) aρ

d) (2 2 - 1 / 2 ) aρ

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15. A circular cylinder of mass m and radius a is free to turn about its axis which is horizontal. A light inextensiblestring is wound around the cylinder, its free end is attached to a freely hanging mass m. The string unwindswithout slipping as the mass m falls. The tension in the string will be

a) mg

b) mg2

c)mg3

d) mg4

16 A charge particle q pases through a region having perpendicular uniform electric field Eur and magnietic field

Bur undeviated. Choose the current alternative —

a) the charged particle must be at rest

b) the componet of velocity vector along Eur must be zero

c) the velocity vector Vur

must be perpendicular to Eur and B

ur together

d) none of these is correct

17. A convex lens of focal length f1 is placed infront of a luminous point P so that the distance of the point P from lens is greaterthan focal length and the image formed is at the shoirtest possible distance. If now a concave lens of very large focal lengthf2 be placed in contact with first, find the shift in the position of the image.

a) 1 22 2 /f f

b) 1 22 /f f

c) 1 22 /f f

d) 21 24f / f

18. A uniform rope of length 12 m and mass 6 kg hangs vertically from a rigid support. A block of mass 2 kg isattached to the free end of the rope. A transverse pulse of wavelength 0.06 m is produced at the lower end ofthe rope. What is the wavelength of the pulse when it reaches the top of the rope.

a) 1. 2 mb) 0. 12 mc) 0.012 md) information is not sufficent to evalute

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19. The figure shows different graphs in case of a thin convex lens for the formation of a real image. u and v arethe object and image distances respectively. fund out the correct identification for the different combinationsfrom the followings.

y

x

(I)

(II)

(III)

(IV)

a) graph I, if x is v and y is u/v(b) graph II, if x is u and y is v(c) graph III, if x is v and y is v/u(d) graph IV, if x =1/u and y is 1/v

20. A throtting process is one in which a fluid, originally at a constant high pressure seeps through a porous wallor a narrow opening into a region of constant lower pressure without a transfer of heat taking place. thephysical quantity that remains constant during this process in the system considered as an ideal gas is

a) Temperature

b) Entropy

c) Enthalpy

d) volume

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21. A charged particle having charge 10-6 C and mass 10-10 kg is fired form the middle of the plate making anangle 300 with plane of the plate. Length of the plate is 0.17 m and it is separated by 0.1 meter. Electric fieldE = 10-3 N/C is present between the plate. Just outside the plates magnetic field is present. Find the velocityof projection of charged particle and magnitude of the magnetic field perpendicular to the plane of the figure,if it has to graze the plate at B and A parallel to the surface of the plate. (Neglect gravity).

AE

300B

a) . 7 m /s , 1.2 mT

b) 1.4 m /s , 2.4 mT

c) 2.8 m /s , 4.8 mT

d) 14m / s , 48 mT

22. Two flat mirrors form an angle close to 1800. A source of light S is placed at equal distances b from themirrors. Find the interval between adjacent interference bands on screen MN at a distance OA = a from thepoint of intersection of the mirror. The wavelength of the light wave is known and equal to λ . Shield C doesnot allow the light to pass directly from the source to the screen

S C

N

A

M

a

O bb

á

a) ( )2a bb

λ +α

b)( )2a bb

λ −α

c)( )a bb

λ +α d)

( )a bb

λ −α

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23. A micro-ammeter has a resistance 100 Ω and full scale deflection current 50µA. It can be used as a voltmeteror as a higher range ammeter provided a resistance is added to it. Chose the correct range and resistancecombinations from the following

(1) 50 V range with 10 k Ω resistance in series (2) 10 V range with 200 k Ω resistance in series

(3) 5 mA range with 1 Ω resistance in parallel (4) 10 mA range with 1 Ω resistance in parallel(a) 1, 3

(b) 2, 4

(c) 1, 4

(d) 2, 3

24. A swing has lengh L and a person is sitting at rest at location A.

A rod is located at a distance x below the point at which the swing is attached (point O). What should be the location of therod (distance x) so that the parson will still make a full revolution around the rod?

O

L A

a) x =L2

b) x =L3

c) x <2L3

d) x > 3L5

25. A parallel plate capacitor filled with a dielectric whose permittivity varies with applied voltagee according tothe law -1 = αV (where α=1 volt ).∈ Another similar caacitor without dielectric is charged to a potential of 156volts and connected in parallel with the uncharged now linear capacitor. What is the common voltage acrossthe two capacitors?

a) 2 V b) 24 V

c) 6 V d) 18 V

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26. A metal bar with length l, mass m, and resistance R is placed on frictionless metal rails that are inclined at anangle φabove the horizontal. The rails have negligible resistance. There is a uniform magnetic field of magnitudeB directed downward in figure. The bar is released from rest and slides down the rails. What is the terminalspeed of the bar?

φ

a

bl

B

B

a) 2 2 2

sincosT

mgRVB l

= φφ

b) 2 2 2

sincosT

mgVB l

= φφ

c) 2

s i nc o s

m g RB l

φφ

d) none of these

27. A standing wave is produced in a steel wire of mass 100 gm tied to two fixed supports. The length of the stringis 2 m and strain in it is 0.4%. The string vibrates in four loops. Assume one end of the string to be at x = 0, allparticle to be at rest at t= 0 and maximum amplitude to be 3 mm. find wavelength and frequency of the wave.

a) 400 Hz

b) 300 Hz

c) 500 Hz

d) 200 Hz

28. A ideal mono-atomic gas is confined by a spring loaded massless pistion of cross-section 8.0 x 10-3 m2.Initially, the gas is at 300 K and occupies a volume of 2.4 x 10-3 m3 and the spring is in its relaxed state. Thegas is heated by an electric heater unitl the piston moves out slowly without friction by 0.1 m. Calculate thefinal temperature of the gas.

a) 800 K b) 600 K

c) 700 K d) 900 K

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29. A mss M sitting on an ice rink is firmly attached to a massless spring with spring constant K and equilibrium

length L. The spring is compressed against the wall of the rink to a length .2L

A second mass M, which is not

attached to anything, is lying a distance 34

L away; the two masses will collide if the spring is extended by 4L

past its equilibrium length.

I) After the spring is released, the masses will collide. If the collision is elastic, the final velocity of the

second mass is 23

16KLM

II) The maximum speed the first mass can reach after the collison is 2

16KL

M

Choose the correct option based on the above information

a) Both statements I & II are correctb) Both statements I & II are wrongc) Data is insufficient to evaluate the statement Id) Data is insufficient to evaluate the statement II

30. In order to increase the resistance of a given wire of uniform cross section to four times its value, a fraction of

its length is stretched uniformlytill the full length of the wire becoems 23

times the original length what is the

value of this fraction?

a)41

b) 81

c) 161

d) 61

K M

L/2

L L/4

M

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31. An electron and a proton are separated by a large distance and the electron approaches the proton with akinetic energy of 2 eV. If the electron is captured by the proton to form a hydrogen atom in the ground state,what wavelength photon would be given off?

a) 793.3Å

b) 703.3Å

c) 603.3Å

d) 593.3Å

32. A road passes at some distance from a standing man. A truck is coming on the road with some acceleration.The truck driver blows a whistle of frequency 500 Hz when the line joining the truck and the man makes anangle of θwith the road. The man hears a note having a frequency of 600 Hz when the truck is closest to him.Also the speed of truck has got doubled during this time. Find the value of ‘θ ’

a) 60º

b) 45º

c) 90º

d) 120º

33. In each of the four sketches below, a round object (either a hoop or a solid disk) of radius r and mass m rollsor slides with linear speed v towards a metal ramp at angle 50°. Two of the aporoaches to the ramps aremetal (M), on which the objects roll without sliding, but the other two are frictionaless Slipperide (S). Rankthe four situations, from highest to lowest, in terms of how high the object rolls up the ramp

A)v

S

M B)v M

M

C)v M

M

D)v M

S

a) C > B > A = D

b) B > C > A = D

c) A = D > B > C

d) None of these

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34. Sound moves faster on a warm day than on a cold day. The Doppler Effect will be greater:

a) On a warm day because the velocities of the source and observeer will be less significant compared tothe velocity of sound

b) On a warm day because the velocities of the soruce and observer will be more significant compared tothe velocity of sound

c) On a cold day because the velocities of the source and observeer will be less significant compared tothe velocity of sound

d) On a cold day because the velocities of the source and observer will be more significant compared tothe velocity of sound.

35. Two parallel long straight conductors lie on a smooth surface. Two other parallel conductors rest on them atright angles so as to form a square of side a initially. A uniform magnetic field B exists at right angles to theplane containing the conductors. They start moving out with a constant velocity V. If r is the resistance per unitlength of the wire the current in the circuit will be

a)r

Bv

b)v

Br

c) Bvr

d) Bv

36. In an agricultural experiment, a solution containing 1 mole of a radioactive material (T1/2 =14.3 days) wasinjected into the roots of a plant. The plant was allowed 70 hours to settle down and then activity wasmeasured in its fruit. If the activity measured was Ci 1 µ , what percentage of activity is transmitted from theroot to the fruit in steady state?

a) 111.26 10 %−×

b) 91.26 10 %−×

c) 61.26 10 %−×d) none of these

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37. A glass bulb whose volume at 00C equals 10 c.c. is filled with mercury. It is then joined to stem of diameter 0.2cm at 00C. What length of the stem will the liquid occupy at 600C.?[Given, coefficient of volume expansion of mercury = 18 × 10-5 0C-1 and coefficient of linear expansion ofglass = 9 × 10-6 0C-1]

a) 2.92 cm

b) 2.90 cm

c) 2.75 cm

d) 2.85 cm

38. Positively charged particle A starts at rest and is pulled from a great distance directly toward negativelycharged particle B by the electric field created by particle B. If particle A has a velocity v when it is a distance4r from particle B, what will be the velocity of particle A when it is a distance r from particle B?

a) v21

b) v

c) 2v

d) 4v

39. The absolute temperature T of a gas is plotted against its pressure P for two different constant volumes V1 andV2 where V1 > V2. T is plotted along x-axis and P along y-axis.

a) Slope for curve corresponding to volume V1 is greater than that corresponding to volume V1

b) Sople for curve corresponding to volume V2 is greater than that corresponding to volume V1

c) Slope for both curves are equal

d) Slope for both curves are unequal such that they intersect at T=0

40. A certain prism is found to produce a minimum deviation of 380. It produces a deviation of 440 when the angleof incidence is either 420 or 620. What is the angle of incidence when it is undergoing minimum deviation?

a) 450

b) 490

c) 400

d) 550

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41. n moles of an ideal gas undergopes a cyclic process in which it absorbs a heat Q1 at at constant temperatureT1 such that the expansion ratio is α . It rejects a heat Q2 at constant temperature T2 (< T1). The efficiency ofthe cyclic process is η , the total work done in the cyclic process is W and dU is the change in internal energyof the process.

1)

−=

1

21TTη 2) αη )( W 2121 InTTRQQ −=−=

3) dU = 0 4) αη 1 InRTdU =

a) 1, 2, 3

b) 1, 2, 4

c) 1, 2

d) None of these

42. One mole of an ideal monoatomic gas is taken round the cyclic process ABCA as shown in figure. Calculatethe maximum temperature attained by the gas-during the cycle.

B

P

CAPO

VO 2VO

V

3PO

a) 0 0258PVR

b) 0 0208PVR

c) 0 020 PVR

d) none of these

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43. A pendulum has a period T for small oscillations. An obstacle is placed directly below the pivot, so that onlythe lowest one fourth of the string can follow the pendulum bob when it swings to the right of its restingposition as shown. The pendulum is released from rest at a certain point. Assuming that the angle between themoving string and the vertical stays small throughout the motion, the time it takes to return to that point is

OA

l43l

4l

a) T

b)2T

c)2

3T

d) 43T

44. A metal ball at 300C is dropped from a height of 6.2 km. The ball is heated due to the air resistance and it completely meltsbefore reaching the ground. The molten substance falls slowly on the ground. Calculate the latent heat of fusion of metal.Specific heat of lead = 126 J kg-1 0C-1. Melting point of metal is 2000C (use g= 10 ms-2)

a) 40.58 kJ/kg

b) 45.48 kJ/kg

c) 48.50 kJ/kg

d) none of these

45. In a double slit experiment light of wave length Å 4800λ = is used. One slit is covered by a thin plate of glass4.1=µ and the other by another plate of same thickness 8 x 10-4 cm but having a value for 7.1=µ . The

central fringe will be shifted on the screen to which position?

a) Position of 5th fringe b) Position 6th fringec) Position 7th fringe d) Position 4th fringe

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Question 46 to 50 are based on the following passage

Springboard diving has become an exact science. The diver strives to achieve maximum air time and enter thewater cleanly. A proper approach and take off from the end of the board are essential elements of a wellexecuted dive. Several steps are involved in the diving process. First, the diver stands at attention. Second,the diver takes three steps forward. At the end of the third step, the diver propels himself upward, with aninitial kinetic energy of W1 (the hurdle energy), and reaches a height of H1 above the diving board, whichremains in the horizontal position. Next, gravity causes the diver to fall back down and return to the board,resulting in depression of the board. the board is elastic and stores the diver’s energy. At maximum depression,both the diver and the board are stationary. The elastic nature of the board causes in to return to its horizontalposition, and the diver once again propels himself upward, increasing his energy by an amount equal to W2(the leap energy), and rises to a hight of H2 above the diving board.

In order to obtain maxmimum height, the diver must leave the board when it is exactly in the horizontalposition. Furthemore, after the diver takes off from the board, the board should have zero velocity. Thisallows the diver to extract all of the energy given to the board during the approach.

(Note : g = 9.8 m/s2 is the acceleration due to gravity)

46. In the perfect dive, the maximum energy of the diver is equal to

a) the leap energyb) the sum of the leap energy and the potential energy due to the height of the board above the waterc) the sume of hurdle energy, the leap energy, and the gravitational potential energy due to the height of the

board above the water.d) potential nergy due to the height of the board above the water, and the potential energy of the board at

maximum depression.

47. A diver dives off a board that is 1 m above the surface of the water. The diver r3eaches a height of 80 cmabove the board. the total time that the diver spends in the air after take off is:

a) 0.2 s

b) 0. 4 s

c) 0.6 s

d) 1.0 s

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48. Striving for maximum height, a diver takes off without any rotational motion and enters the water feet first afterpassing very close to the end of the board. If the driver’s leap energy and urdle energy are the same, then therelationship between H1 and H2 is:

a) H1 = H2

b) 2H2

11H =

c) H1 = 2H2

d) H1 and H2

49. A person with a mass of 70 kg jumps to a height 50 cm above the ground. If the efficiency of human muclesis 50%, how much energy does the diver expend for this jump?

a) 87. 5 J

b) 350 J

c) 700 J

d) 1400 J

50. Assuming that all of the diver’s energy comes from the hurdle and the leap, adding spin to a diver’s upward movementwould

a) decrease the maximum height because some kinetic energy will be in the form of rotational energy.b) not affect the maximum height because translational and rotational motions are independent.c) increase the maximum height by increasing the total energy of the dive.d) increase the time the diver spends in the air.

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Paper - I I :Mathematics - 51 to 100

Questions 51to 55 are based on the following passage Normally, the various propositions you study, e.g., equation of tangent, normal, chord, focal chord, formulafor focal distance etc., are derived for the parabola y2 = 4ax. However, all the results with slight transformationare valid for any parabola.

Suppose we represent the equation of parabola y2-4ax = 0 by S (x, y, a) = 0 and any equation dervied for thisparabola by P (x, y, a) = 0

Now, if the given parabola is y2 = 4ax, i.e., y2+4ax = 0 we can write it S (x, y, -a) = 0, so the correspondingequation of P will be (P (x, y, -a) = 0

Similarly for x2 = 4ay can be written as S (y, x, a) and corresponding transformation is P (y, x, a)(i.e., interchange x and y)

Ans . transformation for x2 = 4ay is P (y, x, -a) = 0

For example, the equation of tangent to y2 = 4ax is y = mx + ma

, so correponding trangent to x2 = 4ay is

mamyx = and the point of contact will be

2,2ma

ma

The equation of normal to y2=4ax is y =mx - 2am - am3. The equation of normal to

x2 = -4ay is x = my + 2 am + am3.

Further, if the coordinates of vertex are not (0, 0) but (h, k) then we replace x by x - h and y by y - k inaddition to above transformation

51. The focal distance of the point (x, y) on the parabola 01682 =+= yxx is

a) 4−y

b) 5−y

c) 2−y

d) 4−x

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52. Normals are drawn from the point (7, 14) to the parabola x2 - 8x - 16y = 0. The slopes of these normals are

1) 1 2) 2 3) 23

4) 23−

a) 1, 2, 3

b) 1, 2, 4

c) 2, 3, 1

d) None of these

53. The coordinates of the feet of normals obtained in previous probem are

1) (0, 0) 2) (-4, 3) 3) (16, 8) 4) (-8, 4)

a) 1, 2, 3

b) 1, 2, 4

c) 2, 3, 1

d) None of these

54. The points on the axis of the parabola x2 + 2x + 4y + 13 = 0 from where three distinct normals can be drawnare given by

1) (-1, k), k∈ (-1, 2) 2) (-1, - 6)3) (-1, k), k∈ (- ∝ , -5) 4) (-1, 1)a) 2, 3

b) 1, 2

c) 0, 1

d) None of these

55. The line pyx =+ αα sin cos touches the parabola x2 + 4a (y+a) = 0 if

a) αsec pa =

b) αα sin cos2 pa =

c) 0sin cos 22 =+ αα pa

d) tan seca pα α=

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Questions 56 to 57 are based on the following passage

Each of the 11 letters A, H, I M, O T, U V W, X and Z appears same when looked at in a mirror. They arecalled symmetric letters. Other letters in the alphabet are asymmetric letters.

56. How many four-letter computer passwords can be formed using only the symmetric letters (no repetitionallowed)?

a) 7920

b) 330

c) 14640

d) 419430

57. How many three-letter computer passwords (no repetition allowed) with at least one symmetric letter?

a) 990

b) 2730

c) 12870

d) 15600

Questions 8 to 45 are independent questions

58. The graph of the arccosine function is the graph of the arcsine function

a) translated horizontally 2 / π units to the rightb) first reflected in the horizontal axis and then translated vertically 2 / π units upwardc) first translated horizontally 2 / π units to the left and then reflected in the horizontal axisd) first translated vertically 2 / π units downward and then reflected in the vertical axis

59. The cubes of the natural numbers are grouped as )....6 ,5,4( ),3,2( ,1 333333 then the sum of the numbers in thenth group is

a) )3(n )1( 81 223 ++nn

b) )4(n )2( 121 223 ++nn

c) )12(n )16( 161 223 ++nn

d) )3(n )1( 121 223 ++nn

(6 mark)

(6 mark)

(3 mark)

(3 mark)


23



60. In a particular dam project, certain barriers have to be raised to prevent the flow of water. But in spite ofraising a barrier, it might happen that the water force can break the barrier. The probability of a barrier failingis 20 percent. Then, what should be the minimum number of barriers ot be raised so that the overall probabilityof the project failing is less than 0.1 percent?

a) 5

b) 7

c) 10

d) 11

61. In a pure radioactive decay model, the rate of change in the mass, M, satisfies the differential equation, dM /dt = m/10. If the initial value of M is M0, find M in terms of M0 after 20 units of time, t, have elapsed.

a) 0M21

b) 0M41

c)2eM0

d) 20

eM

62. A whispering gallery is constructed as part of the surface formed on rotation of the ellipse 1100x 22

=+ky with

x and y in yards. Each whispherer stands at a focus on the x-axis that is three feet from the nearest vertex. Findk.

a) 6

b) 7

c) 18

d) 19

(3 mark)

(3 mark)

(3 mark)


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63. A square ABCD has its centre at the origin. If A is the point Z1, then the centroid of the triangle ABC is

a)3

1Zi±

b) 31Z±

c)

±

3πsin i

3πcos

3Z1

d) 1Z π πcos i sin3 6 6

±

64. How many non zero positive integer solutions are there for the equation x + y + Z = 12?

a)! 12 ! 2

! 14

b) ! 2! 12

c)! 12 ! 2

! 11

d) 211C

65. If A, G and H are the Arithmetic mean, Geometric mean and Harmonic mean between two unequal positive

integers. Then the equation 2 0Ax G x H− − = has

a) both roots fractionsb) at least one root which is negative fractionc) exactly one positive rootd) both (b) and (c)

(3 mark)

(3 mark)

(3 mark)


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66. Let R = the set of real numbers, I = the set of integers, N = the set of natural numbers. If S be the solution set

of the equation ,]1[)1(][)( 2222 ++−=+ xxxx where (x) = the least integer greater than or equal to x and[x] = the greatest integer less than or equal to x, then

a) S = R

b) S = R-1

c) S = R - N

d) None of these

67. theng(x),f(x) and2xtan

2xsec g(x) and

2xcos

2xsinf(x) If 22

n2

n2 =

−

=

+

=

a) Rx ∈

b)

+=−∈

2)12(: πnxxRx

c) π)12(: +=−∈ nxxRx

d) π 2: nxxRx =−∈

68. Ten identical balls have to be distributed among three identical boxes. In how many ways can this be donesuch that every box has atleast two balls?

a) 16

b) 15

c) 81

d) None of these

69. In the given square, a diagonal is drawn, and parallel line segments joining points on the adjacent sides aredrawn on both sides of the diagonal. The length of the diagonal is 2n cm. If distance between consecutive

line segments be , 2

1 cm then the sum of the lengths of all possible line segments and the diagonal is

a) cm 21)n(n +

b) cmn2

c) 2)n(n +

d) cm 2n2

(3 mark)

(3 mark)

(3 mark)

(3 mark)


26



70. 20)73(8RLet += and [R] = the greatest integer less than or equal to R. Then

1) [R] is even 2) [R] is odd

3) 20)738(11][

+−=− RR 4) 21][ RRRR +=+

a) 2, 3, 4

b) 1,2,3

c) 3, 2,1

d) None of these

71. R ba, If ∈ the roots of the equation 010bxax2 =++ are not real and distinct m, n are the values of a and brespectively for which 5a+b is minimum, then the family of lines 0)1()324( =−−+++ yxnyxm are concurrentat

a) (1, -1)

b)

−

67,

61

c) (1,1)

d)

−−

67,

61

72. -2a

f(x)

a -2a

g(x)

-a

a

Mark the correct option ?

a) if f(x) = g(x-a)

b) if f(x) = g(x+a)

c) if f(x) = g (-x)

d) if f(x) = g(x)

(3 mark)

(3 mark)

(3 mark)


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73. If maximum and minimum values of the determinant are2sin1cossin

2sincos1sin2sincossin1

22

22

22

xxxxxxxxx

++

+

then, and βα

1) 4 99 =+ βα

2) 62 173 =+ βα

3) ) ( 22 nn βα + is always an even integer for Nn ∈

4) a triangle can be constructed having its sides as 3βα and βαβ,α ++−

a) 1, 2, 3

b) 1,3

c) 1, 2, 4

d) None of these

74. A B C is a right angle triangle in which o90B =∠ and BC = a. If n points LnLLL ...3,2,1 on AB are such that

AB is divided in (n+1) equal parts and nn MLMLML ,.....,, 22,1,1 are line segments parallel to BC and

1, 2 3, .....M L M Mn are on A C. Then the sum of the length of the sides of nn MLMLML ,.....,, 22,1,1 is

a) 2)1( +na

b) 2)1( −na

c)2

an

d) None of these

75. The vectro C along the bisector of the acute angle between a 7 i-4 j-4k and b 2 i- j 2k= = + where

270C = is given by

a) k2j7-i + b) k01ji13 ++−

c) k2j7i ++− d) k2j7i −−

(3 mark)

(3 mark)

(3 mark)


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76. An executive wrote 5 letters to 5 people A, B, C, D and E and asked his secretary to place them in 5envelopes also marked A, B, C, D and E. The secretary, however, placed the letters at random into theenvelopes such that each envelope received exactly one letter. Then, the number of arrangements in whichexactly 2 leeters are placed in correct envelopes is:

a) 10

b) 20

c) 30

d) Noneof these

77. Which of the following statements are correct?

I) The circular points corresponding with the arc lengths π and - π are the same point.

II) In circular co-ordinates, the numbers 0, ,...4 ,2π π are all equal

III) The circular points corresponding with the numbers 2 and 2π-2 are the same

IV) The circular points corresponding to the arcs 23- and

2π π

are equal

a) I, II and III

b) I, II and IV

c) I, III and IV

d) II, III and IV

78. Consider a curve 2 22 2 0ax hxy by gx+ + + = and a point P (u, v). A line is drawn from the point P, making anangle θ'' with x-axis, intersects the curve at Q and R. Then PQ, PR is

a)sin2θh θsin bθcos a2gubv2huvau

22

22

+++++

b) 2gubv2huvau2θsin h θsin bθcos a

22

22

+++++

c)θsin bθcos a2gubv2huvau 22

22

++++

d) None of these

(3 mark)

(3 mark)

(3 mark)


29



79. A student appears for tests, I, II and III. The student is successful if he passes either in tests I and II or in I and

III. The probabilities of the student passing in tests, I, II, III are respectively p, q and .21

If the probability that

the student is successful is ,21

then

a) p = q = 1

b) p = q = 21

c) p=1, q = 0

d) p=21

, q =1

80. If the slope of one of the lines represented by 02 22 =++ byhxyax be the square of the other, the

=++ab

8hh

bathen 2

a) 4

b) 6

c) 8

d) None of these

81. The equation of a circle is 0)1( 2222 =+−−−+ λλ aayaxyx . If two chords, each bisected by the x-axis canbe drawn to the circle from the point )),1(),1(( +− λλ aa which lies on the circle then λ satisfies

a) 01242 >−− λλ

b) 01242 <−− λλ

c) 04122 >−− λλ

d) 04122 <−− λλ

(3 mark)

(3 mark)

(3 mark)


30



82. If P is any point lying on the ellipse ,12

2

2

2=+

by

ax

whose foci are S and S’.

,' ' βα =∠=∠ SPSandPSSLet then

1) PS + PS’ = 2a, if a > b 2) PS + PS’ = 2b, if a < b

3)ee

+−=

11

2tan

2tan βα

4) bawhen ]ba[ab

ba2βtan

2αtan 22

2

22>−−−=

a) 1, 2, 3

b) 1, 3, 4

c) 1, 2, 4

d) None of these

83. The function f(x) = max 1-x, 1+x, 2, Rx ∈ is

a) discontinuous at all pointsb) differentiable nowherec) differentiable at Rx ∈ -1, -1d) discontinuous at 1 and -1

84. (tan ) (sin ) and ( cosec ) x + (cos ) 1Let x y yα α α α α α+ = = be two variable straight lines, α being theparameter. Let P be the point of intersection of the lines. In the limiting position when ,0→α the coordinatesof P are

a) (2, 1)

b) (2, -1)

c) (-2, 1)

d) (-2, -1)

(3 mark)

(3 mark)

(6 mark)


31



85. ∞++−

−++−

−++

< ....1

841

42xx-1

2x-1 then 1, xIf 84

73

42

3

2 xxxx

xxxx

a) 2

11+ x x+

b) 2

1 2x1+ x x

++

c)2

2

1 x x1+ x x

− ++

d) 1

86. The value of ∫− +

++−−−+2

22

23567

211271032x dx

xxxxxx

is

1) 0 2) 222

516 π+−

3) dxx

xx2

11232 2

262

0 ++−∫ 4) 22

25

14 π+−

a) 2, 3

b) 1, 4

c) 1, 2

d) 3, 4

87. The area of the region bounded by 2

3, ([ . ]10xy

= −

denotes the greatest integer ), y = 1 and the lines x = 1,

10=x is

a) 9 sq. unitsb) 11 sq. units

c) unitssq . )110( +

d) unitssq . )110( −

(3 mark)

(3 mark)

(3 mark)


32



88. Let 1], 1,[R0R:f −−→− defined by ,)( 33

33

xex

xx

e

eexf−−

−+= the f is

1) a one - one function 2) an increasing function3) a decreasing function 4) onto functiona) 1, 3, 4

b) 1, 2, 3

c) 3, 1

d) None of these

89. If for non - zero x, af (x) + bf ,511 −=

xx where ,ba ≠ the dxxf )(2

1∫ is

a) a log 2- 5a + 7b

b)21

(a log 4-10a + 7b)

c) a log 2 - 5a + 7bd) None of these

90. If 24 6 log (9 4) ,9 4

x xx

x x

e e dx Ax B e Ce e

−

−

+ = + − +−∫ then A, B and C will be

a)3 36A=- , B= , C = constant2 35

b)3 35 3A= , B= , C = log 3+c2 36 2

c)3 35 3A=- , B=- , C =- log 3+c2 36 2

d)3 35A=- , B= , C = constant2 36

(3 mark)

(3 mark)

(6 mark)


33



91. If f(x) is a continuous function and attains on ly rational values and if f(1) = 4, then the roots of(2) x2 + f(0)x + f(6) = 0 are

a) imaginaryb) real and distinctc) real and equald) rational

92. Examine the following statement ( s ) and choose the correct option

I. If nnxaxf/1)()( −= where a > 0 and n is a positive integer, then [ ] xxff =)( .

II If the letters of the word “Assassin” are written down at random in a row, the probability that no two S’s occur together is 1/35.

a) only I is correctb) only II is correctc) both I and II are correctd) both I and II are wrong


I. The determinants

abccabbca

111

and 2

2

2

111

ccbbaa

are not identically equal.

II . The equation 01x3x2 2 ==+ has an irrational root.


(3 mark)

(3 mark)

(3 mark)


34




I.If 0C.,0B.,0A. =χ=χ=χ for some non-zero vector, χ , then [A B C] = 0.

II .If the complex numbers, Z1, Z2 and Z3, represent the vertices of an equilateral triangle such that

321 ZZZ == then 0321 =++ ZZZ .


95. The imaginary part of 112

++

iZz

is -2. Then the locus of the point representing Z in the complex plane is

a) a circleb) a straight linec) a parabolad) an ellipse

(6 mark)

(3 mark)


35



Questions 96 to 100 are based on the following passage A series S1 of five positive integers is such that the third term is half the first term and the fifth term is 20 morethan the first term. In series S2, the nth term defined as the difference between the (n+1) term and the nth termof series S1, is an arithmetic progression with a common difference of 30.

96. First term of S1 is

a) 80

b) 90

c) 100

d) 120

97. Second term of S2 is

a) 50

b) 60

c) 70

d) None of these

98. What is the difference between second and fourth terms of S1?

a) 10

b) 20

c) 30

d) 60

99. What is the average value of the terms of series S1?

a) 60b) 70c) 80d) Average is not an integer

100. What is the sum of series S2?

a) 10

b) 20

c) 30

d) 40

(3 mark)

(3 mark)

(3 mark)

(3 mark)

(3 mark)


36



Paper - I I I : Chemistry- 101 to 150

Questions 101 to 105 are based on the following passageA buckyball is large, highly-ordered, nearly spherical configuration of carbon atoms that resembles a molecularcage. Since it contains only carbon, a buckyball is an allotrope of carbon in addition to the naturally occurringdiamond and graphite forms. When buckyballs were first synthesized, they caused a stir in the scientIiccommunity, but practical applications of these unique molecular structures were not immediately obvious.However, buckyballs have recently shown promise as high-temperature superconductors.

A superconductor is an electronic conductor that conducts electricity with zero resistance below its characteristictransition temperature. Above the transition temperature, the substance exhibits normal behavior. While ametal conducts electricity very well, it has a measurable resistance that increases as the temperature is raised.The relationship between resistance and temperature for metallic conductors and superconductors is illustratedin Figures 1 and 2.

Metallic Conductor

Metallic ConductorFigure 1

Res

ista

nce

Superconductor

Figure 2

Res

ista

nce

Since superconductors have no resistance, their use has been proposed for powerful magnets in MagneticResonance Imaging and high-speed trains as well as ultrasensitive detectors. Superconductors have presentedexciting results with transmission lines, where power loss may be minimized by the elimination of electricalresistance. Unfortunately, the main problem has been that the transition temperature for most substances isextremely low, between 4-20K. For this reason, scientists continue to search for superconducting materialsthat work at room temperature.


37



A group of scientists performed an experiment to study the super conducting properties of buckyballs. Asuperconducting transistor made of buckyballs produces an electric field that draws electrons away from thebuckyballs, leaving gaps of positive charge in the superconducting material. The scientists predicted thatseparating the buckyballs with other molecules would increase the number of positive gaps, thereby increasingthe superconductivity of the material.

Two separator molecules were added to the buckyball transistor devices. In the first device, chloroform CH3C1 was added. In the second, bromoform CH3 Br was added. In the third device, no separator moleculeswere added. The highest temperature at which superconductivity was observed for each device is shown inTable 1.

Separator Highest SuperconductingTemperature (0F)

None - 366

Chloroform - 315

Bromoform - 249

101. Bromoform is a better separator molecule than chloroform because bromoform :

a) is heavier than chloroform, making it closer character to the buckyball moleculeb) has greater electron density than chloroform, so it is better able to canel out the positively charged gaps

in the superconducting materialc) is larger than chloroform, so it is better able to separate electrons from the buckyballs.d) contains more atoms than chloroform, so it is better able to separate electrons from the buckyballs.

102. All of the following are groups of allotropes EXCEPT:

a) iron : B (s); B12 (icosohedron)b) Oxygen : O2 (dioxygen); O3 (ozone)c) Phosphorus : P4 (red); P4 (white); P3 (gas)d) Sulfur : S8 (yellow); S2 (blue)

103. Which of the following is the molecular shape of chloroform?

a) Trigonal bipyramidalb) Tetrahedralc) Trigonal planard) Bent

(3 mark)

(3 mark)

(3 mark)


38



104. What is the dipole moment of C60 molecule?

a) Positive, into the cage, because individual carbon atoms each have four valence electrons.b) Positive, out of the cage, because individual carbon atoms form polar bonds with many elements.c) Negative, out of the cage, because of the magnetic field created by the electrons within the cage.d) Zero, because of the symmetry of the molecule.

105. Why does the addition of chloroform and bromoform molecules increase the superconductivity of the buckyballdevice?

a) Separating the bucyball molecules increases the number of positive gaps in the superconducting material.b) Chloroform and bromoform are small enough to insert themselves into the buckyball cages, making the

material denser.c) Chloroform and bromoform have strong dipole moments due to the presence of highly electronegative

halogen atoms.d) The addition of volatile molecules such as bromoform and chloroform decreases the overall density of the

superconducting material

Questions 106 to 144 are independent Question

106. An electric discharge is passed through a mixture containing 40 ml of H2 and 40 ml of O2. The volume of thegases formed at (a) 383 K and (b) at room temp. will be :

a) (a) 60 ml (b) 20 mlb) (a) 40 ml (b) 60 mlc) (a) 20 ml (b) 60 mld) (a) 60 ml (b) 60 ml

107. Which of the following statement(s) is/are correct?

1) when molecule possesses no symmetry, the number of optical isomers is 2n (where n = number of chiralcarbons).

2) when molecule has a plane of symmetry, the number of optical isomers is 2n–1 or 2(n–1) + 2n 12

− .3) when molecule possesses no symmetry, the number of meso isomers is zero.4) lactic acid has four forms and four optical isomers.a) 1, 3, 4

b) 1, 2, 3

c) 2, 3, 4

d) 1, 2, 4

(3 mark)

(3 mark)

(3 mark)

(3 mark)


39



108. The ratio of the energy of electron in the ground state of hydrogen to the electron in the first excited state ofLi2+ is:

a) 9 : 4

b) 4 : 9

c) 2 : 3

d) 1 : 8

109. Which of the following statement(s) is/are correct about aceto-acetic ester?

1) its keto form is more stable than enol form.2) keto form is about 92.7% and enol form is 7.3% in the mixture.3) enol form of aceto-acetic ester is volatile because of intramolecular hydrogen bonding.4) number of σ and π bonds plus lone pair of electrons in both keto and enol forms of aceto-acetic ester

are dIferent.a) 1, 3

b) 1, 2, 3

c) 2, 3, 4

d) 1, 2, 4

110. In the esterIication of a carboxylic acid R1 — COOH by alcohol R2—OH, oxygen atom of the acid isisotopic.

181 2 1 2 2

O O

R C O H R OH R C OR H O− − − + − → − − +

Which of the following statements is correct :

(a) O18 in water(b) O18 is in esterc) O18 is in bothd) O18 is in none

(3 mark)

(3 mark)

(3 mark)


40



111. Benzene, naphthalene and anthracene are aromatic compounds which become stable through resonance.They have 6π , 10π and 14π electrons respectively. The correct statement(s) regarding the resonanceenergies of three compounds is /are

(1) benzene has higher resonance energy than that of naphthalene and anthracene.(2) naphthalene has higher resonance energy than that of benzene and anthracene.(3) anthracene has higher resonance energy than that of benzene and naphthalene.(4) as number of rings increases, resonance energy per ring decreases.a) 1, 2

b) 2, 3

c) 3, 4

d) none

112. Out of CHCL3, SI4 and TeCl4, molecules having regular geometry are :

a) CHCl3 onlyb) CHCl3 and TeCl4

c) SI4 onlyd) SI4 and TeCl4

113. Chlorination of alkanes is carried out in the presence of sunlight while iodination in the presence of strongoxidising agents like conc. HNO3, conc. HIO3, conc. HgO etc. This is because of

a) reversible reaction of iodine with alkane.b) R – I becomes stable in the presence of strong oxidising agent.c) oxidising agent activates l2.d) oxidising agent prevents the formation of side products.

114. For the reaction between permanganate ion and oxalate ion in basic solution, the unbalanced equation is :

2 _ 2 _4 2 4 2(n) 3MnO C O MnO CO ,− + → +

In the balanced equation, the number of OH–ions is :

a) 4 on the rightb) 4 on the leftc) 2 on the rightd) 2 on the left

(3 mark)

(3 mark)

(3 mark)

(6 mark)


41



115. The correct order of reactivity amongst the following compounds towards aromatic electrophilic substitution

I. Chlorobenzene II. BenzeneIII. Aluminium chloride IV. Toluenea) I > II > III > IVb) IV > II > I > IIIc) II > I > III > IVd) III > II > I > IV

116. A solution containing one mole per litre each of Ni(NO3)2, AgNO3, Mg(NO3)2 and Pb(NO3)2 is beingelectrolysed by using inert electrodes. The values of standard potentials are :

2

2

Ni / Ni Ag / Ag

Mg / Mg Pb / Pb

0.25V; _ 0.80V;

2.37V; 0.13V;

Ε° Ε°

Ε° Ε°+ +

++ +

= − =

= − = −

2 2H O / H 0.80V;Ε° =− with increasing voltage, the sequence of deposition of metals on cathode will be :

a) Ni, Ag, Mg, Pb

b) Pb, Mg, Ag, Ni

c) Ag, Pb, Ni

d) Ag, Pb, Ni, Mg

117. Which of the following fact(s) explains(s) as to why p-nitrophenol is more acidic than phenol?

a) –1 -effect of nitro groupb) greater resonance effect of p-nitrophenoxy ionc) steric effect of bulky nitro groupd) None of thesea) 2, 4

b) 2, 3

c) 3, 4

d) 1, 2

(3 mark)

(3 mark)

(3 mark)


42



118. I the pressure on an eqm. mixture of the three gases No, Cl2 and NOCl,

2NO(g) + Cl2(g) 2NOCl(g)

is suddenly decreased by doubling the volume of the reaction vessel at constant temperature, when the systemreturns to equilibrium :

a) The value of Kc will have increasedb) The value of Kp will have increasedc) The concentration of NOCl will have increasedd) The number of moles of Cl2 will have increased

119. Degree of unsaturation in is

a) 3

b) 4

c) 5

d) 6

120. A container contains certain gas of mass ‘m’ at high pressure. Some of the gas has been allowed to escape

from the container and after some time, pressure of the gas becomes half and its absolute temperature 23 rd.

The amount of the gas escaped is :

a)23m

b) 12

m

c) 14

m

d)16 m

(3 mark)

(3 mark)

(6 mark)


43



121. Replacement of most of the hydrogens of an alkene (A) by cyano groups forms a very strong acid (B) asshown below

NC CH—C C

CN3 2C H C H C H− =

NC | CN CN

(A) (B)The sharp increase in acidity in going from A to B is best explained asa) electron withdrawing inductive effect of nitrogen.b) extensive delocalization of the negative charge of the anion resulting from the ionization of B.c) combined electron withdrawing inductive effect and resonance effect of cyano groups.d) the ‘acedic hydrogen’ being positioned alpha to the cyano groups.

122. A mineral having the formula AB2 crystallizes in the cubic close packed lattice with the A atoms occupying thelattice points. The co-ordination number of A atoms, that of B atoms and the fraction of the tetrahedral sitesoccupied by B atoms are :

a) 2, 6, 75%

b) 8, 4, 100%

c) 3, 1, 25%

d) 6, 6, 50%

123. A sample of 2, 3-dibromo-3-methylpentane is heated with zinc dust. The resulting product formed is isolatedand heated with HI in the presence of phosphorous. IdentIy which is the structure that represents the finalorganic product formed in the reaction?

a) 3 2 2 3

3

CH CH CH CH CH|

CH

− − − −

b)

3

2 2 3

CH|

CH CH CH CH CH= − − −

c) 3 2 3

3

CH CHI CH CH CH|

CH

− − − −

d) 2 2 3

3

CH CH C(1) CH CH|

CH

= − − −

(3 mark)

(3 mark)

(3 mark)


44



124. For the reaction, A+2B+C → D+2E, the rate of formation of D is found to be :

(i) Doubled when [A] is doubled keeping [B] and [C] constant

(ii) Doubled when [C] is doubled keeping [A] and [B] constant

(iii) The same when [B] is doubled keeping [A] and [C] constant. Which one is the rate equation for thereaction :

a) Rate = k [A] [B] [C]b) Rate = k [A]0 [B] [C]c) Rate = k [A] [B]0 [C]b) Rate = k [A] [B] [C]0

125. Which of the following is not correctly matched :

a) Terylene : condensation polymer of terephthalic acid and ethylene glycolb) Perspex : A homopolymer of methyl methacrylatec) Teflon : Thermally stable cross linked polymer of phenol and formaldehyded) Synthetic rubber : A copolymer of butadiene and styrene

126. Consider 1 M solutions of two solutes X and Y in a solvent. Solute ‘X’ undergoes 80% dimerisation whilesolute ‘Y’ is 90% trimerised in the solutions. Pick up the correct statement :

a) Boiling point of ‘X’<B.P. of Yb) Osmotic pressure of Y>O.P. of Xc) Freezing point of X<F.P. of Yd) Colligative properties of solutions X and Y are equal

127. Phenol can be converted into salicylic acid using

a) CO2 and alkali under pressureb) CCl4 in alkaline mediumc) CHCl3, in alkaline medium followed by oxidationd) any of the methods indicated in (1), (2) and (3)

128. When 60.00 ml of 0.1 F Ca(NO3)2 and 40 ml of 0.125 F Na2CO3 are mixed, CaCO3 precipitates. IKsp[CaCO3]=5× 10–9, the [CO3

2–] in the resulting solution is :

a) 0.05b) 0.1 Mc) 5 × 10–7 Md) 5 × 10–8 M

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129. Match List-I with List-II and select the correct answer using the options given below the lists

List-I List-II(A)Rosenmund’s reaction 1. Rearrangement of oximes to amides.(B) Reimer-Tiemann’s reaction 2. Conversion of an aldohexose into an aldopentose.(C)Kiliani - Fisher’s synthesis 3. Catalytic reduction of an acid halide to an aldehyde.(D)Beckmann’s rearrangement 4. Conversion of an aldopentose into two aldohexoses.

5. Formylation of a phenol with chloroform and strong base.a) A–3; B–5; C–2; D–1b) A–3; B–5; C–4; D–1c) A–3; B–4; C–2; D–5d) A–5; B–3; C–1; D–4

130. Which of the following mixtures of solutions will act as a buffer solution :

a) 20 ml of 0.1 M CH3COOH + 40 ml of 0.1 N HCl

b) 200 ml of N10 NaOH + 100 ml of

N20 HCl

c) 100 ml of 0.1 N NaOH + 150 ml of 0.1 N HCNd) 100 ml of 0.1 N NaoH + 50 ml of 0.2 N CH3COOH

131. Glucose gives silver mirror test because it contains —CHO group, but fructose (having keto group) gives thistest due to :

a) It is isomer of glucoseb) It undergoes rearrangement in ammoniacal medium to form reducing sugarsc) Bothd) None

132. Standard enthalpies of formation of O3, CO2, NH3 and HI are +142.2, –393.3, –46.2 and +25.9 kJ mol–1

respectively. The order of their increasing stabilities are :

a) O3, HI, NH3, CO2

b) O3, CO2, NH3, HI

c) CO2, NH3, HI, O3

d) NH3, HI, CO2, O3

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133. What is true about amino acids :

1) Ten amino acids are essential 2) They exist as zwitter ion3) All amino acids are optically active 4) There are 24 natural amino acids knowna) 1, 2, 3

b) 2, 3, 4

c) 1, 3, 4

d) 1, 2, 4

134. I 0.193 gram of gold is dispersed in one litre of water as spherical particles of unIorm size of radius1.2× 10–4 cm, then the number of gold particles per mm3 of the solution (density of gold 19.3 gm/cm3) isnearly equal to :

a) 500

b) 790

c) 980

d) 1380

135. Both H2O2 and O3 act as oxidising agents. The oxidising action in which they are similar

(1) PbS to PbSO4 (2) Fe2+ to Fe3+

(3) K4[Fe(CN)6] to K3[Fe(CN)6] (4) decolourising of acidIied KMnO4

a) 1, 2, 3

b) 2, 3, 4

c) 1, 3, 4

d) 1, 2, 4

136. Na2SO4 is water soluble but BaSO4 is insoluble because

(1) the hydration energy of Na2SO4 is higher than that of its lattice energy.(2) the hydration energy of Na2SO4 is less than that of its lattice energy.(3) the hydration energy of BaSO4 is less than that of its lattice energy.(4) the hydration energy of BaSO4 is higher than that of its lattice energy.a) 1, 3

b) 2, 4

c) 1, 2

d) 3, 4

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137. The reaction of an element A with water produces combustible gas B and an aqueous a solution of C. Whenanother substance D reacts with this solution C also produces the same gas B, D also produces the same gaseven on reaction with dilute H2SO4 at room temperature. Element A imparts golden yellow colour to Bunsenflame. Then, A, B, C and D may be identIied as

a) Na, H2, NaOH and Znb) K, H2, KOH and Znc) K, H2, NaOH and Znd) Ca, H2, CaCOH2 and Zn

138. ( ) 2organicCompound

A O X Y Z+ → + +

Compund (A) in pure form does not give ppt. with AgNO3 solution. A mixture containing 70% of (A) and30% of ether is used as an anaesthetic. Compound (X) and (Y) are oxides while (Z) is a pungent smelling gas.(X) is a neutral oxide which turns cobalt chloride paper pink. Compound (Y) turns lime water milky andproduces an acidic solution with water. Compounds (A), (X), (Y) and (Z) respectively will be

a) CH4, H2O, CO2, Cl2

b) CHCl3, H2O, CO2, Cl2

c) CH3OH, H2O, CO2, N2

d) NH2CONH2, H2O, N2O, CO2

139. Which of the following statements is/are correct regarding inter-halogen compounds of ABx types?(1) x may be 1, 3, 5 and 7(2) A is a more electronegative halogen than B(3) FBr3, cannot exit(4) the structure of CI3, and I7, show deviation from normal structures and could be explained on the basis

of VSEPR theorya) 1, 3

b) 2, 3

c) 2, 4

d) 1, 4

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140. Which of the following statements is/are correct regarding B2H6?1) banana bonds are longer but stronger than normal B–H bonds2) B2H6 is also known as 3c–2e compound3) the hybrid state of B in B2H6 is sp3 while that of sp2 in BH3

4) it cannot be prepared by reacting BF3, with LiBH4 in the presence of dry ethera) 1, 2, 3

b) 2, 3, 4

c) 1, 2, 4

d) 1, 3, 4

141. The correct statement(s) about transition elements is/are(1) the most stable oxidation state is +3 and its stability decreases across the period(2) transition elements of 3d-series have almost same atomic sizes from Cr to Cu.(3) the stability of +2 oxidation state increases across the period(4) some transition elements like Ni, Fe, Cr may show zero oxidation state in some of their compoundsa) 1, 2, 3, 4

b) 2, 3, 4

c) 1, 2, 4

d) 1, 4

142. Matallurgical process of zinc involves roasting of zinc sulphide followed by reduction. Metallic zinc distilsover as it is volatile and impurities like Cd, Pd and Fe gets condensed. The crude metal obtained is calledspelter, which may be purIied by

(1) electrolysis process (2) fractional distillation

(3) polling (4) heating with iodine

a) 1, 2

b) 2, 3

c) 2, 4

d) 1, 4

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143. Hoop’s process of purIication of aluminium involves formation of layers during electrolysis. This is because

(1) the three layers have same densities but dIferent materials(2) the three layers have dIferent densities(3) the upper layer is of pure aluminium which acts as a cathode(4) the bottom layer is of impure aluminium which acts as an anode and middle layer consists of cryolite

and BaF2.a) 2, 3, 4

b) 1, 2, 4

c) 1, 3, 4

d) none of these

144. In the separation of Cu2+ and Cd2+ in II group of basic radicals, tetrammine copper (II) sulphate and tetramminecadmium (II) sulphate react with KCN to form the corresponding cyano complexes. Which one of thefollowing pairs of the complexes and their relative stability enables the separation of Cu2+ and Cd2+?

a) more stable K3 [Cu(CN)4] and less stable K2[Cd(CN)4]b) less stable K2 [Cu(CN)4] and more stable K2[Cd(CN)4]c) more stable K2 [Cu(CN)4] and less stable K2[Cd(CN)4]d) less stable K3 [Cu(CN)4] and more stable K2[Cd(CN)4]

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Questions 145 - 149 are based on the following passageThe dissociation of the diatomic halogen into its atoms, which go on to abstract a hydrogen atom from H2 toform the product molecule. This reaction is most vigorous with fluorine and least vigorous with bromine (aliquid at 250C); heat must be provided for the system to approach equilibrium in the latter two cases.

Gaseous hydrogen halides may also be generated by the reaction of halide salts with an appropriate acid. HFis readily formed by reacting sodium flouride with concentrated sulfuric acid, hydrogen chloride is formed inan analogous manner. However. However, concentrate H2SO4 is too strong an oxidizing agent to form HBrand HI form their respective sodium halide salts. Phosphoric acid is a useful substitute here, although thereaction generally must be heated to expel the HBr or HI gas formed.

Table 1 shows a comparison of some of the physical properties of the hydrogen halides.

Property HF HCI HBr HI

Formula weight (g.mol-1) 20.01 36.46 80.92 127.9

Bond-Energy (kJ.mol-1) 565 431 368 297

Melting Point 0C) -83 -114 -87 -51

Boiling Point (0C) 20 -85 -67 -35

Water solubility at 25 0C0. Total 78 210 234(g/100gH2O)

Table - 1

All the hydrogen halides are extremely water soluble, and all except hydrogen fluoride exhibit the “levelingeffect” of water, i.e., even though acid strength is given by all these acids dissociate completely in water.

Alkaline metal halides form regular crystalline solids. Sodium chloride exhibits a simple face-centered cubiclattice structure consistent with ion/counter-ion pairs of dIfering size, while cesium chloride has a primitive(often called body-centered) cubic lattice structure consistent with the almost equal sizes of the cesium andchloride ions. Following a general trend for periodic group analogues, the lattice energy of cesium chloride ismuch smaller than that of sodium chloride due to dIferences in packing efficiency, which is greater for NaCIthan for CsCI. Table 2 shows the boiling points for some ionic alkaline metal halides.

Metal Halide Formula Weight (g.mol-1) Boiling Point (0C)

LI 25.9 1717

NaCI 58.5 1465

KBr 119.0 1398

TbI 212.4 1304

Table - 2


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145. Water solubility, melting point, and boiling point are directly related to formula weight for HCI, HBr and HIwhy are these trends not continued in HF?

a) The lattice energy for HF(s) is much smaller than that of HI(s)b) HCI, HBr, and HI do not form intermolecular hydrogen bondsc) Of the hydrogen halides, HF is the weakest acid.d) hydrogen halides, so it is the most soluble.

146. Why might bromine and iodine need to be heated in order to react with hydrogen?

a) In their elemental states, both bromine and iodine are too viscous for the reaction to occur.b) The formation reactions for HBr and HI are endothermicc) A competing reaction, the photolysis of hydrogen, is quenched by gaseous bromine and iodine.d) The reaction products are lower in enthalpy than the reactants.

147. For the alkaline metal halides listed below:

I) Boiling points are inversely related to molecular size.II) The radius of K+ is greater than that of CI-1.a) I onlyb) I and III onlyc) II and III onlyd) I, II, and III

148. Which of the following best describes the reaction of gaseous hydrogen and chlorine at 250C to form HCI(g)?

a) precipitationb) combinationc) disproportionationd) formation

149. What is the approximate ratio of velocities of HCI(g) and HBr(g), respectively, at 250 C?

a) 2/3b) 1/1c) 3/2d) 9/4

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150. According to the passage, which of the following is a viable initiation reaction for the gaseoushydrogen-chlorine reaction to form According to the passage, which of the following is a viable initiationreaction for the gaseous hydrogen-chlorine reaction to form HCI?

a) +→ H 2H2

b) +→ Cl 2Cl2

c) ++→+ HClHHCl 22

d) ++ +→+ lCClHHCl2

(3 mark)

ai iitjee modeltest 02

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