Ai Iitjee Modeltest 02

IIT-JEE Model Test - 02

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

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1. 2. 3. 4. 5.

Download the test If possible take a print of the test Mark correct option on the test booklet or on a sheet of paper Login to the website open the relevant answer sheet of this test. Enter all your answers and submit the answer sheet online to get Instant score analysis

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Paper - I : Physics - 1 to 50 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 order to 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 - which comes 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 opposite direction 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 sensors are used to determine its velocity. If the speed falls within a predetermined range, the sensors will trigger a gate to accept the coin; otherwise, the coin will be rejected.

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Once comlete, the apparatus is tested using three disks an undamaged quarter, a quarter with a hle of radius 5.5 mm removed from its center, and a non-conducting plastic quarter. The friction in the experiments is negligible. 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. The results of the experiment are summarized in Table - 1.

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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.

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What is the resistance per unit are of an undamaged quarter as it completes the circuit in the apparatus? a) 0.40 Ω/cm 2 b) 0.90 Ω/cm 2 c) 24 Ω/cm 2 d) 4.0 Ω/cm

2

(3 mark)

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2.

(3 mark)

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 hole would increase b) the difference between conductivity of the undamaged quarter and conductivity of the plastic quarter would increase. c) the magnetic force on the undamaged quarter would be double the magnetic force on the quarter with a hole. d) the difference between speed of the undamaged quarter and speed of the quarter with a hole would increase. 3.

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The 1.3 magnet used in the apparatus deflects a a+3.5 µC charge located on the very edge of a quarter. If the particle, traveling in a direction perpendicular to the magnetic field, was deflected with a force of magnitude (3 mark) 4.1 x 10-7N, what is the speed of the particle? a) 0.09 m/s b) 0.18 m/s c) 181 m/s

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d) 12.5 m/s 4.

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

(3 mark)

a) the voltage of the battery was increased b) the resistance of the coin was decreased c) the thickness of the coin was increased d) 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 a (3 mark) greater 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 quarter

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c) 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 a diameter of 1 m. Neglecting air resistance, what will be the balloon’s initial upward acceleration when released (3 mark) from 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.

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A certain element has a density of 10 g/cm3 and half-life 140 days. Over a period of 140 days the average number of α emissions per day is found to tbe 12 x 1012 from a sample of initial mass 1 µ g . Estimate the (3 mark) number of atoms in 1 cm3 of element. a) 2.66 x 1022 b) 3.36 x 1022 c) 12 x 1022

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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 from potential energy, to kinetic energy, electicity if the water in the dam were replaced with mercury, the energy (3 mark) produced by ther dam would. a) Increase b) Decrease c) Remain the same d) Decrease then increase

9.

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

(3 mark)

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

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b) Reduces the glare on the pool surface allowing divers to better see their target at the bottom of the pool c) Increases the surface tension through turbulent flow allowing for cleaner dives d) 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 that its acceleration is always inclined at 450 to the instantaneous inward radius. The speed of the particle after (3 mark) time t will be a)

ur r - ut

b) u 2 c)

d)

11.

u 2 ur 2(r - ut)

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In aeodynamic design, reducing the coefficient of friction is critical to reduced drag Most of the time that means eliminating turbulent flow. Yet pure laminar flow is not ideal. Which of the folllowing is a NOT a reason (3 mark) that a golf ball flies better with asymmetric dimples laid in an isometric pattern?

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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 a capacitor and a dashpot (the piston that slows a door) is the same as a resistor, which system stores more energy at equal tensions, two springs with constants 3 and 4 in series or in parallel? Both systems are equidistant (3 mark) and 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 law (3 mark) F = − kx − bx 2 ,calculate compression distance x of the spring.

h

a) x = 2mgh/k b) x = ( 4mgh /b )1/4 c) x = 2k/b

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d) x = [ 4mgh / b + k 2 / b 2 − k / b ]1/ 2 14.

A length 4a of uniform wire is bent in the form of a square and the opposite angular points are formed with straight pieces of the same wire which are in contact at the intersection. A given current enters at the intersection of diagonals and leaves at an angular point. Find the resistance of the whole network if ρ is the resistance per (3 mark) unit length. a)

( 2 / 2 2 +1) ρa

b) ( 2/2 2 - 1) ρa c) (2 2 +1 / 2 ) ρa d) (2 2 - 1 / 2 ) ρa

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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 inextensible string is wound around the cylinder, its free end is attached to a freely hanging mass m. The string unwinds (3 mark) without slipping as the mass m falls. The tension in the string will be a) mg

16

b)

mg 2

c)

mg 3

d)

mg 4

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ur A charge particle q pases through a region having perpendicular uniform electric field E and magnietic field (3 mark) ur B undeviated. Choose the current alternative —

a) the charged particle must be at rest

ur b) the componet of velocity vector along E must be zero ur ur ur c) the velocity vector V must be perpendicular to E and B together d) none of these is correct

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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 greater than focal length and the image formed is at the shoirtest possible distance. If now a concave lens of very large focal length (3 mark) f2 be placed in contact with first, find the shift in the position of the image.

a) 2 2 f1 / f 2 b)

2 f1 / f 2

c) 2 f1 / f 2 d) 4f12 / f 2

18.

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A uniform rope of length 12 m and mass 6 kg hangs vertically from a rigid support. A block of mass 2 kg is attached to the free end of the rope. A transverse pulse of wavelength 0.06 m is produced at the lower end of (3 mark) the rope. What is the wavelength of the pulse when it reaches the top of the rope. a) 1. 2 m b) 0. 12 m c) 0.012 m

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d) 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 are the object and image distances respectively. fund out the correct identification for the different combinations (3 mark) from the followings. y

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

PAGE x

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

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(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 wall or a narrow opening into a region of constant lower pressure without a transfer of heat taking place. the physical quantity that remains constant during this process in the system considered as an ideal gas is (3 mark) 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 an angle 300 with plane of the plate. Length of the plate is 0.17 m and it is separated by 0.1 meter. Electric field E = 10-3 N/C is present between the plate. Just outside the plates magnetic field is present. Find the velocity of projection of charged particle and magnitude of the magnetic field perpendicular to the plane of the figure, (3 mark) if it has to graze the plate at B and A parallel to the surface of the plate. (Neglect gravity).

B 0

30

E

a) . 7 m /s , 1.2 mT b) 1.4 m /s , 2.4 mT c) 2.8 m /s , 4.8 mT

PAGE A

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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 the mirrors. Find the interval between adjacent interference bands on screen MN at a distance OA = a from the point of intersection of the mirror. The wavelength of the light wave is known and equal to λ . Shield C does (3 mark) not allow the light to pass directly from the source to the screen

N S C

b b

O

A

a

á

PAGE

M

a)

λ ( a + b) 2bα

c)

λ ( a + b) bα

b)

λ ( a − b) 2bα

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23.

A micro-ammeter has a resistance 100 Ω and full scale deflection current 50 µ A. It can be used as a voltmeter or as a higher range ammeter provided a resistance is added to it. Chose the correct range and resistance (3 mark) combinations 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.

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

(6 mark)

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 the rod (distance x) so that the parson will still make a full revolution around the rod?

O

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L 2

a) x =

25.

b) x =

L 3

c) x <

2L 3

d) x >

3L 5

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A parallel plate capacitor filled with a dielectric whose permittivity varies with applied voltagee according to the law ∈ = αV (where α=1 volt -1 ). Another similar caacitor without dielectric is charged to a potential of 156 volts and connected in parallel with the uncharged now linear capacitor. What is the common voltage across (6 mark) the two capacitors? a) 2 V c) 6 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 an angle φ above the horizontal. The rails have negligible resistance. There is a uniform magnetic field of magnitude B directed downward in figure. The bar is released from rest and slides down the rails. What is the terminal (3 mark) speed of the bar?

B

a l

b

B

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a) VT =

mgR sin φ B2l 2 cos2 φ

b) VT =

mg sin φ B2l 2 cos2 φ

c)

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m g R s in φ B 2l co s φ

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 string is 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, all particle to be at rest at t= 0 and maximum amplitude to be 3 mm. find wavelength and frequency of the wave. (3 mark)

a) 400 Hz b) 300 Hz c) 500 Hz d) 200 Hz 28.

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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. The gas is heated by an electric heater unitl the piston moves out slowly without friction by 0.1 m. Calculate the (3 mark) final temperature of the gas. a) 800 K c) 700 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 attached to anything, is lying a distance

L . A second mass M, which is not 2

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

past its equilibrium length.

(3 mark)

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

3KL2 16 M

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

KL2 16 M

Choose the correct option based on the above information

K

M

M

a) Both statements I & II are correct

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b) Both statements I & II are wrong

c) Data is insufficient to evaluate the statement I

L

d) Data is insufficient to evaluate the statement II 30.

L/2

L/4

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

3 times the original length what is the 2 (6 mark)

value of this fraction? a)

1 4

b)

1 8

c)

1 16

d)

1 6

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31.

An electron and a proton are separated by a large distance and the electron approaches the proton with a kinetic energy of 2 eV. If the electron is captured by the proton to form a hydrogen atom in the ground state, (3 mark) 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 an angle of θ with the road. The man hears a note having a frequency of 600 Hz when the truck is closest to him. (6 mark) Also the speed of truck has got doubled during this time. Find the value of ‘ θ ’

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a) 60º b) 45º

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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 rolls or slides with linear speed v towards a metal ramp at angle 50°. Two of the aporoaches to the ramps are metal (M), on which the objects roll without sliding, but the other two are frictionaless Slipperide (S). Rank (3 mark) the four situations, from highest to lowest, in terms of how high the object rolls up the ramp A)

v

M

B)

S

C)

v

M

M

v

M

M

a) C > B > A = D b) B > C > A = D c) A = D > B > C d) None of these

D)

v

M

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34.

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

(3 mark)

a) On a warm day because the velocities of the source and observeer will be less significant compared to the velocity of sound b) On a warm day because the velocities of the soruce and observer will be more significant compared to the velocity of sound c) On a cold day because the velocities of the source and observeer will be less significant compared to the velocity of sound d) On a cold day because the velocities of the source and observer will be more significant compared to the velocity of sound. 35.

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Two parallel long straight conductors lie on a smooth surface. Two other parallel conductors rest on them at right angles so as to form a square of side a initially. A uniform magnetic field B exists at right angles to the plane containing the conductors. They start moving out with a constant velocity V. If r is the resistance per unit (3 mark) length of the wire the current in the circuit will be a)

Bv r

b)

Br v

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c) Bvr d) Bv 36.

In an agricultural experiment, a solution containing 1 mole of a radioactive material (T1/2 =14.3 days) was injected into the roots of a plant. The plant was allowed 70 hours to settle down and then activity was measured in its fruit. If the activity measured was 1 µ Ci , what percentage of activity is transmitted from the (3 mark) root to the fruit in steady state? a) 1.26 × 10 −11% b) 1.26 × 10 −9 % c) 1.26 × 10 −6 % 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 0.2 cm 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 of (6 mark) glass = 9 × 10-6 0C-1] a) 2.92 cm b) 2.90 cm c) 2.75 cm d) 2.85 cm

38.

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Positively charged particle A starts at rest and is pulled from a great distance directly toward negatively charged particle B by the electric field created by particle B. If particle A has a velocity v when it is a distance (3 mark) 4r from particle B, what will be the velocity of particle A when it is a distance r from particle B? a) 1 2 v b) v

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c) 2v d) 4v 39.

The absolute temperature T of a gas is plotted against its pressure P for two different constant volumes V1 and (3 mark) V2 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 angle of incidence is either 420 or 620. What is the angle of incidence when it is undergoing minimum deviation? (3 mark)

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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 temperature T1 such that the expansion ratio is α . It rejects a heat Q2 at constant temperature T2 (< T1). The efficiency of the cyclic process is η , the total work done in the cyclic process is W and dU is the change in internal energy (3 mark) of the process. T 

2 1) η = 1 −  T 

2) W = Q1 − Q2 = η R (T1 − T2 ) In α

3) dU = 0

4) dU = η RT1 In α



1



a) 1, 2, 3 b) 1, 2, 4 c) 1, 2 d) None of these 42.

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One mole of an ideal monoatomic gas is taken round the cyclic process ABCA as shown in figure. Calculate (3 mark) the maximum temperature attained by the gas-during the cycle.

www.aieeepage.com P

3PO PO

a)

25 PV 0 0 8R

b)

20 PV 0 0 8R

c)

20 PV 0 0 R

d) none of these

B A VO

C 2VO

V

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43.

A pendulum has a period T for small oscillations. An obstacle is placed directly below the pivot, so that only the lowest one fourth of the string can follow the pendulum bob when it swings to the right of its resting position as shown. The pendulum is released from rest at a certain point. Assuming that the angle between the moving string and the vertical stays small throughout the motion, the time it takes to return to that point is (3 mark)

3l 4

l

PAGE l 4

A

a) T

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T b) 2

44.

c)

3T 2

d)

3T 4

O

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 melts before reaching the ground. The molten substance falls slowly on the ground. Calculate the latent heat of fusion of metal. (3 mark) 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.

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In a double slit experiment light of wave length λ = 4800 Å is used. One slit is covered by a thin plate of glass µ = 1.4 and the other by another plate of same thickness 8 x 10-4 cm but having a value for µ = 1.7 . The (3 mark) central fringe will be shifted on the screen to which position? a) Position of 5th fringe c) Position 7th fringe

b) Position 6th fringe www.aieeepage.com 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 the water cleanly. A proper approach and take off from the end of the board are essential elements of a well executed 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 an initial kinetic energy of W1 (the hurdle energy), and reaches a height of H1 above the diving board, which remains 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 horizontal position, 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.

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In order to obtain maxmimum height, the diver must leave the board when it is exactly in the horizontal position. Furthemore, after the diver takes off from the board, the board should have zero velocity. This allows 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.

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In the perfect dive, the maximum energy of the diver is equal to a) the leap energy

(3 mark)

b) the sum of the leap energy and the potential energy due to the height of the board above the water c) 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 cm (3 mark) above 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 after passing very close to the end of the board. If the driver’s leap energy and urdle energy are the same, then the (3 mark) relationship between H1 and H2 is: a) H1 = H2 1

b) H1 = H 2 2 c) H1 = 2H2 d) H1 and H2 49.

a) 87. 5 J b) 350 J c) 700 J d) 1400 J 50.

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A person with a mass of 70 kg jumps to a height 50 cm above the ground. If the efficiency of human mucles (3 mark) is 50%, how much energy does the diver expend for this jump?

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Assuming that all of the diver’s energy comes from the hurdle and the leap, adding spin to a diver’s upward movement (3 mark) would

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, formula for focal distance etc., are derived for the parabola y2 = 4ax. However, all the results with slight transformation are 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 this parabola 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 corresponding equation of P will be (P (x, y, -a) = 0

PAGE

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 +

a , so correponding trangent to x2 = 4ay is m

www.aieeepage.com  2a a 

a x = my and the point of contact will be m

 , 2 m m 

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 in addition to above transformation 51.

The focal distance of the point (x, y) on the parabola x 2 = 8 x + 16 y = 0 is a)

(3 mark)

y−4

b) y − 5 c)

y−2

d) x − 4

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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 (3 mark)

1) 1

2) 2

3)

3 2

4) −

3 2

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)

a) 1, 2, 3 b) 1, 2, 4 c) 2, 3, 1 d) None of these 54.

PAGE 3) (16, 8)

(3 mark)

4) (-8, 4)

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The points on the axis of the parabola x2 + 2x + 4y + 13 = 0 from where three distinct normals can be drawn (3 mark) are 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 x cos α + y sin α = p touches the parabola x2 + 4a (y+a) = 0 if a) a = p secα b) a cos2α = p sin α c) a 2 cosα + p 2 sin α = 0 d) a tan α = p secα

(3 mark)

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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 are called 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 repetition (6 mark) allowed)? a) 7920 b) 330 c) 14640 d) 419430

57.

PAGE

How many three-letter computer passwords (no repetition allowed) with at least one symmetric letter? a) 990 b) 2730 c) 12870 d) 15600

(6 mark)

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Questions 8 to 45 are independent questions 58.

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

(3 mark)

a) translated horizontally π / 2 units to the right b) first reflected in the horizontal axis and then translated vertically π / 2 units upward c) first translated horizontally π / 2 units to the left and then reflected in the horizontal axis d) first translated vertically π / 2 units downward and then reflected in the vertical axis 59.

The cubes of the natural numbers are grouped as 13 , (23 ,33 ), (43 ,53 , 63 ).... then the sum of the numbers in the (3 mark) nth group is a)

1 3 2 n ( n + 1) (n 2 + 3) 8

b)

1 3 2 n (n + 2) (n 2 + 4) 12

c)

1 3 2 n (n + 16) (n 2 + 12) 16

d)

1 3 2 n (n + 1) (n 2 + 3) 12

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60.

In a particular dam project, certain barriers have to be raised to prevent the flow of water. But in spite of raising a barrier, it might happen that the water force can break the barrier. The probability of a barrier failing is 20 percent. Then, what should be the minimum number of barriers ot be raised so that the overall probability (3 mark) of 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. (3 mark) a)

1 M0 2

b)

1 M0 4

c)

M0 2e

d)

62.

PAGE

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M0 e2

A whispering gallery is constructed as part of the surface formed on rotation of the ellipse

x2 y2 + = 1 with 100 k

x and y in yards. Each whispherer stands at a focus on the x-axis that is three feet from the nearest vertex. Find (3 mark) k. a) 6 b) 7 c) 18 d) 19

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63.

64.

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

(3 mark)

a) ±

i Z1 3

b) ±

Z1 3

c)

Z1  π π  cos ± i sin  3  3 3

d)

Z1  π π  cos ± i sin  3  6 6

a)

14 ! 2 ! 12 !

12 ! b) 2!

65.

PAGE

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

c)

11! 2 ! 12 !

d)

11

(3 mark)

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C2

If A, G and H are the Arithmetic mean, Geometric mean and Harmonic mean between two unequal positive (3 mark)

integers. Then the equation Ax2 − G x − H = 0 has a) both roots fractions b) at least one root which is negative fraction c) exactly one positive root d) both (b) and (c)

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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 ( x) 2 + [ x]2 = ( x − 1) 2 + [ x + 1]2 , where (x) = the least integer greater than or equal to x and (3 mark) [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.

PAGE

 x   x  x x If f(x) = sin 2  n  + cos 2  n and g(x) = sec 2   − tan 2  and f(x) = g(x), then 2  2  2  2

a) x ∈ R π 2

 

b) x ∈ R −  x : x = ( 2n + 1)  c) x ∈ R − {x : x = ( 2n + 1)π }

(3 mark)

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d) x ∈ R − {x : x = 2n π } 68.

Ten identical balls have to be distributed among three identical boxes. In how many ways can this be done (3 mark) such 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 are drawn on both sides of the diagonal. The length of the diagonal is n 2 cm. If distance between consecutive line segments be

PAGE

1 cm, then the sum of the lengths of all possible line segments and the diagonal is 2

a) n(n + 1) 2 cm b) n 2 cm c) n(n + 2)

(3 mark)

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d) n 2 2 cm

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70.

Let R = (8 + 3 7 ) 20 and [R] = the greatest integer less than or equal to R. Then

1) [R] is even

(3 mark)

2) [R] is odd 1

3) R − [ R] = 1 − (8 + 3 7 ) 20

4) R + R [ R ] = 1 + R 2

a) 2, 3, 4 b) 1,2,3 c) 3, 2,1 d) None of these 71.

PAGE

If a, b ∈ R the roots of the equation ax 2 + bx + 10 = 0 are not real and distinct m, n are the values of a and b respectively for which 5a+b is minimum, then the family of lines m (4 x + 2 y + 3) + n( x − y − 1) = 0 are concurrent

at a) (1, -1)

(3 mark)

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 1 7 b)  − ,   6 6

c) (1,1)  1  6

7 6

d)  − ,− 

f(x)

72.

g(x)

a

-2a

-2a

-a

(3 mark)

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)

PAGE

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

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1 + sin 2 x 2

73.

If maximum and minimum values of the determinant

sin x sin 2 x

cos 2 x

sin 2 x

2

1 + cos x sin 2 x are α and β , then 2 (3 mark) cos x 1 + sin 2 x

1) α + β 99 = 4 2) α 3 + β 17 = 26 3) (α 2n + β 2n ) is always an even integer for n ∈ N

PAGE

4) a triangle can be constructed having its sides as α − β, α + β and α + 3β a) 1, 2, 3 b) 1,3 c) 1, 2, 4 d) None of these

74.

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A B C is a right angle triangle in which ∠B = 90o and BC = a. If n points L1, L2, L3 ...Ln on AB are such that AB is divided in (n+1) equal parts and L1, M 1, L2 , M 2 ....., Ln , M n are line segments parallel to BC and M1, L2 , M 3 .....Mn are on A C. Then the sum of the length of the sides of L1, M 1, L2 , M 2 ....., Ln , M n is

a)

a(n + 1) 2

b)

a(n − 1) 2

c)

an 2

(3 mark)

d) None of these

75.

PAGE

The vectro C along the bisector of the acute angle between a = 7 i-4 j-4k and b = 2 i- j + 2k where C = 270 is given by

a) i - 7j + 2k c) −i + 7 j + 2k

(3 mark)

b) −13i + j + 10k

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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 5 envelopes also marked A, B, C, D and E. The secretary, however, placed the letters at random into the envelopes such that each envelope received exactly one letter. Then, the number of arrangements in which (3 mark) exactly 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?

PAGE

(3 mark)

I)

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

II)

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

III)

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

IV)

The circular points corresponding to the arcs

www.aieeepage.com π - 3π and are equal 2

2

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

78.

Consider a curve ax2 + 2hxy + by2 + 2gx = 0 and a point P (u, v). A line is drawn from the point P, making an (3 mark) angle ' θ' with x-axis, intersects the curve at Q and R. Then PQ, PR is a)

b)

c)

au 2 + 2huv + bv 2 + 2gu a cos 2θ + b sin 2θ + h sin2θ a cos 2θ + b sin 2θ + h sin 2θ au 2 + 2huv + bv 2 + 2gu au 2 + 2huv + bv 2 + 2gu a cos 2θ + b sin 2θ

d) None of these

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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 1 2

III. The probabilities of the student passing in tests, I, II, III are respectively p, q and . If the probability that (3 mark)

1 the student is successful is , then 2

a) p = q = 1 b) p = q =

1 2

c) p=1, q = 0 1 2

d) p= , q =1

80.

PAGE

If the slope of one of the lines represented by ax 2 + 2hxy + by 2 = 0 be the square of the other, the 2

a + b 8h then + = h ab

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(3 mark)

a) 4 b) 6 c) 8 d) None of these

81.

The equation of a circle is x 2 + y 2 − λax − ay − a 2 (λ2 + 1) = 0 . If two chords, each bisected by the x-axis can be drawn to the circle from the point (a(λ − 1), a (λ + 1)), which lies on the circle then λ satisfies

(3 mark)

a) λ2 − 4λ − 12 > 0 b) λ2 − 4λ − 12 < 0 c) λ2 − 12λ − 4 > 0 d) λ2 − 12λ − 4 < 0

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82.

If P is any point lying on the ellipse

x2 a2

+

y2 b2

= 1, whose foci are S and S’.

(3 mark)

Let ∠PSS ' = α and ∠PS ' S = β , then

1) PS + PS’ = 2a, if a > b 3) tan

2) PS + PS’ = 2b, if a < b

α β 1− e tan = 2 2 1+ e

α 2

β 2

4) tan tan =

a 2 − b2 b

2

[a − a 2 − b 2 ]when a > b

a) 1, 2, 3 b) 1, 3, 4 c) 1, 2, 4 d) None of these 83.

PAGE

The function f(x) = max {1-x, 1+x, 2}, x ∈ R is a) discontinuous at all points b) differentiable nowhere

(3 mark)

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c) differentiable at x ∈ R -{1, -1} d) discontinuous at 1 and -1 84.

Let (tan α ) x + (sinα ) y = α and (α cosec α ) x + (cos α ) y = 1 be two variable straight lines, α being the

parameter. Let P be the point of intersection of the lines. In the limiting position when α → 0, the coordinates (6 mark) of P are a) (2, 1) b) (2, -1) c) (-2, 1) d) (-2, -1)

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85.

1 - 2x

If x < 1, then

a)

1 1+ x + x 2

b)

1 + 2x 1+ x + x 2

1- x + x

2

+

2 x − 4x3 2

1− x + x

4

+

4x3 − 8x7 4

1− x + x

8

(3 mark)

+ ....∞

1− x + x2 c) 1+ x + x 2

PAGE

d) 1

2

86.

∫

The value of

2x 7 + 3 x 6 − 10 x 5 − 7 x 3 − 12 x 2 + x + 1 x2 + 2

(3 mark)

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− 2

16

π

14

π

2) − 5 2 + 2 2

1) 0 2

3) 2

dx is

3 x 6 − 12 x 2 + 1

∫

2

x +2

0

dx

4) − 5 2 + 2 2

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

87.

 x2  y = 3, −  ([ . ] denotes the greatest integer ), y = 1 and the lines x = 1, The area of the region bounded by  10  (3 mark) x = 10 is

a) 9 sq. units b) 11 sq. units c) ( 10 + 1) sq. units d) ( 10 − 1) sq. units

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3

88.

Let f : R − {0} → R − [−1, 1], defined by f ( x) =

e x + e− x e

x 3 −e − x

3

3

, the f is

1) a one - one function

2) an increasing function

3) a decreasing function

4) onto function

(3 mark)

a) 1, 3, 4 b) 1, 2, 3 c) 3, 1 d) None of these

89.

PAGE

1 1 If for non - zero x, af (x) + bf   = − 5, where a ≠ b, the  x x

a) a log 2- 5a + 7b 1 (a log 4-10a + 7b) b) 2

2

∫

f ( x) dx is

(3 mark)

1

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

90.

4e x + 6e− x dx = Ax + B log (9e2 x − 4) + C , then A, B and C will be If ∫ x 9e − 4e− x 3 2

36 , C = constant 35

3 2

35 3 , C = log 3+c 36 2

a) A=- , B= b) A= , B= 3 2

c) A=- , B=3 2

d) A=- , B=

35 3 , C =- log 3+c 36 2

35 , C = constant 36

(6 mark)

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91.

If f(x) is a continuous function and attains on ly rational values and if f(1) = 4, then the roots of (3 mark) (2) x2 + f(0)x + f(6) = 0 are a) imaginary b) real and distinct c) real and equal d) rational

92.

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

(3 mark)

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

PAGE

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 correct b) only II is correct c) both I and II are correct d) both I and II are wrong 93.

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

(3 mark)

I. The determinants 1 a a2 1 a bc 1 b b2 1 b ca and are not identically equal. 1 c c2 1 c ab

II . The equation 2 x 2 + 3x = 1 = 0 has an irrational root. a) only I is correct b) only II is correct c) both I and II are correct d) both I and II are wrong

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94.

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

(6 mark)

I.If χ.A = 0, χ.B = 0, χ.C = 0 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 Z1 = Z 2 = Z 3 then Z1 + Z 2 + Z 3 = 0 .

a) only I is correct b) only II is correct c) both I and II are correct d) both I and II are wrong

95.

The imaginary part of

PAGE

2z + 1 is -2. Then the locus of the point representing Z in the complex plane is iZ + 1

a) a circle b) a straight line c) a parabola

(3 mark)

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d) an ellipse

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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 more than the first term. In series S2, the nth term defined as the difference between the (n+1) term and the nth term of series S1, is an arithmetic progression with a common difference of 30. 96.

First term of S1 is

(3 mark)

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.

PAGE

(3 mark)

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(3 mark)

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?

(3 mark)

a) 60 b) 70 c) 80 d) Average is not an integer 100. What is the sum of series S2? a) 10

PAGE

(3 mark)

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b) 20 c) 30 d) 40

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Paper - I I I : Chemistry- 101 to 150 Questions 101 to 105 are based on the following passage A buckyball is large, highly-ordered, nearly spherical configuration of carbon atoms that resembles a molecular cage. Since it contains only carbon, a buckyball is an allotrope of carbon in addition to the naturally occurring diamond and graphite forms. When buckyballs were first synthesized, they caused a stir in the scientIic community, 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 characteristic transition temperature. Above the transition temperature, the substance exhibits normal behavior. While a metal 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 illustrated in Figures 1 and 2.

Resistance

PAGE

www.aieeepage.com Metallic Conductor

Resistance

Metallic Conductor Figure 1

Superconductor

PAGE Figure 2

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

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A group of scientists performed an experiment to study the super conducting properties of buckyballs. A superconducting transistor made of buckyballs produces an electric field that draws electrons away from the buckyballs, leaving gaps of positive charge in the superconducting material. The scientists predicted that separating the buckyballs with other molecules would increase the number of positive gaps, thereby increasing the superconductivity of the material. Two separator molecules were added to the buckyball transistor devices. In the first device, chloroform CH3 C1 was added. In the second, bromoform CH3 Br was added. In the third device, no separator molecules were added. The highest temperature at which superconductivity was observed for each device is shown in Table 1. Separator None Chloroform Bromoform

Highest Superconducting Temperature (0F)

PAGE - 366

- 315

- 249

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

(3 mark)

a) is heavier than chloroform, making it closer character to the buckyball molecule b) has greater electron density than chloroform, so it is better able to canel out the positively charged gaps in the superconducting material c) 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. (3 mark)

102. All of the following are groups of allotropes EXCEPT: a) b) c) d)

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

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103. Which of the following is the molecular shape of chloroform? a) b) c) d)

Trigonal bipyramidal Tetrahedral Trigonal planar Bent

(3 mark)

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104. What is the dipole moment of C60 molecule?

(3 mark)

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 buckyball (3 mark) device? a) Separating the bucyball molecules increases the number of positive gaps in the superconducting material.

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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

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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 the (3 mark) gases formed at (a) 383 K and (b) at room temp. will be : a) (a) 60 ml (b) 20 ml b) (a) 40 ml (b) 60 ml c) (a) 20 ml (b) 60 ml d) (a) 60 ml (b) 60 ml 107. Which of the following statement(s) is/are correct?

(3 mark)

1) when molecule possesses no symmetry, the number of optical isomers is 2n (where n = number of chiral carbons). n   − 1 

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

.

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

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d) 1, 2, 4

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108. The ratio of the energy of electron in the ground state of hydrogen to the electron in the first excited state of (3 mark) Li2+ 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?

(3 mark)

1) its keto form is more stable than enol form.

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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

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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 is (3 mark) isotopic. O

O

R 1 − C − O18 − H + R 2 − OH → R 1 − C − OR 2 + H 2 O

Which of the following statements is correct : (a) O18 in water (b) O18 is in ester c) O18 is in both d) O18 is in none

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111. Benzene, naphthalene and anthracene are aromatic compounds which become stable through resonance. They have 6 π , 10 π and 14 π electrons respectively. The correct statement(s) regarding the resonance (3 mark) energies 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

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112. Out of CHCL3, SI4 and TeCl4, molecules having regular geometry are : a) CHCl3 only b) CHCl3 and TeCl4

(3 mark)

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c) SI4 only d) SI4 and TeCl4 113. Chlorination of alkanes is carried out in the presence of sunlight while iodination in the presence of strong (3 mark) oxidising 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 : MnO −4 + C2 O24 _ → MnO 2(n) + CO32 _ ,

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In the balanced equation, the number of OH–ions is : a) 4 on the right b) 4 on the left c) 2 on the right d) 2 on the left

(6 mark)

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115. The correct order of reactivity amongst the following compounds towards aromatic electrophilic substitution (3 mark)

I. Chlorobenzene

II. Benzene

III. Aluminium chloride

IV. Toluene

a) I > II > III > IV b) IV > II > I > III c) II > I > III > IV d) 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 being (3 mark) electrolysed by using inert electrodes. The values of standard potentials are :

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Ε°Ni2+ / Ni = −0.25V; Ε°Ag + / Ag = _ 0.80V;

Ε°Mg++ / Mg = −2.37V; Ε°Pb2+ / Pb = −0.13V;

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Ε°H 2 O / H 2 =−0.80V; 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?

(3 mark)

a) –1 -effect of nitro group b) greater resonance effect of p-nitrophenoxy ion c) steric effect of bulky nitro group d) None of these a) 2, 4 b) 2, 3 c) 3, 4 d) 1, 2

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118. I the pressure on an eqm. mixture of the three gases No, Cl2 and NOCl, 2NO(g) + Cl2(g)

(3 mark)

2NOCl(g)

is suddenly decreased by doubling the volume of the reaction vessel at constant temperature, when the system returns to equilibrium : a) The value of Kc will have increased b) The value of Kp will have increased c) The concentration of NOCl will have increased d) The number of moles of Cl2 will have increased

119. Degree of unsaturation in a) 3

PAGE is

(3 mark)

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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 2 3

from the container and after some time, pressure of the gas becomes half and its absolute temperature rd. (6 mark)

The amount of the gas escaped is : a)

2 m 3

b)

1 m 2

c)

1 m 4

d)

1 m 6

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121. Replacement of most of the hydrogens of an alkene (A) by cyano groups forms a very strong acid (B) as (3 mark) shown below NC ‹

CH 3 − CH = CH 2

NC

(A)

CH—C |

CN

C

CN CN

(B)

The sharp increase in acidity in going from A to B is best explained as a) electron withdrawing inductive effect of nitrogen. b) extensive delocalization of the negative charge of the anion resulting from the ionization of B.

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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 the lattice points. The co-ordination number of A atoms, that of B atoms and the fraction of the tetrahedral sites (3 mark) occupied by B atoms are :

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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 isolated and heated with HI in the presence of phosphorous. IdentIy which is the structure that represents the final (3 mark) organic product formed in the reaction? a) CH3 − CH 2 − CH − CH 2 − CH3 | CH 3

CH 3 |

b) CH = CH − CH − CH − CH 2 2 3 c) CH 3 − CHI − CH − CH 2 − CH 3 | CH 3

d) CH 2 = CH − C(1) − CH 2 − CH3

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| CH 3

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

(3 mark)

(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 the reaction : 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

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125. Which of the following is not correctly matched :

(3 mark)

a) Terylene : condensation polymer of terephthalic acid and ethylene glycol b) Perspex : A homopolymer of methyl methacrylate

c) Teflon : Thermally stable cross linked polymer of phenol and formaldehyde

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d) 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 while (6 mark) solute ‘Y’ is 90% trimerised in the solutions. Pick up the correct statement : a) Boiling point of ‘X’O.P. of X c) Freezing point of X
(3 mark)

a) CO2 and alkali under pressure b) CCl4 in alkaline medium c) CHCl3, in alkaline medium followed by oxidation

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d) 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. I (6 mark) Ksp[CaCO3]=5 × 10–9, the [CO32–] in the resulting solution is : a) 0.05 b) 0.1 M

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c) 5 × 10–7 M d) 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.

(3 mark)

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

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

(3 mark)

a) 20 ml of 0.1 M CH3COOH + 40 ml of 0.1 N HCl b) 200 ml of

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N N NaOH + 100 ml of HCl 10 20

c) 100 ml of 0.1 N NaOH + 150 ml of 0.1 N HCN d) 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 this (3 mark) test due to : a) It is isomer of glucose b) It undergoes rearrangement in ammoniacal medium to form reducing sugars c) Both d) 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 (3 mark) 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 :

(3 mark)

1) Ten amino acids are essential

2) They exist as zwitter ion

3) All amino acids are optically active

4) There are 24 natural amino acids known

a) 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 radius 1.2 × 10–4 cm, then the number of gold particles per mm3 of the solution (density of gold 19.3 gm/cm3) is (6 mark) nearly equal to : a) 500 b) 790 c) 980 d) 1380

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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

(3 mark)

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

(3 mark)

(1) the hydration energy of Na2SO4 is higher than that of its lattice energy.

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(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

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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. When another substance D reacts with this solution C also produces the same gas B, D also produces the same gas even on reaction with dilute H2SO4 at room temperature. Element A imparts golden yellow colour to Bunsen (3 mark) flame. Then, A, B, C and D may be identIied as a) Na, H2, NaOH and Zn b) K, H2, KOH and Zn c) K, H2, NaOH and Zn d) Ca, H2, CaCOH2 and Zn

138.

A

organic (Compound )

+ O 2  →X + Y + Z

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Compund (A) in pure form does not give ppt. with AgNO3 solution. A mixture containing 70% of (A) and 30% 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 and (3 mark) produces an acidic solution with water. Compounds (A), (X), (Y) and (Z) respectively will be a) CH4, H2O, CO2, Cl2

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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?

(3 mark)

(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 theory a) 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?

(3 mark)

1) banana bonds are longer but stronger than normal B–H bonds 2) B2H6 is also known as 3c–2e compound 3) 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 ether a) 1, 2, 3 b) 2, 3, 4 c) 1, 2, 4 d) 1, 3, 4

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141. The correct statement(s) about transition elements is/are

(3 mark)

(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

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(4) some transition elements like Ni, Fe, Cr may show zero oxidation state in some of their compounds a) 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 distils over as it is volatile and impurities like Cd, Pd and Fe gets condensed. The crude metal obtained is called (3 mark) spelter, 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 (3 mark)

(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

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144. In the separation of Cu2+ and Cd2+ in II group of basic radicals, tetrammine copper (II) sulphate and tetrammine cadmium (II) sulphate react with KCN to form the corresponding cyano complexes. Which one of the following pairs of the complexes and their relative stability enables the separation of Cu2+ and Cd2+? (3 mark)

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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 passage The dissociation of the diatomic halogen into its atoms, which go on to abstract a hydrogen atom from H2 to form the product molecule. This reaction is most vigorous with fluorine and least vigorous with bromine (a liquid 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. HF is readily formed by reacting sodium flouride with concentrated sulfuric acid, hydrogen chloride is formed in an analogous manner. However. However, concentrate H2SO4 is too strong an oxidizing agent to form HBr and HI form their respective sodium halide salts. Phosphoric acid is a useful substitute here, although the reaction 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 Formula weight (g.mol-1) Bond-Energy (kJ.mol-1) Melting Point 0C) Boiling Point (0C)

PAGE HF

HCI

HBr

HI

20.01

36.46

80.92

127.9

565

431

368

297

-83

-114

-87

-51

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

78

210

-35 234

Table - 1 All the hydrogen halides are extremely water soluble, and all except hydrogen fluoride exhibit the “leveling effect” 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 cubic lattice 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 and chloride ions. Following a general trend for periodic group analogues, the lattice energy of cesium chloride is much smaller than that of sodium chloride due to dIferences in packing efficiency, which is greater for NaCI than 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

58.5

1465

119.0

1398

212.4

1304

NaCI KBr TbI

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145. Water solubility, melting point, and boiling point are directly related to formula weight for HCI, HBr and HI (3 mark) why 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 bonds c) 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?

(3 mark)

a) In their elemental states, both bromine and iodine are too viscous for the reaction to occur.

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b) The formation reactions for HBr and HI are endothermic

c) 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.

(3 mark)

147. For the alkaline metal halides listed below:

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I) Boiling points are inversely related to molecular size. II) The radius of K+ is greater than that of CI-1. a) I only b) I and III only c) II and III only d) 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) b) c) d)

(3 mark)

precipitation combination disproportionation formation

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

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2/3 1/1 3/2 9/4

(3 mark)

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150. According to the passage, which of the following is a viable initiation reaction for the gaseous hydrogen-chlorine reaction to form According to the passage, which of the following is a viable initiation (3 mark) reaction for the gaseous hydrogen-chlorine reaction to form HCI? a) H 2 → 2 H + b) Cl 2 → 2 Cl + c) Cl 2 + H 2 → HCl + H + d) Cl 2 + H + → HCl + Cl +

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