Ai Iitjee Modeltest 03

IIT-JEE Model Test - 03

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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 Question 1 to 6 are based on the following passage An orbiting space shuttle provides a unique environment in which to study Newton’s laws of physics. The shuttle is lifted into orbit by a thrust of 24,000 kN provided by two solid rocket boosters (SRB) and the main engine. After the SRBs detach, the orbital maneuvering system engines put the shuttle into a circular orbit with a typical altitude of 300 km and an orbital velocity of 8 km/s. When final orbit is achieved the engines no longer fire, and the shuttle makes 1.85 x 10-4 revolutions per second. Once the space shuttle is in orbit, unfamiliar physical behavior is observed. For example, the astronauts float and appear to be weightless. However, this does not mean that there is no gravity. Bot the shuttle and the astronauts are in orbit about the Earth, and it is gravity that is keeping them there. The astronauts appear to be weightless because the shuttle and everything in it are in free fall and all are accelerated at the same rate.

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In general, objects revolving about a more massive body need not follow a circular path. Planets revolving around the Sun, for example, move in elliptical orbits. The geometry of a generic ellipse is shown below.

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-a

-c

c

a

-b

Figure -1

The length of the ellipse, known as the major axis, is 2a, and its width is 2b. The points at c and -c are the foci of the ellipse, where c satisfies the relationship.

c = a 2 − b2 Different planets will move in orbits with different values of a and b, but the Sun always occupies one of the foci. The minimum distance between the Sun and a planet is therefore (a-c), while the maximum distance between the two is (a+b). the value of a for different planets are listed in table 1. Planet

a

Mercury Venus Earth Mars Jupiter Satum Uranus Neptune

5.8 x 1010 m 1.1 x 1011 m 1.5 x 10 11 m 2.3 x 1011 m 7.8 x 1011 m 1.4 x 1012 m 2.9 x 1012 m 4.5 x 1012 m

Pluto

5.9 x 1012 m

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 GM s T 2   1/3 2  4π 

The period of a planet, T, is related to the value of a by : a =  Where Ms is the mass of the Sun.

In addition, a planet moving in an elliptical orbit has a total energy that is related to its major axis : E=−

GM s m p 2a

Where E is the total energy (kinetic and potential) of the system, and mp is the mass of the planet. A circular orbit can be treated as a special case where a is the radius. 1.

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Approximately, how long does it take the suttle mentioned in paragraph 1 to circle the Earth once (3 mark) when it is in its final orbit? a) 90 min b) 4 hrs c) 10 hrs

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d) 2 days 2.

(3 mark)

What is the magnitude of the accleration due to gravity g, at the altitude of the shuttle?

a) g = 0 because everything is weightless. b) g = 9.8 m/s2 because g is a constant everythere. c) g = Gme/r2, where G is the gravitational constant, from the shuttle to the center of the Earth. g = Gme/Re2, where G is the gravitational d) Constant, me is the mass of the Earth, and Re is the radius of the Earth. 3.

Why is a space shuttle unable to maintain a circular orbit at an altitude of 1 km above the Earth’s (3 mark) surface once its engines are shut off ? I. The force of gravity is too strong at an altitude of i km to allow a stable circular orbit to exist.

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II. Air resistance would quickly degrade its orbit.

III. The centripetal force is zero once the engines are turned off. a) I only b) II only c) I and II only d) II and III only

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4.

A pendulum clock operates on Earth with a period of 1 s. If the clock is taken on board the shuttle, (3 mark) what will be its new period when in orbit? a) 10-4s b) 1 s c) 1012 s d) Infinity

5.

A comet is revolving around the Sun with an orbit of major axis 2a and a total energy of E1, while a second comet of the same mass follows a circular orbit of radius r and has a total energy of E2. If (3 mark) a = 2r, what is the ratio of the magnitude of E1 to the magnitude of E2? a) 1 : 1 b) 1 : 2 c) 2 : 1 d)

6.

2 :1

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The orientation of an elliptical orbit actually changes over time. The major axis of the Earth’s orbit, for example, rotates by about 100 seconds of arc in each century, with all else remaining the same. Which (3 mark) of the following is a possible explanation for this? a) A centrifugal force exists because the rotating planet is a non-intertial reference frame. b) The gravitational attraction of the Sun provides the centripetal acceleration causing the orbit to rotate. c) Energy is dissipated as a planet moves through space. d) the other planets also exert attractive gravitational pull on one another.

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Questions 7 to 46 are independent Question 7.

Refer to the elevator shown below. The mass of the elevator and everything in it is 1000 kg. The man in the elevator has a mass of 90 kg. The box that he holds has a mass of 10 kg. The floors of the building in which the elevator operates are separated by 5m. The elevator accelerates and decelerates (3 mark) at 1 m/s2, and moves at a maximum velocity of 5 m/s. The scale reads in newtons.

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On a trip from the 1st to the 6th floor, the man wondered if he could throw the box into the air the moment the elevator leaves the 1st floor, and catch it the moment the elevator arrives at the 6th floor. What would the initial vertical velocity of the box have to be in order for this to work? a) 5 m/s b) 10 m/s c) 37 m/s d) 55 m/s

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8.

The problem below is an example of what we consider a challenging problem in mechanics. We provide a comprehensive solution. (6 mark) puck

h r

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Figure 1 : Frictionless track with a circular loop-the-loop.

A small puck of mass m is released from rest a height h above the ground and slides along a frictionless track. The track contains a circular “loop-the-loop” of radius as in Figure1. The angle θ0 relative to the vertical at which the puck loses contact with the track is θ0 and it is a function of the height h, the radius r, the mass m and the gravitational field g. The puck has a chance to fall off at h > r.

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Which of the following statement(s) is/are correct/wrong with respect to the given illustration. h  I. The tracks exerts a normal force N = mg  r − 2 − 3cos θ  and the total radial force is equal to 



− N − mg cos θ .

II. N ≥ 0 and one loses contact with the track at the moment N vanishes. This occurs at an angle θ0   given by cos θ0 = 3  r − 1   2

h

III. If the puck is released from the same height as the top of loop-the-loop θ0 is approximately 48º. IV. For the puck to reach the top of loop-the-loop you must have h ≥ (a) I & IV are wrong (b) II, III & IV are correct (c) I, II & IV are correct (d) All are correct

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5r 2

.

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9.

Rising hoop: Two beads of mass m are positioned at the top of a frictionless hoop of mass M and radius R, which stands vertically on the ground. The beads are given tiny kicks, and they slide down the hoop, one to the right and one to the left, as shown. What is the smallest value of m/M for which the hoop will rise (3 mark) up off the ground at some time during the motion?

m

m

M

(a) >

1 2

(b) >

1 3

(c)

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2 > 3

(d) > 10.

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3 2

A stone of M s and volume V s is inside a boat and the boat (with the stone) is floating in a pool of water (density ρ). The boat along has mass M b and volume V b . If the stone is thrown out from the boat into the pool will the water level in the pool change, and if so in what direction (increase or (3 mark) decrease) ? I) The water level do not change II) The water level in the pool change and it decreases III)The water level in the pool change and it increases IV) Mass densities of water, store one very important in conclusion.

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Which of the above given statements are correct ? a) I only b) II & IV only c) III & IV only d) I & IV

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11.

A boat with a man is moving near a dock. At a certain instant the boat is connected to a fixed point A on the shore by a rope. Initially the length of rope between the boat and point A is l1=25m and the boat has velocity v1=5m/s perpendicular to the rope. The man in the boat pulls the rope with a constant force F=500N to draw the boat near the dock. The boat and the man have a combined mass M=200kg. At the moment the length of the rope between the boat and point A is l2=20m, find the speed of the (3 mark) boat. a)

45 m / s

b)

50 m / s

c)

90 m / s

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d) none of these

12.

(3 mark)

Three charges 1.00µC , 2.00µC and 3.00µC are arranged as shown in the fig.

www.aieeepage.com 3.5 cm 4.5 cm 1.0µC

O

3.0µC

2.5 cm 2.0µC

1) Total number of electric field lines that leave a sphere centered at the origin and having a radius 2.00 cm is 0.0 Nm2C–1 2) Total number of electric field lines that leave a sphere centered at the origin and having a radius 3.00 cm is 2.2 ×105 Nm2C −1 3) Total number of electric field lines that leave a sphere centered at the origin and having a radius 4.00 cm is 3.3 ×105 Nm2C −1 4) Total number of electric field lines that leave a sphere centered at the origin and having a radius

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5.00 cm is 0.0 Nm2C −1 . Which of the above statement(s) are correct ? a) 1,2,3,4 b) 1, 2, 3 c) 1, 2, 4 d) None

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13.

The average life time of an excited state of hydrogen is of the order of 10–8 sec. How many times an electron makes when it is in state n=2 before it falls to the ground state? Given Bohr radius = 5.3 × 10−11 m, (3 mark)

velocity of electron in ground state v1 = 2.19 ×106 m/s . a) 3×106 b) 5 × 106 c) 8 × 106 d) 9 × 106 14.

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A man puts springs on the bottoms of his shoes and jumps off a 10 m cliff. Assuming the springs follow Hooke’s law, from the moment the springs touch the ground to when they are fully compressed, (3 mark) the magnitude of the man’s acceleration will: a) decrease then increase

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b) increase then decrease c) remain constant at 10 m/s

2

d) remain constant of zero 15.

A block of mass M1 with a circular cut of radius R is at rest on a frictionless surface. A smaller mass, M2 is released from rest at the top of the cut and slides without friction along the circular surface. As it slides, momentum is imparted to the block and it starts moving to the left. The speeds v1 and v2 of the block and the small mass just as M2 leaves the block. (6 mark)

initial

M2

final v1

M1

a) V1 = M 2

(c) V1 =

M1

M2 v2

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2 gR 2 gR 2 gR 2 gR ; V2 = M1 ; V2 = M1 (b) V1 = M 2 M1 ( M1 + M 2 ) M 2 ( M1 + M 2 ) M1 + M 2 M1 + M 2

2 gR M 22 ; V2 = M1 ( M1 + M 2 )

2 gR M1 M1 + M 2

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16.

In Thomson’s experiment, if the velocity of electron is greater than the ratio of electric field (E) and (3 mark) magnetic field (i.e.v > E/B), then I) the electron will move to the undeflected spot II) the electron will not reach the undeflected spot III)the electron will move to a spot above the undeflected position IV)the electron will move to a spot below the undeflected position Which of the above statement are correct a) I & III only

17.

b) II & IV only

c) III & IV only

d) I & IV only

A cylinder of radius r and thermal conductivity K1 is surrounded by a cylindrical shell of inner radius r and outer radius 2r, whose thermal conductivity is K2. There is no loss of heat across cylindrical surfaces, when the ends of the combined system are maintained at temps T1 and T2. The effective (3 mark) thermal conductivity of the system, in the steady state is

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K1 K 2

a) K + K 1 2

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b) K1 + K 2 c)

K1 + 3K 2 4

d) 3K1 + K 2 4

18.

Below are four equations expressing relationships between physical quantities. g is a gravitational field strength, r a radius, ρ a density, G the universal constant of gravitation, m a mass and T a time (3 mark) period. Which of the equations is (are) homogeneous. 1) gT 2 = 4πr 2

2)

g =

4 πρG r2 3

3)

g r 2 = Gm

4

4) g = 3 πρ G r

Which of the above statement(s) are correct ? a) 3, 4 b) 1, 2 c) 1, 3 d) none

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19.

Monochromatic light λ =5893 A0 produce fringes in a biprism in the focal plane of eyepiece at a distance 1 metre from slits. A convex lens introduced between biprism and eyepiece gives images of slits in two positions. The respective distance between the images of slits are 4.05 × 10−3 m and 2.9 ×10−3 m . (6 mark) The fringe wide will be a) 1.72 × 10−4 m b) 0.86 ×10−4 m c) 2.2 × 10−4 m d) 1.1× 10−4 m

20.

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Refer to the diagram below. A person dangles a rope and makes small circular motions with his hands. (3 mark) The rope takes on the shape as shown. L is the distance between the first two nodes.

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If increasing the frequency of the revolutions increases the tension in the rope, might the increased tension make it possible to generate the same harmonic at more than one frequency on the same rope? a) No, because a harmonic can have only one frequency for a given medium

(3 mark)

b) No, because greater tension would produce the harmonic at a lower frequency c) Yes, because greater tension would produce the harmonic at a higher frequency d) Yes, because greater tension would produce the harmonic at a lower frequency 21.

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Suppose the potential energy between electron and proton at a distance ‘r’ is given by − Ke2 . 3r 3

Application of Bohr’s theory to hydrogen atom in this case shows that :

(3 mark)

i) energy in nth orbit is proportional to n6

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ii) energy is proportional to m–3 (m: mass of electron) Then : a) both (i) and (ii) are correct c) only (ii) is correct

b) only (i) is correct

d) none are correct

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22.

A thin concavo-convex lens has two surfaces of radii of curvature R and 2R. The material of the lens (3 mark) has a reflective index µ . When kept in air, the focal length of the lens 1) will depend on the direction from which light is incident on it 2) will be the same, irrespective of the direction from which light is incident on it R

2R

3) will be equal to µ − 1

4) will be equal to µ − 1

Which of the above statement (s) are correct ? a) 2, 4 b) 1, 3

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c) 1, 4 d) 2, 3 23.

Three rods of identical cross-sectional area and made from the same metal form the sides of an isosceles triangle ABC right angled at B, Fig.9.56. The points A and B are maintained at temperatures T and 2 T respectively in the steady state. Assuming that only heat conduction takes place, (3 mark) temperature of point C will be

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a) b) c) d)

24.

T 2 −1 T 2 +1 3T 2 +1 T 3 ( 2 − 1)

If we use permitivity ε , resistance R, gravitational constant G and voltage V as fundamental physical (3 mark) quantities, then

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1) [angular displacement] = ε 0 R 0 G 0 V 0

3) [velocity] = ε –1R –1G 0 V 0

2) [dipole moment] = ε1R 0 G 0 V1

4) [force] = ε1R 0 G 0 V 2

Which of the above statement(s) are correct ? a) 1, 2, 4 b) 1, 2, 3

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c) 1, 2 d) 2, 3

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25.

r

An object of mass m is moving with velocity u towards a plane mirror kept on a stand as shown in the figure. The mass of the mirror and stand system is m. A head-on elastic collision takes place between (3 mark) the object and the mirror stand, the velocity of image before and after the collision is

r

r

a) u , 2 u r

r

b) – u , –2 u r

r

c) – u , 2 u r

r

d) u , 2 u

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26. As a hot air ballon rises into the atmosphere its volume does not change. It is opened at the bottom to allow air exchange with the atmosphere. Ignoring the weight of the ballon and the undercarriage, (3 mark) which of the following will stop a hot air balloon from rising? a) the pressure inside the balloon is equal to the pressure of the surrounding atmosphere b) the volume inside the balloon is equal to the volume of the surrounding atmosphere displaced by the balloon c) the temperature inside the balloon is equal to the temperature of the surrounding atmosphere d) the number of moles of air inside the balloon is equal to the number of moles of air in the surrounding atmosphere 27.

A pure radioactive material has a half-life of 109 years, and a sample of it undergoes 10,000 decays per second.

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The result of this decay is another element that is itself radioactive with a half-life of 2 days. The result of this decay is still another element that is radioactive with a half-life of 5 years, finally decaying to something stable. After one month and After 100 years about how many decays per second are occuring in this sample? (a) none of these (b) 5,000, 7,500

(3 mark)

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(c) 10,000, 15,000 (d) 20,000, 30,000

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28.

The conductor ABCDE has the shape shown in below figure. It lies in the yz plane, with A and E on the y-axis. When it moves with a velocity u in a magnetic field B, an emf e is induced between A and (3 mark) E Z B a

E

C

A

O

a

Y

D X

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1) e = 0, if v is in y-direction and B is in the x-direction

2) e = 2B a v, if v is in the y-direction and B is in x-direction 3) e = B λ v, if v is in z-direction and B is in x-direction

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4) e = B λ v, if v is in x-direction and B is in z-direction Which of above statement(s) are correct ? a) 1, 3, 4 b) 1, 2, 3 c) 1, 2 d) 1, 4 29.

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

(3 mark)

I) A thin uniform circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with an angular velocity ω . Another disc of the same dimensions but of mass M/4 is placed gently on the first disc coaxially. The angular velocity of the system now is 2ω / 5 . II) In a photoelectric emission process the maximum energy of the photo-electrons increases with increasing intensity of the incident light. 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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30.

A thick plate is made of a transparent material whose refractive index changes from n1 on its upper (3 mark) edge to n2 on its lower edge. A ray of light from a medium with refractive index n. 1) Angle at which the ray of light leaves the plate depends on the angle of incidence and refractive indices of the media on both sides of the plate. 2) Angle at which the ray of light leaves the plate depends on the angle of incidence and variation of refractive index of the medium inside the plate. 3) The angle θ at which the ray of light is incident to the vertical is related to the refractive index ‘n’ at any point in the plate by the relation n sin θ =constant. 4) If the refractive index reaches a value n = n0 sin α at any where inside the plate, then total internal reflection will take place inside the plate.

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Which of the above statement (s) are correct ? a) 1, 3, 4 b) 1, 2, 3 c) 1, 2, 4 d) none 31.

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At constant volume, the molor heat capacity of oxhydrogen gas (mechanical mixture of hydrogen and oxygen) is greater than that of water produced by chemical combination by n. The value of n is (3 mark)

a) 5/6 b) 2/3 c) 1/6 d) 1/3 32.

Which of the following is required in order for momentum to be conserved in a system of objects that (3 mark) collide? (a) Unbalanced forces act only between the objects in the system (b) Two or fewer objects are in the system

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(c) Contact time between the objects in the system is very short (d) Objects in the system are elastic

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33.

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

(3 mark)

I) A conducting rod AB moves parallel to the x-axis 9see fig.) in a uniform magnetic field pointing in the positive z-direction. The end A of the rod get positively charged. y B V A

PAGE 0

x

II) A simple pendulum with a bob of mass m swings with an angular amplitude of 40º. When its angular displacement is 20º, the tension in the string is greater than mg cos 20º. a) only I is correct

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b) only II is correct c) both I and II are correct d) both I and II are wrong 34.

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

(3 mark)

I) A projectile fired from the ground follows a parabolic path. The speed of the projectile is minimum at the top of its path. II) A plane wave of sound travelling in air is incident upon a plane water surface. The angle of incidence is 60º. Assuming snell’s law to be valid for sound waves, it follows that the sound wave will be refracted into water away from the normal. 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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35.

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

(3 mark)

I) A source of sound with frequency 256 Hz is moving with a velocity V towards a wall and an observer is stationary between the source and the wall. When the observer is between the source and the wall he will hear beats. II) Electron in a conductor have no motion in the absence of a potential difference across it. a) only I is correct b) only II is correct c) both I and II are correct d) both I and II are wrong 36.

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A spherical drop of mercury with charge 8Q splits into eight identical spherical droplets, each with the same charge and radius. The electrical energy, in joule, of a conducting sphere with radius r and charge q is (4.5 ×109 )

q2 . After the droplets are separated far apart so that they no longer interact, the r

percentage of the electrical energy that has been converted to other forms of energy is a) 12.5%

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(3 mark)

b) 25% c) 50% d) 75% 37.

A spherical iron ball of radius r is placed on a large block of dry ice at 0ºC. The ball sinks into the ice until it is half submerged. What was the temperature of iron ball if the density of iron is ρ , the specific (3 mark) heat of iron is s, density of ice is ρ ´ and later heat of fusion of ice is L? ρ´L

a) θ = 2ρs ρL

b) θ = 2ρ´s ρ´L

c) θ = ρs

2ρ´L

d) θ = ρs

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38.

Common fluorescent light bulbs consist of glass tubes containing low-pressure mercury vapor. Electrodes at each end allow current to flow, which converts the mercury vapor to a plasma. The plasma can reach temperatures of 104K. Which of the following best explains why the fluorescent (3 mark) bulb feels cool to the touch? (a) The light emitted is in the visible range, so little is infrared radiation. (b) The plasma exists for a short time, so the heat is quickly dissipated. (c) The pressure in the bulb is low, so heat is not conducted to the glass. (d) The density of the plasma is low, so the amount of heat is small.

39.

(6 mark)

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

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I) A beam of white light passing through a hollow prism give no spectrum. II) A ring of mass 0.3 kg and radius 0.1 m and a solid cylinder of mass 0.4 kg and of the same radius are given the same kinetic energy and released simultaneously on a flat horizontal surface such that they begin to roll as soon as released towards a wall which is at the same distance from the ring and they begin to roll as soon as released towards a wall which is at the same distance from the ring and the cylinder. The rolling friction in both cases is negligible. The cylinder will reach the wall first.

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a) only I is correct b) only II is correct c) both I and II are correct d) both I and II are wrong 40.

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

(3 mark)

I) Water in a closed tube (see Fig) is heated with one arm vertically placed above a lamp. Water will begin to circulate along the tube in counter-clockwise direction.

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II) Two identical metallic spheres of exactly equal masses are talen. One is given a positive charge Q coulombs and the other an equal negative charge. Their masses after charging are different. 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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41.

A long solenoid of cross - sectional radius 5 cm is wound with 10 turns per centimetre. It is placed in the middle of a closely wrapped coil of 5 turns and radius 10 cm along its axis. The electric field induced in the coil when the current through the solenoid is decreasing at the rate of 0.2A/s, is (6 mark)

a) 10–7V/m b) 2 × 10–7V/m c) zero d) 4 × 10–7V/m 42.

A block of ice with mass m=10.2kg is moved back and forth over the flat top horizontal surface of a large block of ice. Both blocks are at 0ºC and the force that produces the back and forth motion acts horizontally. The co-efficient of kinetic friction (wet ice on ice) is µ =0.06. The total distance travelled by the upper block relative to the supporting block to produce 18gm of water is nearly equal (3 mark) to

PAGE

a) 10km b) 0.1km

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c) 0.5km d) 1km 43.

Use the diagram below to answer the question that follows. v1

The diagram shows a wave pulse with velocity v1 travelling in a light string attached to a heavy string. Which of the following best represents the shape of the string after the pulse has passed the boundary (3 mark) between the two strings? v1

v2

(a)

(b)

v2

v2

PAGE v1

(c)

v2

(d)

v1

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44.

A tennis ball with (small) mass m2 sits on top of a basketball with (large) mass m1. The bottom of the basketball is a height h above the ground, and the bottom of the tennis ball is height h+d above the (3 mark) ground. The balls are dropped. To what height does the tennis ball bounce?

h

(a) d + 3h (c) d + 9h

PAGE (b) d + 6h

(d) d + 18h

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Note: Work in the approximation where m1 is much larger than m2, and assume that the balls bounce elastically. 45.

A charge q is uniformly distributed on a hollow sphere of radius R. It is rotated with an angular speed about an axis pasing through the centre of mass of the hollow sphere. The magnetic moment of the (3 mark) hollow sphere is a)

q 2 R ω 5

b)

q 2 R ω 4

c)

q 2 R ω 3

d) qR 2 ω 46.

PAGE

On a day when the velocity of sound in air is v, a whistle moves with velocity u towards a stationary wall. The whistle emits sound with frequency f. The frequency of reflected sound heard by an (3 mark) observer travelling along the whistle will be v−u

  a) f  v + u   

c) f

b)

 v  f   v−u 

www.aieeepage.com  v+u  d)

f   v−u 

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Question 47 to 50 are based on the following passage .

Refer to the diagram shown below. When an instrument plays a note, the resulting sound is a combination of all the possible harmonics for that instrument in its momentary configuration. For instance, a musician changes notes on a violin by pressing the strings against the neck of the instrument, thus shortening the string length and changing the possible harmonics. A given shortened string will play at one time all the possible harmonics allowable by its string length. A given note is the same set of harmonics for all instruments. The diagram below shows the sound waves of the same note played by three different instruments.

Flute

PAGE

Oboe

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Saxophone

47.

Which of the following explains why a human can distinguish between the sound waves of the same (3 mark) note played by different instruments? a) The frequency is different for each instrument b) The wavelength is different for each instrument c) The relative intensities of each harmonic vary differently for the same instrument d) The relative wavelengths of each harmonic vary differently for each instrument

48.

How does the period of the first harmonic for the note played by the flute compare with the period of (3 mark) the wave form shown?

PAGE

a) The period for the first harmonic is half as great b) The period for the first harmonic is the same

c) The period for the first harmonic is twice as great

d) The period for the first harmonic is four times as great

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49.

How does the period of the second harmonic for the note played by the oboe compare with the period (3 mark) of the wave form shown? a) The period for the second harmonic is half as great b) The period for the second harmonic is the same c) The period for the second harmonic is twice as great d) The period for the second harmonic is four times as great

50.

How does the period of the third harmonic for the note played by the oboe compare with the period of (3 mark) the wave form shown?

PAGE

a) The period for the third harmonic is one fourth as great b) The period for the third harmonic is one third as great c) The period for the third harmonic is half as great d) The period for the third harmonic is the same

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Paper - I I : Mathematics - 51 to 100 Questions 51 - 55 are based on the following passage Let f : x − y be a bijective function. We define a function. g : y → x such that

(I)

f ( x) = y ⇔ g ( y ) = x, x ∈ X , y ∈ Y then g is called inverse of f & is denoted by f –1.

51.

If [x] denotes the integral part of x, then the domain of f ( x) = cos−1 ( x + [ x]) is

(3 mark)

(a) (0, 1)

PAGE

(b) [0, 1) (c) [0, 1] (d) [–1, 1]

52.

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(3 mark)

If f ( x) = 2 cos2 x + 3 sin 2 x + 1 then f −1 ( x) is 1

−1

1

−1

(a) 2 sin  (b) 2 sin  −1 (c) sin

x −2 π 1  −1 x − 2 π  −  or −  cos 2 6 2  2 3 x −2 π 1  −1 x − 2 −  or + cos 2 3 2  2

x−2 π − 2 3

or cos −1

π 6 

x−2 π + 2 6

(d) does not exist

53.

 x2 + 1 

Range of sin −1  2  is x +2 



π

(a) 0, 2    π

  (b) 0, 6   

(c)  π 6 , π 2

(3 mark)



)

(d) none of these

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54.

The inverst of

 x,  f ( x) =  x 2 ,  8 x ,

  x,  −1 (a) f ( x) =  x ,  2 x ,  64

  x,  −1 (b) f ( x) =  x , x  , 8

x <1

(3 mark)

1≤ x ≤ 4 x>4

x <1 1 ≤ x ≤ 16 x > 16

PAGE

x <1 1≤ x ≤ 4

1  , x 1 −1 (c) f ( x) =  2 , x  8 ,   x

x>8

www.aieeepage.com x <1 1≤ x ≤ 4 x>4

(d) does not exist

55.

Let g :[1,3] → Y be a function defined as g ( x) = log( x 2 + 3x + 1) then g −1 ( x) is

(3 mark)

x (a) −3 ± 5 + 4e

2

x (b) −3 + 5 + 4e

2

x (c) −3 − 5 + 4e

2

(d) does not exist

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Questions 56 - 93 are independent questions

56.

The common roots of the equation z 3 + 2 z 2 + 2 z + 1 = 0 and z1985 + z100 + 1 = 0 are

(3 mark)

a) 1, ω b) 1, ω 2 c) ω , ω 2 d) none of these

57.

PAGE

If 3 cos x − sin x ≥ 2,0 ≤ x ≤ 2π , then the solution set for x is π

19π

    a) 0, 12  ∪  12 , 2π      π



(3 mark)

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b) 0, 12    π

5π

    c) 0, 4  ∪  4 , π      7π d)  , 2π   4

58.



Vijay wishes to call a friend from a public phone booth which accepts only one-rupee coins. Vijay can remember all the digits except the last digit of his friend’s number. He has 2 one-rupee coins in his pocket. He selects the last digit at random. If he gets a wrong number, he again selects the last digit at random from among the unused digits. The probability that he dials the correct number before (3 mark) running out of one-rupee coins is a)

2 10

b)

8 9

c)

9 90

d)

3 90

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59.

The position vectors of the vertices of a ∆ ABC are a, b, c . Then the position vector of the circumcentre (3 mark) of the triangle is a)

Σ a sin 2 A Σ sin 2 A Σ a sin A

b) Σ sin 2 A

60.

c)

Σ a sin A Σ sin A

d)

Σa 3

PAGE

Let A = {1, 2,3} and B = {a, b, c} . If f is a function from A to B and g is a one-one function from A to B then the maximum (3 mark) number of definitions of

I) f is 9

II) g is 9

www.aieeepage.com III) f is 27

IV)g is 6

Which of the above statement(s) are correct ? a) I & II b) II & III c) III & IV d) I & IV

61.

If log10 x + log10 y ≥ 2 , then the smallest possible value of x+y is

(3 mark)

a) 10 b) 30 c) 20 d) none of these 62.

PAGE

The locus of the point of intersection of tangents to the parabola y 2 = 4( x + 1) and y 2 = 8( x + 2) which (3 mark) are perpendicular to each other is a) x = −3 b) x + 7 = 0 c) x = 3

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d) x − y = 3

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63.

If the fourth term in the expansion of 

 1  1    log x +1   12 +x   x    

I) 10

2

II) 10

6

is equal to 200 and x > 1, then x is equal to

(3 mark)

III) 104

IV)none of these

Which of the above statement(s) are correct ? a) I & II b) II & III c) III & IV d) I & IV 64.

PAGE

The circle with its centre at the focus of the parabola x2=4by and touching its directrix intersects the (3 mark) parabola at a) (± 2b, b)

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b) (± b, b) c) (2 3b, − 3b) d) (0, 0)

65.

 

Let R = {( x, y): x, y ∈ , x 2 + y 2 ≤ 25} R ' = ( x, y ): x, y ∈ , y ≥

4 2 x  then 9 

I) dom R ∩ R ' = [−3,3]

II) Range R ∩ R ' ⊃ [0, 4]

III) Range R ∩ R ' = [0, 5]

IV) R ∩ R ' defines a function

(3 mark)

Which of the above statement(s) are correct ? a) I, II, III b) II, III, IV c) III, II d) IV, III, I

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66.

In a sequence of (4n+1) terms, the first (2n+1) terms are in A.P. whose common difference is 2 and the (3 mark) last (2n+1) terms are in G.P. whose common ratio is 0.5. If the middle terms of the A.P. and G.P. are equal, then the middle term of the sequence is a)

b)

n ⋅ 2n +1 2n − 1

n ⋅ 2n +1 22 n − 1

c) n ⋅ 2n d) none of these

67.

PAGE

(3 mark)

C is the centre of the ellipse 9 x 2 + 16 y 2 − 54 x − 128 y + 193 = 0 and A and B are two points on the ellipse such that ACB = 90º . Then a)

144 25

b)

25 144

c)

7 12

d)

12 7

1 www.aieeepage.com = = CA CB 1

2

2

(6 mark)

68.

 x

If f ( x) = 

 x

4

2

<1

2

≥ 1

x x

a) 1, –1 b) 1, 0 c) 0, 1 d) 1, does not exist

, then lim x →1

f ( x)

f ( x) are equal to and xlim →−1

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69.

−1 −1 −1 −1 If cos x + cos y = sin y − sin x =

π , then the number of ordered pairs (x, y) is 3

(3 mark)

a) 0 b) 1 c) 2 d) 4

70.

A particle is moving in a straight line such that its distance at any time t is given by S =

I) velocity is max at t =

PAGE

(6 − 2 3) 3

t4 − 2t 3 + 4t 3 + 7 , then 4 (6 mark)

III) acceleration is min at t = 2

III)the distance is min at t = 0. 4

IV) none of these

Which of the above statement(s) are correct ?

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a) I, II, III b) II, III, IV c) IV, II d) IV, III, I 71.

If a denotes the number of permutations of x+2 things taken all at a time, b the number of permutations (3 mark) of x things taken 11 at a time and c the number of permutations of x–11 things taken all at a time such that a = 182 bc. Then the value of x is a) b) c) d)

72.

10 12 15 18

When a right-handed rectangular Cartesian system oxyz is rotated about the z-axis through an angle r π in the counter clockwise direction, it is found that a vector a has components 2 2,3 2 and 4. the 4 components of

r a

PAGE

(3 mark)

in the oxyz system are

a) 5, –1, 4 b) 5, –1, 4 2 c) –1, –5, 4 2

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d) –1, 5, 4

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73.

The family of curves represented by

dy x 2 + x + 1 = dx y 2 + y + 1

and the family represented by

dy y 2 + y + 1 = =0 dx x 2 + x + 1

(3 mark)

a) touch each other b) are orthogonal c) are one and the same d) none of these

x

74.

∫

Let f ( x) = (5 + ⋅ | 1 − † |) dt 0

= 5x+1 Then

if x > 2

PAGE

(3 mark)

if x ≤ 2

a) f ( x) is not continuous at x = 2

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b) f ( x) is not differentiable everywhere except at x = 2 c) f ( x) is differentiable at x = 2 d) f ( x) is differentiable and continuous everywhere

75.

A mirror and a source of light are situated at the origin O and at a point on OX respectively. A ray of light from the source strikes the mirror and is reflected. If the D.R.´s of the normal to the plane are (3 mark) 1 –1 1 then D.C.´s of the reflected ray are a)

1 2 2 , , 3 3 3 1 2 2 , 3 3 3

b) − , 1 3

2 3

1 3

2 2 3 3

c) − , − , −

2 3

d) − , − ,

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76.

The serial number of the term in the expansion of the binomial a

  a  x   a  y   B = exp.  log  1/ c   + exp  log  1/ b   which contain same power of x and y is  x   c  y    b 

77.

a)

a (c − 1) +1 b+c+2

b)

a (c − 1) −1 b+c+2

c)

a (c + 1) b+c+2

d)

a (c − 1) +2 b+c+2

The minimum value of

PAGE

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1   1    π ⋅ x ∈  0,  1 +  1 + n n   sin x   cos x   2

(3 mark)

(3 mark)

a) 1 b) 2 c) (1 + 2n / 2 )2 d) (1 + 2n / 2 ) 78.

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

(6 mark)

I) For real numbers x and y, we write x*y if x–y+ 2 is an irrational number. Then, the relation* is an equivalence relation. II) For every integer n > 1, the inequality (n!) l / n < a) only I is correct b) only II is correct c) both I and II are correct d) both I and II are wrong

n +1 2

holds.

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79.

The solution of the differential equation

dy = cot x cot y dx

where y =

π 4

when x =

π 4

is given by

(3 mark)

a) cos x = 2cosec y b) 2sin x = cos y c) 2sin x = sec y d) cos x = 2 sin y 80.

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

(6 mark)

PAGE

I) Let A, B and C be unit vectors suppost that A. B = A. C =0, and that the angle between B and C is π / 6 . Then A = ±2(B × C) .

II) For complex number z1 = x1 + iy1 and z 2 = x2 + iy 2 , we write z1 ∩ z 2 , if x1 ≤ x2 and y1 ≤ y 2 . Then 1− z

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∩0. for all complex numbers z with 1 ∩ z , we have 1+ z

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

81.

If a, b, c are non-zero numbers and the system

ax + by + (a + c) z = 0 (2b − c) x + by + 2bz = 0 ax + by + az = 0

(3 mark)

has a non-trivial solution, then a,b, c are in a) A.P.] b) G.P. c) H.P. d) none of these

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82.

 x2  = + 2  , y = x − 1 and x = 0 above the x-axis is ([.] denotes the y  The area bounded by the curves   64  (3 mark)

greatest integer function) a) 2 b) 4 c) 3 d) 5 83.

Examine the following statement ( s ) and choose the correct option 2a

I) The value of the integral

(3 mark)

PAGE



f ( x)



∫  {f ( x) + f (2a − x)} dx is equal to a 0

II) The product of any r consecutive natural numbers is always divisible by r!. a) only I is correct b) only II is correct

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c) both I and II are correct d) both I and II are wrong

84.

If f ( x) = bx 2 + cx + d and if f ( x + 1) − f ( x) is identically equal to 8x + 3, then the roots of the equation (3 mark)

x 2 + bx + c = 0 are

a) imaginary b) real and equal c) irrational d) rational 85.

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

(3 mark)

PAGE

I) If x − r is a factor of the polynomial f ( x) = an x4 + .... + a0 , repeated m times (1 < m ≤ n) , then r is a root of f ' ( x) = 0 repeated m times.

II) If tan A=(1–cosB) sin B, then tan 2A=tan B. a) only I is correct b) only II is correct

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c) both I and II are correct d) both I and II are wrong

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86.

A box contains n pairs of shoes and 2r shoes are selected. (r < n). The probability that there is exactly (3 mark) one pair is n −1

Cr −1

2n

C2 r

a)

b)

n ⋅n −1 Cr −1 2n

C2 r

n −1 r −1 c) ( n ⋅ 2nCr −1 ) 2

C2 r

d) none of these

87.

The value of the integral

PAGE

where [ . ] denotes the greatest integer function is    πx    (6 mark)  x 1 + cos    + 1  dx 2        −2 1

∫

a) 0

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b) 1 c) 2 d) 3 88.

Examine the following statement ( s ) and choose the correct option (3 mark)

I) The derivative of an even function is always an odd function.

II) The straight line 5x + 4 y = 0 passes through the point of intersection of the straight lines x + 2 y − 10 = 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 89.

PAGE

The line x + 3 y − 2 = 0 bisects the angle between a pair of straight lines of which one has the equation x − 7t + 5 = 0 . The equation of the other line is a) 3x + 3 y − 1 = 0 b) x − 3 y + 2 = 0 c) 5x + 5 y − 3 = 0

(3 mark)

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d) 5x + 5 y + 3 = 0

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90.

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

(3 mark)

Lt g (x) exist. I) If Lt [ f ( x) g ( x)] exists then both and Lt f (x) and x→ a x→ a x→ a

II) No tangent can be drawn from the point (5/2,1) to the circumcircle of the triangle with vertices (1, 3 ) (1,− 3 ), (3,− 3 ) .

a) only I is correct b) only II is correct c) both I and II are correct d) both I and II are wrong 91.

PAGE

The largest interval in which x12 − x9 + x 4 − x + 1 > 0 is a) − 4 < x ≤ 10 b) 0 < x < 1 c) −100 < x < 100

(3 mark)

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d) − ∞ < x < ∞ 92.

Rolle’s Theorem cannot be applied to the function f(x) = |x| in the interval [–1,1] because a) f(x) is not continuous at x = – b) f(x) is not continuous at x =

(3 mark)

1 2

1 2

c) f(x) is not continuous at x = 0 d) f(x) is not differentiable at x = 0 93.

π  π 2 2 If f ( x) = sin x + sin  x + 3  + cos x cos  x + 3  and g    

5 =   = 1 , the ( gof ) ( x) is equal to 4

(3 mark)

PAGE

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

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Questions 94 - 95 are based on the following passage f ( x, y ) = x 2 + y 2 + 2 xy

g ( x, y ) = x 2 + y 2 − 2 xy

h ( x, y ) = x + y

94.

(3 mark)

Which of the following statements is true? a) f ( x, y ) + g ( x, y ) ≥ 2h( x, y ) for all x ∈ R, y ∈ R b) f ( x, y ) + g ( x, y ) ≤ 2h( x, y ) for all x ≤ 1, y ≤ 1

PAGE

c) f ( x, y ) + g ( x, y ) ≤ 2h( x, y ) for all 0 ≤ x ≤ 1, 0 ≤ y ≤ 1

d) f ( x, y) + g ( x, y) ≤ 2h( x, y) for all 0 ≤ x ≤ 1, 0 ≤ y ≤ 1 95.

(3 mark)

Which of the following is not true?

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a) g ( x, y ) = f (− x, y ) for all x ∈ [3, − 2] b) f ( x, y ) = g (− x, y ) for all x ∈ [3, − 2]

c) f ( x, y ) ≤ g ( x, y ) for all x ≥ 0, y ≥ 0 d) none of these

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Questions 96 to 100 are based on the following passage (II)A system of circles is said to be coaxal when every pair of the circles has the same radical axis. It follows from this definition that 1. The centres of all circles of a coaxal system lie in one straight line, which is ⊥ r to common radical axis. 2. Circles passing through two fixed points form a coaxal system with the line joining points as common radical axis. 3. The equation to a coaxal system of which two members are S1 = 0, S2 = 0 is S1 + λS2 = 0 , λ is a parameter. If line of centres is X-axis, radical axis as Y-axis then the simplest form of equation of coaxal

PAGE

circles is x 2 + y 2 + 2 gx + C = O , Where C is fixed & g is parameter.

Radius of this circle is g 2 − C , if g 2 − C = 0 i.e., g = ± C then centre is ( C , O) , (− C , O) which are called limiting points (obtained by equating radius to ‘O’) 96.

Limiting points exist when (a) C < O

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(3 mark)

(b) C < g (c) C > g (d) C ≥ O 97.

For the circle x 2 + y 2 + 2 x − 3 y − 4 + λ( x + y − 1) = 0 , radical axis is

(3 mark)

(a) x + y − 1 = 0 (b) x − y + 1 = 0 (c) 2 x − 3 y − 4 = 0 (d) 2 x − 2 y + 5 = 0 98.

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The equation of line of centres for Question (2) is (a) x + y − 1 = 0 (b) x − y + 1 = 0 (c) 2x −2y +5 = 0 (d) 2x −2y +3 = 0

(3 mark)

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99.

From points P&Q on radical axis of a circle belonging to coaxal system Tgts.. are drawn with lengths (3 mark) α & β then (a) α < β (b) α > β (c) α = β (d) nothing can be said

100. If limiting points exist for circles belonging to a coaxal system represented by x 2 + y 2 + 2 gx + c = 0 , then how many circles belonging to the same system exists b/w − C and C . (a) O (b) infinite (c) finite (d) nothing can be said

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(3 mark)

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Paper - I I I : Chemistry - 101 to 150 Questions 101 to 105 are based on the following passage Quantm mechanics is the study of matter and radiantion at the atomic level. Four atomic models have been proposed over the last century. A British scientist conducted experiments with cathode ray emissions in the presence of electric and magnetic fields. Based on this data he devised the “PlumPudding Model” of the ato, where electrons and protons are uniformly distributed throughout the atom.

PAGE Figure 1

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Next, a New zealand scientist revised the “Plum-pudding Model” and put forth the “Planetary Model” of the atom. The “Planetary Model” was developed as a result of experiments where alphaparticles (helium particles) are collimated by a lead box as they accelerate towards a thin gold foil. The scientist then measured the angles of deflection, as detected by a fluorescent zinc sulphide film. They majority of alpha particles were deflected through small angles, but a much smaller fraction were scattered through larger angles, including back scattered through 180 degrees. Scattered particles

Most particles are undeflected

Beam of particles

Source of

Thin gold foil

Circular fluorescent screen

α particles

n=

16C( Z 2 ) N (K 2 ) (sin θ) 4

PAGE

....Equation (1)

“n” represents the number of particles deflected at eh particular angle F. K represents the kinetic energy of the alpha-particles. C is a constant value that depends on the strength of the alpha-particle source and the geometry of the particle detector. N is the numebr of nuclei per unit area of the foil. Z is the atomic number of the gold atom) The third model of the atom was the Bohr atom, built on spectroscopic data. Spectroscopic data had noted that an atom could only absorb certain energies,

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being excited to a higher state. Then these electrons would return to thier gound state (low energy state), releasing the exact same amount of energy that they absorbed. The “Bihr Model” differs from the “Planetary Model” by quantifying the energies of electrons orbiting the nucleus in specific orbits. Each orbit possesses a particular amount of energy, based on its distance from the nucleus. n=4

n =3 n=2 n =1

PAGE Line Spectrum

Wavelength

Figure 3 : Planetary Model

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The fourth model of the atom, the “Quantum Model” incorporates the premise that electrons act as both particles and waves. A set of equations describing the wave functions of the electrons was derived. As a result, the “Quantum Model” redefines electron “orbits” as electron “orbitals”, the area where an electron with a certain amount of energy has the highest probability of being found. Nucleus

2s orbital

2p orbital

3s orbital

1s orbital

PAGE 1s

2s

2p

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101. Which of the following will result in an electron moving to an excited state ?

(3 mark)

I) Heating the atom II) Colliding the electron with another atom or electron III)Bombarding the electron with a photon with energy equal to the exact difference between two orbits of the Bohr Model. Which of the above statement(s) are correct ? a) I only b) II & III only c) I, II, & III d) I & II only

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102. Based on the passage, which of following would the NewZealand scientist be able to conclude ? (3 mark)

a) The backscattered alpha-particles underwent elastic collisions with the nucleus of the gold atoms. b) The backscattered alpha-particles underwent inelastic collisions with the nucleus of the gold atoms.

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c) The backscattered alpha-particles underwent elastic collisions with the orbiting electros of the gold atoms d) The backscattered alpha-particles underwent inelastic collisions with the orbiting electrons of the gold atoms. 103. The Bohr Model was a response to the drawbacks in the Planetary Model”. Which of the following (3 mark) is a drawback of the “Planetary Model”? a) The electrons of the Planetary Model have no electrical potential energy. b) The electrons of the Planetary Model would gain electrical potential energy and spiral into the nucleus. c) The electrons of the Planetary Model would lose electrical potential energy and spiral into the nucleus. d) The electrons of the Bohr Model would lose electrical potential energy and spiral into the nucleus.

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104. At which of the following angles would the New Zealand scientist expect the greatest # of scattered (3 mark) alpha particles? a) 1 b) 45

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c) 60 d) 90

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105. According to the Quantum Model, how many electrons can be held in the principal quantum numebr (3 mark) n=4? a) 8 b) 16 c) 18 d) 32 Questions 106 to 145 are independent Question 106. According to LeChatelier’s Principle the addition of heat to the following reaction CO2 ( g ) + 2 H 2O( g ) → CH 4 ( g ) + 2O2 ( g ) will cause it to shift to the right. This reaction can therefore be (3 mark) described as

PAGE

a) spontaneous b) endothermic c) unimolecular

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d) exothermic

107. Amongst

Ni(CO)4 , [Ni(CN)4 ]2–

and

(3 mark)

[Ni(Cl) 4 ]2– :

2– a) Ni(CO)4 and NiCl2– 4 are diamagnetic and [Ni(CN) 4 ] is paramagnetic

b)

[Ni(Cl) 4 ]2–

and

c) Ni(CO)4 and

[Ni(CN)4 ]2– are

[Ni(CN)4 ]2– are

diamagnetic and Ni(CO) 4 is paramagnetic

diamagnetic and [Ni(Cl)4 ]2– is paramagnetic

d) Ni(CO)4 is diamagnetic and [Ni(Cl)4 ]2– and [Ni(CN) 4 ]2– are paramagnetic 108. Why are the intermolecular forces in water ice stronger than the intermolecular forces in dry ice (3 mark) (CO2)? a) Water can exist in the liquid phase at one atmosphere, while carbon dioxide cannot b) Water has a much lower molecular weight than carbon dioxide c) Water is polar, while carbon dioxide is nonpolar d) Water molecules have less kinetic energy than carbon dioxide molecules

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109. Monatomic hydrogen gas is placed in a container of fixed volume, initially at STP. As the temperature is slowly raised, spectral lines corresponding to electrons in energy levels above the ground level appear. No matter how far the temeprature is raised, however, no spectral lines for electrons above the n = 7 level are ever found. Which of the following is a possible explanation for this phenomenon? (3 mark)

a) No elements have electrons in levels above n = 7 b) Energy levels above n = 7 correspond to orbitals so large that the hydrogen atoms would overlap, disrupting the spectal lines c) At the temperatures required to raise electrons to orbitals above n = 7, hydrogen nuclei would decompose d) Beyond n = 7, STP cannot be maintained

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110. Which of the following is a good test for an electrolyte?

(3 mark)

a) Place two leads into the substance, and connect the leads with a resistor. If the substance is an electrolyte, a current will flow. b) Place two leads into the substance, and connect the leads with a battery. If the substance is an electrolyte, a current will flow.

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c) Dissolve the substance in water. Place two leads into the solution, and connect the leads with a resistor. If the substance is an electrolyte, a current will flow. d) Dissolve the substance in water. Place two leads into the solution, and connect the leads with a battery. If the substance is an electrolyte, a current will flow. 111. Which of the compounds below is the product of the following reaction?

CO(CH2)4 CH3

(3 mark)

KOH

?

H2 NNH2

COH(CH2)4 CH3

CO(CH2)3 CH3

PAGE

a)

b)

OC(CH2)4 CH3

(CH2)5 CH3

d) www.aieeepage.com

c)

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112. Which of the following could be used to estimate the value of absolute zero?

(3 mark)

a) Plot pressure vs. temperature values for an ideal gas at constant volume, and extrapolate the resulting line to low temperature. The intercept with the temperature axis is an estimate of absolute zero. b) Plot volume vs. temperature values for an ideal gas at constant pressure, and extrapolate the resulting line to low temperatures. The intercept with the temperature axis is an estimate of absolute zero. c) Allow both volume and pressure to vary, and plot the product of pressure and volume vs. temperature. The intercept with the temperature axis is an estimate of absolute zero. d) All of the above techniques would work.

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113. A student pours 100 ml. of pure water into a 500 ml. beaker. The student adds 10 ml. of Fluid X stirs and allows the mixture to come to equilibrium. The students repeats this process until the beaker is full. If the entire experiment is performed at temperature T1, which of the following describes the (3 mark) system during this experiment?

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a) Initially Fluid X dissolves completely in water to form a single phase. When enough Fluid X is added, a second phase of water dissolved in Fluid X begins to form. As the amount of Fluid X increases, the water from the first phase is dissolved into the Fluid X to form a single phase. b) A two phase system with Fluid X in one phase and water in the other phase remain separate throughout the experiment. c) Initially Fluid X dissolves completely in water to form a single phase. As more Fluid X is added, the Fluid X begins to predominate so that water is dissolved in Fluid X. One phase is maintained throughout. d) Initially Fluid X dissolves completely in water to form a single phase. As the solution nears the critical solution temperature, equal amounts of Fluid X and water form two seperate phases. As the amount of Fluid X increases still further, the water from the first phase is dissolved into the Fluid X to form a single phase. 114. In a 1 M solution of acetic acid (pKa=4.7), the vast majority of the acetic acid is undissociated. Aspartic acid residues in proteins, which have an extremely similar molecular structure to acetic acid, (3 mark) are generally almost completely dissociated. Why?

PAGE

a) In aspartic acid, nearby hydrophobic residues activate the acid.

b) Proteins are generally found in extremely acidic environments, increasing the dissociation of residues such as aspartic acid. c) Proteins contain basic residues stronger than water which deprotonate the aspartic acid. d) The many acidic residues found in a typical protein increase the effective concentration to above1M.

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115. Suppose a student said, “The standard potential of a half-reaction can be used to calculate the equilibrium constant of the half-reaction.” Which of the following statements most accurately (3 mark) characterizes the student’s comment? a) The statement is a consequence of the Nernst equation, and is therefore true. b) The statement is a consequence of the definition of standard potential, and is therefore true. c) The equilibrium constant cannot be calculated unless the conditions under which the standard potential was measured is known. d) It is meaningless to refer to the equilibrium constant of a half-reaction. 116. The rate constant of a chemical reaction is characterized by all of the following except :

(3 mark)

PAGE

a) It is always dependent upon the composition of the reaction mixture. b) It depends exponentially upon the temperature.

c) It is proportional to e − Ea / Rt (where E is the reaction’s activation energy). d) the Eurim equation can be used to calculate it.

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117. Use the following information to answer the following question.

(3 mark)

Using calculus, the rate law for a first order reaction can be transformed to : log[ A]t = − kt / 2.303 + log[ A]0 where [ A]t is the concentration of A at time, t, [ A]0 is the initial concentration of A, and k is the rate constant of the reaction. Methyl isonitrile is converted to acetonitrile in a first order process as follows: CH 3 NC ( g ) → CH 3CN ( g )

c)

Pressure, CH 3NC

Time

Pressure, CH3NC

b)

Time

PAGE d)

Pressure, CH3NC

a)

Pressure, CH3NC

Which of the following graphs best illustrates the partial pressure of methyl isonitrile as the reaction goes forward?

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Time

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118. A pH meter can be thought of as a hydronium concentration cell. The reference half-cell is kept at a pH of 2.0. The other half-cell consists of a platinum probe placed into the sample being tested. If electrons flow from the reference half-cell into the sample, which of the following is true? (The (3 mark) applicable half-reaction is: 2 H + + 2e− → H 2 ) a) The probe is the anode and the sample solution has a pH less than 2.0. b) The probe is the anode and the sample solution has a pH greater than 2.0. c) The probe is the cathode and the sample solution has a pH less than 2.0. d) The probe is the cathode and the sample solution has a pH greater than 2.0.

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119. In formamide the nitrogen has a bond angle of 120º, indicating sp2 hybridization rather than the (3 mark) expected sp3 hybridization. The best explanation for this observation is

O || H–C–NH2

www.aieeepage.com in one of the resonance structures the nitrogen has a double bond. formamide

a)

b) nitrogen always has sp2 hybridization. c) the lone pair of electrons on the nitrogen indicates sp2 hybridization. d) the nitrogen has three atoms attached therefore it must have sp2 hybridization.

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120.

(3 mark)

115 110

Vapor

100

0

T( C)

105

95 90 85

Liquid

80

PAGE 0

.2

(Toluene)

.4

.6

.8

1.0

mole fraction Benzene

(Benzene)

The graph above is a temperature-composition diagram for mixtures of benzene and toluene at 1 atm. pressure. Given a 50 mole % mixture of the two liquids we could obtain a mixture that is 25 mole % benzene by : a) simple distillation b) fractional distillation with two theoretical plates c) fractional distillation with three theoretical plates d) boiling in an open flask until the boiling point reaches 100ºC

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121. For a second order reaction all of the following are true except:

(3 mark)

a) the half life is not independent of the initial concentration. b) the rate can have a first order dependence on each of the two reagents. c) no expression for the variation in the concentrations of the two reagents can be derived. d) a plot of 1/[A]t against t is linear. 122. In considering the reaction: 3NO2 ( g ) + H 2O(l ) → 2 HNO3 (aq) + NO ( g ) student A writes the equilibrium expression as:

K=

[ NO][ HNO3 ]2

true statement?

[ NO2 ]3

while student B writes:

K=

PNO [ HNO3 ]2 [ NO2 ]3

PAGE

. Which of the following is a (3 mark)

a) Student B is incorrect; it is not permissible to mix concentrations and partial pressures in one equilibrium expression. b) Student A is incorrect; gases should always appear as partial pressures in equilibrium expressions.

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c) Both students are correct, and will arrive at the same value of K.

d) Both students are correct, but they will arrive at different values of K.

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123. Paraffin “wax” is composed of solid alkanes. Which of the following alkanes would be the best (3 mark) choice use in the manufacture of paraffin. a) CH4 b) C5H12 c) C4H10 d) C25H52 124. One mole each of A and B and 3 moles each of C and D are taken in a 1L container, If Ke=2.25 for the (6 mark) reaction A+B C+D, the eqm. concentrations of A and C will be in the ration: a) 3 : 2 b) 2 : 3 c) 2 : 1 d) 1 : 2

PAGE

www.aieeepage.com MgO( s ) + CO ( g ) . Experiments carried out

125. In the preparation of MgO, the reaction is MgCI 3 ( s)

2

between 850ºC and 950ºC led to a set of Kp values fitting an empirical equation log K p = 7.310 −

8500 . T

If the reaction is carried out in quiet air, what temperature would be predicted from the equation for (3 mark) the complete decomposition of the MgCO3? a) 890ºC b) 790° c) 990° d) 860°

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126. The amount of chloride in a water supply is determined by titrating the sample against AgNO3 as follows: AgNO3 (aq.) + Cl − (aq.) → AgCl ( s) + NO3− (aq.) What percentage of chloride is present in the water if 26.7 ml of 0.30M AgNO3 is necessary to react with all of the chloride in a 14.0g sample? (Atomic (3 mark) weight Cl=35.5) a)

26.7(.3) (1000) 35.5(14)

b)

26.7(.3) (35.5) (100) 1000(14)

c)

26.7 (35.5) (.3) (1000) (14)

d)

26.7 (14) (.3) (1000) (35.5)

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127. Fuel cells have been created that employ the following reaction to produce energy: 2 H 2 + O2 → 2 H 2O These fuel cells produce a considerable amount of usable energy without creating any pollution, and they require only the plentiful elements hydrogen and oxygen. Oxygen is plentiful in our atmosphere, and hydrogen is readily produced by the electrolysis of water. Based on this description, are fuel cells a viable alternative to other energy sources, such as fossil fuel, nuclear power, or solar power? (3 mark)

a) Yes, because it is a highly exothermic reaction b) Yes, because electrolyzing water to provide hydrogen would require less energy than the fuel cell would produce, since oxygen is so readily available c) No, because the entropy of the reaction is unfavourable d) No, because electrolyzing water to provide hydrogen will require as much energy as the fuel cell would produce 128. Oil of celery is an alkene with the molecular formula C15H24. After hydrogenation with an excess of H2 the molecular formula is C15H28. What can be concluded about the structure of oil of celery?

PAGE

(3 mark)

a) Oil of celery has two double bonds and two rings. b) Oil of celery has four double bonds and no rings.

c) Oil of celery has no double bonds and four rings. d) Nothing can be determined about the structure.

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129. The approx. time required to coat a metal surface of 80 cm2 with 5 × 10–3 cm thick layer of silver (density 10.5 gm/cm3) with a passage of 1.5A current through a silver nitrate solution is: (6 mark) a) 2500 sec. b) 125 sec. c) 115 sec. d) 145 sec. 130. Chloroacetic acid, a monoprotic acid, has a Ka (ionisation constant) of 1.36 × 10−3 . Calculate boiling point of 0.01M aqueous solution Kb (molal elevation constant) = 0.51 mol–1 kg K, b.p. (H2O) = 100ºC. Assume 0.01 molar = 0.01 molal.

PAGE

PLAN : Chloroacetic acid is ionised hence, x can be calculated using Ostwald’s dilution law x=

Ka c

. Thus, i ( = (1+x)) is known, hence ∆ Tb is calculated.

a) 100.007ºC

(3 mark)

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b) 100.005°C c) 100.000°C d) None

131. To convert bromobenzene into methyl benzoate a certain sequence of steps is required. These steps are listed below. Arrange them in the appropriate order and then choose the corresponding response. Note: Each one of the steps may be used once, more than once, or not at all. 1) dry ether

2) excess methanol

3) carbon dioxide

5) magnesium

6) HBr

7) Sodium bicarbonate

(3 mark)

4) mineral acid catalyst

a) 6,1,5,3,5,7,2 b) 1,5,6,6,3,2,4 c) 5,1,6,3,7,2,7 d) 6,5,1,3,2,7,4

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132. In which of the following cases does the internal energy of the desribed system increase? I. A clay ball is dropped and sticks to the ground II. Hydrogen and Oxygen react exothermically to form water III. A car is driven at a constant speed (consider the effect of air resistance) Which of the above statement(s) are correct ? a) II only

(3 mark)

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

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133. Hydroboration and oxidation of an alkene results in an anti-Markovnikov addition of a hydroxyl (3 mark) group. What is the product of the hydroboration and oxidation of 2-isopropyl-2butene? a) 3-isopropyl-2-butanol b) 2-isopropyl-2-butanol c) 2-isopropyl-3-butene d) 2-isopropylbutane

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134. A straight glass tube of length 200 cm has two inlets x and y at the two ends. HCl and NH3 are allowed to enter the tubes through the inlets x and y respectively at the same time. White fumes of NH4Cl (6 mark) appear at a point P inside the tube. The distance of P from the end ‘x’ is: a) 40.57 cm b) 121.71 cm c) 80.95 cm d) 60.85 cm 135. When photons of energy 4.25 eV strike the surface of a metal A, the ejected photoelectrons have maximum kinetic energy, TA (expressed in eV) and de Broglie wavelength λ A . The maximum kinetic energy of photoelectrons liberated from another metal B by photons of energy 4.20 V is TB = TA − 1.503eV . (3 mark) If the de Broglie wavelength of these photoelectrons is λ B = 2λ A , then which is not correct:

PAGE

a) The work function of A is 2.25 eV

b) The work function of B is 3.70 eV c) TA = 2.00 eV d) TB = 2.75eV

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(3 mark)

136. The name of the compound pictured below is: CH3 N

CH3

CH3 CH CH3

a) N, N–methylisopropyl–p–methyl aniline b) p–isopropyl–p–methylaminotoluene c) N, N-dimethyl–p–methylaminotoluene

PAGE

d) p-methylisopropylamine–phenyl methane

137. When heat is added to potassium chlorate, it generally disproportionates into potassium perchlorate and potassium chloride. If manganese dioxide is present during the process, however, the products (3 mark) are potassium chloride and oxygen gas. Which of the following is a possible explanation for these observations?

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a) In the absence of manganese dioxide, the first set of products is more stable than the second. Manganese dioxide is a catalyst that stabilizes the second set of products. b) Although the second set of products are more stable than the first, in the absence of manganese dioxide the second reaction occurs at a negligible rate. Manganese dioxide is a catalyst that in creases the rate of the second reaction. c) Manganese dioxide cannot be a catalyst, since it changes the products of the reaction; it must be actively involved with the second reaction. d) Manganese dioxide cannot be a catalyst, since the presence of a catalyst would affect the reverse reaction as well; it must be a kinetic promoter of the second reaction.

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(3 mark)

138. How does the rate of step I in the mechanism shown below compare to the rate of step II?

Step I

Step II a) Step I is faster than step II. b) Step II is faster than step I.

R | R–C–X | R

Nu

R | R–C + | R R | R–C + | R

+ X

––

R | R–C–Nu | R

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c) Step I and Step II happen at the same rate. d) The relationship cannot be determined.

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139. The surface tension of water is 72.8 dynes cm–1. Calculate the energy required to disperse one spherical drop of radius 3.0 mm into spherical drops of radius 3.0 × 10−3 mm. PLAN : If there are total N smaller drops (r = 3 ×10−3 mm) in one large drop (R = 3.0 mm) then 4 4 π (3 × 10 −3 )3 N = π (3.0)3 . 3 3

(6 mark) Also surface area of one large drop = 4 π R 2 . Total surface area of N smaller

drops = 4 π N r 2 hence, energy required = γ × change in surface area. a) 8.2252 × 10–3 J b) 8.2250 ×10−3 J c) 8.2249 × 10−3 J d) None

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(6 mark) 140. Calculate the energy required to excite one litre of hydrogen gas at 1 atm and 298 K to the first excited –1 state of atomic hydrogen. The energy for the dissociation of H–H bond is 436 kJ mol .

a) 98.17 kJ b) 99.07 kJ c) 88.17 kJ d) 89.07 kJ

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141. In an isolated system this reaction: Zn(s) + 2 H + (aq) place than this reaction Zn(s) + Cu 2+ (aq) possible to conclude this?

H 2 ( g ) + Zn2++ (aq) is much more likely to take (3 mark)

Cu ( s) + Zn2++ (aq) . Which one of the following makes it

a) Third Law of Thermodynamics b) First Law of Thermodynamics c) Dulong and Pett’s Law d) Second Law of Thermodynamics

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(3 mark)

142. An experimenter finds that, at room temperature, exposing solid silver to oxygen gas at a pressure of 1atmosphrere for 1 hour produced no observable reaction. What can be concluded from this? a) The results of the experimenter agree with the graph, since the graph shows silver oxide production being nonspontaneous under standard conditions at room temperature b) The graph is probably in error, since it shows silver oxide production being spontaneous under standard conditions at room temperature

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c) The experimenter probably performed the experiment under nonstandard conditions d) Although the reaction is spontaneous under standard conditions at room temperature, the rate is too low to produce a measurable effect in one hour (3 mark)

143. The iodoform test shown below is used to identify methyl ketones. A positive test gives the yellow crystalline CHI3. Use the equation shown below to answer the question. O || R–C–CH3 + 3I2 + 4OH

O || – R–C–O + CHI3 + 3H2O

Why does the hydroxide substitute for the carbon group only after three iodine ions have added? a) The presence of the iodide atoms forms a much better leaving group. b) Iodide is a good leaving group. c) HI is a strong acid.

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d) Water is a good leaving group.

144. Both carbon-oxygen bonds in formate are 1.26Å compared to 1.20Å for a carbon-oxygen double (3bond mark) and 1.34 Å for a carbon-oxygen single bond. What is the best explanation for this observation?

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a) The negative charge shortens the carbon oxygen single bond.

b) The negative charge lengthens the carbon oxygen double bond. c) The negative charge creates a larger dipole moment.

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d) The actual structure is a combination of two significant resonance structures.

(3 mark)

145. A cell that is described as being “without a liquid junction:” a) cannot exist b) has only one electrode c) has two electrodes in the same electrolyte d) has a flowing g junction modification

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Questions 146 to 150 are independent Question The discovery that silver nanoclusters can exhibit photoactivated fluorescence has potential applications to the electronics industry for data storage and enhanced imagery for photography. Silver nanoclusters are formed from a photoreaction of Ag 2 O on the surface of an extremely thin silver film (~20 nm thick). When the clusters are irradiated with wavelengths shorter than 520 nm, multicolored fluorescence results with silver nanoparticles being activated indidually. After being photoactivated, the particles fluoresce under both blue and green excitation. When the particles are illuminated with blue light, “blinking” intermittent fluorescence results and when irradiated with gree light, the particles emit a brighterred fluorescence.

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As the particles undergo photoactivation, electrons are raised from the singlet ground state, S0 , to the singlet excited state, S1 and energy is absorbed. The particle can undergo vibrational relaxation to its lowest vibrational state in the excited state or ground state. The energy of the excited state may be emitted as fluorescence of equal energy as the absorption process. Conversion to a triplet state (T1 ) of lower energy or return to the ground state via nonradiative internal conversion may also occur.

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S1 excited

internal conversion

vibrational

II.

Fluoresence

I.

absorption

IV.

III.

T1 triplet

Phosphorescence

V S0

grond

vibration relaxation

(3 mark)

146. Which of the following has the lngest wavelength ? a) gama radiation b) infrared radiation c) visible light d) ultraviolet light

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147.

In which fo the following equations is the energy transferred dependent upon the color of light usued to photoactivate the (3 mark) nanocluster ? I. E =

1 mv 2 2

II.

E = hv

III. E = hc / λ

Which of the above statement(s) are correct ? a) I only b) III only c) II and III only d) I, II and III

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148. Which of the processes in Figure I result(s) in a change of energy ? a) I only b) II only c) I, II, V only

(3 mark)

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d) I, II, III, IV, V 149. Which of the followign statements is TRUE regarding the diagram in Figure 1 ?

(3 mark)

a) The absorption of energy from the So state to the S1 state is quantitized b) Fluorescence results from the internal conversion from the S1 state to the So state. c) Phosphorescence results from the internal conversion frm the T1 state to the So state. d) Conversion from the T1 to the So state is called vibrational relaxation. 150. Which of the following processes would emit the photon with the longest wavelength ?

(3 mark)

a) fluorescence b) intersystem crossing c) internal conversion d) phosphorescence

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