Ai Iitjee Modeltest 04

IIT-JEE Model Test - 04

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

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www.aieeepage.com Figure - 1

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

(T / ρ)1/ 2 λ

Equation - 1

Where f is the frequency, T is the tension on the string, p is the linear density of the string, and λ is the wavelength. In wind instruments, though the mechanism of sound production differes from that of the string instruments, the basic principles of a vibrating medium are retained. These instruments use a column of air, open at one, both, or neither end, to propagate a sound wave. Nodes and antinodes are crreated along the length of the column of air. A node exists when some value is maximally restricted from change; whereas an antinode exists where some value can maximally change. For example, a mode of vibration in terms of displacement of air would have a node at a closed end, since air is not free to move there, resulting in no change in displacement, for example a mode in terms of air pressure. Analogously to the string instrument, the wind instrument may have its air column shortened or elongated by a skilled musician, producing specific notes, which are arranged in a specific way to produce music. 1.

a) 77.8 m sec

-1

2.

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It is known that some note D# roughly corresponds to a frequency of 311 sec-1. A musician attempts to play that some note in an octave lower. If the wavelength of the vibrating string is 0.25 m, how fast must the wave be moving to achieve this note? (3 mark) c) 332 m sec www.aieeepage.com

b) 155.5 m sec-1

-1

d) 777.5 m sec-1

Which of the following is true regarding a vibrating string that is fixed at both ends? a) Thefirst harmonic has 1 more displacement node than the third overtone has. b) The third overtone has 2 more displacement antipodes than the fifth harmonic has. c) the fifth harmonic has 3 fewer displacement nodes than eighth overtone has. d) The eighth overtone has 4 fewer displacement antipodes than the thirteenth harmonic has.

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(3 mark)

3.

What is the most likely explanation for using strings of different densities to achieve different sounds, rather (3 mark) thanrelying solely on different string lengths? a) b) c) d)

4.

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

A student suspends a block vertically from a string, and when the string is plucked, it vibrates at some frequency. Which of the following can the student change in order double the frequency of vibration, assuming all other (3 mark) variable remain unchanged? a) have the mass of the string b) double the wavelength c) decrease the length of the string one -fourth isoriginal length

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d) quadruple the mass of the block 5.

A spherical particle is travelling horizontally when it collides with a portion of a vibrating string with both ends fixed. Assuming the string was propagating a horizontal wave, and that this collision is completely inelastic, which (3 mark) set of information allows for the determination of the particle’s velocity before the collision? a) The final velocity of the particle.

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

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c) the length of the portion of string contributing to the collision, the linear density of the string, the mass of the particle, and the final velocity of the particle. d) the linear density of the string, the density of the particle, the volume of the particle, and the final velocity of the particle. Questions 6 to 45 are independent Question 6.

A homogeneous copper disc of mass ‘m’ kg and radius ‘r’ mt is placed with its centre at ‘O’ in a magnetic field of induction B Tesla so that the disc is perpendicular to the magnetic field. When the circuit is closed the disc begins to rotate in t sec acquiring a velocity of ‘n’ revolution per second. The current in the circuit is — (3 mark)

O B

a)

7.

2π n m Bt

b)

+

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πnm Bt

c)

πnm 2 Bt

d)

πnm 2 Bt

In a circular motion of a particle the tangential acceleration of the particle is given by at = 2t

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m . The radius of the s2

circle described is 4m. The particle was initially at rest. Time after which total acceleration of the particle makes (3 mark) 45º with radial acceleration is — a) 1 sec

b) 2 sec

c)

3 sec

d) 4 sec

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8.

Three non-zero vectors will have zero resultant only when

(3 mark)

a) the cross product of resultant of any 2 vectors with third vector is zero b) the dot product of resultant of any two vectors with the third is zero c) all the 3 vectors are collinear d) none of these 9.

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

10.

1 300

b)

1 200

c)

1 600

d)

1 900

The two ends of a uniformly tapered nod are maintained at temperatures 100ºC and 0ºC respectively. Under steady (3 mark) state, the temperature of the section AA’ is —

PAGE L 2

A

100ºC

OºC

www.aieeepage.com L

a) 50ºC 11.

b) > 50ºC

A1

c)

∠ 50ºC

d) none of these

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

U = Ke 2 log r , where K is a constant. Given e– the charge of electron/proton, m = mass of electron then (3 mark)

according to Bohr’s theory its velocity in nth orbit is —

a) 12.

b)

2π

L g

b)

π L

Two waves

b) 1 m

d)

Ke2 m

c)

g

2⋅ L

g

d)

L

g

PAGE c)

0.25 m

(3 mark)

d) 0.125 m

π  y1 = a sin(3.14 x − 50t ) and y2 = a sin  3.14 x + 50t +  superposed, then the first two nodes 3 (3 mark) 

(x > 0) for the standing wave is — a) 0.833 m, 1.833 m 15.

c)

Ke2 nm

Sound waves of frequency 660 Hz fall normally on a perfectly reflcting wall. The shortest distance from the wall at which the air particles vibrate with maximum amplitude is ——— (Given velocity of sound in air = 330 m/s) a) 2 m

14.

nh 2π m r 2

A rope of mass M and length L hangs vertically. The time needed for a pulse to travel from the bottom to the (3 mark) support is —

a) 13.

h 2π m r

www.aieeepage.com c) 0.677 m, 1.677 m

b) 0.415m, 0.930 m

d) 0.1667 m, 1.667 m

A radio active isotope is being produced at a constant rate A. The isotope has a half-life T. After a time l >> T, the (3 mark) member of nuclei become constant. The value of this constant is — a)

AT l n2

b)

AT ⋅ l n 2

c)

A ⋅ l n2 T

d)

AT

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16.

The daughter nucleus in a nuclear decay is itself radioactive. Let λ p and and the daughter nuclei. Also, let N p and

λ d be the decay constant of the parent

N d be the number of parent and daughter nuclei at time ‘t’. Then (3 mark)

condition for which the number of daughter nuclei becomes constant is —

a) 17.

λ p N p > λd N d

b)

λ p N p < λd Nd

λ p N p = λd Nd

c)

d)

λp Np

=

λd Nd

A cubical vesel with non transparent walls is so located that the eye of an observer does not see its bottom but see all of the wall CD. The height of liquid (µ = 13 / 8) should be poured into the vesel for the observer to see an (3 mark) object ‘O’ located at a distance ‘b’ from the corner S is — Q

R

PAGE O

P

b a) 2 18.

S

b

www.aieeepage.com b) b

c)

2b

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

d) 3b

λ , where λ = wavelength of light used. Then 2 (3 mark)

central fringe of fring pattern forms at — Screen S1 S

O S2 D

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a) point O

c) a distance 19.

λD below the point O 2d

λD above the point O 2d

b)

a distance

d)

none of these

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A parallel sided slab has its refractive index variying linearly with the distance from one parallel side, from

µ1 , at

µ 2 , at the opposite side. The slab is placed in a medium of refractive index µ 0 . If a parallel beam mono-chromatic light is incident on the first surface from the outside medium at an angle of incidence α , the angle

the first side to

of emergence from the second face is —

a)

µ1 ⋅α µ2

b)

(3 mark)

µ  sin −1  1 ⋅ sin α   µ2 

c)

µ  sin −1  1 sin α   µ2 

d)

α

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20.

Two lenses A and B are placed at closer seperation as shown. The focal length of combination of these two lenses is f. An opaque screen ‘SS’ is introduced between them as shown, blocking half the space. The resulting focal (3 mark) length of combination in — S

S

a) 21.

f 2

b)

f

c)

d) cannot be determined

A beam of light consisting of two wavelengths 650nm and 520nm is used to obtain interference fringes in Young’s double slit experiment. The distance between slits is 2mm, and between the planes of slits and screen is 120cm. The least distance from the central maximum, where the bright fringes due to both waveleng coincide is — (3 mark) a) 156 mm

22.

2f

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b) 1.56 cm

c)

1.44 cm

d) 144 mn

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

(3 mark)

R www.aieeepage.com R

L

L

a) 23.

L R

b)

4L R

L 2R

c)

d)

3L 4R

Magnetic flux linked with a stationary loop of resistance R varies with respect to time (t) during the time period T as : φ = at (T − t ) , where a is a constant. Calculate the amount of heat generated in the loop during that time. (3 mark) Assume the inductance of the coil as negligible.

aT 3 a) 4R 24.

a 2T 3 b) 4R

c)

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a 2T 3 d) 3R

In a certain polytropic process, the volume argon was increased by 4 times and pressure decreased by 8 times (3 mark) simultaneously. The molar heat capacity of argon in this process is ——(Assume argon to be ideal) a)

4.2J

k − mol

b)

−4.2J

8.4J

c)

k − mol

G

25.

a 3T 3 3R

k − mol

d)

−8.4J

k − mol

G

(4i + 4 j ) m/s. A constant force of −20 Gj N is applied on the www.aieeepage.com

The initial velocity of a particle of mass 2kg is

particle. Initially the particle was at (0, 0). The x-coordinates of the point where its y-coordinate is again zero is — a) 3.2m

b) 6 m

c)

4.8 m

d) 1.2 m

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(3 mark)

26.

A small ball of mass ‘m’ is connected to a wire (AB) and a cord (BC) as shown. If the cord is cut then ratio of tension in supporting wire immediately after the cord is cut to that in the wire before the cord is cut is — (3 mark)

A

B

C

m a) 0 27.

θ

d) sin

2

θ

4 3

b)

3 4

PAGE c)

5 4

d)

4 5

A billiard ball rolls without slipping across a horizontal table and hits a vertical wall. During the impact both the ball and the wall deform elastically. The coefficient of friction of the ball against the wall is µ . If both gravity and rolling friction during impart neglected, the angle to the horizontal at which the ball will rebound from the wall is (3 mark) —

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a) 29.

2

Orbital velocity is a certain orbit (1) is same as the escape velocity from some other orbit (2). The ratio for the amount of energy to be imparted to a satellite in order to transfer it from circular orbit (2) to (1), to gravitational (3 mark) potential energy is orbit (1) will be — a)

28.

c) cos

b) 1

tan −1 µ

b)

1 tan −1   µ

c)

µ tan −1   2

d)

tan −1 (2µ)

A uniform circular disc which rolls without slipping with a velocity ‘v’ encounters an abrupt change in the direction of its motion as it rolls on to the incline ‘ θ ’. The new velocity v1 of the centre of the disc as it start up the (3 mark) incline is —

V

a) 30.

V (1 + 2 cos θ) 3

b)

V (1 − 2 cos θ) 3

PAGE c)

V (sin θ)

d) V cos θ

A particle executes SHM in a straight line. In the first second starting from rest it travels a distance ‘a’ and in the (6 mark) next second a distance ‘b’ in same direction. The amptitude is —

a)

2a 2 3a − b

b)

a2 3a − b

c)

2a − b

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d)

a −b

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31.

Calculate the natural frequency of the oscillation of spring (spring constant = K) loaded with a mass ‘m’ when it is (3 mark) set in motion. Both the springs are identical and are in tension all time.

K

K

m

a) 32.

1 K 2π m

b)

1 2K 2π m

c)

1 K 2π 2 m

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d)

1 2π

m K

Two point charges q1 and q2 are placed at A and B curve drawn represent the distribution of potential due to the (3 mark) charges along the line connecting the charges. The curve indicates that V

V

www.aieeepage.com q1

33.

P

q2

a) charges q1 and q2 are same in nature

b)

charges q1 and q2 are opposite in nature

c) electric field intensity at point P is zero

d)

none of the above

A metallic wire PQR in the shape of a radius ‘a’ slides with constant velocity ‘v’ is a uniform magnetic field of (3 mark) induction ‘B’ as shown resistance ‘R’ is —

P V

R

PAGE Q

a) 34.

π BV a R

b)

BV a R

2BV a R

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d) zero

A cylindrical container of height h and area A, is immersed in water to a depth ho. A small hole of area A2 appears in the bottom of the container. The time in which the container sinks is ——(Neglect atmospheric pressure) (6 mark)

a)

A2 (h = ho) A1 2 gho

b)

A1h A2 2 gho

c)

A1 (h − ho) A2 2 gho

d)

A2

A1 h 2 g (h − ho)

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35.

A uniform elastic plank moves over a smooth horizontal plane due to a constant force F distributed uniformally over the end face. The surface of the end face is equal to A and Young’s modulus of the material to Y. The strain (3 mark) of the plank in the direction of the acting force is — a)

36.

F 3 AY

b)

F 2 AY

c)

F AY

d)

3F 2 AY

A uniformly charged semi circular loop of radius R carries a uniformly distributed positive charge q as shown. The (6 mark) net electric field at the centre of loop is —

+

+ Y

+ + +

X

PAGE +

+

+

a) zero

c) 37.

q along Y axis 4π ε 0 R 2

d)

q along x- axis 2π ε0 R 2

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2q along x - axis π ε0 R 2 2

2

2

Gas at pressure P0 is contained in a vessel of the masses of all the molecules are halved and their speed doubled, the (3 mark) resulting pressure P will be — a) 4 P0

38.

b)

b) 2 P0

c)

P0

d) P0/2 (3 mark)

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

r3

C

V

r2 r1

a) 39.

V (r1 + r2 ) r1 + r2 + r3

b)

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V (r1 + r2 ) r2

c)

V r2 r1 + r2

d)

V r1 r1 + r2

Two wires A and B of the same material, having radii in the ratio 1 : 2 are carrying curents in the ratio 4:1. The ratio (3 mark) of the drift speed of electrons in A and B is — a) 4 : 1

b) 1 : 4

www.aieeepage.com c) 1 : 16

d) 16 : 1

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40.

A cell of emf ε and internal resistance r is connected in series with a variable resistance. The potential difference (V) of the cell is measured for different values of current (I) external resistance. V and I is shown in figure. Internal (3 mark) resistance is —

o, q V

p, o I a) P 41.

b) q

P q

c)

d)

q

P

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Consider a circuit that consists of four ressitors (each with R = 1 MΩ ), a capacitor (C = 1 µΩ). and a battery (V = 10 MV) as shown. If the capacitor is fully charged and then the battery is removed, find the current at t = 0.5 s as (6 mark) the capacitor discharges. R

R

www.aieeepage.com R

R

C V a) 40 A 42.

b) 20 A

c)

d) 5.4 A

The propagation of sound in a gas may be modeled as adiabatic in nature. For a three degree of freedeom ideal gas, (3 mark) by what factor does the sound speed change when the presure is doubled at constant density ? a) increases by factor

2 b)

decrease by factor

c) increases by factor 2 43.

24.3 A

d)

2

decrease by factor 2

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

µk. A B

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(6 mark)

A

C

B

C

v=0

BEFORE

2

a)

v 6µ k g

2

b)

AFTER

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v 4µ k g

c)

v2 2µ k g

d)

v2 µk g

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44.

Refer to the diagram below. A very large, charged plate floats in deep space. Due to the charge on the plate, a constant electric field E exists everywhere above the plate. An object with mass m and and charge q is shot upward from the plate with a velocity v and at an angle θ . It follows the path shown reaching a height h and a range R. (3 mark) Assume the effects of gravity to be negligible.

E

h

θ R

Which of the following is true concerning the flight of the projectile shown ? a) Increasing the mass m decreases the maximum height h.

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b) Increasing the charge q increases the maximum height h

c) Increasing the mass m decreases the downward acceleration.

d) Increasing the charge q decreases the downward acceleration 45.

Refer to the diagram below. inside a vacuum chamber, a point charge q1 is separated by a distance d from the surface of a hollow sphere with a radius r and made from a conducting material. The sphere has a charge q 2 . (3 mark) (Note: k is the Coulomb’s law constant).

www.aieeepage.com q1

d q2.

When q1 is removed, the force on the sphere charges. Which of the following represents the time between the moment q1 is removed and the moment the sphere experiences any change in force ? a) The sphere feels the change instantaneously b)

d /(3 × 108 )

c)

(3 × 108 ) / d

d)

( d + r ) /(3 × 108 )

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Questions 46 - 50 are based on the following passage

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

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I = I 0 − bx

(Equation - 1)

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

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Unlike solar power, where solar energy is directly converted into electricity, both wind and hydroelectric power generation requires the conversion of kinetic energy into mechanical power, which is then used to create electrical power. A wind turbine converts the kinetic energy of passing air molecules while a hydroelectric turbine converts the kinetic energy of passing water molecules. Both forms of energy production proceeds through the use of a large rotor connected to an induction generator. A siple induction generator is comprised of a flat rectangular coil rotating in magnetic field, and the emf, ε , produced by such a generator can be calculated with the following formula. ε = ε max sin(2 πft) (Equaton 2) ε max = NBA f (Equation 3

Where ε max is the peak emf produced, N represents the number of turns in the coil, B is the constant magnetic field, A is the area covered by the coil, f represents the number of complete rotations the coils executes per second, and t is the duration of time that the generator is operating. 46.

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

PAGE

a) Increase the magnetic field. c) Increase the rotational speed of the generator 47.

b) Increase the number of turns in the coil d) Increase the overal coil size

(3 mark)

Current investigation into improving the efficiency of solar power conversion includes maximizing the amount of photons that are absorbed within the surface of collector panels. According to the passage, which of the following (3 mark) would NOT be useful for this purpose:

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a) Increasing the number of conducting elements to maximize electrical transmission. b) Increase the thickness of the semiconductor plates. c) Using mirrors to combine and concentrate more sunlight onto the panel surface. d) Minimizing reflective loses from conducting elements. 48.

Any photon striking an electron in a solar panel semiconductor must have sufficient energy to liberate that electron without causing heat because heat significantly decreases the conductivity and lifespan materials. Currently, the best photovoltaic substances require light in the visible range. Which of the following the would best help to (3 mark) maximize energy generation a) Use semiconductive material whose electrons are liberated at the lowest possible frequencies. b) Coat the surface to remove infrared radiation c) Coat the surface to remove UV radiation d) Use a coolant to maintain a constant operating temperature.

49.

A marooned physicist creates a crude hydroelectric generator hoping to use the kinetic energy of a small waterfall as a source of energy for his radio. Given a mechanical efficiency of 75%, power and AC cycling frequency requirement of 20 watts and 60 Hz respectively, along with a voltage requirement of 120Vrms' how far below the top of the waterfall should he place his generator ? (NOTE: Assume that 1kg of water strikes the surface of the rotor (3 mark) per second, and neglect air resistance) a) 2 . 04 m c) 6 . 44 m

50.

PAGE b) 2 . 72 m

d) 27 . 2 m

Wind turbines are giant fans mounted high above the ground. They are subject to shear forces from high winds on their rotor blades and mounting poles. To minimize the possible damage due to bending from extreme winds, (3 mark) engineers may employ all of the following EXCEPT.

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

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Paper - I I : Mathematics - 51 to 100

Questions 51 - 54 are based on the following passage Let f ( x ) be a function and a be a point within or without the domain of f ( x ) . Then we say that 1.

Lt − f ( x) or Lt + f ( x) is infinite. f ( x) has an infinite discontinuity at x = a if x → a x →a

2.

Lt − f ( x) and Lt + f ( x) lie in a certain range but do not f ( x) has oscillating discontinuity at x = a if x → a x →a approach to a definite value at x = a .

3.

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

PAGE

jump function at x = a . 4.

Lt − f ( x) & f ( x) has a removable discontinuity at x = a if x → a

Lt

x → a+

Lt

x→a−

f ( x) −

Lt

x→a+

f ( x) =

f ( x) both exist finitely & their values

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

Lt − f ( x) = x = a so that x → a

51.

52.

53.

f ( x) = f ( a) .

www.aieeepage.com

 x−a , x≠a  1 = ( ) f x  e x −a + 1 The function defined by at x = a .   O , x = a

(3 mark)

(a) is constant

(b) has removable discontinuity

(c) has jump discontinuity

(d) has infinite discontinuity

1  cos , f ( x) =  x The function  O , 

x≠0 x=0

at x = 0 .

(3 mark)

(a) is constant

(b) has removable discontinuity

(c) has jump discontinuity

(d) has oscillating discontinuity

sin (loge x ) ,

The function f ( x) =  

O

(a) is constant



1 x m sin , x  O ,

 The function f ( x) = 

(a) m ≥ O

,

x≠0 x=0

at x = 0 .

(3 mark)

PAGE

(b) has removable discontinuity

(c) has jump discontinuity 54.

Lt

x →a +

(d) has oscillating discontinuity

x≠0 x=0

is constant at x = 0 if

www.aieeepage.com (c) m ≥ 1

(b) m > O

(3 mark)

(d) both (b) & (c)

Questions 55 - 95 are independent questions 55.

If the square root of a) 2

x y i  x 2 y 2 1  x y  31 is ±  + −  , then m is + 2 +  + + 2 y x 2i  y x  16  y x m b) 3

c)

4

(3 mark)

d) none of these

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56.

57

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

(3 mark)

a)

Re(a) Im (a) tan θ = (Re(a ))2 − (Im(a ))2

b)

⋅ Re  a  Im (a)   tan θ = (Re(a )) 2 + (Im( a )) 2

c)

tan θ =

2Re (a) Im (a) (Re(a ))2 − (Im(a ))2

d)

none of these

Let I be the incenter of triangle ABC. Let the incircle of ABC touch the sides BC, CA and AB at K, L and M respectively. The line through B parallel to MK meets the lines LM and LK at at R and S, respectively. (3 mark)

Angle RIS is a) acute 58.

b) obtuse 1

c)

right angle

d) any of these

-

Two circles I and I 2 intersect at M and N.

PAGE

Let l be the common tangent to I -1 and I- 2 so that M is closer to l than N is. Let l touch I -1 at A and I - 2 at B. Let the line thorugh M parallel to l meet the circle I -1 again at C and the circle I- 2 again at D. Lines CA and DB meet at E; lines AN and CD meet at P; lines BN and CD meet at Q, then a) MP = MQ b) EP = EQ c) AP = CP d) both a & b n

Ck = k = 0 n ( k + 3) n

59.

∑ Show that nlim →∞ a) (2 - e)

60.

b) 0

1 , 1, 2 2

b)

1

d) 2

1 1 , where u = u2 + u − 2 x −1

1 , − 1, 2 2

b) 790

b)

232

12 65

b)

c)

0, 1

(3 mark)

d) 1, 2

c)

791

(3 mark)

d) none of these

232 − 1

c)

232 + 1

PAGE

d) none of these

53 65

c)

1 65

d) none of these

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If ‘head’ means one and ‘tail’ means two, then coefficient of quadratic equation ax 2 + bx + c = 0 are chosen by (3 mark) tossing three fair coins. The probability that roots of the equations are imaginary is a) 5/8

66.

(6 mark)

To avoid detection at customs, a smuggler has placed six narcotic tablets in a bottle containing nine vitamin pills that are similar in appearance. If the customs official selects three of the tablets at random for analysis, then the (3 mark) probability that smuggler will be arrested for illegal possession of narcotics is a)

65.

d) e

In a city no person have identical set of teeth and there is no human person without a tooth. Also no person has more than 32 teeth. If we disregard the shape and size of tooth and consider only the positioning of the teeth, then (3 mark) the maximum population of the city is a)

64.

e-2

The number of rectangels excluding squares from a rectangle of size 9 × 6 is a) 789

63.

c)

c)

Find the points of discontinuity of y = a)

62.

b) does not exist

(3 mark)

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

61.

www.aieeepage.com

k

(3 mark)

b) 3/8

c)

7/8

d) 1/8

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

c b + <0 a a

b) 1 +

c b + <0 a a

c)

1+

c b + <0 a a

d)

b+c <0 a

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(3 mark)

67.

1 -1 −1 −1 Find the value of : cos(2 cos x + sin x) at x = , where 0 ≤ cos x ≤ π and − π/2 ≤ sin -1 x ≤ π/2. 5

a)

68.

±

2 6 5

Evaluate

2 6 5

b)

∫ ( x + a)

c)

a)

c)

7  x+a 7   +c ( a − b)  x − b 

(3 mark)

1

b)

7  x+a 7   +c ( a + b)  x − b 

d)

7  x−b  7   +c ( a − b)  x + a 

1

− sin 4 t

a) 70.

1 1 2 − sin 2t 2 4

d) does not exist

dx ( x − b) 6 / 7

7  x −b  7   +c ( a + b)  x + a 

Solve I = ∫cos4 t

2 6 5

8/ 7

1

69.

−

(3 mark)

1

f ( z ) dz f (cos 2t − z ) +

b)

PAGE

(3 mark)

f (z)

1 1 − + sin 2 2t 2 4

c)

1 −1 + sin 2 2t 2

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d)

1 1 − + sin 2 2t 2 2

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

x+

x

Y y=

y=x-x x

O

1/2

1

2

x=1

a) 0 71.

73.

4 5

c)

2 5

d)

1 5

Find the equation of the curve such that the square of the intercept cut off by any tangent from the y-axis is equal to (3 mark) the product of the coordinates of the point of tangency.

a) y = ce 72.

b)

b)

PAGE

log y = ±2

x y

c)

x = ce

y x

d)

x = ce

+2

y x

The sum of the torques about any point in the plane of the polygon of forces represented by the sides of the polygon (3 mark) taken in order is. a) twice the vector area b) vector area of closed plane c) nothing can be said d) proportional to area of polygon Given that vectors, A, B, C from a triangle such that A = B + C. Find a, b, c, d such that the area of the triangle

www.aieeepage.com

(3 mark)

is 5 6 where A = ai + bJ + cK. B = di + 3j + 4k, C = 3i + j - 2k. a) -8, 4, 2, -11

b) 8, -4, -2, 11

c)

3, 4, 2, 5

d) 3, -4, 2, 5

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74.

The curves y 2 = 4ax and ay 2 = 4 x 3 intersect each other at an angle of tan −1 (1/ 2) and also if PG1 and PG2 be the normals to the two curves at common point of intersection (which is not orgin) meeting the axis of x in G1 and G 2 , (6 mark)

then G1 G 2 = ? a) 5a 75.

b)

2

d) 10a y is equal to 2

(3 mark)

d) none of these

± 2

c)

3x

(3 mark)

d) 4x

A variable line thro’ P with co-ordinates (-2, 1) cuts the axis in A, B resp. Q is a point on AB such that PA, PQ and (6 mark) PB are in H.P. Then the locus of Q is a straight line.

PAGE

b) x = 2y + 1

c)

x = 2y + 2

d) x = y + 2

If the line y = 3 x cuts the curve x 3 + y 3 + 3 xy + 5 x 2 + 3 y 2 + 4 x + 5 y − 1 = 0 at the points A, B, C, then OA.OB.OC (3 mark) is a)

79.

c)

− 2

b) 2x

a) x = 2y 78.

2a

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

77.

c)

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

76.

b) 4a

4 (3 3 − 1) 13

b)

2 +7 www.aieeepage.com c) 3

3 3 +1

d) none of these

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

(3 mark)

80.

a)

( 2 − 1)a or ( 2 + 1) a

b)

2 2a

c)

(2 − 2)a

d)

(2 + 2)a

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

(3 mark)

a) 81.

a > 2b 2

2

If the polar of a) parabola

82.

a < 4b

2

c)

a > 8b 2

2

d)

a = 7b 2

2

x2 y2 x2 y 2 + = + = 1, then the locus of the pole is 1 is always touching the curve a 2 b2 b2 a 2 b) ellipse

c)

hyperbola

(3 mark)

d) circle

If the sum of the slopes of the normal from a point ‘P’ to the hyperbola xy = c 2 is equal to λ(λ ∈ R + ), then locus of (3 mark) point ‘P’ is a)

83.

b)

2

x2 = λ c2

b)

PAGE

y2 = λ c2

c)

xy = λ c 2

d) none of these

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

(6 mark)

The axes being rectangular, find the equation of the perpendicular from the origin to the line a) 84.

x y z = = 2 1 4

x y z = = 2 −1 −4

c)

x y z = = 2 −1 4

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d)

x y z = = −2 1 4

Graph of the equation y 2 + z 2 = 0 in three dimensional space is a) x-axis

85.

b)

b) y - axis

c)

z-axis

(3 mark)

d) yz-plane

If sum of the first 2n terms of the A.P., 2, 5, 8,.......is equal to the sum of first n terms of the A.P. 57, 59, 61...., then (3 mark) n equals a) 10

b) 12

c)

11

d) 13

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86.

a) 87.

a 2 + c 2 > 2b2

89.

b)

c)

b3 + d 2 > 2c3

a 5 + c 5 > b5

d) all of these

The expression 4 x 2 + 4 x | sin θ| - cos 2 θ attains the minimum value a) -2

88.

(3 mark)

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

b) -1

c)

-1/2

(3 mark)

d) 0

 A If A = 840°, then 2 sin   euqals 2

(3 mark)

a)

1 + sin A + 1 − sin A

b)

− 1 + sin A + 1 − sin A

c)

1+ sinA - 1 - sinA

d)

− 1+ sinA - 1 - sinA

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

(3 mark)

PAGE

There is at leat one value of x in (1, 3) which satisfies a) x log x = 3 - x 90.

Let f ( x) =

b) x log x = 3 + x

c)

d) x log x = - 3 -x

x2 + 1 ,1 ≤ x ≤ 4. [.] denotes the greatest integer function. Then [ x]

a) f(x) is monotonically decreasing [1, 3, 9] c) The greatest value of f(x) is 91.

x log x = x - 3

(3 mark)

b)

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

d)

The least value of f(x) is 2

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17 2

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

(6 mark)

(i) f(0) = 2, f(1) = 1; (ii) f has a minimum value at x = 5/2 and

2ax 2ax − 1 2ax + b + 1 b b +1 −1 iii) For all x f ' ( x) = 2(ax + b) 2ax + 2b + 1 2ax + b The constants a, b respectively will be a)

92.

1 5 , 4 8

Number of solutions of sin a) 0

93.

1 5 , 4 4

c)

1 5 − , 4 4

d)

1 5 − ,− 4 4

x + 2π x = x 2 + π 2 + 1 is 2

b) 1

(3 mark)

PAGE c)

2

d) none of these

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

94.

b)

n3

Cr

b)

n

Cr 3

Solution set of the inequality 5 a) (-2, 0)

c)

3n

Cr

d)

3.2 n Cr

 1  www.aieeepage.com >  is

x+2

b) (-2, 2)

(3 mark)

1/ x

(3 mark)

 25 

c)

(-5, 5)

d)

(0, ∞)

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x

95.

1 1 If 372      3  3

a)

x

> 1, then

x ∈ [0,1)

b)

(3 mark)

x ∈ [0,16)

c)

x ∈ [0,64)

d) none of these

Questions 96 - 100 are based on the following passage (IV) f ( x) = ax3 + bx 2 + cx + d , a > 0 then f 1 ( x) = 3ax 2 + 2bx + c . Case:1 f 1 ( x) = 0 has no real roots. Then f ( x) always increases as x increases & f ( x ) = 0 has one real root.

PAGE

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

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Case:3 f 1 ( x) = 0 has two distinct roots α & β (α < β) . If f (α ) f ( β) < 0 then the equation f ( x ) = 0 has three real roots. Case:4 f 1 ( x) = 0 has two distinct roots α & β (α < β) , but f ( β) = 0 , also in this case f ( x ) = 0 has repeated root & one other root. (β, 0)

In general, the equation g ( x) = 0 has a repeated root x = α, if g (α) = g1 (α) = 0 . 96.

97.

The equation x 3 − 3 x + 1 = 0 has (a) three distinct real root

(b) one repeated & one different root

(c) only one real root which is not repeated

(d) only one repeated root

The no. of integral roots of the equation in previous question is (a) 3

98.

(b) 2

PAGE

(d) 0 (3 mark)

(b) 1

(c) –1

(d) not defined as all roots are not real

The equation 8 x3 − 20 x 2 + 6 x + 9 = 0 has

(3 mark)

(b) all distinct real roots www.aieeepage.com

(a) one repeated root (c) all roots repeated 100.

(c) 1

(3 mark)

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

99.

(3 mark)

(d) only one real root which is not repeated

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

 −1 1 3   , ,   2 6 2

b)

1 3  ,  6 2

(3 mark)

c)

 −1 3   ,   2 2

d)

3   2

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Paper - I I I : Chemistry - 101 to 150

Questions 101 to 105 are based on the following passage A chemist is studying the boiling points of various silanes. Due to similarities in reactivity, many silanes exist as mistures with a variety of molecular formulas. In order to determine the boiling point of a pure silane, individual compounds must be separated by distillation. Experiment - 1 : A mixture of silanes is placed in a distillation apparatus at - 1150 C. The temperature is slowly raised. Between - 1130 C and -1090C, a colorless vapor boils off the liquid mixture. This is collected and labeled Flask A. the chemist continues to raise the temperature, and another vapor is collected between -170C and -120C. This is labeled Flask B. Between 500C and 540C, a third sample is collected and labeled Flask C. Finally, the remainder of the mixture boils between 840C and 850C. This is collected in Flask D.

PAGE

Experiment - 2 : The chemist injects 25 µL of the sample from Flask D into a gas chromatograph. Analysis of the results shows that the sample is a mixture of straight-chain and branched-chain isomers. Expriment 3 Flasks A, B, C, and D are analyzed individually to give the boiling point data in Table - 1 Silane SiH4 Si2H6

Normal Boiling Point (0C) -111.8

www.aieeepage.com -14.5

Si3H8

52.9

Si4H10

84.3 Table -1

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

Normal Boiling Point (0C)

CH4

- 164

C2H6

- 88.6

C3H6

- 44

C4H10

- 05 Table - 2

101.

Many low-molecular weight hydrocarbons are gases under standard conditions, making a determination of the boiling point difficult. What might a chemist do to determine the boiling point of a low - molecular weight (3 mark) hydrocarbon?

PAGE

a) Lower the temperature at which the determinations are made b) Pressures, then extrapolate the curve to I atm c) Mix the hydrocrbons with suitably highermolecular weight compounds, then determine the boiling point of the mixture. d) Determine the boiling point at lower pressures, then extrapolate the curve to 1 atm. 102.

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Compared with hydrocarbons of the same general moelcular formula, the boiling points of silanes are:

(3 mark)

a) Higher, because of the greater number of electrons and stronger intermolecular forces in silicon-based compounds. b) Higher, because of the lower number of electrons and weaker intermolecular forces in silicon-based compounds. c) Lower, because of the lower number of electrons and weaker intermolecular forces in siliconbased compounds. d) Lower, because of the greater number of electrons and stronger intermolecular forces in siliconbased compounds.

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103.

104.

Which of the following quantum numbers correspond to the outermost valence electron of silicon? a) n = 2; ℓ = 2

b) n=2; ℓ = 1

c) n = 3; ℓ = 1

d) n = 3; ℓ = 2

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

(3 mark)

(3 mark)

a) The straight-chain isomer, because there are more sites for hydrogen bonding. b) The straight-chain isomer, because there is more opportunity for V an der Waals interactions. c) The branched-chain isomer, because V an der Waals interactions are more significant with substituted structures. d) Neither, the structure does not affect the boiling point. 105.

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

(3 mark)

I. minute differences in the structure of each compound cause differences in the boiling points.

PAGE

II. Each additional compound in the mixture acts a solute III. The substance that boils off is impure a) I only

b) II only

c) I and III only

d) II and III only

Questions 106 to 145 are independent Question 106.

Both

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H 2O2 and O3 acts as oxidising agents. The oxidising action in which they are similar

1)

PbS to PbSO4

2)

Fe 2+ to Fe3+

3)

K 4 [ Fe(CN ) 6 ] to K 3[ Fe(CN )6 ]

4)

decolourising of acidified

(3 mark)

KMnO4

Which of the given statement(s) match with the main statement. a) 1, 2, 3 107.

b) 2, 3, 4

c)

1, 2, 4

d) none

Na 2SO 4 is water soluble but BaSO 4 is insoluble because

(3 mark)

1) The hydration energy of Na 2SO 4 is higher than that of its lattice energy 2) the hydration energy of Na 2SO 4 is less than that of its lattice energy 3) the hydration energy of BaSO 4 is less than that of its lattice energy 4) the hydration energy of BaSO 4 is higher than that of its lattice energy

PAGE

Which of the given statement(s) match with the main statement. a) 1, 2 108.

b) 1, 3

c)

2, 3

d) 2, 4

C(OH) 4 is unstable because a carbon atom cannot hold more than one -OH groups but Si(OH) 4 is a stable compound because 1) C-O bond energy is low 3) Si-O bond energy is low

(3 mark)

2) C-O bond energy is high

www.aieeepage.com 4) Si-O bond energy is high

Which of the given statement(s) match with the main statement. a) 1, 4

b) 1, 3

c)

1, 2

d) none

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109.

Which of the following statements concern with transition metals ?

(3 mark)

1) Compounds containing ions of transition elements are usually coloured 2) the most stable oxidation state is + 3. 3) they show variable oxidation states, which differ by two units only 4) they easily form complexes. a) 1, 2, 3 110.

b) 2, 3, 4

1, 2, 4

d)

none

In electrorefining of metals, anode and cathode are made-up of impure metal and a strip, a pure-metal respectively while the electrolyte is solution of a complex metal salt. This method cannot be applied for the refining of (3 mark) a) Copper

111.

c)

b) Sodium

c)

Aluminium

d) Zink and Silver

A white sodium salt dissolves readily in water to give a solution, which is neutral to litmus. When silver nitrate solution is added to this solution, a white precipitate is formed which does not dissolve in dilute HNO 3 . The (3 mark) acidic would be a)

112.

CO 32-

b)

PAGE

Cl -

c)

SO 32-

d)

Br -

Amongst the following, choose the correct statement(s)

(3 mark)

1) atomic hydrogen is obtained by passing hydrogen through an electric arc. 2) hydrogen gas will not reduce heated aluminium oxide.

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3) finely divided paladium absorbs large amount of hydrogen gas

4) pure nascent hydrogen is the beast obtained by reacting Na with C 2 H 5 OH a) 1, 2, 3 113.

b) 2, 3, 4

c)

1, 2, 4

d) none

If one measures the gradient of the e.m.f of a cell with respect to temperature the end result will be a value for (3 mark)

114.

a)

∆H of the cell reaction

b) the heat of the cell reaction

c)

∆S of the cell reaction

d)

∆G of the cell reaction

The average osmotic pressure π ,of blood is 12.3 atm at 27°C . What concentration of glucose , C 6 H12 O 6

(6 mark)

will be isotonic with blood ? a) 2.0M 115.

c) 0.5M

d) 1.5M

A balloon initially contains 20 grams of helium at a pressure of 1000 torr . After some helium is let out of the balloon ,the new pressure is 900torr ,and the volume is half of what is was .If the temperature has not changed ,how (3 mark) much helium is now in the balloon ? a) 9 grams

116.

b) 0.025M

b) 10 grams

c)

11 grams

d) cannot

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

PAGE

2HCl+Na 2 CO 3 U H 2 CO 3 +2NaCl

(gNa 2 CO3 ) (2) a) (mol.wt.Na 2CO 3 ) (ml HCl/1000)

c)

1 ( moles Na 2 CO3 )    2 (ml HCl/1000)

b)

1 ( gNa 2 CO3 )    2 (mol HCl/1000)

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moles Na 2 CO3 (ml HCl/1000)

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(6 mark)

117.

Which of the following explains the pressure and volumes deviations in a real gas compared to an ideal gas ? I

Ideal gas molecules don’t have volume and real gas molecules do

II

Ideal gas molecules don’t exert forces on one another and real gas molecules do

(3 mark)

III Ideal gas molecules all move at the same speed for a given temperature , whereas the speed of real gas molecules varies within a sample of gas at a given temperature a) I only 118.

119.

b) II only

c)

I and II only

d) I , II and III

Reaction chambers A and B both contain equal amounts of pure 1-butene. A catalyst for the isomerization of 1-butene to 2 - butene is added to chamber A . Assuming there are no other products ,and that both chambers (3 mark) eventually reach equilibrium: a) chamber A will always contain at least as much 2-butene as chamber B, with the difference increasing over time. b) chamber A will always contain at least as much 2- butene as chamber B, with the difference first increasing, but then decreasing over time. c) chamber A will always contain at least as much 2-butene as chamber B, with the difference first decreasing, but then increasing over time. d) chamber B will always contain at least as much-2 -butene as chamber A, with the difference increasing over time. Direction : Use the following information to answer the question Objects radiate heat at a rate given by the (3 mark) following equation.

PAGE

P = σεAT 4

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where P is the rate at which heat is radiated, σ is the Stefan-Boltzman constant (5.67 × 10 −8 W m −2 K −4 ), ε is the emissivity of the object’s surface having a value between zero and one, A is the surface area, and T is the temperature in Kelvin. The rate at which objects absorb heat from their environment is given by the same equation except that T is the temperature of the environment. The net rate of energy exchange due to radiative processes is given by :

Pn = σεA(Tenv 4 − T 4 ) where Pn is the net rate of energy exchange and Tenv is the temperature of the environment. A black body radiator has an emissivity of :

120.

a) 0

b) 0.5

c) 1.0

d) The emissivity of a blackbody radiator may vary.

Hexane is infinitely soluble in octane Why ?

(3 mark)

a) Because hexane and octane have similar molecular weights b) Because the hexane-octane intermolecular bond is much stronger than either the hexane-hexane or the octane-octane intermolecular bonds c) Because hexane can hydrogen bond to octane

PAGE

d) Because the entropy increase upon mixing the two materials is the dominant factor in the free energy change when the two are mixed. 121.

Suppose the amount of material undergoing an oxidation reduction reaction doubles, but all other conditions (3 mark) remain the same. Which of the following also doubles ? I)

Free energy changes

II) Total change flow III) Potential a) I only

www.aieeepage.com c) I and II only

b) II only

d) II and III only

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122.

Direction : Cocaine is stimulant that is isolated from coca leaves Refer to the structure of cocaine shown below (3 mark) to answer question 9

CH 3

8N O 7

O

6

CH 3

12

3 O

4

11 10 O 1

H 5

How much p character is in the hybridised orbital on the N8 nitrogen in the cocaine structure ? a) 33.3% 123.

b) 50%

PAGE c)

66.6%

d) 75%

Direction : A lower heat of hydrogenation indicates a more stable alkene. Refer to the table below to answer (3 mark) question

Molar heat Of hydrogenation

www.aieeepage.com Alkene

ethylene

137 kJ

propene

126 kJ

1-butene

127 kJ

cis-2-butene

120 kJ

trans-2-butene

116 kJ

cis-2-pentene

120 kJ

2-methyl-2-butene

113 kJ

2, 3-dimethyl-2-butene

111 kJ

Which of the following alkenes is the Most stable ? a) ethylene 124.

b) cis-2-butene

c)

d) 2, 3-dimethyl-2-butene

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

O

O

4

2

PAGE 3

125.

2-Methyl-2-butene

1

a) The carbon atom labeled 1. b) The cabon atom labelled 2. c) The carbon atom labeled 3. d) The carbon atom labeled 4 The neurotransmitter shown below contains what functional groups ?

www.aieeepage.com O N O

a) a primary amine and a carboxylic acid

b)

a tetriary amine and a carboxylic acid

c) a tertiary amine and an ester

d)

a quaternary amine and an ester

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(3 mark)

(3 mark)

126.

127.

The stability of most cycloalkanes (which is indicated by their higher boiling and melting points) as welll as their (3 mark) non-planar structure is not dependent upon : a) Baeyer strain

b) Strecker strain

c) Pitzer strain

d) nonbonded interactions. (6 mark)

Catechol is treated with four reagents, as follows :

O catechol Cl

C - CH 2 Cl

- HCl

A

POCl 3

B

CH 3 NH 2 − HCL

H2

D

C Pd

What is the structure of D ?

OH

OH OH

a)

b)

H 2 C − CH 2 − CH 3

PAGE c)

H - C - CH 2 − CH 3

d)

H - C - CH 2 − NH − CH 3

O = C - NH - CH 3

OH

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Calculate the number of carbon atoms in 27.3 g of trichloroacetic acid. (Atomic weights : C = 12.0, = 35.5, (6 mark) O = 16.0, H = 1.0) a)

c) 129.

CHO

OH

OH 128.

OH

OH

COOH

27.3( 2) (6.02 × 10 23 ) / 163.5

163.5(27.3) 2(6.02 × 10 23 )

b)

27.3(2) 163.5

d)

27.3 (6.02 × 1023 ) 163.5

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

Fe 2 O 3 ⋅ xH 2 O. This precipitate is filtered, washed and ignited to Fe 2 O 3 . The Fe 2 O 3 weighs 0.29 g. the reaction is : 2Fe3+ → Fe2O3 (s) and the atomic weights of iron and oxygen are 55.9 and 16.0, respectively. The (6 mark)

percentage of iron in the sample would be equal to :

130.

a) 100 ×

0.56 (55.9)2 × 0.29 159.8

c) 100 ×

0.29 0.56 × 2(55.9) 159.8

b)

100 ×

0.29[(2 × 55.9) / 159.8] 0.56

PAGE d)

100 ×

55.9[(2 × 159.8) / 0.29] 0.56

Which of the following statements is true of isotopes ?

(3 mark)

a) They have different atomic numbers and the same atomic masses. b) Their electronic configurations differ

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c) slight differences in chemical behavior of isotopes (called isotope effects) influence rather the kind of reaction than the rate of reaction itself. d) The first ones discovered were those of neon. 131.

Based on the Third Law of thermodynamics we know that all perfect crystals at absolute zero have : a) the same enthalpy

b) the same crystal lattices

c) differing ∆ A values.

d) two of the above, (a) and (c)

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(3 mark)

132.

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

#carbon atoms

133.

134.

#carbon atoms

#carbon atoms

#carbon atoms

A perpetual motion machine capable of generating increasing amounts of energy without interacting with its (3 mark) surrounding cannot exist. This is best explained by the a) First Law of Thermodynamics

b)

Third Law of thermodynamics

c) Energy conservation principle

d)

Gibbs-Helm holtz equation

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

PAGE

s) -2.3, -5.1, -5.3, -8.2, -14.9 c) 2.3, 5.1, 5.3, 8.2, 14.9 135.

d)

log VR

c)

log VR

b)

log VR

a)

log VR

(3 mark)

b)

0.2, 2.8, 2.9, 6.7

d)

6.7, 9.6, 9.8, 12.6, 15.0, 16.1

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

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log[A] t = − kt / 2.303 + log[A]0

(3 mark)

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 accetonitrile in a first order process as follows :

CH 3 NC(g) → CH 3CN(g) The rate constant for the conversion of methyl isonitrile is 5 × 10 −5 s −1. A scientist has a container containing methyl isonitrile gas with a partial pressure of 100 torr. After 12.8 hours (approx. 46,000 seconds), what is the partial pressure of methyl isonitrile gas inside the container ? a) 1 torr

25 torr

P (atm)

d) 50 torr

PAGE

P (atm)

P (atm)

d)

Free energy, G 298 (kj)

c)

Free energy, G 298 (kj)

b)

Free energy, G 298 (kj)

a)

137.

c)

The free energy of a gas depends on its partial pressure according to the expression G = G o + RT In (P/P o ). (3 mark) Which of the following plots below shows agreement with this relationship? Free energy, G 298 (kj)

136.

b) 10 torr

1n

P (atm)

Suppose a certain reaction has the rate law :

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

Which of the following can be concluded about the reaction ?

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

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(3 mark)

For question refer to Habeer process shown below :

(3 mark)

Concentration

138.

A

B

C

Time → N 2 (g)+3H 2 (g) U 2NH 2 (g) In 1912 Fritz Haber developed the Habber process for making ammonia from nitrogen and hydrogen. His development was crucial for the German war effort of World wat I, providing the Germans with sample fixed nitrogen for the manufacture of explosives.

PAGE

The Haber process takes place at 500°C and 200 atm. It is an exothermic reaction. The graph below shows the change in concentrations of reactants and products as the reaction progresses. Even at the high temperatures, the conversion of nitrogen and hydrogen to ammonia was slow. In order to make the process industrially efficient Fritz Haber used a metal oxide catalyst. Which of the following was accomplished by use of the metal oxide catalust ? I)

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The rate of production ammonia increased

II) The energy of activation was raised III) The equilibrium shifted to the right a) I only 139.

b) II only

c)

I and II only

d) I, II, and III

Given the fact that the standard free energies of formation of water vapor and liquid water are -229 kJ/mol and -237 kJ/mol respectively, what is the free energy of the vaporization of water? Assume all measurements were (3 mark) preformed at 25°C. a) -466 kJ/mol

140.

141.

b) -8 kJ/mol

c)

+ 8kJ/mol

d) +466 kJ/mol

When slat X is dissolved in water to form a 1 molar unsaturated solution, the temperature of the solution is seen (3 mark) to drop. From this information, we can conclude that for dissolving this salt in water : a)

∆H o , ∆S o , and ∆G o are all positive

c)

∆H o is positive; ∆G o is negative

d)

∆H o is positive; no conlusion can be reached about ∆G o

b)

∆H o , ∆S o , and ∆G o are all negative

Which of the following structures is an amide ? H2 N

a)

b) OH

O

PAGE c)

(3 mark)

HO

d)

O

O

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142.

(3 mark)

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

HO

3β - cholestanol How many tertiary carbons are in 3β -cholestanol ? a) 3 143.

b) 5

c)

7

PAGE

d) 9

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

Br

HBr

1, 2 - addition 1, 4 - addition www.aieeepage.com

Br

Which product is more thermodynamically stable ? a) 1, 2-addition product b) 1, 4-addition product c) The products have the same stability d) The relative stability cannot be determined. 144.

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

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

O

(3 mark)

O

R - C - CH 3 + 3I 2 + 4OH − → R − C − O + CHI3 + 3H 2 O 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

PAGE

b) Iodide is a good leaving group. c) HI is a strong acid. d) Water is a good leaving group. 145.

In the protein hemoglobin, the histidine residue is attached to the Fe of the heme group. The formation of the (3 mark) bond between the histidine and the Fe is a : a) Lewis acid-base reaction b) condensation reaction

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c) dehydration reaction d) hydrogenation reaction

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Questions 146 to 150 are independent Question Water is often referred to as the “universal solvent”. Most compounds are at least partially soluble in water. The efficiency of water as a solvent makes the purifying of water and the handling of water difficult for certain applications. Even in state of the art research facilities, sterile and deionized water is usually neither sterile nor devoid of solutes. The pH of this water, for example, is often as low as 5 instead of the expected 7 for pure water. Distillation of water 9the process of evaporating and condensing water to remove impurities) is not a perfect method for purifying water, as distilled water will leach substances out of any container or tubing in which it is placed. Furthermore, water will dissolve gases from the air. While nitrogen gas (the main constituent in air) is inert for most purposes, oxygen in the water can lead to oxidation of any solutes. Carbon dioxide complexes with water to form carbonic acid, H2CO3H2CO3. Even though carbonic acid is a weak acid, the pH of a standing body of pure water will drop steadily if left exposed to air. Purification standards for drinking water are much less rigorous than those used in the laboratory. Techniques such as distillation are much too energy inefficient to perform on the large scale needed for a public water supply. Instead, water purification for drinking water mainly involves slight chlorination to kill bacteria and the removal of most solids and particulates by sedimentation. As a result, drinking water is not pure by any real measure. The majority of drinking water supplied to the public has a very hight mineral content consisting mostly of sodium and calcium salts in additon to fluoride ions which are added for dental health. The presence of impurities can contribute to proplems such as corrosion, precipitation, and bad tasting water. 146.

a) NaCI

(3 mark)

b) Na2SO4

d) CaSO www.aieeepage.com If the pH of carbonated water (water with dissolved carbon dioxide) is 5, what is the hydrogen ion concentration? c) CaCI2

147.

PAGE

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

4

(3 mark)

148.

a) 1 x 10-5 M

b) 5 M

c) 5 x 10-5 M

d) 1 x 10-9 M

Water softeners replace calcium ions in “hard” water with sodium ions. By doing so, water softeners do all of the (3 mark) following except? a) Add more cations to the solution b) Decrease the freezing point of the solution c) Decrease the osmotic pressure of the solution d) Increase the boiling point of the solution

149. Which of the following would affect the boiling point of and aqueous solution without altering (3 mark) its electrical conductance?

150.

a) Methanol

b) Acetic acid

c) Sodium chloride

d) Sodium benzoate

Under what conditions will liquid water have absolutely no ions in solution? a) b) c) d)

PAGE

In equilibrium with ice at 00 C As a 90% sucrose solution Perfectly buffered pH 7.00 solution None

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(3 mark)