Ai Iitjee Modeltest 05

IIT-JEE Model Test - 05

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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 X-ray diffraction can be used to determine the inner structure of crystals, as the wavelengths of X-rays are roughtly equal to the interatomic spacing in crystalline matter, on the order of 10-10 m. X-rays, upon entering the highly ordered lattice structure of a crystal, will diffract off of the different atoms. Analysis of the wave interference effects of the Xrays as they leave the crystal alows for precise calculation of the distance between layers of atoms. This type of wave phenomena is called Bragg diffraction. Students can study the effects of Bragg diffraction without being exposed to potentially harmful X-rays. By scaling the wavelength of the incoming radiation up from 1-10 m to 10-2 m, relatively harmless microwaves can be beamed into periodic layers of steel balls, each separated by a small number of centimeters.

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Figure 1 is a schematic showing two microwaves bouncing off of consecutive layers of the lattice. The angle of incidence (and reflection), θ , is varied as the experiment is carried out. Because the space between layrs is d, the difference in path length between the two rays is 2d, sin θ . The experimenter can use a microwave detector to locate the angles at which constructive interference occurs. As the difference in path length between two waves undergoing constructive interference is a interger multiple of the wavelength, the following equation can be used to determine d for the lattice.

nλ = 2d sin θ, n − 1, 2, 3... 1.

What is the spacing between the planes of steel balls if 3-cm microwaves generate constructive interference 190? (3 mark) (sin 190 = 0.33) a) 1.5 cm

2.

b) 2.0 cm

3.0 cm

d) 4.5 cm

The detector is moved to a fixed angle, θ , where an maxima of reflected microwave intensity occurs. How does the (3 mark) intensity of the reflected signal change if the consecutive layers of steel balls are moved apart? a) The intensity falls c) The intensity rises, then falls

3.

c)

b) The intensity rises d) The intensity falls, and then rises.

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A decrease in the intensity of the incoming microwaves would?

(3 mark)

a) increase the values of the angles at which constructive interference occurs.

b) decrease the values of the angles at which constructive interference occurs. c) have no effect on the results of the experiment.

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d) decrease the distance between the layers of steel balls. 4.

Which of the following is the equation that describes the angles at which microwaves reflecting off of consecutive (3 mark) layers of steel ball undergo destructive interference? a)

5.

nλ = d sin θ

b)

nλ = 2d sin 2θ

c)

( n + 1)λ = d sin θ

d)

(n + 1 / 2)λ = d sin θ

Which of the following is an example of the frequency of oscillation of microwaves? a) 3.3 x 10 Hz -12

b) 1.0 x 10 Hz

c)

-2

3.0 x 10 Hz 6

(3 mark)

d) 3.0 x 10 Hz 10

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Questions 6 to 45 are independent Question 6.

The number of possible overtones of air column in a closed pipe of length 83.2cm and of a diameter 6cm whose (3 mark) frequencies lie below 1000 Hz will be — (velocity of sound = 340m/s) a) 5

7.

b) 2

c)

6

d) 3

A bar of mass M=5 kg is held between four disks, each of mass, m=2 kg and radius r. If the normal forces exerted on the disks are sufficient to prevent slipping, then the acceleration of the bar immediately after it has been released from (3 mark) rest is —

M

a) 8.

3g 7

b)

4g 9

PAGE c)

5g 11

d)

5g 9

A uniform circular disc of mass m and radius ‘a’ rotates freely is a vertical plane about its centre. Initially the disc is rotating with angular velocity W0 and is reduced to rest in a time T by a constant force ‘F’ applied tangentially at rim. (3 mark) The F will be equal to —

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a) 9.

maW0 4T

b)

maW0 2T

c)

2maW0 T

d)

3maW0 4T

A sound wave is represented by y = a sin(1000 π t − 3 x ) . The distance between two points having a phase (3 mark)

π difference of is — 3 a)

10.

2π 9

b)

π 18

c)

A hollow cone floats with its axis vertical upto

π 9

d)

5π 18

1 of its height in a liquid of density d1 with its apex submerged. When 3 (3 mark)

a liquid of density d2 is filled in it, it floats with

d2 1 = of its height submerged. The ratio d1 — 2

PAGE h

a) 57 : 147 11.

c) 57 : 648 www.aieeepage.com

b) 47 : 349

d) 2 : 3

A thermally insulated vessel containing a diatonic gas whose molar mass is M moves with a velocity v. The (3 mark) temperature rise in the gas resulting from the sudden stoppage of vessel would appropriately be :

a)

2mv 2 5R

b)

mv 2 R 5

c)

2mv 2 R 5

d)

mv 2 5R

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12.

Three moles of an ideal gas (monoatomic) perform a cycle as shown. The temperatures in different states are,

T1 = 400 K , T2 = 800 K , T3 = 2400 K and T4 = 1200 K . The work done during the cycle is nearly ———K (3 mark)

.Joules

P

3

2

1

4 T

a) 13.

b) 1.5 × 10 2

103

c)

20

d) 10

A cyclic process ABCA is shown in V – T diagram as shown. The same process on the P – V diagram is — (3 mark)

V

C

B

PAGE A

T

P

P

I)

II) A

A

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14.

C

B V

V

V

b) II

c)

III

d) IV

A parallel plate an capacitor is charged to a certain potential difference. A dielectric bar is put into the capacitor. The charge on the plates is needed to be increased three times to restore the former potential difference. The relative permittivity of the bar is — a) 0.333

15.

A

IV)

C

C

V

P

B

A

III)

B

a) I

P

B

C

b) 3

c)

0.166

(3 mark)

d) 6

A parallel plate air capacitor is charged by a battery so that the plates of the capacitor acquire a potential difference equal to the emf of the battery. The ratio of the work done by the battery and the energy stored in the capacitor — (6 mark)

a) 1 : 1 16.

b) 1 : 2

c)

2:1

d) 1 : 4

The potential difference between A and B is 23V. The potential difference across 3 µ F capacitor is —— volts. (3 mark) 3ì F

2ì F +

4ì F

+

+

B

A

5V

8V

a) 7 17.

b) 8

PAGE c)

23

The flux through a loop varies with time according to the relation φ

d) 4

= 0.1(t 2 − 6t ) . Tesla – m2 where t is in seconds. (3 mark)

The induced emf in the loop varies in the time according to the graph — E

E

a)

b) t

18.

E

E

c) www.aieeepage.com

t

t

d) t

Two coils are wound on the common core. The inductance of the first coil is 0.2H, and that of the second is 0.8H. The resistance of second coil is 600 Ω . The current that will flow through the second coil if the current of 0.3A in the first (3 mark) coil is switched off during 0.001 sec ——. a) 1A b) 0.4A c) 0.2A d) 0.1A

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19.

A coil of inductance 0.25 µ and negligible resistance is connected to a source of supply whose voltage is given by

V = 2t + 3t 2 . If the voltage is applied, when t = 0 and switched off at t = 2 sec., the energy stored in the inductor (3 mark)

will be —— a) 125 J 20.

b) 250 J

c)

288 J

d) 144 J

A current of 2 Amp flows in a pure inductance of 4 µ . The coil is suddenly disconnected from the source and almost simultaneously connected across a 10 Ω resistance. The initial rate of change of current is ——— Amp/sec a) 0.25

21.

(3 mark)

d) 1.0

π b) 16

c)

π2 8

d)

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π 8

b) 2r

c)

r

d)

r 2

Sixteen thin convex lenses of focal lengths f , 2 f , 4 f ,8 f ,.......... are placed in contact with each other. The (3 mark) combination will behave as a convex lens of focal length (approximately) ——

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a) 24.

0.75

Two cells, each of emg ‘E’ and internal resistance ‘r’ are connected in parallel across a resistance R. The power (3 mark) delivered to the resistance will be maximum, if R = —— a) 4r

23.

c)

A current of 2 Amp flows through a square frame ‘x’ of wire 2m long. The same amount of current also flows through (3 mark) a circular coil ‘y’ of perimeter 2m. The ratio of the magnetic fields at the centres of y and x is ——

π2 a) 16 22.

b) 0.50

136 f

b)

39 f

c)

2f

d)

f

2

A U–tube of uniform cross sectional area containing a liquid is mounted on a horizontal turn table notating with an (6 mark) angular speed ω about the axis shown. Then h = ?

h

L

a) 25.

ωL2 2g

ω 2 + L2 b) 2g

c)

ω 2 L2 2g

d)

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ω 2 − L2 2g

In the arrangement shown in figure, mass of block B and A is 2m and m respectively. Surface between B and floor is smooth. The block B is connected to the block C by means of a pulley system. If the whole system is released. Find the minimum value of mass of the block C so that the block A remains stationary with respect to the block B. (3 mark) Coefficient of friction between A and B is µ .

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B C

a)

m µ

b)

2m µ +1

c)

3m µ −1

d)

6m 2µ − 1

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A prism of refractive index µ and angle A is placed in the minimum deviation position. If the angle of minimum (3 mark) deviation is equal to A, then the value of A is —— a)

27.

Sin −1

µ 2

b)

2Sin −1

(µ − 1) / 2

c)

2 cos −1

2 a) µ(µ − 2)

1 b) µ(µ − 2)

R

µ µ +1

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b) 3

c)

µ2 − 1 d) µ2 + 3

c)

4

d) 5

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The plot of the number (N) of left over atoms versus activity (A) of a radio active substance is —

N

N

N

II)

I)

a) I

IV)

A

A

b) II

c)

(3 mark)

N

III)

A

A

III

d) IV

An electron, in a hydrogen like atom, has total energy –3.4eV. Its kinetic energy is —— a) –3.4 eV

b) +3.4 eV

c)

–1.7 eV

(3 mark)

d) +1.7 eV

zzzzz

zzzzz

A

B

zzzz

D

C

z zzz z

zzzzz

zzzzz

Use the diagram below to answer the question. 40 spheres of equal mass make two rings of 20 spheres each. The (3 mark) ring on the right has a radius twice as large as the ring on the left.

zzzzz

PAGE zzzzz

31.

µ 2

In Youngs expermient the wavelength of red light is 7800 Aº and that of blue light is 5200Aº. The value of n for which (3 mark) the (n+1)th blue bright band coincides with the nth red band is —— a) 2

30.

2sin −1

Q

R

mR

29.

d)

A quarter cylinder of radius R and refracture index µ is placed on a table at a distance mR from a point P. The value (3 mark) of m for which a ray from P will converge at a point Q distant R from curved surface is —

P

28.

µ 2

r

z

26.

2r

1 2 3 4 www.aieeepage.com If the position of the spheres approximates two uniformly dense rings, which of the following is true concerning a 0

mass placed at position D? a) The net gravitational force due to the spheres of the larger ring would be zero. b) The net gravitational force due to the spheres of the smaller ring would be zero. c) The net gravitational force due to the spheres of both rings would be zero. d) If the smaller ring were removed, the mass would move toward the center of the larger ring.

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32.

The bottoms of two vertical cylinders of different cross sections are connected by a thin pipe. Each cylinder contains gas at constant temperature and is covered by a movable piston. The mass of one piston is m1=1.0kg. the other m2=2.0kg. Initially, the pistons are at the same height h=0.40m. What would be the difference in the heights of the pistons (H) if an extra load of m=1.0kg is placed on the lighter piston? Assume the entire arrangement is placed in (3 mark) vaccum. a) 1.5 m

33.

b) .90 m

c)

d) No difference

Consider a cone, with a light bulb at the vertex, cut by a plane making an angle of 30º with base. The area of the plane inside the cone has an image of area s on the base. If the area of the base is A and the average light intensity at the (3 mark) base is I, what is the average light intensity on the inclined plane?

PAGE A

a) 34.

.60 m

IA 2s

b)

I2 As

S

c)

3 IA 2s

d)

IA s

www.aieeepage.com A ray parallel to the optic axis passes through the focus.

Which of the following is NOT true for a converging lens in optics? a)

(3 mark)

b) A ray originating at the focus is bent parallel to the optic axis. c) A ray through the center of the lens is bent parallel to the optic axis. d) An object placed at the focus has image at infinity. 35.

A photon strikes a free electron at rest and is scattered straight backward. If the speed of electron after collision is (3 mark) α c , where α << 1 then, a) electron’s kinetic energy is a fraction α of photon’s initial energy. b) electron’s kinetic energy is a fraction

1 of photon’s initial energy. α

c) electron’s kinetic energy is a fraction α 2 of photon’s initial energy. d) electron’s kinetic energy is a fraction 36.

1 α2

of photon’s initial energy.

When a monochromatic point source of light is at a distance of 0.2m from a photoelectric cell, the cut-off voltage and the saturation current are respectively 0.6V and 18.0 mA. If the same source is placed 0.6m away from the (3 mark) photoelectric cell, then

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1) the stoping potential will be 0.2V

2)

the stopping potential will be 0.6V

3) the saturation current will be 6.0 mA

4)

the saturation will be –1 mA

Which of the given statement(s) match with the main statement. a) 2, 4 37.

b) 1, 4

c)

3, 4

d) 2, 3

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A stationary 10 kg box is lifted and placed at rest on top of a 10 m shelf. The move takes 2 s. A student argues that (3 mark) the minimum average power is greater than 500W. The student is : a) right because the box must have a change in kinetic energy in addition to the change in potential energy. b) right because the box had to be accelerated which requires a force greater than mg. c) wrong because the box can be moved at an infinitely slow constant velocity, and thus the work done is equal to the weight times the distance. d) wrong because the force on the box could be twice the weight for the first half of the trip, and zero for the second half of the trip.

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38.

Direction : Refer to the below diagram an ideal fluid with a specific gravity of 1.0 flows through the pipe in the direction from c to a. The pipe has the same diameter at a and c. The vertical pipes are vacuum sealed at the top. The (3 mark) height of the fluid at h1, h2 and h3 are measured from the center of the pipe, and are not drawn to scale.

h3 c

h2

h1

b

a

floor Heights h1, h2 and h3 not drawn to scale

If a second ideal fluid with a specific gravity of 2.0 were passed through the pipe at the same volume flow rate, the height h1 would; a) decrease by a factor of 2. b) remain the same. c) increase by a factor of 2.

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d) more information is required to predict the change in h1. 39.

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Direction : Refer to the diagram below a sphere with mass m is placed at the surface of a very shallow pool (depth h) of a fluid with density ρ and oscillated a distance y every t seconds. Waves with a frequency f and amplitude A are generated on the fluid surface and propagate away from the sphere with a velocity v. The distance between the wave (3 mark) crests is given by x.

y

x m

h If the wave generating apparatus were placed on the moon, and y remained the same, which of the following would occur? a) 40.

ρ would decrease b) f would increase

c)

x would increase

d) v would decrease

A metallic chain of length L and mass M is vertically hung above a surface with one end in contact withit. The chain is then released to fall freely. If x is the distance covered by the end of the chain, how much force (exerted by the (6 mark) bottom surface) will the chain experience at any instance during the process?

PAGE X

L

www.aieeepage.com X

a)

N = Mg − Mx ''

b)

N = 3Mg

c)

N = Mg − 2Mx ''

d)

N = (3M / L ) gx

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41.

A movable heavy piston is supported by a spring inside a vertical cylindrical container as shown. When all air is pumped out of the container, the piston is in equilibrium as shown in Diagram1, with only a tiny gap between the pistorn and the bottom of the container. When a portion of gas at temperature T is introduced under the piston, the latter rises to a height h as shown in Diagram 2. What would be the height of the piston above the bottom of the container if the gas is then heated to temperature 2T? (3 mark) Assume that the piston moves without friction and that the spring obeys Hooke’s law.

h Diagram 1

a) 42.

1 h 2

b)

h

Diagram 2

PAGE c)

2h

d)

2h

Direction : Refere the digram below E is the electric field created by q1. V is the voltage at a given point in the field E. Assume that the electric field created by q2 is negligible compared to E. k is Coulomb’s Law constant, m1 is the (3 mark) mass of q1and m2 is the mass of q2.

www.aieeepage.com 2r d

q1

r

q2

If q1 is positive, then when q2 is mvoed from its present location to a distance r from q1, the magnitude of the voltage experienced by q2 due to E:

43.

a) decreases by a factor of 4.

b)

remains the same

c) increases by a factor of 2.

d)

increases by a factor of 4.

Two cylinders are rapidly spinning in the opposite directions as shown. The axes of the cylinders are a distance d apart. A uniform board of mass M is placed horizontally on the cylinders as shown. The coefficient of kinetic friction between the board and the cylinders is µ s . Which of the following statements correctly describe the subsequent (6 mark) motion of the board.

I)

PAGE

d The center of the board will oscillate with period T = 2π 2µ , so the board will begin the oscillation moving kg

to the left.

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d II) The center of the board will oscillate with period T = 2π 2µ , so the board will begin the oscillation moving kg

a) b) c) d)

to the right. only I is correct only II is correct both are wrong cannot describe the motion with the given information

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44.

Recall the equation for a series RLC circuit. Compare this to the parallel resonant circuit shown and find Rp if a series RLC circuit and the parallel RLC circuit are to have the same equations for the potential of capacitor while they both (6 mark) have the same L, C and Q. I2

I1

C

a) 45.

Rp = R

b)

Rp = L

L

Rp

R p = 1/ C

c)

d)

R p = L / RC

Direction : Refer to the diagram below. A conducting bar is slid at a constant velocity v along two conducting rods. The rods are separted by a distance l and connected across a resistor R. The entire apparatus is placed in an external (3 mark) magnetic field B directed into the page.

R

PAGE B in

v

l

www.aieeepage.com How will the current in the apparatus shown above be generated? a) sinusoidally b) clockwise c) counterclockwise d) There is not enough information to determine the direction of the current

PAGE

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Questions 46 - 50 are based on the following passage Magnetic resonabce, first discovered in 1946, has found its way into many scientific arenas as a diagnostic tool. Its usefulness lies in its ability to create images of the interior of structures without the use of ionizing radiation like xrays. The two main drawbacks of using x-rays are their high-energy bound breaking potential, as well as their reliance on the presence of contrast enhancing material. Modern day MRI machines used in clinical imaging create a standing magnetic field aligned with the patient from head to toe. These machines use the proton of a hydrogen atom as their target, due to its abundance in the human body. When the field is applied, the magnetic moment of the protons exposed to the field will dynamically align with or against the field, according to the equation. N-N+ = -E/kT (Equation 1) Where N+ is the number of protons in the lower energy level, N- is the number of protons in the higher energy level, E is the energy difference between the two states, k is Boltzmann’s constant (1.38 x10-23 j/K), and T is the temperature in Kelvins.

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In the presence of such a large magnetic field, a proton will precess, or wobble, about the axis through its magnetic moment, at a specific frequency called the Larmor frequency.

f 0 = γB0' (Equation - 2)

Where B0 is the strength of the magnetic field in Tesla, and γ is the gyromagnetic ratio, a constant unique to every atom ( γ for 1 H is 42.56 MHz/Tesla)

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Once aligned, an electromagnetic radio frequency (RF) pulse is applied at the specific Larmor frequency for the target proton, causing the protons to become excited to the higher energy state Various measurements can then taken as the RF pulse is removed and the protons release the absorbed energy. (Note : planck’s constant h =6.6 x10-34 j.s.) 46.

47.

How much power is required to excite a single proton exposed in a 1.5-T field by a 2 second RF pulse? a) 4. 22 x 10-26 W

b) 1. 44 x 10-24 W

c) 6.36 x10-38 W

d) 2.11 x 10-26 W

All ofr the following will affect the ratio of protons given in Equation 1 EXCEPT:

(3 mark)

(3 mark)

a) Increasing the magnetic field b) Decreasing the temperature. c) Targeting other elemental protons other than 1H d) Increasing the wavelength of the RF pulse. 48.

If the magnetic field strength were doubled, how would the energy required to excite a proton from the lower energy (3 mark) to the higher energy spin change? a) It would double

b) There would be no change

c) It would decrease by one-half 49.

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A uniform magnetic field, B, runs at a height h parallel to the ground. A free electron (mass me) is placed in the field, initially moving at speed v in the opposite direction to the field. Neglecting air resistance, what is the magnitude of (3 mark) the net force on the electron? a) meg + evB

50.

d) It would increase by one-half.

b) meg - evB

c)

meg

d)

(m e g ) 2 + (evB) 2

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How many times greater is the energy of a 1019 Hz X-ray photon than the energy of the RF photon used in the MRI (3 mark) described in the passage, when the applied field is 1.5T? a) 6. 39 x 106

b) 1.57 x 1017

c)

2.35 x 1011

d) 3.52 x 1011

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Paper - I I : Mathematics - 51 to 100

Questions 51 - 54 are based on the following passage Consider a series of the form

f11 ( x) f 21 ( x) f31 ( x) + + + ............. the sum of such a series can be obtained in the following way; f1 ( x) f 2 ( x ) f3 ( x) Step1: Obtain the product f1 ( x ) f 2 ( x )......... f n ( x) = g ( x ) (say) Step2: Take log of both the sides, then log f1 ( x) + log f 2 ( x) + ............. + log f n ( x) = log g ( x)

PAGE

Step3: Differentiate bothe sides w.r to x,

f 1 ( x ) g1 ( x) f11 ( x ) f 21 ( x) + + ............. + n = f1 ( x) f 2 ( x) f n ( x) g ( x )

The above method can be extended for the sum of infinite returns of the series provided the series is convergent.

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51.

1 2x 4 x3 8 x7 + + + + ..... is The sum of n terms of the series 1 + x 1 + x 2 1 + x 4 1 + x8

n−1

n −1

a)

1 2n x 2 − n 1 − x 1 − x2

c)

−

b)

1 2n x 2 + n 1 − x 1 + x2

d)

−2n x 2

n−1

52.

n −1

 1 1  +  n  2n 1 + x2  1 − x

1 1− x

b)

1 1+ x

c)

1 x −1

(3 mark)

d) 1

If sin θ1 sin θ2 sin θ3 ...........sin θn = f (θ) then cot θ1 + cot θ2 + cot θ3 + ..........cot θn =

a) 54.

1 2n x 2 − 1 − x 1 − x 2n

If x <1 then the sum to infinite terms of the series given in above question is a)

53.

(3 mark)

f (θ) f 1 (θ)

b)

− f 1 (θ) f (θ)

log f (θ)

PAGE c)

f 1 ( θ)

d)

(3 mark)

f 1 (θ) f (θ)

n −1

The value of the product (1 + x ) (1 + x 2 ) (1 + x 4 ) (1 + x8 ) ....... (1 + x 2 ) is n

a)

1 − x2 1− x

n

b)

1 + x2 1− x

c)

2n

(1 − x) (1 − x )

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(3 mark)

d)

1 − x2

n

1 + x2

n

Questions 55 - 95 are independent questions 55.

f(x) = ax2 + bx + C, where a ≠ 0 . If f(-1) < + 1, f(1) > -1 and f(3) < - 4, the a) b + 1 > 0

b) 8a + 1 < 0

c)

a is negative

(3 mark)

d) b is positive

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56.

In a class tournament, where the participants have to play each one game with another, two players fell ill after playing three games each. If the total number of games played is 84, the number of players at the beginning was (3 mark)

a) 12 57.

58.

b)

Z1 + Z 2 Z1 Z2

c)

2Z1 Z 2 Z1 + Z 2

d)

Z1 + Z2 2Z1 Z 2

b) 2A = B

(3 mark)

c)

2B = A

PAGE

d) A = -B

The line y = m1x, y = m2x and y = m3x meet the line x + y = 1 at A, B, C respectively. If AB = BC, then 1 + m1, 1+ m2, 1+ (6 mark) m3 are b) in G.P.

d) not the terms of a progression

3 3

b)

π and AB= 12. The middle point of AC is (4, 12). Then the radius 3 (3 mark)

www.aieeepage.com

In a ∆ABC, co-ordinates of A are (4, 6), BAC=

a)

c)

2 3

 576 49  ,−   25   25

b)

7   576 ,−   25   25

d)

4 3

3

x2 y2 + = 1 is 576 49

A point of contact of a tangent of slope 1 to the ellipse

a)

63.

(3 mark)

If A = cor 84o cot 48o and B = tan 24o tan 12o, then

of the incircle of the ∆ABC is

62.

d) 18

Z1 Z2 Z1 + Z2

c) in H.P.

61.

15

a)

a) in A.P.

60.

c)

If the tangents at Z1 and Z2 on the circle Z = r meet at P(Z3 ), then Z3 is

a) A = B 59.

b) 10

c)

(3 mark)

7   576 ,−  − 25   25

7   24  ,−   25 25 

d)

The points with position vectors a + b , a − b , and a + k b , are collinear

(3 mark)

a) for a finite number of real values of k

b) for no real value of k

c) for all real values of k

d) for infinite number of real values of k

If the position vectors of A, B, C, D on a plane are a , b , c , d and if (b + c − 2d). (b − c )

(3 mark)

= (c + a − 2d) . (c − a ) = 0 then D is a) circumcentre of ∆ABC c) orthocentre of ∆ABC 64.

d) centroid of ∆ABC

G

G

G G

G

G

G

G

G

The position vectors of P, Q, R with respect to O are 3i - 2 j + k, i + 3 j+ 4 k and 2i + j - 2 k respectively. (3 mark) Then the distance of P from the plane OQR is a) 2

65.

PAGE b) incentre of ∆ABC

b)

11 3

www.aieeepage.com c) 1

d) 4

An ordinary die is rolled n times. The probability of getting an odd number 2 times is equal to the probability of getting an even number 3 times. Then the probability of getting an odd number, odd number of times is equal to (6 mark)

a)

1 16

b)

1 32

c)

3 16

d)

1 2

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66.

67.

The domain of definition of y given by x 2 − cos −1 y = π is a)

- 2π,- π  ∪  π, 2π     

b) [−2π , −π ] ∪ [π , 2π ]

c)

 2π π  π 2π  ,− , − ∪  2   2 2   2

d)

π 6

b)

69.

sin θ + 2cos θ 2

d

tan 2 θ − 1 is equal to

(3 mark)

b) log  tan θ − 1 − tan θ + 2  + c www.aieeepage.com  

c)

tan −1 (tan 2 θ + 2)

The value of nLt →∞

∫

5π 6

)

(

a)

3π

f(x) is not differentiable at x =

d) None of these

log  tan 2 θ − 1 + tan 2 θ + 2  + c  

a)

70.

cosθ 2

(6 mark)

PAGE

 5π 

c) f(x) is continuous for x ∈  0,   4 

∫

π  π    −4π , − 4  ∪  4 , 4π     

5π , then 4

If f(x) = Max {1, cos x + sin x, sin x - cos x} 0 ≤ x ≤

a) f(x) is not differentiable at x =

68.

(3 mark)

1 14

2

d)

n

n r (3 r + 4

∑ 1

b) 2

2

cot −1 (tan 2 θ + 2) (3 mark)

n )2 c)

1 2

d)

3 2

cot −1 cot x dx is equal to

(3 mark)

−π

a) 71.

72.

2π 2

3π 2

c)

9π 2

d) 16π 2

The differential equation of all those lines which are at a unit distance from the origin is 2

2

a)

dy    dy   y − x  =1−   dx    dx  2

2

c)

dy    dy   y − x  =1+   dx    dx 

If 32 cos a) 2

73.

b)

2θ −1,

6, 34− 2 cos

2θ

(3 mark)

2

dy  dy  b)  y + x  =1+ dx  dx 

PAGE 2

dy    dy  d)  y − x  = 1 −   dx    dx 

2

are the first three terms of an A.P, then the common difference of A.P is c) 1 www.aieeepage.com

b) 3

d) 4

The number of ways in which 18 dice can be thrown so that each face is displayed exactly thrice is

( 3)

6

a)

3

6

b)

( 3)

6

c)

18

18 d)

( 3)

6

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(3 mark)

(3 mark)

74.

(

3 The number of terms with rational coefficients in the expansion of x + 2 y + 3 z

a) 6 75.

b) 7

a) [ x ]

[ z + 1]

[ y]

b) [ y ]

d)

8

29

d) 01 (3 mark)

is c)

[z]

PAGE

d) 0

The number of points in the complex plane satisfying the conditions Z − 2 = 2 and Z (1 − i ) + Z (1 + i) = 4 a) 1

b) 2

c)

0

(3 mark)

d) more than 2

If x sec α + y tan α = y sec β + y tan β = a then sec α sec β =

a +y x2 + y2 2

a)

2

b)

x +y www.aieeepage.com c)

a + y2 x2 − y2 2

2

(3 mark)

2

a2 + y2

d)

x2 − y 2 a2 − y2

If the two circles x 2 + y 2 + 2 gx + 2 fy = 0 and x 2 + y 2 + 2 g ' x + 2 f ' y = 0 touch each other, then a)

80.

c)

[z] [ z]

is

79.

5

(3 mark)

If [.] denotes the greatest integer function and if −1 ≤ x < 0,0 ≤ y < 1,1 ≤ z < 2, then the

[ x]

78.

is

(3 mark)

b) 43

[ x + 1] [ y ] volue of [ x] ( y + 1]

77.

6

The last two digits of the number 3400 are a) 81

76.

c)

)

ff' = gg'

b)

f'g = fg'

c)

f 2 g 2 = f'2 g 2

d)

(3 mark)

fg' + f'g = 0

A B C is a triangle formed by the common tangents to the circles x 2 + y 2 − 6 x = 0 and x 2 + y 2 + 2 x = 0. Then

(3 mark)

81.

82.

a) the centroid of the ∆ABC is (-1, 0)

b) circumradius of the ∆ABC is

c) area of the ∆ is 2 3

d) the angle BAC is 90o

x2 y2 If 2 + 2 = 1, (a > b) and x 2 − y 2 = c 2 cut at right angles, then a b a)

a 2 = b 2 = 2c 2

c)

a 2 − b 2 = 2c 2

b)

b 2 − a 2 = 2c 2

PAGE d)

(6 mark)

a 2 b 2 = 2c 2

The period, if it exists, of f, defined by f ( x + 2) = − f ( x + 6)(∀x ∈ R ) is a) 2

83.

4 3

b) 8

c)



4

(3 mark)

d) period does not exist

 {x}   {x}    + cos    is maximum is ({x} denotes the fractional a    a  (3 mark)

The set of values of ‘a’ for which f ( x ) =  sin 



www.aieeepage.com

part of x) a)

(0, ∞)

b)

π   , ∞ 4 

c)

 1  0,   π

d)

 4  0,   π

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84.

The chord joining the points where x = P and x = q on the curve y = ax 2 + bx + c is parallel to the tangent at the (3 mark) point on the curve whose abscissa is a)

85.

1 ( p + q) 2

b)

b) ST2 = 2SP . SQ

a≠b

b)

89.

c)

y = f ( x)2 + 4 represents a parabola

b)

(3 mark)

d) 2ST2 = SP . SQ

c≠a

d)

(6 mark)

c>a (3 mark)

1

d) none of these (3 mark)

y = f ( x) represents a hyperbola

d) none of these

www.aieeepage.com

b) 5 : 8

c)

2:3

d) 3 : 2

a a 2 1  sin 2 t  − e dt esin t dt  is (Here, a is a constant)  ∫ ∫ x→0 x x+ y  y 

Lt

b)

esin

2

c)

y

(3 mark)

sin 2 y esin

2

y

d) none of these

If f is a continuous function such that f (0) = f (1) = 0, f '(1) = 2 and y ( x) = f (e x )e f ( x ) then y '(0) is b) 1

c)

2

(3 mark)

d) None of these

There are three piles of identical red, blue and green balls and each pile contains at least 10 balls. The number of (3 mark) ways of selecting 10 balls if twice as many red balls as green balls are to selected is b) 3

The straight line

c)

4

d) 5

x − 3 y − 2 z −1 = = is 3 1 0

PAGE

(3 mark)

b) parallel to y-axis

c) parallel to z-axis

95.

1 (q − p) 2

The area of the region bounded by the curve a 4 y 2 = (2a − x) x5 is to that of the circle whose radius is a, is (3 mark) given by the ratio

a) parallel to x-axis 94.

St = SP . SQ

PAGE

f ( x) > 2 ∀ x ∈ R.

a) 2 93.

c)

a)

a) 0 92.

c)

c)

Let f ( x) = e x + e − x , x ∈ R. . Then

a) 0 91.

b≠c

b) 4

a) 4 : 5

90.

d)

If ( 2) x + ( 3) x = ( 13) x / 2 , then the number of values of x is : a) 2

88.

pq 2

The function f(x) = ax − b + c x , x ∈ R (where (a, b, c > 0) assume its minimum value at x = 0, if a)

87.

c)

The tangents at P and Q on the parabola x2 = 4y meet at T. If S is the focus, then a) ST2 = SP . SQ

86.

1 ( p − q) 2

d) perpendicular to Z-axis

The equation of the sphere inscribed in a tetrahedron whose faces are x = 0, y = 0 and 2x - y + 2z = 4 is a)

x2 + y2 + z 2 − 4 x + 4 y − 4 z + 8 = 0

c)

x2 + y2 + z 2 + 4 x − 4 y + 4 z + 8 = 0

b)

x2 + y2 + z 2 − 4 x − 4 y − 4 z + 8 = 0

www.aieeepage.com d) x + y + z − 4 x − 4 y + 4 z + 8 = 0 2

2

2

3 2 2 If x + x + 1 is a factor of ax 3 + bx 2 + cx + d , then the real root of ax + bx + cx + d = 0 is

a)

(3 mark)

−

d a

b)

c a

c)

b a

d) none of these

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(3 mark)

Questions 96 - 100 are based on the following passage The graph of derivative of a function f ( x ) is given (i.e. y = f 1 ( x) ) Analyse the graph in the given domain and answer the following questions if it is given that f (0) = 0 .

y

-a

96.

The function f 1 ( x) is a) even

97.

b) odd

The graph of y = f ( x ) has a) no inflexion point

0

x

a

PAGE c)

indefinite

(3 mark)

d) neithr even nor odd (3 mark)

www.aieeepage.com b) one point of inflexion

c) one extreme point

d) two extreme points a

98.

∫ f ( x) dx is

The value of the integral

(3 mark)

−a

(a) 0 99.

b) a

c)

2a

d)

2

∫

a

0

f ( x) dx

The function f ( x ) for −a ≤ x ≤ a is

(3 mark)

a) always decreasing b) always increasing c) increasing for (−a, 0) & decreasing for (0, a ) d) increasing for (0, a ) & decreasing for (−a, 0) 100.

The function f ( x ) is a) even c) neither even nor odd

PAGE b) odd

d) indefinite

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(3 mark)

Paper - I I I : Chemistry - 101 to 150

Questions 101 to 105 are based on the following passage Just prior to World War I,the German chemist Fritz Haber developed a method for the large-scale production of ammonia from atmospheric nitrogen and hydrogen. Reaction 1 shows the equilibrium that is established between nitrogen, hydrogen, and ammonia gases.

N 2 (g) + 3H 2 (g)

2NH3 (g)

(Reaction 1)

At 298 K, the quilibrium constant for this reaction is about 6 ∞ 105 . The reaction however proceeds very slowly. From the kinetic aspect, the solution to this problem was to raise the temperature at which the reaction is carried out. However, raising the temperature favours the formation of the reactants. the van’t Hoff equation provides a way of estimating the dependence of the equilibrium constant on the temperature. In

K2 ∆H 0 =− K1 R

 1 1  −  T T 1  2

PAGE (Equation 1)

Where K1 and K2 are the equilibrium constants at T1 and T2 respectively,

∆H 0 is the standard change in enthalpy

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of the reaction, presumed to be temperature-independent, and R is the universal gas constant. Using this equation with T1=298 K, the ratio of the equilibrium constant at 800 K to that 298 K is

K 800 = 7 × 10 −11 K 298

(Equation 2)

The Haber process makes use of a catalyst composed of partially oxidized iron with a small amount of aluminum added. As gaseous nitrogen and oxygen are circulated over (and adsorb onto) the catalytic surface, ammonia is condensed out of the misture. Because the iron oxide catalyst is in a different phase than the reactant species, this process is an example of heterogeneous catalysis.

101.

Which of the following is the most likely role of the catalytic iron oxide surface in the Haber process? a) b) c) d)

102.

PAGE

Cool the reaction bulb in an ice bath and increase the overall pressure. Remove some of the ammonia as it is formed. Transfer the gases to a larger bulb that is being heated on a hot plate. Transfer the gases to a smaller bulb at room temperature

www.aieeepage.com

What is the approximate equilibrium constant of Reaction 1 at 800 K? a) 1 x 10-16

105.

(3 mark)

Its equilibrium constant at 298 K is less than 1. Its equilibrium constant at 800 K is less than 1 It is endothermic It leads to an increase in entropy

A scientist tries to synthesize ammonia in the laboratory?. If she wants to force the reaction to completion, which of (3 mark) the following methods should she NOT use? a) b) c) d)

104.

It facilitates the desorption of gaseous ammonia from the surface It interacts with the adsorbed N2 molecules and facilitates their dissociation It interacts with the ammonia molecules and weakens the N-H bonds. It stabilizes the ammonia, making the reaction more thermodynamically favorable.

Which of the following statements about the decomposition reaction of ammonia into nitrogen hydrogen is FALSE? a) b) c) d)

103.

(3 mark)

b) 4 x 10-7

c)

1 x 10-6

(3 mark)

d) 4 x 10-5

Which of the following molecules will react with H2O4 and have the highest Keq for the reaction? a) CH3CONH2

b) CH3CH2NH2

c)

(CH3CH2)2 NH

d) C6H5NH2

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(3 mark)

Questions 106 to 110 are independent Question 106.

Which of the following factors does not contribute to the energy (ε α ) of a system that has a large number of (3 mark) molecules (N) ? a) Electronic

107.

b) Nuclear

c)

Vibrational

d) Thermal

Eugenol is a dental anesthetic that is isolated from oil of cloves . The structure is shown below . What functional (3 mark) group are present in this toothache remedy ?

H 2C = C − C H H2

OH OCH 3

108.

PAGE

a) aromatic ring ,alkene , alcohol ,and ether

b) cycloalkyl ring , alkene , alcohol , and ester

c) aromatic ring , alkyne , ether and ester

d) aromatic ring ,alkene , alcohol and ester

The following values of a sample of gas were measured in the lab : P = 1.5 atm ; V = 10.3 L ; T = 298.0 K . Based on these measurements ,a student calculated the number of moles using the equation PV = nRT. Which calculated value has the correct number of significant figures ? (Note : the value of R is 0.08206 L atm K -1 mol −1 ) a) 0.63 mol

109.

c) 0.6318 mol www.aieeepage.com

b) 0.632 mol

(3 mark)

d) 0.63180 mol

∂ T

The Joule-Thompson experiment is a constant-enthalpy process measuring  ∂ P  as real gases undergo :  H

(3 mark)

110.

a) an isothermal compression

b)

an isentropic expansion

c) a throttled adiabattic expansion

d)

an adiabatic compression (3 mark)

What is the length of the bond between C1 and C2 in the structure shown below ? 1

6

2

5 4

3

a) the length of a carbon-carbon bond in an alkane b) the length of a carbon-carbon double bond in an alkene c) shorter than the length of a carbon-carbon double bond in an alkene

PAGE

d) between the length of a carbon-carbon bond in an alkane and the length of a carbon-carbon dould bond in an alkene. Questions 111 to 112 are based on the following passage Refer to the structures of D-aldoses below that are syntheized from D-glyceraldhyde to answer question 6 - 7 CHO

CHO

CHO

www.aieeepage.com

H HO

OH

HO

H

HO

H

HO

H

H

OH

H

OH

H

OH

H

OH

CH 2 OH

D - Glucose

CH 2OH

D - Mannose

H

H OH

H HO

H

OH

HO

H

OH

H

CH 2 OH

D - Altrose

CHO OH H H OH CH 2 OH

D - Galactose

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111.

what is the most specific relationship between D-glucose and D-altrose ? a) diastereomers

112.

b) enantiomers

c)

(3 mark)

epimers

d) not stereoisomers

Of the four structures shown, which are diastereomers of D-glucose ?

(3 mark)

a) D-mannose

b) D-galactose and D-mannose

c) D-mannose, D-altrose, and D-galactose

d) D-altrose

Questions 113 to 117 are independent Question 113.

Which of the following statements about chemical equilibrium is accurate ? I)

(3 mark)

Equilibrium is reached when ∆G (free energy change) equals zero.

II) ∆G o (standard free energy change) = -RT in K eq (where T = temperature, R = gas constant, K eq = equilibrium constant.) III) ∆G o is Independent of pressure. a) I only 114.

PAGE

b) II and II

c)

I and II

d) I, II, and III

Which of the following alcohols would undergo dehydration by an E1 mechanism the fastest ? OH

(3 mark)

b)

a)

www.aieeepage.com

OH

c)

d) OH

115.

HO

Many chemists consider the electronegativity of helium to be undefined. Why ?

(3 mark)

a) The small size of helium makes its electronegativity difficult to measure b) Helium does not have inner-shell electrons c) Helium atoms are electrically neutral d) Helium does not form bonds with other elements 116.

Use the van der Waals equation given below to answer question . The van der Waals equation is used to predict the behavior of real gases. a and b are constants specific for a particular gas. Their values can be obtained by (3 mark) experiment or from a reference book. 2    P + n a (V − nb) = nRT  V 2  

PAGE vander Waals Equation

The constant a and b have positive values. What is the expected difference between using the ideal gas law, PV = nRT, to calculate the pressure from measured variables, and using van der Waals equation to calculate pressure from measured variables ? a) The pressure will always be lower when calculated with van der Waals equation. b) The pressure will always be greater when calculated with van der Waals equation. c) The pressure will always be the same when calculated with van der Waals equation. d) Whether the value for pressure is lower or greater when calculated with van der Waals equation will depend upon the real volume and temperature.

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117.

Use Kohlrausch’s law to calculate the conductivity (λ o ) of NH 4 OH.

λ o(NH 4Cl) = 150, λ a) 525

o(NaOH) =

Use the fact that

248 and λ o(NaCl) = 127. The units of λ o are Ohm-1cm 2 mol−1.

b) 29

c)

271

d) 98

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(3 mark)

Questions 118 to 119 are based on the following passage

(3 mark)

Friedel-Crafts acylation is a reaction of an acid chloride with an activated aryl ring. Use the example reaction OH

OH O AlCl3 C  → Cl CH 2 CH 3

118.

The Friedel-Crafts acylation is a(n): a) substitution reaction c) addition reaction

119.

OH C =O

C=O

CH 2 CH 3

CH 2 CH 3

PAGE b)

d)

elimination reaction

(3 mark)

redox reaction

Which of the following aryl compounds would be most reactive with an acid chloride to form an aryl ketone ?

b)

a)

NO www.aieeepage.com c) OCH

2

(3 mark)

CN d)

NC Questions 120 to 145 are independent Question 120.

The following an unbalanced reaction :

(3 mark)

C12 H 22 O11 (l) + O 2 (g) → CO 2 (g) + H 2 O(g) How many moles of oxygen gas are required to burn one mole of C12 H 22 O11? a) 1 121.

b) 6

c)

12

d) 24

An unknown compound is oxidized to a carboxylic acid, in the presence of potassium permanganate. The same compound is oxidized to an aldehyde, losing an α - hydrogen in the pressence of pyridinium chloro-chromate

(C 5 H 5 NH CrO 3Cl − ). The compound is also known to exhibit mild acidic properties since it reacts with active metals (e.g. Na) liberating hydrogen gas, Based on these facts this compound is most likely :

122.

a) a primary amine.

b) a secondary ketone

c) a primary alcohol

d) a primary ketone

PAGE

What is true about an S N 2 reaction ? I)

A carbocation intermediate formed

II) The rate determing step is bimolecular III) The mechanism has two steps

www.aieeepage.com b) II only

Which of the given statement(s) match with the main statement. a) I only c) I and III only

d) I, II, and III

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(3 mark)

(3 mark)

For question refer to Habeer process shown below :

Concentration

123.

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 ample fixed nitrogen for the manufacture of explosives.

PAGE

The Habber process takes plae 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 processes. Instead of developing a catalyst, why don’t Haber increase the rate of the reaction by raising the temperature ? a) The Haber process is exothermic, so raising the temperature would have lowered the rate of the reaction. b) The Haber process is exothermic, so raising the temperature would have reduced the yield of the reaction.

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c) Higher temperatures would have caused an increase in pressure lowering the yield of the reaction. d) Higher temperatures might have decomposed the hydrogen. 124.

Direction : Use the following information to answer question . Objects radiate heat at a given by the following (3 mark) equation.

P = σεAT 4 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 emmissivity fo 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 process is given by :

Pn = σε A(Tenv 4 − T 4 ) where Pn is the net rate of energy exchange and Tenv is the temperature of the environment. An object 10 degrees warmer than the room in which it sits. In which of the following circumstance will the object reach room temperature the fastest ?

125.

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a) The room is 0°C and the object is white.

b)

The room is 0°C and the object is black

c) The room is 10°C and the object is white

d)

The room is 10°C and the object is black

Which of the following statements concerning Michael addition is not true ? a) The process involves nucleophilic addition

b) Carbanions are added to α, β - unsaturated carbonyl compounds forming carbon-carbon bonds.

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c) A base is necessary to initiate the addition

d) Compounds such as ammonia, primary and secondary amines oftern tend to inhibit Michael addition

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(3 mark)

126.

Cyelohexanol is a solid in a cool room, while cyclohexane is a liquid, what is the explanation for the different (3 mark) states ? a) Cyclohexanol has greater London Dispersion force than cyclohexane b) Cyclohexanol has weaker London Dispersion forces than cyclohexane c) Cyclohexanol has hydrogen bonding and cyclohexane does not d) Cyclohexane has hydrogen bonding and cyclohexanol does not

127.

A researcher wishes to have two 20.0 L chambers containing equal amounts (moles) of oxygen gas, one at 5 atm and (3 mark) the other at 3 atm. Is this possible ? a) Yes, if the oxygen samples in the contains have different densities b) Yes, if the oxygen samples in the containers are at different temperatures c) No, because once the volume and the number of moles of an ideal gas are known, all other parameters are determined

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d) No, because volume and pressure are inversely proportional for an ideal gas 128.

Direction : Use the diagram below to answer question . The isotherms of H 2 O are shown as solid lines on pressure (3 mark) vs. molar volume phase diagram below

P/atm

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218 85

liquid

15

r vapo 300°C

liquid + vapor

200°C

V What is the name for H 2 O at 219 atm and 375°C ? a) liquid 129.

b) vapor

c)

d) ice IX

15.0 A were passed through a lead storate cell for 1.25 hours. During this time how much electricity (q) passed (3 mark) through the cell. (Note “q” = coulombs of electricity.) a) q = (15. 0A) (1.25 hr)

c) 130.

supercritical fluid

q = (15.0A) (1.25hr) (3600 sec hr −1 )

15.0A

b)

1.25hr(3600 sec hr -1 )

d)

q=

(1.25hr) (3600 sec hr −1 ) 15.0A

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The rate of precipitate formation increases for the reaction of 1-bromobutane with Nal as the concentration of Nal is increased. When the concentration of NaI is increased in the reaction of 2-chloro-2-methylpropane. no rate change (3 mark) is observed. Why is there a change in rate in the first case and not in the second ? a)

− Cl− is a better leaving group than Br .

b)

− Br is a better leaving group than Cl −

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c) 1-bromobutane proceeds via a S N 2 mechanism, while 2-chloro-2-methylpropane proceeds via a S N 1 mechanism. d) 1-bromobutane proceeds via a S N 1 mechanism, while 2-chloro-2-methylpropane proceeds via a S N 2 mechanism.

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An aromatic compound contains 69.4% carbon and 5.8% hydrogen. A sample of 0.303 g of this compound was analysed for nitrogen by Kjeldahl’s method. The ammonia evolved was absorbed in 50 ml. . of 0.05 M sulphuric acid. The excess of acid required 25 ml. of 0.1 M sodium hydroxide for neutralization. Determine the molecular formula of the compound if its molecular weight is for neutralization. Determine the molecular formula of the compound if its (6 mark) molecular weigh is 121. a)

C 6 H 5 NO

c)

C 5 H 5 CH 2 NO

n =5→n =2

b)

n = 5 → n =1

c)

n = 4 → n =1

d)

n = 3 → n =1

Which of the following graphs below best represents the distribution of the blackbody radiation at several temperatures ? (3 mark)

PAGE

30 0

E n e r g y

K 00 15

10

00

b)

K

1500K 1000K

Wavelength

2000K

1500K

d)

00

E n e r g y

25

2500K

30 00 K

3000K

c)

2500K 2000K

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Wavelength

E n e r g y

3000K

E n e r g y

K

a)

K 00 20

K 00 15 10

K 00

Wavelength

Wavelength

134.

d) None of these

One emission line in the spectrum of the hydrogen atom occurs at a wavenumber of 23,032. Assuming the Rydberg (3 mark) constant is 109, 678, the line represents a transition between which two quantum levels ? a)

133.

b)

0K 25 00 K

132.

C 7 H 7 NO

20 00 K

131.

Usae the table shown below to answer question

Acid

(3 mark)

pK a

CH 3CH 2COOH

4.87

CH3 COOH

4.74

CH 3CH 2 CH 2 COOH

4.82

ClCH 2CH 2 CH 2COOH

4.52

ClCH 2 COOH

2.86

Cl 3CCOOH

0.64

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Which of the following has the most acidic proton ? a)

CH 3CH 2 COOH

c)

ClCH 2 COOH

b)

CH 3COOH

d) Cl CCOOH www.aieeepage.com 3

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135.

When 16.8 g of white solid X were heated, 4.4 g of acid gas A that turned lime water milky was driven off together with 1.8 g of a gas B which condensed to a colourless liquid. The solid that remained, Y, dissolved in water to give an alkaline solution, which with excess barium chloride solution gave a white precipitate Z. Thje precipitate effervesced (6 mark) with acid giving off carbon dioxide. Which of the following statement(s) give the correct result of the identification I)

X is NaHCO 3

II) A is CO 2 and B is H 2 O

III) X is BaCO 3

IV) Y is Na 2 CO 3

a) II & III b) only III c) I, II & IV d) The given information is not sufficient for identification. 136.

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A metal complex having composition Cr(NH 3 ) 4 Cl 2 Br has been isolated in two forms (A) and (B). The form (A) reacts with AgNO 3 to give a white precipitate readily soluble in dilute aqueous ammonia, whereas (B) gives a pale yellow precipitate soluble in concentrated ammonia. Calculate their magnetic moments (spin - only value).

137.

a)

2 15 BM

c)

15 BM

b)

2 5 BM

d)

5 BM

(3 mark)

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Several types of organics compounds undergo elimination to form alkenes when heated to relatively high temperatures. Which of the compounds below does not exhibit this tendency ? (3 mark)

O a)

R

S

− C - OCH 2 CHR '2

(an ester)

b)

R - S - C - OCH 2 CHR '2 (a xanthate) O

(CH 3 )3C

H

S

H 2C

OCSCH 3

H

c)

d)

H 2C

C

OH OH C O

138.

The polymerization reaction with adipic acid to form Nylon 6.6 is shown below, Nylon 6.6 is a(n) (3 mark)

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nH 2 N(CH 2 ) 3 NH 2 + nHOOC(CH 2 ) 4 COOH O

O

H NH(CH 2 ) 6 NHC(CH 2 ) 4 C OH

(2n − 1)H 2 O

Nylon 6.6

a) polyster c) dicarboxylic acid

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139.

The Haber process can be represented by the following scheme :

(3 mark)

Identify A, B, C, D CaCO 3

CO 2 CaO NH 3 , H 2 O

H 2O

B

A

NaHCO 3 + D

NaCl

C + H 2O

140.

a)

Ca(OH) 2

CaCl 2

b)

NH 4 HCO 3

c) d)

NH 3 + H 2 O + E

CaCO 3

Ca(HCO 3 ) 2

(NH 3 ) 2 CO 3

NH 4 Cl

NH 3

Na 2 CO 3

NaHCO 3

NaOH

NaCl

NH 4 Cl

NH 4 OH

NH 3

(NH 3 ) 2 CO 3

PAGE

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Find the equilibrium constant for the reaction,

(3 mark)

In 2 + Cu 2 + → In 3+ + Cu + at 298 K

0 0 Given : E Cu 2+ /Cu + = 0.15V; E In 2 + /In + = −0.40V, E In 3+ /In + = −0.42 V

a) 141.

1010

b) 108

c)

106

d) none of these

The reactions below represents a possible mechanism for the chlorination of methane. Indicate which of the (3 mark) statements below is (are) true. Mechanism uv ligh

1)

Cl 2   → 2Cl.

2)

Cl ⋅ + CH 4 → HCl + ⋅CH 3

3)

CH 3 ⋅ + Cl 2 → Cl + ⋅CH 3Cl

4)

Cl ⋅ + Cl⋅ → Cl 2

5)

CH 3 ⋅ + Cl⋅ → CH 3Cl

I.

Steps (2), (3) and (4) represents the chain propagating steps,.

II. If we add oxygen to the reaction vessel, the series of reactions shown above would proceed more rapidly, oxygen would catalyst the reaction.

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III. Step (4) is most likely the rate determinant step.

IV. Step (5) represents a possible termination step for the reaction a) I only 142.

b) II only

c)

IV only

d) II and IV only

The density of mercury is 13.6 g/ml. Calculate approximately the diameter of an atom of mercury assuming that (6 mark) each atom is occupying a cube of edge length equal to the diameter of the mercury atom. a)

2.91 A cm

b)

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2.44 A cm

d) 1.98 A cm

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143.

144.

The vaour pressure of the two miscible liquids (A) and (B) are 300 and 500 mm of Hg respectively. In a flask 10 moles of (A) is mixed with 12 moles of (B). However, as soon as (B) is added , (A) starts polymerizing into a completely insoluble solid. The polymerization follows first-order kinetics. After 100 minutes, 0.525 mole of a solute is dissolved which arrests the polymerization completely. The final vapour pressure of the solution is 400 mm of Hg. Estimate the rate of constant of the polymerization reaction. Assume negligible volume change on mixing and poilymerization and (6 mark) ideal behaviour for the final solution. a)

2.303 × 10 −5 min −1

b)

2.303 × 10 −4 min −1

c)

1.005 × 10 −4 min −1

d)

.905 × 10 −4 min −1

Nitro benzene is formed as the major product along with a minor product in the reaction of benzene with a hot mixture of nitric acid and sulphuric acid. The minor product consists of carbon : 42.86%. hydrogen : 2.40% nitroge : 16.67%, and oxygen : 38.07% (i) Calculate the empirical formula of the minor product. (II) when 5.5 g of the minor product is dissolved in 45g of benzene, the boiling point of the solution is 1.84 °C higher than that of pure benzene. The molar (6 mark) mass of the minor product and its molecular and structurral formula is.

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a) The Molar mass is 184 g mol−1 and the product is m-dinitrobenzene b) The molar mass is 184 g mol−1 and the product is 2 2(C 3 H 2 N O 2 ) c) The molar mass is 168 g mol −1 and the product is C 6 H 4 (NO 2 ) 2 d) The molar mass is 253 g mol−1 and the product is C 6 H 4 (NO 2 ) 2 145.

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The standard molar enthalpies of formation of cyclohexane(l) and benzene (l) at 25°C are -156 and +49 kJ mol-1 respectively. The standard enthalpy of hydrogenation of cyclohexene (l) at 25°Cis -119 kJ mol-1 . Use these data to (3 mark) estimate the magnitude of the resosnance energy of benzene a)

- 357 Jmol -1

b)

- 205 Jmol -1

c)

- 152 Jmol -1

d)

- 562 Jmol -1

Questions 146 to 150 are based on the following passage One technological application of thermodynamics in our society is in the form of heat packs and cold packs. These devices contain chemicals, which react in an endothermic or exothermic chemical reaction. Commonly, cold packs contain ammonium nitrate and water in two separate compartments. When the contents of the separate compartments are mixed, a chemical reaction occurs due to the high solubility of ammonium nitrate in water. The associated enthalpy change is referred to as enthalpy of solution or heat of solution. The process of dissolution (Reaction 1) of ammonium nitrate is highly endothermic and the cold pack absorbs heat from its surroundings, making it feel “cold”. the enthalpies of solution and solubility values for a number of ionic compounds are listed in Table 1.

→ NH 4 (aq ) + NO3− (aq), Standard ∆H rxn = +25.69kJ / mol NH 4 NO3 (s) 

Compound Silver chloride Sodium Chloride Lithium Fluoride Rubidium Fluoride

Reaction 1

PAGE ∆H Solution (kJ/mol)

Solubility in water (g/100 mL)

61

0.000089 (10 degrees C)

26

35 . 7 (0 degrees C)

-3

130 . 6 (18 degrees C)

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The chemical processes which take place in hot packs are varied. One style of hot pack utilizes the energy changes which are associated with the crystallization of sodium acetate (NaCH3CO2) in the presence of water (Reaction 2)

Na + (aq) + CH 3CO 2 - aq) + 3H 3O(1)  → NaCH 3CO 2 .3H 2O(s) Standard ∆H rxn = −387.6kJ / mol

Reaction 2

Alternatively, the oxidation of transition metals, which is often exothermic, may be used to produce “heat” in a hot pack. When elemental Iron reacts with oxygen in the atmosphere, it oxidizes (Fig.3). One advantage of this reaction is the ability to package and store the iron in an environment void of oxygen unitl it is ready to use. If oxygen flow is somewhat restricted, hot packs of this type can maintain a temperature of 58 to 68 degrees Celsius for hours.

→ 2Fe2O 2 (s) 4Fe(s) + 3O 2 (g) 

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Standard ∆H rxn = −1648.4 kJ/mol 146.

From the information given in the passage, the molar solubility of solubility of sodium chloride in water at 0 degrees (3 mark) Celsius would be a) 35.7 moles/L

147.

c)

6.11 moles/L

d) 1.64 moles/L

If 61.11 g of ammonium nitrate were dissolved in an excess of water, the amount of energy released would be a) 61.1 kJ

148.

b) 0.611 moles/L

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b) 0.764 kJ

(3 mark)

d) 25.69 kJ

The reason silver chloride would not be practical if used in a cold pack is

(3 mark)

a) Silver chloride is not an ionic compound and is therefore not soluble in water. b) Silver chloride has an enthalpy of solution that is too high c) The solubility of silver chloride in water is too low d) The dissolution of silver chloride in water is exothermic 149.

What is the freezing point of a saturated aqueous solution of Lithium Fluoride (Kb=-1.86 K/m)? a) -1.86 degrees Celsius c) 0.186 degrees Celsius

150.

(3 mark)

b) -0.186 degrees Celsius d) -0.1 degrees Celsius

The entropy change involved in the oxidation of iron (Reaction 3) would have which of the following thermodynamic (3 mark) effects? a) At very high temperatures, the oxidation of iron would be non-spontaneous. b) At very low temperatures, the oxidation of iron would be non - spontaneous c) At very high temperatures, the entropy change would be favorable.

PAGE

d) The entropy change would have no effect on the oxidation of iron.

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