Ai Iitjee Modeltest 01

IIT-JEE Model Test - 01

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

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1. 2. 3. 4. 5.

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

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Paper - I : Physics - 1 to 50 Questions 1 - 5 are based on the following passage A bimetallic strip is a simple device that capitalizes on the difference between the thermal expansion properties of two metals. When the strip is heated, one metal expands more than the other, causing the strip to bend. An important application of the bimetallic strip is the ‘thermal switch’ usd in electrical circuits. some kitchen toasters use a thermal switch as a timing device. Figure -1 shows a simplified version of a toaster circuit, with the thermal switch labeled S”. the toaster is plugged into a wall outlet supplying alternating current with Vms=120 volts.

PAGE Magnet

r

R

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120 V

Figure - 1

Depressing the spring-loaded toaster handle lowers the toast tray and closes switch S, a mechanical switch that is unaffected by temperature. The toast tray is held down against the opposing upward force of the spring by an electromagnet, which creates a magnetic field varying linearly with current. Meanwhile, the bread is being toasted by radiative heat transfer from the resistance R, a long wire that runs back and forth on the sides of the toast tray. This resistor is made from a wire of high resistivity to keep the current within acceptable limits. As the temperature within the toaster rises, the bimetallic strip S’ starts to bend, and at a sufficiently high temperature, bending of the thermal switch is enough to break the circuit, cutting off current to the electromagnet. The tray pops up and the toasting process is ended.

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Alternatively, the function of the bimetallic strip as a timing device can be fulfilled by a capacitor connected in series with the electromagnet. When the switch S is closed, the capacitor begins to charge and the current in the electromagnet decreases, eventually dropping below the critical value necessary to hold the handle assembly down magnet 120 V S R r S’ 1.

If the heating element of the simplified toaster in Figure-1 is a cylindrical wire of resistivity ohm-meters, length 0.5 m and diameter 0.2 cm, the power dissipated by the resistor will be most nearly (3 mark) equal to:

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a) 0.1/p

b) 120/p

c) 500/p

d) 14500/p

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2.

Each of the following changes to the capacitor-based toaster discussed in the passage would produce (3 mark) darker toast EXCEPT. a) Using a spring with a smaller spring constant in the toast tray. b) Using a stronger electromagnet. c) Using a capacitor with a smaller separation between the plates. d) Using a higher resistance wire as the heating element.

3.

It takes 10 J of energy to depress the handle of toaster 1 a given distance. If it takes 60 J of energy to the handle. of toaster 2 twice this distance, then the ratio of the spring constant of Toaster 1 to that of Toaster 2 is : (3 mark) a) 1 : 6

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b) 6 : 1 c) 2 : 3 d) 3 : 2 4.

Which of the following represents the magnitude of the maximum voltage supplied by the wall outlet (3 mark) discussed in the passage ?

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a) 120 2 V b) 120 / 2 V c) 120 V d) 60 V 5.

Rank the following combinations of resistors in order of DECREASING current supplied by a battery (3 mark) connected between points x and y .

R 1)

R

R R R

3)

R

2)

PAGE 4)

R a) 1, 2, 3, 4 c) 3, 4, 2, 1

R

R

R

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Questions 6 to 45 are independent Questions 6.

A cylinder of length 76 cm, has two flexible diaphragms at its ends and one at its middle. The two parts contain hydrogen and oxygen gas separately. The two end diaphragms are set into vibrations by the same source. Determine the minimum frequency of the source, whic will render th middle diaphragm (3 mark) motionless. Speed of sound in H2 and O2 are 1100ms-1 and 310 ms-1 respectively. a) f= 568 Hz b) f = 569 Hz c) f = 570 Hz d) f = 569 Hz

7.

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A charge Q is divided into two parts such that charge on each part is q and

Q = 2 . The Coulombic q (3 mark)

force betwen the two charges q and q when placed some distance apart 1) is maximum irrespective of the medium in which they are placed 2) is minimum

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3) is equal in magnitude for both but opposite in direction 4) is dependent on the medium in which charges areplaced Which of the given statement(s) match with the main statement. a) 1, 2, 3 b) 1, 3, 4, c) 2, 3, 4 d) None of these 8.

A uniformly stretched string is made to vibrate in its fundamental mode. Maintaining the same fundamental frequency, the length (l) of the string is adjusted according to the tension (T). \the two are (3 mark) plotted on a log-log scale, adopting length on the Y axis. The slope of the line will be : a) 2 b) 1/ 2 c) 1 d) 1/4

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9.

In the circuit shown:

(3 mark)

2Ω 3Ω

4Ω

PAGE 0.2 µ F

6 V

2.8Ω

1) a current of 0.9A flows through 2Ω resistor when steady state is reached

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2) a potential drop of 4.2 V appears across the resistance of 2.8 Ω 3) a potntial drop of 1.8 V appears across the capacitor C 4) a potential of 4.2 V appears across the capacitor C

Which of the above given statements are correct with reference to the figure. a) 1, 2, 3 b) 1, 2, 4, c) 2, 3, 4 d) None of these

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The emission spectrum of a black body at two different temperatures are shown by curves P and Q. The ratio of the areas under the two curves P and Q will be: (3 mark)

Intensity

10.

Q P

PAGE 1987 2980 Wavelength (nm)

a) 1 : 16 b) 4 : 9

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c) 81 : 256 d) 16 : 81 11.

A proton moving with a constant velocity passes through a region of space without any change in velocity. If E and B represent electric and magnetic fields, respectively, the region of space may have 1) E = 0; B = 0

2) E = 0; B ≠ 0

3) E ≠ 0; B = 0

4) E ≠ 0; B ≠ 0

(6 mark)

Which of the given statement(s) match with the main statement. a) 1, 2, 3 b) 2, 3, 4, c) 1, 2, 4, d) None of these

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12.

In a thermodynamic process the final volume and pressure of an ideal gas are same as the initial (3 mark) volume and pressure. It ncessary follows that: a) The net change in internal energy of the gas is zero b) The net work done by the gas is zero c) The net heat supplied to the gas is zero d) None of the above

13.

When photons of energy 4.25 eV strike the surface of a metal A, the ejected photoelectrons have maximum kinetic energy, TA expressed in eV and de Broglie wavelength λ A . The maximum kinetic eenergy of photoelectrons liberaated from another metal B by photons of energy 4.70 eV is TB =

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(TA - 1.50 eV). If the de Broglie wavelength of these photoelectrons is λB = 2λ A , Then 1) the work function of A is 2.25 eV

2) the work function of B is 4.20 eV

3) TA= 2.00 eV

4) TB = 2.75 eV

(3 mark)

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Which of the given statement(s) match with the main statement. a) 1, 2, 3 b) 2, 3, 4, c) 1, 2, 4, d) None of these 14.

A steel drill making 180 revolutions per minute is used to drill a hole in a block of steel. \the mass of the steel block and drill is 180 g. If the entire mechanical work is used up in producing heat and the rate of rise of temperature of the block is 0.50C/s, then the torque required to drive the drill is: (Spe(3 mark) cific heat capacity of steel =0.1 cal/g-oC) a) 0.5 N-m b) 1 N-m c) 1.5 N-m d) 2 N-m

15.

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To produce a minimum reflection of wavelengths near the middle of visible specctrum (550 nm) how (3 mark) thick should a coating of MgF2 ( µ = 1.38). be vacuum - coated on a glass ssurface: a) 10-7 m b) 10-10 m c) 10 m

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-9

d) 10-8m

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16.

One mole of an ideal gas is taken from state A to state B as shown in figure. The maximum temperature attained during the process is: (3 mark)

P A

2P0 P0

B

PAGE Vo

a)

3 Pθ V0 2 R

9 Pθ V0 b) 4 R

c)

2Pθ V0 R

d)

Pθ V0 2R

2Vo

V

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17.

A small conducting sphere of radius a mounted on an insulating haandle and having a positive charge q is inserted through a hole in the walls of a hollow conducting sphere of inner radius b and outer radius c. The hollow sphere is supported on an insulating stand and is initially uncharged and the small sphere is placed at the centre of the hollow sphere. Neglect any effect of hole. Which of the following statements will be true for this system? 1) The electric field at a point in the region between the spheres at a distance r from the centre is equal to ( q / 4πε 0 r 2 ) 2) The electric field at a point outside the hollow sphere at a distance r from the centre is equal to ( q / 4πε 0 r 2 )

3) No work will be done in carrying a small charge from the inner conductor to the outer conductor

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4) The potential of the inner sphere with respect to the outer sphere is given by: Vab =

(6 mark)

Which of the given statement(s) match with the main statement. a) 1, 2, 4 b) 1, 2, 3

q 1 1  −  4πε 0  a b 

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c) 1, 2 d) 2, 3, 4 18.

A liquid rises to a height h in a long vertical capillary tube, when immersed in it. If the liquid be made to rise in a capillary of length nh (n < 1) projecting out, the angle between the capillary surface and the free meniscus at the point of contact will be : (Assume the liquid to completely wet the tube) (3 mark) a) cos −1 (1 − n) b) cos −1 (n) c) cos −1 (2n) d) cos −1 (1 − 2n)

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19.

r A particle of charge -q and mass m enters in a uniform magnetic field B (perpendicular to paper inwards) at P with a velocity V0 at an angle α and leaves the field at Q with velocity v at angle β as shown in figure. Then (6 mark)

x P x

x

x

x

x

x

V β

1) α = β 2) v = v0 3) PQ=

v0 x B

PAGE x Q x

x

x

x

x

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2mv0 sin α Bq

2m(π − α ) Bq Which of the above given statements are correct with reference to the figure. a) 1, 2, 3, 4

4) particle remains in the field for time t =

b) 1, 2, 3 c) 1, 2 d) None of these 20.

A beaker containing water with a total mass of 10 kg is placed on the pan of a balance ‘A’. A solid body of mass 5 kg and density 50 g/cc suspended from a spring balance B is gently lowered in the water contained in the beaker, so that it gets fully immersed without any contact with the baker. The readings shown by the balance A and B will be respectively as: (3 mark) a) 10 kg and 5 kg b) 9 kg and 6 kg c) 11 kg and 4 kg d) 10.1 kg and 4.9 kg

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21.

As the position of an object (u) from a concave mirror is varied, the position of the image (v) also varis. By letting u change from 0 to + ∞ the graph between v and u will be: (3 mark)

v f

a)

v f

b)

u

PAGE u

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v f

c)

u

v f

d)

22.

u

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A block is resting on a piston which executes simple harmonic motion with a period of 2.0 s. The maximum velocity of the piston, at an amplitude just sufficient for the block to separate from the piston is: (3 mark) a) 1.57 ms-1 c) 2.0 ms

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23.

A conducting sphere of radius R has a charge. Then:

(3 mark)

1) the charge is uniformly distributed over its surface, if thre is no external electric field 2) distribution of charge over its surface will be non-uniform, if an external electric field exists in the space 3) the electric field strength inside the sphere will be equal to zero only when no external electric field exists 4) potential at every point of the spehere must be same Which of the given statement(s) match with the main statement. a) 2, 3, b) 1, 2 c) 1,3 d) None of these 24.

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A unform thin ring of mass M1 and radius R is kept with its plane horizontal, vertially above a uniform solid sphere of mass M2 and radius R. The centre to centre distance between them is 2 2 R . The gravitational force acting between them is: (3 mark)

25.

a)

2 GM1M 2 9R2

b)

2 2 GM1M 2 27 R 2

c)

GM1M 2 16 R 2

d)

2 2 GM1M 2 9R2

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In a household electric circuit:

(3 mark)

1) all electric appliances drwing power are joined in parallel 2) a switch may be either in series or in parallel with the appliance which it controls 3) if a switch is in parallel with an appliance, it will draw power when the switch is in the off position (open)

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4) if a switch is in parallel with an appliance, the fuse will blow (burn out) when the switch is put on (closed) Which of the given statement(s) match with the main statement. a) 1, 3, 4 b) 1, 2, 3

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c) 1, 2 d) None of these

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26.

A uniform rod AB rests on a smooth floor leaning against a smooth wall. The rod AB is released when (3 mark) θ is small. The instantaneous centre of rotation always lies in the: Y B

A

a) First quadrant b) Second quadrant c) Third quadrant d) Fourth quadrant 27.

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Which of the following statements are correct?

(3 mark)

1) A mirror cannot give rise to chromatic aberration 2) A lens gives risee to chromatic aberration 3) A lens gives rise to spherical aberration 4) A mirror can give rise to spherical aberration Which of the given statement(s) match with the main statement. a) 1, 2, 3, 4 b) 1, 2, 3 c) 1, 2, 4 d) None of these 28.

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A hollow conical vesel is filled with water at a constant rate.The rate at which the centre of mass of water in the cone rises is plotted against the height of water in the cone on a log - log scale, by taking them on Y and X-axis respetiely. The slope of the line will be : (3 mark) a) -1 b) -2

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c) -3 d) -

3 2

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29.

In the ccircuit shown in the figure, switch S is closed at time t=0. Select the correct statements: (6 mark)

2R

C

2C

R

PAGE S

E

1) rate of increase of charge is same in both the capacitors

2) ratio of charge stored in capacitors C and 2C at any time t would be 1 : 2 3) time constants of both the capacitors are equal

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4) steady state charge in capacitors C and 2C are in the ratio of 1: 2 Which of the given statement(s) match with the main statement. a) 2, 3, 4, b) 1,2,3 c) 2, 1 d) None of these

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30.

Two identical balls A and B lie on a smooth horizontal surface, which gradually merges int a curve to a height 3.2 m. Ball A is given a velocity of 10 m/s, to collide headon with ball B, which then takes up the curved path. The mnimum coefficient of restitution e for the collision between A and B, in order (3 mark) that ball B reaches the highest point C of the curve is (g = 10 m/s2):

C

3.2 m

A O

31.

a)

1 4

b)

3 5

c)

1 2

d)

3 4

PAGE B O

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1 floats on water in a large tank. The work done in 2 pressing the ball down, in order that, the ball just gets immersed in water is : ( ρ = density of water)

A small ball of radius r and specific gravity

(6 mark)

2 4 a) π r ρ g 3

b)

1 4 πr ρg 3

c)

5 π r4ρ g 12

7 4 d) π r ρ g 8

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32.

Two identical double convex lenses each of focal length f are made of glass of µ = 1.5. If R is the (3 mark) radius of ccurvature of each of the four faces: 1) the focal length of combination is half the radius of curvature of any of the four faces 2) the focal length of combination increases if the lenses are separated by a distance f and the new focal leength is twice is focal length when the lenses are in contact 3) the focal length of combination decreases when the lenses are separated by a distance f and the new focal length is half of the focal length when the lenses are in contact. 4) none of the Which of the given statement(s) match with the main statement. a) 1, 2 b) 1, 4 c) 3, 2 d) None of these

33.

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A train p runs along the direction east to west and another train Q runs from west to east along parallel tracks placed at the equator. If both the trains move with the same speed and the thrust offered by the (3 mark) two trains on their respective tracks be T1 and T29 then

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a) T1 = T2 b) T1 < T2 c) T1 > T2 d) The given information is not enough to establish any relation between T1 and T2. 34.

ABCD is a square of side a metres and is made of wires of resistance x ohm per metre. Similar wires are connected across the diagonals AC and BD. The effective resistance between the corners A and C (3 mark) will be

12 B

A 11

PAGE D

a) (2 − 2)ax b) 6ax c) 3ax

C

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d) (3 − 2)ax

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35.

A particle of mass 500 gm moves with an intial velocity of (5iˆ + 2 Jˆ ) m/s on X - Y plane. A force  1  F=  iˆ − Jˆ   8  N acts on the particle. If the initial position of the particle be (2m, 3m) then the position at the instant (3 mark) when the particle is moving purely along X - axis is:

a) (38 m, 7 m) b) (2 m, 8 m) c) (72 m, -2 m) d) (6 m, 39 m) 36.

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The electric field at the centre of a uniformly charged ring is zero. What is the electric field at the (3 mark) centre of a half ring if the charge on it be Q and its radius be R? 1 Q a) 4πε π R 2 0

1 Q b) 4πε R 2 0

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1 2Q c) 4πε π R 2 0 1 2Q d) 4πε R 2 0

37.

A ball strikes the horizontal X - Y plane with a velocity of (10iˆ + 30 Jˆ − 2okˆ ) m/s, and rebounds (3 mark) elastically. Its velocity after t = 2 sec will be: a) 10iˆ + 30 Jˆ + 2okˆ b) 10iˆ + 30 Jˆ c) 10iˆ + 30 Jˆ − 2okˆ d) −10iˆ − 30 Jˆ + 2okˆ

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38.

An equilateral triangular loop ADC having some resistance is pulled with a constant velocity v out of a uniform magnetic field directed into the paper. At time t = 0, side DC of the loop is at the edge of the (3 mark) magnetic field. The induced current (I) versus time (t) graph will be as:

x

x

x x

x

x

x

x

x

x

x

x

xD x

I a)

t

A

x Cx v

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I

b) t

I

c) t I

d) t

PAGE

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39.

A projectile is projected at an angle θ . When the projectile reaches to a height three-fourth that of maximum height, the angle made by the velocity with the horizontal is complimentary to the angle of (3 mark) projection. The value of θ is a) cot -1 ( 2)  3 -1 b) tan  2     1 -1 sin   c)  2  1 -1 d) cos  3   

40.

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In the circuit shown in the figure, if both the bulbs B1 and B2 are identical:

(3 mark)

B1 L=10mH

B2

220v, 50 Hz 1) their brightness will be the same 2) B2 will be brighter than B1 3) as frequency of supply voltage is increased, brightness of B1 will increase and that of B2 will decrease

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4) only B2 will glow because the capacitor has infinite impedance Which of the given statement(s) match with the main statement. a) 2,3 b) 2,4

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c) 1,2 d) None of these

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41.

Two particles P and Q are projected from two different points simultaneously as shown in figure 5.63. (3 mark) The instant when they will be minimum distance apart is: (g = 10 m/s2)

10 2 m / s

20 2 m 20 2 m / s

a)

1 sec 2

b)

1 sec 3

c)

4 sec 5

450

PAGE

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d) 1 sec 42.

(3 mark)

Whenever a hydrogen atom emits a photon in the Balmer series: 1) it may emit another photon in the Balmer series 2) it must emit another photon in the Lyman series 3) the second photon, if emitted, will have a wavelength of about 122 nm 4) it may emit a second photon, but the wavelength of this photon cannot be predicted. Which of the given statement(s) match with the main statement. a) 2, 3 b) 2, 4 c) 1, 2 d) None of these

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43.

Suppose the frequency of emitted photon is f0 when electron of a stationary hydrogen atom jumps from a higher state m to a lower state n. If the atom is moving with a velocity v(<< c) and emits a photon of frequency f during the same transition, then which of the following statements are possible? 1) f may be equal to f0

2) f may be greater than f0

3) f may be less than f0

4) f cannot be equal to f0

(3 mark)

Which of the given statement(s) match with the main statement. a) 1, 2, 4 b) 1, 3, 4 c) 1, 2, 3 d) None of these

44.

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r Given that the force (Lorentz force) F experienced by a particle havig a charge q and velocity vr in a r r r r magnetic field B is given by F = q (v × B) . What is the direction of force acting on electrons falling (3 mark) vertically, at a place where the earth’s magnetic field is horizontal pointing towards notht?

a) East

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b) West c) South d) Vertically up 45.

The threshold wavelength for photoelectric emission from a material is 5200Å. Photoelectrons will be emitted when this material is illuminated with nonochromatic radiation from a: (3 mark) 1) 50 watt infrared lamp

2) 1 watt infrared lamp

3) 50 watt ultraviolet

4) 1 watt ultraviolet lamp

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

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Questions 46 - 50 are based on the following passage The compound pulley is a machine used to lift a heavy object (load); its essential components are shown in Figure - 1

Pulley 2

Pulley 1

PAGE Applied force, F

Load

Figure 1 Compound pulley

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A rope, which supports the load,is attached to the ceiling, passes around pulley 1, and is then redirected by pulley 2 so that a downward tension force, F, can be applied as shown. When this force acts, pulley I moves up with the load, it is referred to as a moveable pulley. Pulley 2, on the other hand, is a fixed pulley. It remains stationary. The mechanical advantage, MA, of a pulley system is the ratio of the force produced on the load to the force applied to the main rope: MA =

force on load applied force

In this system, the theoretical mechanical advantage is 2. By adding additional moveable pulleys, the reqired force can be further diminished. While an ideal compound pulley reduces the force needed to lift an object, it does not reduce the work. this is because the reduced force must be applied over a correpondingly greater distance. In reality, the work done on the load is somewhat less than the work done by the applied force. The difference arises because soem energy is lost to friction, both in the contacts between rope and pulley and in the internal bearings of the pulleys themselves. The magnitude of this effect is represented by the efficiency of the system, which is defined as the ratio of work output to work input. efficiency =

Work output Work input

PAGE

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For any real pulley system, the efficiency is less tan one, and the mechanical advantage is less than it would be in an idealized system.

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46. The upper limit on mechanical advantage for the pulley system shown below is :

(3 mark)

PAGE

a) 3 b) 5 c) 6

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d) 7

47. In a particular compound pulley system, 20% of the energy is dissipated as heat. The ratio of the distance over which the force is applied to the distance the load moves is 6. What force would be (3 mark) required to move a load weighing 1000 Newtons? a)

1000 (0.8) N 6 1000

b) (0.8) 6 N c)

(0.8) 6 N 1000 (0.8)

d) 1000 (6) N

PAGE

48. The absolute value of the work done by the normal force on a perosn in an elevator moving downward (3 mark) over a fixed distance with decreasing speed is: a) greater than the work done by gravity because the normal force is larger than the gravity force. b) zero because the normal force is always perpendicular and therefore can do no work

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c) less than the work done by gravity because the normal force is less than the gravity force. d) less than the work done by gravity because the elevator is moving down.

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49. A compound pulley composed of one moveable pulley and one fixed pulley is used to lower a load. The (3 mark) applied force necessary to keep the load from accelerating as it moves downwards : a) must be more than the applied force necessary to keep the same load moving upwrds at a constant speed. b) must be less than the applied force necessary to keep the same load moving upwards at a constant speed. c) must be equal to the applied force necessary to keep the same load moving upwards at a constant speed. d) could be either more, less, or equal to the applied force necessary to keep the same load moving upwards at a constant speed.

PAGE

50. A pulley mounted at the top of a flagpole enables a person standing at the bottom to raise and lower the (3 mark) flag. The mechanical advantage of this system, assuring friction, is : a) 0 b) 1

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c) - 1 d) 1/2

PAGE

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Paper - II : Mathematics - 51 to 100 Questions 51 to 52 are based on the following passage

A player ‘A’ plays a game against a machine. At each rooud he deposits one rupeee in a slot and then flips a coin which has a probability p of showing a head. If a head shows, he gets back the rupee he deposited and one more rupee from the machine. If a tail shows, he loses his rupee. Let A starts with 10 rupee and q = 1 -p 51.

The probability that he is left with no money by the tenth round or earlier is

(3 mark)

a) q10 10

b) ∑ 10 C r p r q10+ r r =1

c) pq 9 d) 1 - p10

52.

PAGE

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The probability that he is left with no money by the 14th round or earlier is

(3 mark)

a) q10 (1 + 10pq + 45p2 q 2 ) b) q14 (p 2 q + 36pq + 7) c) q12 + 3pq13 + 3p13q + p12 d) 1 −10 C1 pq11 −10 C 2 p 2 q12 Questions 53 to 97 are independent questions 53.

Let PM be the perpendicular from the point P(1, 2, 3) to x - y plane. If OP makes an angle θ with the positive direction of the z-axis and OM makes an angle φ with the positive direction of x-axis, where (6 mark) O is the origin then (θ and φ are acute angles)

PAGE

Which of the following is statement(s) are correct ? 1) tan θ =

5 3

3) tan φ = 2 a) 1, 2, 3 c) 1, 4

2) sin θ sin φ =

4) cos θ cos φ =

2

14 1

14 www.aieeepage.com

b) 2, 3, 4 d) none

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2

54.

The solution of 1) y −

dy  dy  = y2   + 2 y cot x dx  dx 

(3 mark)

is

c =0 1 + cos x c

−1 3) x = 2 sin 2 y

c 1− cos x

2)

y=

4)

x = 2 cos −1

c 2y

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

55.

Let a)

 f : 0, 

π →R 2 

PAGE

π 1 . If a < f   < b, then a and b can be www.aieeepage.com 1 + cos x 2

be such that f(0) = 3 and f ' ( x) =

(3 mark)

π ,π 2

b) 3, 4 π 4

π 2

π 2

3π 4

c) 3 + , 3 + d) 3 + , 3 +

56.

(3 mark)

For the curve y = be x | a 1) the subtangent is of constant length 2) the subnormal is of constant length

PAGE

3) the subnormal varies as the square of ordinate 4) the subtangent varies as the radius vector

Which of the above statement(s) match with the main statements. a) 1, 3 b) 1, 2 c) 1, 4

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d) none

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57.

If n is an integer, 1) −

lim

n →∞

− 3n + (−1) n

(3 mark)

is

4 n − (−1) n

3 4

2) 0 if n is even

3 4

4) None of these

3) − if n is odd

Which of the above statement(s) match with the main statements. a) 1, 3 b) 2, 1 c) 1, 4 d) none 58.

PAGE

If (5, 12) and (24, 7) are the foci of a conic passing through the origin then the eccentricity of conic is 1)

386 12

2)

386 38

(3 mark)

386 25

www.aieeepage.com 3)

4)

2

Which of the above statement(s) match with the main statements. a) 1, 3 b) 1, 2 c) 1, 4 d) none 59.

If θ is the angle subtended by the circle S ≡ x 2 + y 2 + 2 gx + 2 fy + c = 0 at the point P( x1 , y1 ) and (3 mark)

S1 ≡ x12 + y12 + 2gx1 + 2 fy1 + c, = 0 then

1) cot θ =

3)

2 S1 g2 + f 2 − c

θ = 2 tan −1

g2 + f 2 −c S1

S

θ

1 2) cot 2 = 2 2 g + f −c

PAGE 4)

cos θ =

S1 + c − g 2 − f

2

S1 − c + g 2 + f

2

Which of the above statement(s) match with the main statements. a) 2, 3, 4 b) 1, 2, 3 c) 1, 2

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d) none

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60.

If the sides a, b, c of a triangle A B C form successive terms of G.P. with common ratio r ( >1), then which of the following statements is/are not correct (3 mark) 5 +1 2

1) r >

2)

π 3

3) B >

A< B<

4) C >

π 3

π 3

a) 1, 2, 3 b) 1, 2, 4 c) 1, 2 d) none 61.

In a triangle A B C 1) sin A sin B sin C ≤

3 3 8

PAGE

2) sin 2 A + sin 2 B + sin 2 C ≤

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3) sin A sin B sin C is always positive

(6 mark)

9 4

4) sin 2 A + sin 2 B = 1 + cos C

Which of the above statement(s) match with the main statements. a) 1, 2, 3, 4 b) 1, 2, 3 c) 1, 2, 4 d) 2, 3, 4

62.

Let P (X = r) = pq r and P(Y = r) = pq r , where r = 1, 2,...............,0 < p < 1, q = 1 - p. Suppose X and Y (3 mark) are independent. Let Z = max (X, Y). Then 1) P(Z ≤ m) = (1 − q m ) 2 1

3) m∑≥1 P(Z = m) = p

2) P(Z = m) = 2pq m −1 - p(1 + q)q 2m-2 4) P(X ≤ m) = 1 − q m

PAGE

Which of the above statement(s) match with the main statements. a) 1, 2, 3 b) 1, 2, 4 c) 2, 3, 4 d) none

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63.

Which of the following is correct ?

(6 mark)

1) (101)100 > (100)101

2) (26)25 < (25) 26

3) (300)299 < (299) 300

4) (199)198 = (198)199

Which of the above statement(s) match with the main statements. a) 1, 2 b) 2, 3 c) 1, 4 d) none 64.

PAGE

Complex numbers whose real and imaginary parts, x and y are integers and satisfy the equation 3x 2 − | xy | −2 y 2 + 7 = 0

1) do not exist

(3 mark)

2) exist and have equal modulus

4) do not form conjugate pairs www.aieeepage.com Which of the above statement(s) match with the main statements. 3) form two conjugate pairs a) 1, 2, 3 b) 1, 2, 4 c) 2, 3, 4 d) none

65.

Consider the quadratic equation x 2 − 2 px + p 2 − 1 = 0 where p is parameter, then

(6 mark)

1) Both are roots of the equation are less than 4 if p ∈ (−∞, 3) 2) Both the roots of the equation are greater than -2 if p ∈ (−∞, − 1) 3) Exactly one root of the equation lies in the interval (-2, 4) if p ∈ (−1, 3) 4) 1 lies between the roots of the equation if p ∈ (0, 2)

PAGE

Which of the above statement(s) match with the main statements. a) 1, 3 b) 1, 4 c) 2, 3 d) 2, 4

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66.

If the absolute value of the difference of roots of the equation x 2 + px + 1 = 0 exceeds 3 p , then (3 mark)

a) p < -1 or p > 4 b) p > 4 c) −1 < p < 4 d) 0 ≤ p < 4 67.

There are m points on one straight line AB and n points on another straight line AC, none of them being A. The number of triangles formed with these points as verticies (3 mark) a)

mn(m + n) 2

b)

mn(m + n − 1) 2

c)

mn(m + n − 2) 2

PAGE

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d) none of these

68.

13 + 3 ∆ = 15 + 25 3 + 65

2 5 5 15

5 10 is 5

(3 mark)

a) real rational b) real irrational c) complex and rational d) complex and irrational

69.

π

tan x2

If 0 < x1 < x2 < , then tan x is 2 1 a) > x1 x2 x

2 b) > x 1

x

1 c) > x 2

PAGE

(3 mark)

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d) none of these

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70.

1

The graph of f ( x) = | x | − n − n lies in the (where n > 0).

(3 mark)

a) Ist and IIIrd quadrant b) IInd and IIIrd quadrant c) IIIrd and IVth quadrant d) Ist and IInd quadrant 71.

If

∫

x ex 1+ ex

dx = 2( x − 2) f ( x) − 2 log g ( x) + c, then

x a) f ( x) = 1+ e and g(x) =

b)

f ( x) = 1 + e x , g ( x) =

x

c) f ( x) = 1 − e , g ( x) =

(3 mark)

PAGE

1+ex -1

1+ex +1

1+ ex +1 1 + e x −1

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1+ ex +1 1+ ex −1

d) none of these 72.

The area of the region bounded by the curve a 4 y 2 = (2a − x ) x 5 is to that of the circle whose radius (3 mark) is a, is given by the ratio a) 4 : 5 b) 5 : 8 c) 2 : 3 d) 3 : 2

73.

If A, B, C are acute positive angles such that A + B + C = π and cot A cot B cot C = K, then a) K ≤ b) K ≥

1 3 3 1 3 3

c) K <

1 9

d) K >

1 3

PAGE

(3 mark)

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74.

a) n π +

7π 6

b) nπ + (-1) n

π 2

n c) nπ + (-1)

5π 6

n d) nπ + (-1)

75.

(3 mark)

The general values of θ satisfying the equation 2sin 2θ - 3sinθ - 2 = 0 is

7π 6

PAGE

r The vectors ar, b , cr, are of the same length and the angle between any two of them is the same. If r r a = iˆ + ˆj , b = ˆj + kˆ, 1 r 3

then cr is

r

r

r

1) − (i − 4 j + k ) 3)

(3 mark)

r

2) i + k

www.aieeepage.com r r r

r r 1 r ( −i + 4 j + k ) 3

4) (i + 2 j + 3k )

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

76.

If I n = ∫

π/4

0

tan n x dx,

1) I n + I n − 2 =

I n −1

3) I n +1 < 2 I n <

(3 mark)

then

I n −1

2)

I n −1 + I n +1 =

I n

PAGE 4) I n =

n I n−2 n−2

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

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d) none

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77.

 xe ax : x≤0 = ( ) f x  Let  x + ax 2 − x 3 : x > 0

where a is positive constant. The interval in which f’(x) is increasing is

(3 mark)

a) (−∞, ∞) −2



a



b)  − ∞, a  ∪  3 , ∞      c) a > 5 d) −∞ < a < ∞ 78.

PAGE

(3 mark)

If F ( x) = f ( x) g ( x) and f ' (x)g' (x) = c, then f

g

1) F ' = c  f ' + g '  

3)



F"' f"' g" = + F f g

2)

F " f " g " 2c = + + F f g fg

www.aieeepage.com 4) none of these

Which of the above statement(s) match with the main statements. a) 1, 2, 3 b) 1, 3, 4 c) 1, 2, 3, 4 d) none

79.

 2 Let R = {( x, y) : x, y ∈ R. x 2 + y 2 ≤ 25} and R' = ( x, y ) ; x, y ∈ R, y ≥ 9 x  then is   4

1) dom R ∩ R' = [−3, 3]

2) Range R ∩ R'⊃ [0, 4]

3) Range R ∩ R'= [0, 5]

4)

(3 mark)

R ∩ R' defines a function

PAGE

Which of the above statement(s) match with the main statements. a) 1, 2, 3 b) 1, 3, 4 c) 1, 2, 3, 4 d) none

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80.

Consider the parabola y 2 = 4ax and x 2 = 4by . The straight line b1/ 3 y + a1/ 3 x + a2/ 3 b2/ 3 = 0 , 1) touches y 2 = 4ax

2) Touches x 2 = 4by

3) Intersects both parabolas in real points

4) Touches first and intersects other

(3 mark)

Which of the above statement(s) match with the main statements. a) 1, 3 b) 1, 2 c) 1, 4 d) none

81.

PAGE

If θ1 and θ 2 be the angles which the lines (x2 + y2 ) (cos2 θ sin2α + sin2θ) = (x tanα-y sin θ)2 make with the π 6

axis of x, and θ = , then tan θ1 + tan θ 2 is equal to a)

(3 mark)

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8 − sin α 3 8 3

b) − cos ec 2α c) − 8 3 cos ec 2α d) −4 cos ec 2α 82.

The coordinates of the points A and B are respectively (-3, 2) and (2, 3). P and Q are points on the line joining A and B such that AP = PQ = QB. A square PQRS is constructed on PQ as one side, the (6 mark) coordinates of R can be  4 7

1)  − 3 , 3   



13 

2)  0, 3   

1 8

3)  3 , 3   

2



4)  3 , 1  

Which of the above statement(s) match with the main statements. a) 2, 4 b) 1, 2 c) 1, 3 d) none

PAGE

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83.

If tan −1 y = 4 tan −1 x, then y is not finite if

(3 mark)

1) x 2 = 3 + 2 2

2)

x2 = 3 − 2 2

3) x 4 = 6 x 2 − 1

4)

x 4 = 6x 2 + 1

Which of the above statement(s) match with the main statements. a) 1, 2, 4 b) 1, 2 c) 1, 2, 3 d) none ex

84.

If

sin x

1

PAGE

∆ = cos x log e (1 + x 2 ) 1 = a + bx + cx 2 x

1) a = 0

x2

1

2) a = 1

(3 mark)

then the value of b is 3) b = -1

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4) b = -2

Which of the above statement(s) match with the main statements. a) 1, 2 b) 1, 3 c) 1, 4 d) none

85.

If 10 ! = 2 p 3q 5r 7s , then 1) P = 7

2) q = 4

(3 mark)

3) r = 2

4) s = 2

Which of the above statement(s) match with the main statements. a) 2, 3 b) 1, 2 c) 1, 3 d) 3, 4

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86.

If x, y, z are positive numbers in AP., then 1) y 2 ≥ xz

2) xy + yz ≥ 2xz

(3 mark)

3)

x+ y y+z + ≥4 2y − x 2y − z

4) None of these

Which of the above statement(s) match with the main statements. a) 1, 2, 3 b) 1, 2, 4 c) 2, 3, 4 d) none

87.

If | k − 1 |log 3 k

2

− 2 log k

9

= ( k −1) 7 ,

1) 0 < sin −1 k + cos −1 (k − 1) < −1 3) 0 < cot k <

π 6

PAGE

(3 mark)

then which of the following is/are correct ? π 4

−1 2) 0 < tan k <

π 6

π π < tan k < 4) www.aieeepage.com 4 2 −1

Which of the given statement(s) match the main question a) 3, 4 b) 1, 2 c) 1, 3 d) none 88.

If a complex number z is satisfying the relation | z - 8 - 6i | + | z - 14 - 6i| = 10, then maximum value (3 mark) of arg (z) is a) tan −1

33 − 609 48

b) tan −1

33 + 609 48

−1 c) tan

33 48

d) none of these

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89.

The sum of three consecutive terms in a G.P. is 14. If 1 is added to the first and the second term and 1 is subtracted from the third, the resulting new terms are in A.P. The the lowest of the original terms is (3 mark)

a) 1 b) 2 c) 4 d) 8

90.

In the expansion of (3− x / 4 + 35 x / 4 ) n , the sum of the binomial co-efficients is 64 and the term with the (3 mark) greatest binomial co-effecient exceeds the thrid by (n, -1), then the value of x must be

PAGE

a) 1 b) 2 c) 0 d) -1 91.

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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 tossing three fair coins. The probability that roots of the equations are imaginary is (3 mark)

a) 5/8 b) 3/8 c) 7/8 d) 1/8

1/ 2

92.

If x is very small in magnitude compared with a such that

 a    a+ x

1/ 2

 a  +  a−x

= 2 + k.

x2 a2 '

value of k is a)

1 4

b)

1 2

c)

3 4

then the (3 mark)

PAGE

d) 1

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93.

For any quadratic function px 2 + qx + r over [a, a+h], the value of c ∈ (a, a + h) in Lagrange’s Mean (3 mark) Value Theorem is a) dependent on p, q, r b) independent of p but depends upon q, r c) independent of p, q but depends upon r d) independent of p, q, r

a

94.

equal to a) a b)

a 2

c) f (a) d) 95.

dx

Let f(x) be a continuous function such that f(a - x) + f (x) = 0 for all x ∈ [0, a]. Then ∫ 1 + e f ( x ) is 0

PAGE

(3 mark)

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1 f (a) 2

Solution of the differential equation

dy = sin( x + y ) + cos( x + y ) dx

is

(3 mark)

 x+ y a) log 1 + tan 2  = y + c    x+ y b) log 2 + sec 2  = x + c  

c) log 1 + tan( x + y ) = y + c d) none of these 96.

PAGE

r

r

rr

r

The position vectors of the vertices A, B, C of a tetrahedron ABCD are i + j + k, i and 3i respectively, the altitude from vertex D to the opposite face ABC at a point E, If length of the side AD is 4 and volume of the tetrahdron is a) 6

2 2 3

, then AE 2 is equal to

(3 mark)

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b) 9 c) 12 d) none of these

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97.

The value of the determinant  log a  

x   log z  y 

 log b  

x y z  log b   log b   is z x    y

(3 mark)

y z  log a   z  x

 x z  y log c   log c   log c   x y   z  

a) 1 b) -16

PAGE

c) log z xyz d) none of these

Questions 98 to 100 are based on the following passage

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A system of circles is said to be coaxal when every pair of the cirlces has the same radical axis. It follows from this definition that 1. The centres of all circles of a coaxal system lie in one straight line, which is perpendicular to the common radical axis 2. Circles passing through two fixed points from a coaxal system with line joining the points as common radical axis 3. The equation to coaxal system of which two members are S1 = 0 and S2 = 0, is S1 +λS2 = 0 , λ is parameter. If we choose the line of centres as x-axis and the common radical axis as yaxis, then the simplest form of equation of coaxal circles is x 2 + y 2 + 2 gx + c = 0

....(1)

where c is fixed and g is variable If g = ± c , then the radius g 2 − c vanishes and the circles become point circles. The points (± c ,0) are called the limiting points of the system fo coaxal circles given by (1).

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98.

If origin be a limiting point of a coaxal system one of whose member is x2 + y2 − 2αx- 2 βy + c = 0, then (3 mark) the other limiting point is 



cα cβ a)  α 2 + β 2 ,− α 2 + β 2    







cα cβ b)  α 2 + β 2 , α 2 + β 2    αβ cα c)  α 2 + β 2 , α 2 + β 2    



cβ cα d)  − α 2 + β 2 , α 2 + β 2   

99.

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The equation of the radical axis to the system of coaxal circles

(3 mark)

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x 2 + y 2 + 2ax + 2by + c + 2λ(ax - by + 1) = 0 is

a) ax - by + 1 = 0 b) bx + ay - 1 = 0 c) 2(ax + by ) + 1 = 0 d) 2(bx - ay) + 1 = 0 100. The equation of the lines of centres of the system given in previous problem is

(3 mark)

a) ax - by + 1 = 0 b) bx + ay + ab = 0 c) bx + ay + 2ab = 0 d) bx + ay + a 2 + b 2 = 0

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Paper - III : Chemistry - 101 to 150 Questions 101 to 104 are independent Questions 101. Which of the following is (are) true for the above nuclear stability graph?

(3 mark)

160 140

Number of neutrons

120 100 80 60 40 20

PAGE 0 20 40 Number of protons

60

80

100

120

a) Isotopes that fall to the left or right of the stability curve have unstable nuclei and are referred to as being radioactive. b) All isotopes with atomic number higher than 83 are radioactive.

c) The curve indicates that the lighter, stabler nuclei tend to have equal numbers of protons and neutrons.

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d) All of the above. 102. An aqueous solution of a substance gives a white ppt. on treatment with dilute hydrochloric acid which dissolves on heating. When hydrogen sulfide is passed through the hot acidic solution, a black (3 mark) ppt. is obtained. The substance is a a) Hg2++salt b) Cu++ salt c) Ag+ salt d) Pb++ salt 103. A sample of hydrazine sulphate ( N 2 H 6SO 4 ) was dissolved in 100 ml of water , 10 ml of this solution was reacted with excess of ferric chloride solution and warmed to complete the reaction .Ferrous ion formed was estimated and it required 20 ml .of M/50 potassium permanganate solution .Estimate the (3 mark) amount of hydrazine sulphate in one litre of the solution Reaction

PAGE

4Fe3+ + N 2 H 4 → N 2 +4Fe 2+ +4H +

MnO-4 +5FE 2+ +8H + → MN 2 +5FE3+ 4H 2 O a) 6. 5 g b) .65 g

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c) 0.065 g d) .0065 g

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104. On treatment of [Ni(NH3)4]2+ with concentrated HCI , two compunds I and II having the same formula. Ni(NH3)2Cl2 are obtained. I can be converted into II by boiling with dilute HCI. A solution of I reacts with oxalic acid to form [Ni(NH3)2(C2O4) whereas II does not react. Point out the correct statement of (3 mark) the following a) I cis, II trans; both tetrahedral b) I cis, II trans; both square planar c) I trans, II cis; both tetrahedral d) I trans, II cis; both squar planar

PAGE

Questions 105 to 109 are based on the following passage

Alcohols can be prepared by reacting alkyl halide with hydroxid ions. However, this reaction is not always synthetically useful because of competing elimination reactions. This problem can be overcome by choosing a less basic nucleophile. Figure 1 illustrates the formation of butanol through as S N 2 reaction of sodium ethanoate with 1-broobutane, followed by ester hydrolysis. Ester hydrolysis can benefit from the presence of an acid. The acid functions in two ways: First, it protonates the carbonyl oxygen, activating eh carbonyl group to nucleophilic attack; second, it may protonate the leaving group (in this case the alcohol), promoting its leaving group ability.

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O

Step 1 :

+

Br

Na CH 3COO

−

O

DMF

C

CH 3

O

Step 2 : O

C

CH 3

H 2 O,H +

OH

Ester hydrolysis can also be promoted by strong bases. Base-promoted ester hydrolysis proceeds through the nucleophilic addition of hydroxide to the carbonyl group followed by elimination. This reaction is shown in Figure 2.

PAGE

Step 2 : (alternate) :

O

O

C

CH 3

NaOH, H 2 O

OH

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105. The IUPAC name for the ester formed in Step 1 is :

(3 mark)

a) butyl ethanoate b) ethyl butanoate c) ethyl acetate d) butane carboxylate 106. Acid-catalyzed ester hydrolysis leads to the formation of an alcohol. The other product (not shown) of (3 mark) the reaction is : a) ethanol b) diethyl ether

PAGE

c) acetic acid d) sodium acetate

107. DMF, the solvent used in Step 1, is the abbreviation for N, N-dimethylformamide. Its structure and (3 mark) that of another related compound are shown below .

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O

HCN(CH 3 ) 2 N,N-dimethylformamide

HCNH(CH 3 ) N − dimethylformamide

If N-mthylformamide is used as the solvent instead of DMF, the rate of Step 1 will be : a) b) c) d)

somwhat increased. significantly decreased remain the same Cannot be determined

108. Which of the following would be the most useful synthesis of an alcohol from a tertiary halide? (3 mark) +

a)

-

Na CH3COO H+/H2O Br

H2O/2

b)

Br

Br

PAGE OH

Mg

c)

OH

DMF

H+/H2O

OH

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NaOH

d)

Br

H2O

OH

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109. If the isotopically labeled ester shown below were subjected to base-promoted hydrolysis in aqueous NaOH, the expercted product(s) would be (3 mark)

O18

H3C

NaOH H2O

18

OH

O

a)

+

NaO

OH

O

b)

+ 18

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NaO

OH

c)

CH3

CH3 18

O

+

O

NaO

OH

CH3

18

Na O

CH3

18

O

d)

+

NaO

O

CH3

18

Na O

CH3

Q. 110 to 145 are independent Questions 110. Which of the follwing statements is / are coreect ?

(3 mark)

1) Anhydrous ferric chloride can be obtained by heating hydrated ferric chloride.

PAGE

2) A solution of ferric oxalate in dilute H2SO4 will decolorise KMnO4. 3) Ferric salts are more stable than ferrous salts.

4) The Mohr’s salt is resistant to oxidation by atmospheric oxygen. a) 1 , 2 , 4 b) 1 , 3 , 4

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

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111. According to Bhor’s theory , the electronic energy of hydrogen atom in the Bhor’s orbit is given by En =

- 21.76 × 10-19 J Calculate the longest wavelength of light that will be needed to remove an n2

electron from the third Bhor orbit of the He + ion.

(3 mark)

a) 2055Å b) 1855Å c) 2055 ×10−20 m d) 1855 ×10−20 m

PAGE

112. Match the following mixtures with the respective solution used for their separation : a) N2 & CO

(i) Water

b) N2 & O2 c) N2 & NH3 d) PH3 & NH3

(3 mark)

(ii) H2So4 (iii)

Ammonical Cuprous chloride

www.aieeepage.com (iv) Pyrogallol

a) A - iv, B - iii, C - II, D - i b) A - iii, B - iv, C - ii, D - i c) A - iii, B - iv, C - i, D - ii d) A - iii, B - ii, C - iv, D - i 113. Which of the following electropilic aromatic substitution (s) is (are) correct? SO3H (1)

(3) H2SO4

X

X2

X=C1,Br

FeX 3

O (2)

(3 mark)

R C

O

(4) HNO3

NO2

PAGE RC-C1

A1 C1 3

a) (1) and (3) only b) (2) and (4) only c) (1) , (2) and (3) only

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d) All of the aboive. (1) , (2), (3) and (4)

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114. The dipole moment of KCl is 3.336 × 10-29 Coulomb meters which indicates that it is a highly polar molecule . The interatomic distance between K + and Cl- in this molecule is 2.6 × 10-10 m . Calculate the dipole moment of KCl molecule if there were opposite charges of one fundamental unit located at each nucleus .Calculate the percentage ionic character of KCl . (3 mark) a) 80.09% b) 80.08% c) 80.07% d) 80.06 %

PAGE

115. The solubility of hydroxides, fluorides or oxalates of the metals of Group II A a) increases down the group b) decreases down the group c) varies randomly d) is constant

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116. Of the following elements, which possesses the highest electron affinity ? a) b) c) d)

(3 mark)

(3 mark)

As O S Se

117. At room temperature ,ammonia gas at 1 atm pressure and hydrogen chloride gas at P atm pressure are allowed to effuse through identical pin holes from opposite ends of a glass tube of one metre length and of uniform cross -section . Ammonium chloride is first formed at a distance of 60 cm from the end (3 mark) through which HCl gas is sent in . What is the value of P ? a) 2.197 atm b) 1.023 atm c) 0.976 atm d) 0.454 atm

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118. Match the following :

(3 mark)

1) Smelting

i) Copper Glance

2) Self reduction

ii) Malachite

3) Electrolytic reduction

iii) Haematite

4) Hydrometallurgy

iv) Bauxite

a) (1) - (iii), (2) - (i), (3) 0 (iv), (4) - (ii) b) (1) - (ii), (2) - (i), (3) - (iii), (4) - (iv) c) (1) - (iii), (2) - (i), (3) - (ii), (4) - (iv) d) (1) - (iii), (2) - (iv), (3) - (ii), (4) - (i)

PAGE

119. Positive beilistein test for halogens shows that

(3 mark)

a) a halogen is definitely present b) a halogen may be present c) a halogen is absent d) none of these.

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120. At a certain temperature equilibrium constant ( Kc ) is 16 for the reaction SO 2 (g) + NO 2 (g)

(3 mark)

SO3 (g) + NO(g)

If we take one mole each of all the four gases in a one litre container ,what whould be the equilibrium concentrations of NO (g ) and NO 2 (g) ? a) 1.6 moles , 0.4 moles b) 0.2 moles , 0.8 moles c) 1.4 moles , 1.6 moles d) 0.8 moles , 0.2 moles

O (3 mark)

H 2SO 4 121. Following reaction is an example of R − C − OH + HN 3   → R − NH 2

a) Hofmann reaction b) Curtius reaction c) Schmidt reaction d) Lossen reaction

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122. When a hydrophilic sol like gelatin is subjected to electric field, the sol particles move

(3 mark)

a) towards cathode at pH less than the iso-electric point b) towards anode at pH greater than the iso-electric point c) in both directions at iso-electric pH d) in neither direction at iso-electric pH 123. The standard molar enthalpies of formation of cycloheane ( l ) and benzene ( l ) at 25°C are -156 and +49 kJ mol-1 respectively . The standrd enthalpy of hydrogenation of cyclohexene ( l ) at 25°C is - 119 kJ mol-1 . Use these data to estimate the magnitude of the resonance energy of benzene

a) - 152 kJ mol-1 b) - 148 kJ mol-1 c) - 205 kJ mol-1 d) - 357 kJ mol-1

(3 mark)

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124. In a Born-Haber cycle, the total energy involved in the preceding hypothetical preparation of NaCI is equal to the experiment tally determined heat of formation (Q) of the compound from its elements. Which of the following thermochemical values is not used to calculate the total energy of formation of (3 mark) NaCI? 1) Heat of fusion and vaporization (S) 2) Dissociation energy of molecular chlorine (D) 3) Ionization energy of sodium atom (I) 4) Electron affinity of chlorine atom (E) 5) Lattice energy of NaCI (U) a) (1) and (2) b) (2), (3) and (5) c) (1), (2), (3) and (4) d) All of the above

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125. A monobasic acid is dissociated in o.1 M solution. When 200ml of the acid solution is neutralized by 0.1 M NaOH, heat evolved is 244 cal. If the heat of neutralization of a strong acid with a strong base (3 mark) is - 13. 7 kcal, the molar heat of dissociation of the acid is a) 2.20 k cal mol-1 b) 1.50 k cal mol -1 c) -1.50 k cal mol -1 d) 2.0 k cal mol -1

126. The molar volume of liquid benzene ( ( density = 0.877 g mL -1 ) increase by a factor of 2750 as it

PAGE

vaporises at 20°C and that of liquid toluene ( density = 0.867 g mL -1 ) increase by a factor of 7720 at 20°C . A solution of benzene and toluene at 20°C has a vapour pressure of 46.0 Torr . Find the mole (6 mark) fraction of benzene in the vapour above the solution a) 0. 27

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b) 0.46 c) 0.73 d) none of these

127. Select the rate law that conforms to the following data for the reaction : A+B Products → Products Exp No.

[A] (mol L-1)

[B](mol L-1)

Initital rate(mol L-1s-1)

1

0.0012

0.0035

1 x 10-4

2.

0.024

0.070

8 x 10-3

3.

0.024

0.035

1x10-3

4.

0.012

0.070

8 x 10-3

a) − b) −

d [ A] = k[ A]2 [ B] dt

c) − d)

d [ A] = k[ A][ B]2 dt

d [ A] = k[ A][ B]3 dt

d [ A] − = k[ B]3 dt

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(3 mark)

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128. At certain temperature, a compund AB2 dissociates as : 2AB2(g) → 2AB(g) + B2(g) with a degree of dissociation α , which is very small compared to unity. The expression of Kp in terms of α and total pressure p is (6 mark)

129.

a)

α2P 2

b)

α2P 3

c)

α 3P 3

d)

α 3P 2

234

TH90 disintegrates to give during this process ?

206

PAGE

Pb82 as the final product .How many alpha and beta particals are emitted

a) 14 , 12

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(3 mark)

b) 12 , 14 c) 7 , 6 d) 6 , 7 130. The enthalpies associated with the reaction A + B + C → D + E + F is shown above. The fact that the (3 mark) enthalpy of D + E + F is higher than that of A + B + C tells us that

Enthalpy

Activated complex D+E+F

A+B+C

Reaction coordinate

a) the reaction is exothermic b) the reaction is endothermic

PAGE

c) the activation energy required for the reverse reaction is higher than for the forward reaction d) a catalyst for the reaction is unnecessary

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131. Pick up the correct statement(s)

(3 mark)

(i) A reaction catalyzed by an enzyme always gives an optically active product (ii) When an achiral molecule is conveted to a chiral molecule, the product is always racemic (iii) Racemization of an enantiomer can only occur by breaking of at least one bond to the chiral center (iv) Conversion of an erythro to threo stereioisomer always occurs by inversion at one chiral carbon (v) A D enantiomer rottes the plane of polarized light to the right and an L enantiomer to the left a) (i), (ii), (iii) and (v) b) (iii) and (iv)

PAGE

c) (i), (ii), (iii) and (iv) d) all of these

132. The density of mercury is 13.6 g / ml . Calculate approximately the diameter of an atom mercury assuming that each atom is occupying a cube of edge length equal to the diameter of the mercury atom ? a) 2.44× 10-23

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(6 mark)

b) 24.4 ×10-23 cc c) 2.905×10-9cm d) 2.91 Å cm

133. The increasing order of Ag+ ion concentration in

(3 mark)

I. Saturated solution of AgCl

II. Saturated solution of Agl

III. l M Ag(NH3) +2 in 0.1 MNH3

IV. l M Ag (CN) −2 in 0.1 MKCN

Given K sp of AgCl = 1.0 × 10 −10

K d of Ag ( NH 3 ) 2+ = 1.0 × 10 −8

a) I < II < III < IV b) IV < III < II < I c) IV < II < III < I d) IV < II < I < III

K sp of Agl = 1.0 × 10 −16

PAGE

K d of Ag (CN ) −2 = 1.0 × 10 −21

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134. During the discharge of a lead storage battery the density of sulphuric acid fell from 1.294 to 1.139 g / ml .Sulphuric acid of density 1.294 g/ml is 39% by weight and that of 1.139 g /ml is 20% H 2SO 4 by weight .The battery holds 3.5 litres of the acid and the volume remained practically constant during the discharge . Calculate the number of ampere- hours for which the battery must have been used .The charging and (6 mark) discharging reactions are Pb + SO 2-4 = PbSO 4 +2e - (charging) PbO 2 +4H + + SO 42- + 2e − = PbSO 4 +2H 2 O(discharging)

a) 265.02 b) 265.01 c) 265.04 d) 265.03

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135 Which of th e following cells give the cell potentials to be their standard values ?

(3 mark)

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1) Zn( s ) | Zn(2aq+ ) (0.01M ) || H 3O(+aq ) (0.1M ) | H 2( g ) (1atm) , pt 2+ + (0.25M) || Ag (aq) (0.5M) | 2) Cu (s) |Cu (aq)

2+ (0.01M) || pH = 1| H 2(g) (1 atm) , Pt 3) Cd (s) | Cd(aq)

2+ (0.1M) || pH = 1| H 2(g) (1 atm) , Pt 4) Zn (s) | Zn (aq)

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

(3 mark) 136. O.5 g sample of oxalate salt required 30 ml of 0.05 M KMnO 4 in acidic medium for complete oxidation . The precent of oxalate ion in the sampl is

a) 33 % b) 50% c) 66% d)13.2%

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137 A metal complex having composition Cr(NH 3 ) 4 Cl2 Br has been isolated in two forms ( A ) and ( B ) . The form (A) reacts with AgNO3 to give a white precipitate readily soluble in dilute aqueous ammonia (3 mark) ,whereas ( B ) gives a pale yellow precipitate soluble in concentrated ammonia .Calculate their magnetic moments ( spin - only value ) a) 3.87 BM b) 3.86 BM c) 3.85 BM d) 3.84 BM (6 mark)

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138 Predict the possible number of alkenes and the main alkene in the following reaction . (i) excess CH 1

heat

3     → [ ]  → Product

NHCH2CH3

(ii) Ag2O

a) 2 and b) 2 and

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c) 3 and H 2 C = CH 2 d) 2 and H 2 C = CH 2 139. A solid dissolves in water exothermically .If its sturated solution at 20°Cis cooled to 0°C,then

(3 mark)

a) some solid seperates out b) some ice separates out c) both the solid and ice separate d) neither the solid nor the ice separates out

0

(3 mark)

0

140. The radius ratio of Cs + to Cl- is is 0.90 A .If the radius of Cl- ion is 1.80 A ,the false statement regarding the CsClstructure is

PAGE 0

a) the distance between the centres of Cl- ion is greater than 3.60 A 0

b) the distance between the centres of two Cl- ion is 3.60 A 0

c) the distance between Cs + ion and Cl- is 3.24 A

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0

d) the distance between two Cs + ions is greater than 3.24 A

(3 mark)

141. The correct order for the basic character of the compounds I to IV should be

N I a) IV < III < I < II b) IV < I < III < II c) IV < II < III < I d) IV < III < II < I

CH 3 |

N H II

CH 3CN

PAGE

www.aieeepage.com CH 3

Br

|

|

(3 mark)

142. CH3CH 2 CHCH 2CH=CH 2 HBr → CH3CH 2 CHCH 2 CHCH3 (R) - 4 - Methyl - 1 - hexene

X

a) A mixture of two enantiomers in 50 : 50 ratio b) A mixture of two enantiomers in non - 50 : 50 ratio c) A mixture of two diastereomers in 50 : 50 ratio d) A mixture of two diastereomers in non - 50 : 50 ratio (3 mark)

143. Which of the following ions does not involve pπ - dπ bonding ? a) SO32b) PO3-4 c) NO3d) XeOF4

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Cl Cl

144. Predict the product ,if any for the following reaction

aq.OH -

(3 mark)

 →

Cl

OH CI a) CI CI OH b)

PAGE

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CI CI CI c) OH d) No reaction 145. Photoelectric work function of a metal is 1 e V .If a light of wavelength 300 Å falls on the metal ,the (3 mark) velocity of the photoelectron ejected will be a) 10ms -1 b) 103 ms -1 c) 10 4 ms -1 d) 10 6 ms -1

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Questions 146 - 150 are based on the following passage Permanent hair dye products may be divided into two classes: progressive and oxidation hair dyes. Oxidation hair dyes involve organic chemistry, but progressive hair dyes can be analyzed from a general chemistry perspective. The active ingredient in progressive hair dye products can be either lead acetate or bismuth citrate. Both of these chemicals react with the sulfur in hair keratin to change hair from a light color to near black. These reactions are shown in Equations 1 and 2 Pb(CH 3COO) 2 (aq) + S2 − aq) → Pb(s) + 2CH 3COO − (aq)

(Equation -1)

2Bi(HOC(CH 2CO 2 H) 2 + 3S2 - (aq) → Bi 2S3 (s) + 3 HOC(CH 2 )

(Equation -2)

PAGE

Many commercial hair dye products also contain detergents, molecules that sequester hard metal ions such as calcium and magnesium 146. Equation 1 is best characterized as

(3 mark)

a) a Lewis acid-base reaction, because the electron pair on the sulfur ion attacks the positively charged lead ion.

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b) an Arrhenius acid-base reaction, because the electron pair on the sulfur ion attacks the positively charged lead ion. c) an oxidation - reduction reaction, because the sulfur changes oxidation state from - 2 to +2 d) a neutralization reaction, because the acetate ion will be converted to acetic acid in the aqueous solution used to apply the hair dye. 147. Why might calcium and magnesium ions interfere with progressive hair dyes?

(3 mark)

a) Hard metal ions react with acetate and citrate ions, making them unavailable for dyeing. b) Hard metal ions react with sulfide in the hair, making it unavailable for dyeing c) the presence of additional ions in solution decreases the effectiveness of the dye because it reduces the number of collisions between dyeing agents and sulfide ions d) Calcium and magnesium precipitate in elemental form to leave a whitish residue

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148. Why does bismuth adopt a + 3 oxidation state instead of a+5 oxidation state?

(3 mark)

a) Bismuth is transition metal, so it can adopt either state, but losing more electrons brings it closer to a noble gas configuration b) Bismuth is a metalloid, so it prefers to keep some of its valence electrons in order to maintain a stable half-full subshell

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c) Bismuth loses all of its valence p electrons, but these electrons are in a much lower energy state, so the ion is more stable without losing them d) Bismuth can a dopt the noble gas configuration of radon by gaining three electrons

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149. What will be the effect of adding sodium acetate to the aqueous hair dye solution in Equation 1 ? a) Decreased dye effectiveness, because the equilibrium will be shifted to the right

(3 mark)

b) Increased dye effectiveness, because the equilibrium will be shifted to the right c) Increased dye effectiveness, because the equilibrium will be shifted to the left. d) Decreasd dye effectiveness, because the equilibrium will be shifted to the left 150. What is the equilibrium expression for Equation2?

(3 mark)

[HOC(CH 2 CO 2 H) 2 CO 2 − ]3

a) Bi(HOC(CH CO H) CO ) ]2 [S2- ]3 2 2 2 2 3

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3[HOC(CH 2 CO 2 H) 2 CO 2 − ]

b) 2[Bi (HOC(CH CO H ) CO ) ] 3 [S2- ] 2 2 2 2 3 [Bi 2 S3 ] [HOC(CH 2 CO 2 H ) 2 CO 2 − ]3

c) [Bi (HOC(CH CO H ) CO ) ]2 [S 2- ]3 2 2 2 2 3

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[HOC(CH 2 CO 2 H) 2 CO 2 − ]

d) [Bi (HOC (CH CO H ) CO ) ] [S 2- ] 2 2 2 2 3

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