Ai Aieee Modeltest 02

MODEL TEST TEST CODE - Fow

AIEEE PAGE 180 QUESTIONS TIME ALLOWED : 180 MINUTES

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STUDENT’S NAME :

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Read the instructions on the ANSWER SHEET. Fill in your NAME, TEST CODE and AIEEE Application form Number. Use the information provided to choose the BEST answer from the four possible options. On your ANSWER SHEET fill in the oval that matches your answer. Mark only ONE answer for each question. Q. 1 to 8, 61 to 68 & 121 to 130 carries1 12 marks each, Q. 9 to 52, 69 to 112 & 131 to 170 carries 3 marks each and Q. 53 to 60,113 to 120 & 171 to 180 carries 412 marks each. For each incorrect response,one-third of the total marks alloted to the question would be deducted from the total score.

PAGEPAGE You are NOT allowed to use a calculator

TM

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Questions - 180

1.

PHYSICS

Time - 180 Min

Which of the following is a dimensional constant : a) Refractive index b) Poisson’s ratio c) Relative density

d) Gravitational constant

2.

A car moving with a speed of 40 km/hour can be stopped by applying brakes in 2 meters. If the same car is moving with a speed of 80 km/hour, what is the minimum stopping distance : a) 8 m b) 6 m c) 4 m d) 2 m

3.

A pulley with a radius of 3.0 cm and a rotational inertia of 4.5 × 10 −3 kg.m 2 is suspended from the ceiling. A rope passes over it with a 2.0 -kg block attached to one end and a 4.0-kg block attached to the other. The rope does not slip on the pulley. At any instant after the blocks start moving, the object with the greatest kinetic energy is : a) the heavier block b) the lighter block c) the pulley

4.

PAGE d) either block

A β - particle is emitted by a radioactive nucleus at the time of conversion of a) A neutron into a proton

b) A proton into a neutron www.aieeepage.com

c) A nucleon into energy 5.

When blue light is made incident on a metallic, then electrons are emitted by it. But electrons are not emitted by green light. By which of the following radiations the photo-electric emission will be possible ?

a) Yellow

7.

b) Red

c)

Violet

d) Infrared

The A.M range of radiowaves have frequency a) less than 30 MHz

b) more than 30 MHz

c) less than 20000 MHz

d) more than 20000 MHz

Equal masses of two liquids A and B contained in vessels of negligible heat capacity are supplied heat at the same rate. The temp. time graphs for the two liquds are shown in figure. If S represents SP heat and L represents latent heat of liquid, then

Y

B A

TEMP

6.

d) A position into energy

PAGE O

a) SA > SB ; LA < LB

TIME

X

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b) SA > SB ; LA > LB

SA < SB ; LA < LB

d) SA < SB ; LA > LB

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8.

A cable carrying a direct current is burried in a wall which stands in a north-south plane. A horizontal compass needle on the west side of the wall is found to point towards south instead of north. The coil is laid a) vertically upwards and the current is also flowing upwards b) vertically upwards and the current if flowing downwards c) horizontally with current from south to north d) horizontal with current from north to south

9.

If 100 N force is applied to 10 kg block as shown in diagram, then acceleration produced for slab :

µ s = 0.6 100 N

µ k = 0.4

PAGE 10 kg

Slab

40 kg

a) 1.65 m/s2

b) 0.98 m/s2

c)

1/2 m/s2

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d) 0.25 m/s2

10.

For a planet having mass equal to the mass of the earth but radius is one fourth of the earth, then escape velocity for this planet will be : a) 11.2 km/sec b) 22.4 km/sec c) 5.6 km/sec d) 44.8 km/sec

11.

One end of a steel wire of length 1 m and cross-sectional area 1mm2 is clamped at rigid support. The increase in its length when 1 kg-wt. is suspended from it will be, if Y = 20 x 1010 pascal : a) 5 cm b) 0.5 mm c) 0.25 mm d) 0.05 mm

12.

Two springs A and B (KA = 3KB) are stretched by same suspended weight, then ratio of work done in stretching is : a) 1 : 2 b) 2 : 1 c) 1 : 3 d) 1 : 4

13.

Two identical cyllinders are released from the top of two identiacl inclined planes. If one rolls without slipping and the other slips without rolling, then a) sliding cylinder reaches the bottom first with greater speed b) rolling cylinder reaches the bottom first with greater speed c) both reach the bottom simultaneously and with the same speed d) both reach the bottom simultaneously but with different speeds.

14.

a) v / 2 NE c) v/ 2 NW 15.

PAGE

A particle of mass m moving eastward with a speed v collides with another particle of same mass moving northwards with same speed v. The two particles caolesce on the collision. The new particle of mass 2m will move in direction with the velocity b) v/ 2 SW d) v/ 2 SE

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In Young’s double slit experiment, the constant phase different between two sources is π/2 . The intensity at a point equidistant from the slits in terms of max. intensity I o is a) I o

b) I o / 2

c)

3I o / 4

d) 3I o

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16.

Two conducting slabs of heat conductivity K1 and K2 are joined as shown in fig. The temp. of ends of slabs are θ1 and θ2 ( θ1 > θ2 ), the final temp. of junction ( θ m ) is : K2

K1 θ1

a)

K 1θ1 + K 2 θ 2 K1 + K 2

b)

θm

K 1θ1 + K 2 θ1 K1 + K 2

c)

θ2

K 1θ1 − K 2 θ 2 K1 + K 2

d) none

17.

A capacitor is charged with a battery and energy stored in U. After disconnecting battery another capacitor of same capacity is connected in parallel with it. Then energy stored in each capacitor is : a) U/2 b) U/4 c) 4U d) 2U

18

Calculate the net resistance of the circuit between A and B :

PAGE

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8 Ω 3

b)

14 Ω 3

c)

16 Ω 3

d)

23 Ω 3

19.

Three equal resistors connected across a source of e.m.f. together dissipate 10 W of power. What will be the power dissipated if the same resistors are connected in parallel across the same source of e.m.f. : a) 5 W b) 10 W c) 30 W d) 90 W

20.

A bar magnet is held at right angles to a uniform magnetic field. The couple acting on the magnet is to be halved by rotating it from this postion. The angle of rotation is a) 60° b) 45° c) 30°

21.

d) 75°

Resonance frequency of a circuit is f. If the capacitance is made 4 times the initial value, then the resonance frequency will become a) f/2 b) 2f c) f

d) f/4

PAGE

22.

For a plane convex lens for which µ = 1.5, has radius of curvature 10 c.m. It is silvered on its plane surface. Find focal length after silvering : a) 10 cm b) 20 cm c) 15 cm d) 25 cm

23.

A ball of mass m moving with a velocity V undergoes an oblique elastic collision with another ball of the same mass m but at rest. After the collision, if the two balls move with the same speeds, the angle between their directions of motion will be : a) 30° b) 60° c) 90° d) 120°

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24.

An inclined plane makes an angle of 30° with the horizontal. A solid sphere roling down the inclined plane from rest without slipping has a linear acceleration equal to : a)

25.

5g 14

b)

5g 4

c)

2g 3

d)

g 3

A body of mass 1 kg. is realeased from the top of an inclined place shown in the figure and reaches the bottom in 2sec. With what force it should be pulled up from the bottom of the plane to reach the top of the plane in 1 second moving with uniform acceleration :

C

5m

a) 4N 26.

b) 8N

c)

35 N

d) 17.5 N

www.aieeepage.com d) Non-uniform illumination.

In the circuit in the fig. The current through :

3Ω

A 2Ω

2Ω

C

8Ω

9v

28.

B

In case of diffraction at single slit if the wavelength of light becomes equal to the aperture of slit, on the screen we shall observer : a) Image of slit b) Diffraction band c) Uniform illumination

27.

30°

PAGE A

B

2Ω

2Ω

8Ω 4Ω D

2Ω

a) The 3Ω resistor is 0.50 A

b) The 3Ω resistor is 0.25 A

c) The 4Ω resistor is 0.50 A

d) The 4Ω resistor is 0.25 A

A student determined to test the law of gravity for himself walks off a scraper 320 m high with a stop watch in hand and starts his free fall (zero initial velocity), 5seconds later, Super man arrives at the secne and dives off the roof to save the student. What must be the Superman’s initial velocity in order that he catches the student just before the ground is reached (g = 10m/s 2 ) : a) 67.23 m/s

PAGE

b) 91.66 m/s

c)

102.91 m/s

d) None

29.

The period of oscillation of a magnetic needle in a magnetic field is 1.05. If the length of the needle is halved by cutting it, then the time period will be : a) 1.0 sec b) 0.5 sec c) 0.25 sec d) 2.0 sec

30.

Two objects A and B when placed in turn in frong of concave mirror of focal length 7.5 cm, given images of equal size. If A is three times the size of B and is placed 30 cm from the mirror, what is the distance of B from the mirror ? a) 10 cm b) 12.5 cm c) 2.4 cm d) 17.5 cm

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31.

A small box of 100g is pressed against a horizontal spring fixed at one end to compress the spring through 5.0cm. The spring constant is 100 N/m. When released, the block moves horizontal till it leaves the spring. Where will it hit the ground 2m below the spring. from the free end of the spring ? a) 1 m b) 2 m c) 2.5 m

32.

A proton and will be :

d) 3 m α-

particle are accelerated through same voltage. The ratio of their de-broglie wavelength

a) 1 : 2 33.

b) 2 2 : 1

c)

The resultant of two equal foroces is double of either of the force. The angle between them is a) 0° b) 60° c) 90°

34.

d) 120°

The resultant capacitance between A and B is

PAGE 3µ F

A

3µ F

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B

3µ F

3µ F

3µ F

3µ F

a) 1 µ F

b) 3 µ F

c) 2 µ F

d) 1.5 µ F

The rate of change of current is 500 As-1 at the instant the key is pressed in the circuit shown in figure. The current through the circuit is

60 V

10 mH

K a) 2 A 36.

3µ F

2µ F

2µ F

35.

d) 2 : 1

2 :1

55Ω

PAGE

b) 1 A

c)

0.5 A

d) 1.5 A

A charged particle moving in a uniform magnetic field penetrates a layer of lead and loses half of its kinetic energy. The radius of curvature changes to a) twice the original radius b)

2 times to original radius

c) half the original radius d)

1 2

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times the original radius

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37.

Initial pressure and volume of gas are P and V respectively. First its volume is expanded to 4V by isothermal process and then its volume makes to be V by adiabatic process, then its final pressure is ( γ =1.5) a) 8P

38.

b) 4P

c)

40.

41.

d) 2P

The radiant energy from the sun incident normally at the surface of earth is 20 kcal/m2 - min. What would have been the radiant energy incident normally on the earth if the sun had a temperature twice of the present one : a) 40 kcal/(m2 -min) b) 80 kcal/(m2 - min) c) 160kcal/(m2 - min)

39.

p

d) 320kcal/(m2 - min)

Maximum frequency of emission is obtained for transition : a) n = 2 to n = 1 b) n = 6 to n = 2 c) n = 1 to n = 2

d) n = 2 to n = 6

A photon is a) A quantum of light energy

b) A quantum of matter

c) A positively charged particle

d) An instrument for measuring light intensity.

PAGE

A double star consists of two stars, one of mass M and the other 2M. Distance between them is r. The two stars revolve under their mutual gravitational force. Then a) The kinetic energy of the heavier star is 2 times the kinetic energy of the Lighter star. b) The two stars will revolve around the point of trisection of the straight line joining their mass centres, nearer to the heavier star.

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c) The two stars have equal periods of revolution d) both (b) and (c) are correct 42.

In a reasonance - column experiemnt, along tube, open at the top, is clamped vertically. By a separate device, water level inside the tube can be moved up or down. The section of the tube from the open end to the water level acts as aclosed organ pipe. A vibrating tuning fork is held above the open end, and the water level is gradually pushed down. The first and the second resonances occur when the water level is 24.1 cm and 74.1 cm respectively below the open end. The diameter of the tube is a) 2 cm b) 3 cm c) 4 cm d) 5 cm

43.

A gas is filled in a cylinder. Its temperature is increased by 20% on kelvin scale and volume is reduced by 10%. How much percentage of the gas has to leak for pressure to remain constant ? a) 30% b) 40% c) 15% d) 25%

44.

Two heating coils, one of fine wire and the other of thick wire made of same material and of same length are connected in series and then in parallel. Which of the following statement is correct. a) In series, fine thin wire liberates more energy while in parallel, thic wire liberates more energy. b) In serieis, fine thin wire liberates less energy while in parallel, thick wire liberates less energy.

PAGE

c) In series, thic wire liberates more energy while in parallel, it liberates less energy. d) Both wires liberate equal energies in series and parallel. 45.

In youngs double slit experiment, interference pattern is found to have an intensity ratio between bright and dark fringes as 9. Then 1) Intesities on the screen due to two slits are 5 units and 4 nits respectively 2) amplitude ratio is 2 c) amplitude ratio is 9

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4) Intensities at the screen due to two slits are 4 units and 1 units respectively a) 1, 2

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46.

S and falls vertically at the rate of 2 kg s-1 on to a conveyor belt moving horizontally with a velocity of 0.2 ms-1. The extra power required to keep the belt moving is a) 0.08 W b) 0.04 W c) 4 W

47.

d) 1 W

A piece of cork of mass m and density ρo is completely immersed in a liquid of density ρ, where ρ > ρo . It is attached to the bottom of the vessel containing the liquid by a light string. The whole system moves up with an acceleration = a. The tension in the string is  ρo  a) m(g + a)1− ρ  

 ρ





c) mg ρ −1  o  48.

 ρ







b) m(g + a) ρ −1 o  ρ



 o



d) m(g - a) ρ −1

PAGE

At a certain point and a certain time the electric field of an electromagnetic wave is in the negative z direction and the magnetic field is in the positive y direction. Which of the following statements is true ? a) Energy is being transported in the positive x direction but half a cycle later, when the electric field is in the opposite direction, it will be transported in the negative x direction.

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b) Energy is being transported in the positive x direction but half a cylce later, when the electric field is in the opposite direction, it will be transported in the positive x direction c) Energy is being transported in the negative x direction but half a cycle later, when the electric field is in the opposite direction, it will be transported in the positive x direction d) Energy is being transported in the negative x direction and half a cycle later, when the electric field is in the opposite direction, it will still be transported in the negative x direction. 49.

A long straight cylindrical shell has inner radius Ri and outer radius R0 . It carries current i, uniformly distributed over its cross section. A wire is parallel to the cylinder to the cylinder axis, in the hollow region (r < Ri ) . The magnetic field is zero everywhere outside the shell (r > R0 ) . We conclude that the wire. a) is on the cylinder axis and carries current i in the same direction as the current in the shell b) may be anywhere in the hollow region but must be carrying current i in the direction opposite to that of the current in the shell c) may be anywhere in the hollow region but must be carrying current i in the same direction as the current in the shell d) is on the cylinder axis and carries currnt i in the direction opposite to that of the current in the shell

50.

Find the equivalent capacitance between points M and N

PAGE C1

M

N

C2

www.aieeepage.com a) infinity

C

2 b) C1 + C

c)

1

C1C 2 C1 + C 2

d) none of these

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51.

Calculate the plate resistance. If for 5 kΩ of load the value of voltage gain of an amplifier be 1/3 of the amplification factor a) 12 kΩ

52.

c)

15 kΩ

d) 5 kΩ

In a common base amplifier the phase difference between input signal voltage and output voltage is a) 0

53.

b) 10 kΩ

π 4

b)

π 2

c)

d) π

A wire of mass 9.8× 10-3 kg per metre passes over a frictionless pulley fixed on the top of an inclined frictionless plane which makes an angle of 30° with the horizontal. Masses M1 and M2 are tied at the two ends of the wire. The mass M1 rests on the plane and mass M2 hangs freely vertically downwards. The whole system is in equilibrium. Now a transverse wave propagates along the wire with a velocity of 100 meter per seconds. Find M1 and M2 . a) 10, 20

54.

PAGE

b) 20, 10

c)

10, 10

d) 10, 5

Two spheres each of mass M and radius R/2 are connected with a massless rod of length 2R as shown in fig.) What will be the moment of inertia of the system about an axis passing through the centre of one of the sphere and perpendicular to the rod ?

Y

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M

R/2

M

R/2

O

2R

O' Y'

21

2 a) 5 M R

55.

2

b) 5 M R

5

2

c) 2 M R

2

5

d) 21 M R

2

The spring balance A reads 2 kg with a block of mass m suspended from it. A balance B reads 5 kg when a beaker with liquid is put on the pan of the balance. The two balances are now so arranged that the hanging mass is inside the liquid in a beaker as shown in fig.

A m

PAGE B

a) The balance A will read more than 2 kg b) The balance B will read less then 5 kg

c) The balance A will read less than 2 kg and B will read more than 5 kg d) The balance A will read more than 2 kg and B will read less then 5 kg

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56.

A bird in air looks at a fish vertically below it and inside water h1 is the height of the bird above the surface of water and h 2 the depth of the fish below the surface of water. If refractive index of water with respect to air be µ then the distance of the fish as observed by the bird is h

2 b) h1 + µ

a) h1 + h 2 57.

c)

d) µh1 + µh 2

µh1 + h 2

The maximum energy in the thermal rediation from a hot source occurs at a wavelength of 11×10-5 cm. According to Wien’s law, the temperature of this source (on Kelving scale) will be n times the temperature of another source (on Kelvin scale) for which the wavelength at maximum energy is 5.5 × 10-5 cm. The value n is a) 2 b) 4 c) 1/2 d) 1

58.

Two bar magnets of the same mass , same length and breadth but having magnetic moments M and 2M are joined together pole for pole and suspended by a string . The time period of assembly in a magnetic field of strength H is 3 seconds . If now the polarity of one of the magnets is reversed and combination is again made to oscillate in the same field , the time of oscillation is

PAGE

a) 3 sec

b) 3 3 sec

c) 3 sec 59.

d) 6 sec

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Two forces, one with a magnitude of 3N and the other with a magnitude of 5 N, are applied to an object. For which orientations of the forces shown in the diagrams is the magnitude of the acceleration of the object the least ?

3N

a)

5N

3N

5N b)

3N

c)

60.

3N

5N

d)

5N

PAGE

The electric field inside a conductor a) must be zero

b) may be non-zero

c) must be non-zero

d) (a) and (c) are orrect

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CHEMISTRY

61.

A colloidal solution is subjected to an electrical field. The particles move towards anode. The coagulation of same sol is studied using NaCl, BaCl2 and AlCl3 solutions. Thier coagulating power should be a) NaCl > BaCl2 > AlCl3

b) BaCl2 > AlCl3 > NaCl

c) AlCl3 > BaCl2 > NaCl

d) BaCl2 > NaCl > AlCl3

62.

An atom withatomicnumber 20 is most likely to combine chemically with the atom whose atomic number is a) 11 b) 16 c) 18 d) 10

63.

N 2 and O 2 are converted into mono cations, N +2 and O+2 respectively. Which of the following is wrong ?

64.

b) In O+2 , O -O bond order increases

c) In O+2 , Paramagnetism decreases

d) N +2 becomes diamagnetic

The order of solubility of lithium halides in non polar solvents follows the order : a) Lil > LiBr > LiC > LiF b) LiF > Lil > LiBr > LiCl d) LiBr > LiCl > LiF > Lil www.aieeepage.com Electronegativity of Oxygen is more then sulphur yet is acidic while water is neutral. This is because c) LiCl > LiF > Lil > LiBr

65.

66.

67.

PAGE

a) In N +2 , N-N bond weakness

H 2S

a) Water is highly associatet compound

b) Molecular mass of H2S is more than H2O

c) H 2S is gas while H 2O is a liquid

d) H-S bond is weaker than H - O bond

Which of the following nuclear proceosses are identical ? a) β + emission and β - emission

b) α emission and γ radiation

c) β + emission and electron capture

d)

γ

radiation and production of X-rays

In the forth floatation process for the purification or ores, the ore particles float because a) They are light b) Their surface is hydrophobic i.e., not easily wetted by water c) They bear electrostatic charge d) They are insoluble

68.

Which of the following elements represents highly electropositive as well as highly electronegative character in its period ? a) Hydrogen b) Nitrogen c) Fluorine d) None

69.

If the density of liquid water is 1.0 g cm-3 and that of water vapour is 0.0006 cm -3 at 100°C and 1 atm, then the volume occupied by water molecules in litre of steam at this temperature is a) 6 cm-3

70.

PAGE

b) 60 cm-3

c)

0.6 cm-3

d) 0.06 cm-3

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When the product of pressure and volume is plotted against pressure for a given amout of the gas, the line obtained is a) parallel to X - axis b) parallel to Y - axis c) linear with positve slope

d) linear with negative slope

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71.

Which of the following electronic configuratins have the highest exchange energy ? a)

c)

↑

↑

3d

4s

↑

↑

3d

4s

↑↓ ↑↓ ↑↓

↑↓

↑

b)

d)

↑

3d ↑

↑

↑

4s ↑

↑

↑

3d ↑↓ ↑↓ ↑↓

4s ↑↓ ↑↓

↑

72.

How much water should be added to 200 c.c of seminormal solution of NaOH to make at exactly decinormal ? a) 200 cc b) 400 cc c) 800 cc d) 600 cc

73.

Identify the correct statement regarding entropy a) At absolute zero of temperature, theenetropy of p[erfectly crystalline substance is positive b) At absolute zero of temperature, entropy of perfectly crystalline substance is taken to be zero

PAGE

c) At 0°C the entropy of a perfectly crystalline substance istaken to be zero d) At absolutezero of temperature, theentropy of all crystalline substances is taken to be zero. 74.

What will be the H + ion concentration in a solution prepared by mixing 50 mL of 0.20 M NaCl, 25 mL of 0.10 M NaOH and 25 mL of 0.30 M HCl ? a) 0.5 M b) 0.05 M c) 0.02 M d) 0.10 M

75.

How many kilojoules of energy is expended during the passage of current of 0.1 A for 100 s under a potential of 150 V ? a) 1.50 b) 0.15 c) 2.50 d) 9.65

76.

The reaction between NO 2 andCO to produce NO and CO 2 is believed to occur in two steps

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Step 1 NO 2 + NO 2 → NO + NO 3

Step 2 NO 3 + CO → NO + CO 2

The intermediate product and the rate-determining step are a) No andstep 1 b) NO and step 2 c) NO3 and step1 77.

d) NO3 and step 2

From the following which does not show correct order of the given property : a) Sc3+ > Cr3+ > Fe3+ > Mn3+; Stability of + 3 ion b) FeO > CoO > NiO > CuO; Basic property c) M n2+ < Ni2+ < CO2+ < Fe2+; Magnetic motion d) Sc < Ti < Cr < Mn; Number of oxidation state

PAGE

(Given atomic number : Sc = 21, Cr = 24, Mn = 25, Fe = 26, Ti = 22, Co = 27, Ni = 28, Cu = 29) 78.

Which of the following is high-spin (spin (spin-free) complex ? a) [Co(NH3 ) 6 ]3+

b) [Fe(CN) 6 ]4−

c) [CoF6 ]3− 79.

X is converted into a) 9

d) [Zn(NH3 ) 6 ]2+

14 7 N

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by emitting two β -particles. Then the number of neutrons in X will be :

b) 7

d) 3

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80.

81.

In which of the following compounds lassaigne test of nitrogen will be wrong : a) H 2 N − NH 2 .2HCl

b) H 2 N − CONH − NH 2 − HCl

c) H 2 N − CO − NH 2

d) C6 H 5 NH − NH2 2HCl

Arrange the compounds CH 2 = CH − CH 3 (I), CH 2 = CH − CH = CH 2 (II), HC ≡ C − CH = CH 2 (III) and HC ≡ C - C ≡ CH(IV) in order of increasing c-c single bond length

82.

a) I > II > III > IV

b) II > I > IV > III

c) IV > III > II > I

d) I > II > IV > III

In preparation of alkene from alcohol using Al 2 O 3 which is effective factor ? a) Porosity of Al 2 O 3 c) Concentration

83.

b) Temperature

PAGE

d) Surface area of Al 2 O 3

Which of the following alkyl hallides will you expect to given the highest yeild of substitution products under conditions faccourable to a bimolecular reaction ? a) CH 3CH 2 CH 2 CH 2 Br

b) CH 3CH 2 CH 2 CH - CH 3

www.aieeepage.com Br Br

c)

d) CH 3CH 2 − C − CH 3

CH 3CH 2 CH − CH 2 Br

CH 3

CH 3

84. 85.

The IUPAC name of acraldehyde is a) Prop-2-en-1-al b) Propenyl aldehyde

c)

But-2-en-l-al

d) Propenal

The major product obtained in the reaction NC-CH = CH 2 HBr  → a)

NC - CH - CH 3 Br

b) NC - CH 2 − CH 2 Br c) an equimolecular mixture of (a) and (b) d) none of these 86.

PAGE

Monomer of natural rubber is : a) CH 3 − −C = CH − −CH 3 | CH 3

c) CH 2 = C − −CH = CH 2 | CH 3

b) CH3 -- CH = CH -- CH3

d) | www.aieeepage.com CH

CH 2 = C − − − −C = CH 2 | CH 3 3

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87.

In DNA, the complementary bases are : a) uracil and adenine : cytosine and guanine b) Adenine and thymine : Guanine and cytosine c) Adenine and thymine : guanine and uracil d) Adenine and guanine : thymine and cytosine

88.

89.

90.

91.

Commonly used dettol is a mixture of : a) Chloroxylenol + Terpenol

b) Ortho-chlorophenol + Terpenol

c) Ortho-cresol + Terpenol

d) Phenol + Terpenol

The van’t Hoff factor for 0.1 M Ba(NO3 )2 solutions is 2.74. The degree of dissociation is a) 91.3%

b) 74%

c) 87%

d) 100%

PAGE

Internal energy does not include a) nuclear energy

b) energy arising by gravitational pull

c) rotational energy

d) vibrational energy

Look at the following reactions carried out in closed vessels 1) PCl5 → PCl3 + Cl2

2) 2KClO3 → 2KCl + 3O2

3) Fe3+ + SCN − → Fe(SCN) 2 +

4) www.aieeepage.com

N 2 + O2 → 2NO

Which one of them is irreversible ? a) 3 b) 4 92.

c)

2

d) 1

The reaction in which hydrogen peroxide acts as a reducing agent is a) Pbs + 4H2O2 → PbSOl4 + H2O b) 2FeSO4 + H 2SO4 + H2O2 → Fe2 (SO4 )3 + 2H2O c) Ag2O + H 2O2 → 2Ag + H 2O + O2 d) 3Kl + H2O2 → 2KOH + l2

93.

+2 When KMnO4 acts as an oxidising agent and ultimately forms MnO-2 4 , MnO2 , Mn 2O3 and Mn , then the number of electrons transferred in each case respectively is a) 1, 3, 3, 5 b) 1, 5, 3, 7 c) 3, 5, 7, 1 d) 4, 3, 1, 5

94.

The compound which gives the most stable carbocation is

95.

PAGE

b) CH 3 CHCH 3 | OH

a) CH 3CH 2 OH

c) CH 3 CHCH 2 OH | CH 3

CH 3 |

d) CH 3 - C - CH 3 | OH

The one which is unimolecular reaction is 1

a) N 2O5 → N 2O 4 + 2 O 2

www.aieeepage.com b)

PCl3 + Cl2 → PCl5

c) 2Hl → H 2 + l2

d) H2 + Cl2 → PCl5

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96.

Solid oxygen has pale blue colour which is attributed to a) Electronic transitions from the tiplet ground state to anti bonding d 2 pz molecular orbital b) Electronic trnaisition from the triplet ground state tothe excite singlet state c) Electronic transitions from the singlet ground state to the triplet excitied state d) Electronic transitions fromantibonding

97.

molecular orbits to bonding d 2pz M.O.s

When CuSO4 solution is added to K 4[Fe(CN)6 ] the formula of the product formed is ? a) KCN

98.

π

b) Cu(CN)2

c)

Cu2 Fe (CN)6

d) Cu (CN)3 117.

Mercury is the only metal which is liquid at 0°C. This is due to its a) Weak metalic bond & weak covalent bond b) strong covalent bond c) weak metalic bond and absence of covalent bond d) none of these

99.

PAGE

Among Ni(CO)4 , [Ni(CN)4 ]2− and NiCl24−

a) Ni(CO)4 and NiCl24- are diamagnetic and [Ni(CN)4 ]2− is paramagnetic

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b) Ni(CO)4 and [Ni(CN)4 ]2− and diamagnetic and NiCl24− is paramagnetic c) NiCl24− and Ni(CN)4 ]2− are diamagnetic and NiCl24− is paramagnetic d) Ni(CO)4 is diamagnetic and NiCl24- and [Ni(CN4 )]2− are paramagnetic 100. A mixture of 0 - hydroxyacetophenone and p - hydroxy acetophenone can be separated by a) Steam distillation b) Distillation c) Fractional crystallization

d) Sublimation

101. The structures (CH3 )3 CBr and CH3 (CH 2 )3 Br present a) Functional isomerism

b) Chain isomerism

c) Position isomerism

d) Both (b) & (d)

102. Domestic cooking gas (LPG) mainly contains a) Ethylene and carbon monoxide

b) Methane and ethane

c) Liquefied butane and isobutane

d) Hydrogen and acetylene

103. Industrial preparation of chloroform employs acetone and a) clorine gas b) Calcium hypochlorite c) Sodium chloride

PAGE d) Phosgene

104. Ethylamine reacts with nitrosyl chlorid (NOCl) to form a) Ethyl nitrite b) Nitro ethane c) Etyle chloride

d) Ethyl acohol

www.aieeepage.com b)

105. At the isoelectric point, amino acids are present as a) NH2 − CHR − COO−

H 2 N − CHR − COOH +

c) H3N − CHR COO-

d) H3 N − CHR − COOH

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106. Morphine is used as an a) Insecticide

b) Analgesic

c) Antiseptic

d) Antipyretic

107. A cube of any crystal A-atom is placed at every corners and B-atom placed at every centre face. The formula of compound : a) AB b) AB3 c) A2B2 d) A2B3 108. In steam distillation of toluene, the pressure for toluene in vapour is : a) equal to pressure in barometer b) less than pressure of barometer c) equal to vapour pressure of toluene in simple distillation d) more than vapour pressure of toluene in simple distillation 109. Which one/ones of the following reactions will yield 2-propanol ? I.

PAGE

H+

CH 2 = CH − CH 3 + H 2O → 

(i )CH 3 MgI → II. CH 3 − CHO (ii )H O 2

(i )C2 H 5 MgI → III. CH 2O (ii )H O 2

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Neutral KMnO4 IV. CH 2 = CH − CH 3    →

a) I and II

b) II and III

c) III and I

d) II and IV

110. An organic compound X (molecular formula C6H7O2 N ) has six carbon atoms in a ring system, two double bonds and a nitro group as substituent, x is a) Homocyclic but not aromatic b) Aromatic but not homocyclic c) Homocyclic and aromatic d) Haterocyclic and aromatic 111. The metal with highest electrical resistance at room temperature is a) Pb b) Te c) Po

d) Fe

112. Which of the following is not affected by pressure change ? a) 2NO2 (g) c) H2 (g) + I2 (g)

N 2O4 (g) 2HI(g)

PAGE

b) CO2 (g) + H2O(l) d) 2O3 (g)

CO2 solution

3O3 (g)

113. 14 g of element X combine with 16 g of Oxygen. On the basis of this information. Which of the following is a correct statement (Atomic weight of oxygen = 16) a) The element of X could have an atomic weight of 7 and its oxide the formula XO

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b) The element X could have an atomic weight of 14 and its oxide the formula X 2 O c) The element X could have an atomic weight of 7 and its oxide the formula X 2 O d) The element X could have an atomic weight of 14 and its oxide the formula XO 2

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114. A solution is obtained by dissolving 6 gm of urea (mol. we = 60) in a litre of water. Another solution is obtained by dissolving 34.2 gm sucrose (mol. wt = 342) in 1 litre of water at the same temperature. The loweiring of vapour pressure in first solution is a) nearly one-seventh of second solution b) seven times of second solution c) same as that of second solution d) double than that of second solution 115. The pH of a 0.01 M HCN solution for which pK is 4 is a) 0.47 116

b) 1.2

c)

3.0

d) 4.0

The emf of the cell Cu(s) | Cu 2_ (aq) || Ag + (aq) | Ag is 0.46 V. The standard reduction potential of Ag + /Ag is 0.80 V. The standard reduction potential of Cu 2+ /Cu will be a) -0.34 V b) +0.34 V c) -1.26 v

PAGE

d) +1.26 V

117. Equal weights of hydrogen and oxygen are mixed in an evacuated container at room temperature. The pressure exerted by the mixture is 680 mm. The pressure exerted by oxygen is a) 640 mm b) 40 mm c) 340 mm d) 510 mm 118. A freshly prepared radioelement has a half-life of 2 hours. It emits radiation whose intensity is 64 times the permissible safe level. The minimum time after which it would be possible to work with this sample is a) 3 hours b) 9 hours

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c) 24 hours

d) 12 hours

119. What conclusions can be drawn from the following reactions ? H 2 + 4.5eV → H + H

H + 13.6eV → p + + e −

a) It is more difficult to break up an H 2 molecule that it is to break up a hydrogen atom b) It is easier to break up an H 2 molecule than it is to break up a hydrogen atom c) The average energy of formation of H and p + are the same d) Electron and proton attraction in an H 2 molecule as well as an H atom are the same O H 120. The major product obtained in the reaction is CH 2 = CH − C − CH 3 + HCN O→ 

OH

a)

CH 2 = CH − C − CH 3 CN OH

c)

CH 2 = CH − C − CH 3 COOH

PAGE b)

O

NC - CH 2 − CH 2 − C − CH 3

d) none of these www.aieeepage.com

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MATHEMATICS 121. Let A and B be two finite sets having m and n elements respepctively. If m ≤ n, the total number of injective frunctions from A to B is b) n m

a) m n c)

n! (n − m)!

d) n !

122. Consider an infinite geometric series with first term a and common ratio r. If its sum is 4 and the second term is

3 then : 4

a) a =

3 7 ,r= 7 4

c) a =

3 1 ,r= 2 2

b) a = 2, r =

123.

∫ (sin

3

x cos 2 x)dx is

−π

a) 0

PAGE d) a = 3, r =

π

b)

3 8 1 4

π www.aieeepage.com c)

π4 4

4

2

d) 1

124. If in a triangle PQR, sin P, sin Q, sin R are in A.P., then a) the altitudes are in A.P. b) the altitudes are in H.P. c) the medians are in G.P.

d) the medians are in A.P.

125. The area of the curve x 2 + y 2 = 2 a x is a) π a 2 126.

b) 2 π a 2

1 π a2 2

c)

4π a2

d)

c)

0

d) does not exist

lim −1 is equal to x → 1 sin x

a)

π 2

π

b) − 2 2π

−1   127. sin sin 3  is equal to  

a)

2π 3

PAGE π

b) − 3

c)

−

2π 3

π

d) 3

128. The total number of permutations of n different things not more then r at a time , when each thing maybe repeated any number of times is a) n + n 2 + n 3 + ..... + n r

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b) p(n , 1 ) + p(n , 2 ) + p(n , 3) + .....p(n , r)

c) C(n , 1 ) + C(n , 2 ) + C(n , 3) + .....C(n , r) d) none of these - A Premier Institution for IIT - JEE & AIEEE at the National PAGE www.iitjeepage.com www.aieeepage.com www.bitsatpage.com 18

129. Let A = {1, 2, 3, 4}. The function f : A → A and g : A → A are defined in the table given below x

1

2

3

4

f(x) g(x)

3 4

2 3

4 2

1 2

The value of x, for which (fog) (x) = (gof) (x), is : a) 1

b) 2

c)

3

d) 4

130. If ∫ sin 3 xcos5dx = Asin 4 x + Bsin 6 x + Csin8 + D. Then 1 4

1 3

1 8

1 8

a) A = , B = − , C = , D ∈ R 1 6

1 4

1 3

b) A = , B = , C = , D ∈ R

PAGE

1 8

c) A = 0, B = − , C = , D ∈ R

d) none of these

131. ABCD is a quadrilateral and O is any point in its plane such that OA + OB + OC + OD = 0, then O is a) the point of intersection of the lines joining the mid-points of the opposite sides of ABCD b) the point of intersection of the diagonals of ABCD

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c) any point anywhere in the plane of ABCD d) None of these

132. The number of pairs (x, y) satisfying the equation x + y = a) 0

b) 1

c)

2π 3 and cosx + cosy = is : 3 2

2

d) ∞

133. Two persons throw a die alternately till one of them gets a ‘three’ and wins the game. The ratio of their respective probabilities of winning is a) 6 : 5 b) 4 : 5 c) 3 : 2 d) 3 : 5 134. Two mutually perpendicular straight lines are drawn from the origin to form an isosceles traingle with the striaght line xcosα + ysinα − p = 0 . Then the area of this triangle is a) independent of α b) independent of p c) independent of both α and p d) a function of α and p

PAGE

135. The number of negative integral solutions of the equation x1 + x2 + x3 + x4 + 15 = 0 is a) 364

b)

15

c)

C3

14

C4

d) None of these

136. The solution for the differential equation y d x - x d y = x y d x is a)

c)

x = c ex y x2 y2

www.aieeepage.com b) x y = c e x

= c log x

d) none of these

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137. If the point (a, a + 1) belongs to the interior of the region bounded by the curve y = 5 − x 2 and the x - axis then a belongs to a) (-2, 1) b) (-1, 1) c) (-2, 0)

d) (0, 1)

138. If the length of a chord of a circle is equal to that of the radius of the circle, then the angle subtended in radians at the centre of the circle by the chord is : a) 1

b)

π 2

π 3

c)

d)

π 4

139. In a ∆ ABC, the value of sin A cos B cos C + sin B cos C cos A + sin C cos A cos B is equal to a) cos A cos B cos B

b) sin A sin B sin C

c) 0

d) none of these

PAGE

140. The slope of the tangent to the cruve y = f(x) at (x, f(x) is 2x+1. If the curve passes through the point (1, 2), then the area of the region bounded by the curve, the x-axis and the line x = 1 is a)

5 6

c)

1 6

6 5

b)

d) 6 www.aieeepage.com

G

141. If aG and b are vectors, each of magnitude 5, one pointing fowards north-east and the other towards north G

G

west, then a − b is a) 5

b) 10

c)

0

d) 5 2

142. The moment about the point M ( -2, 4, -6) of the force represented in magintude and position by AB where the points A and B have the cco-ordinates (1, 2, -3) and (3, -4, 2) respectively, is a) − 16 ˆi − 2ˆj + 4 kˆ

b) − 3 ˆi + 2ˆj − 3 kˆ

c) − 5 ˆi + 8 ˆj − 8 kˆ

d) 2 ˆi + 2 ˆj − kˆ

143. In a third order determinant, each element of the first column consists of sum of two terms, each element of the second column consists of sum of three terms and each element of the third column consists of sum of four terms. Then, it can be decomposed in n determinants, where n has the value a) 24 b) 16 c) 9 d) 1 144. The harmonic mean of the roots of the equation (5 + 2 ) x2 - (4 + a) 2

b) 4

PAGE c)

5 ) x + 8 + 2 5 = 0 is :

6

d) 8

145. Let AB be a chord of the circle x2 + y2 = r2 subtending a right angle at the centre. Then , the locus of the centroid of the triangle PAB as P moves on the circle is : a) a parabola b) a circle c) an ellipse

d) a pair of straight lines

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146. If the difference between mean the mode is 63 the difference between mean and median is : a) 21 b) 31.5 c) 48.5 d) 189 - A Premier Institution for IIT - JEE & AIEEE at the National PAGE www.iitjeepage.com www.aieeepage.com www.bitsatpage.com 20

dx

147. A particle moves in a straight line with velocity given by dt = x + 1 (x being the distance described). The time taken by the particle to describe 99 metres is b)

a) log10 e

c)

2 log e 10

148. A particle acted upon by forces 3ˆi + 2ˆj + 5kˆ and respective position vectors are

2 ˆi + ˆj - 3 kˆ

d)

2 log10 e

2 ˆi + ˆj - 3 kˆ is

1 log e 2 10

displaced from a point P to a point Q whose

and 4ˆi − 3ˆj + 7kˆ . The work done by the force is

a) 17 units

b) 24 units

c) 33 units

d) 42 units

149. Let A be the set of first ten natural numbers and let R be a relation in A defined by (x, y) ∈ R if and only if x + 2 y = 10. Which of the following is true ? a) R = {(2, 4), (4, 3), (6, 2), (8, 1)}

b) Domain of R = {2, 4, 6, 8}

c) Range of R = {1, 2, 3, 4}

d) All the above

PAGE

150. If all the roots of z3 + az 2 + bz + c = 0 are of unit modulus, then a)

b)

| a |≤ 3

c)

| b |> 3

d) none of these

| c |≤ 3

151. For positive integers n1, n2 the value of the expression (1 + i )n1 + (1 + i 3 ) n1 + (1 + i 5 ) n2 + (1 + i 7 )n2 , where i = − 1 is real numbers if and only if

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b) n1 = n2 − 1

a) n1 = n2 + 1

c)

d) n1 > 0, n2 > 0

n1 = n2

n

1+ i   = 1 is 152. The smallest positive interger n for which  1− i 

a)

4

b) 3

c)

2

d) 1

153. A ray of light is sent along the line which passes through the point (2, 3). The ray is reflected from the point P on x-axis. If the reflected ray passes through the point (6, 4), then the coordinates of P are  26





a)  7 , 0    154.

∫

26 

b)  0, 7    dx

2

4sin x + 4sin x cos x + 5cos2 x

a)

1 tan −1 (2tanx + 1) + C 4

c)

1 tan −1 (2tanx + 1) + C 2

c)

 26   − , 0  7 

d) None of these

is b)

1 1 tan −1 (tanx + ) + C 4 2

PAGE 1



1

−1 d) 2 tan  tanx + 2  + C  

155. The number of ways in which 5 male and 2 female members of a committee can be seated around a round table so that the two females are not seated together is : a) 840 b) 720 c) 600 d) 480

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156. The number of numbers that can be formed by the digits 1, 2, 3, 4, 3, 2, 1, with odd digits at odd places, is given by : a) 430 b) 36 c) 18 d) none - A Premier Institution for IIT - JEE & AIEEE at the National PAGE www.iitjeepage.com www.aieeepage.com www.bitsatpage.com 21

157. The area bounded by the curves y 2 − x = 0 and y − x 2 = 0 is a)

7 3

b)

1 3

c)

158. If f(a)=3, f ' (a) = -2, g(a) = -1, g' (a) = 4, then xlim →a a) -5

5 3

d) 1

g(x)f(a) − g(a)f(x) x −a

b) 10

c)

-10

d) 5

159. Let A, B, C be three events such that P(A) = 0.3 P (B) = 0.4, P(C) = 0.8, P(A ∩ B) = 0.08, P(A ∩ C) = 0.28, P(A ∩ B ∩ C) = 0.09. If P(A ∪ B ∪ C) ≥ 0.75, then

a) 0.23 ≤ P(B ∩ C) ≤ 0.48 b) 0.23 ≤ P(B ∩ C) ≤ 0.75 c) 0.48 ≤ P(B ∩ C) ≤ 0.75 d) none of these

PAGE

160. If 7 points out of 12 are in the same straight line, then the number of triangles formed is a) 19 b) 158 c) 185 d) 201

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161. The normal to the curve represented parametrically by x = a (cos θ + θsin θ) and y = a (sin θ − θ cos θ) at any point θ , is such that it a) makes a constant angle with x-axis b) is at a contant distance from the origin c) touches a fixed circle d) satisfies (b) and (c) 162. A rod AB of length 16 cm. rests between the wall AD and a smooth peg, 1 cm from the wall and makes an angle θ with the horizontal. The value of θ for which the height of G, the mid point of the rod above the peg is minimum, is a) 15° b) 30° c) 60° d) 75°

163. The value of

a−b−c 2a 2b b−c−a 2c

a) (a + b + c) 2 164. If b = 3, c = 4 and B = a) infinite

2c

2a 2b c−a −b

will be

b) (a + b + c) 3

c)

(a − b − c) 2

PAGE

d) (a + b − c) 2

π , then the number of triangles that can be constructed is 3

b) two

c)

one

d) nill

165. Area of the parallelogram formed by the lines y = mx, y = mx + 1, y = nx and y = nx + 1 equals : a) c)

|m+n| ( m − n)

2

b)

2 |m+n|

d)

1 |m−n|

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1 |m+n|

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166. A particles covers S metres in t ses given by S = t 3 + 3t 2 + 2t + 5 . The velocity of the particle after 3 sec is a) 40 m / sec b) 57 m /sec c) 47 m /s

d) 65 m /s

167. A rocket of height h metres in tried vertically upwards. Its velocity at time t seconds is (2t+3)m/s. If the angle of elevationof the top of the rocket from a point on the ground after 1 second of firing is π/6 and after 3 seconds it is π/3 then the distance of the point from the rocket is a) 14 3 metres

b) 7 3 metres

c) 2 3 metres

d) cannot be found without the value of h

168. If in a

∆ABC, sinA = sin 2B

and 2 cos2A = 3 cos2B, then the triangle is

PAGE

a) right angled

b) obtuse angled

c) isosceles

d) equilateral

169. A body whose true weight is 13 gm appears to weight 12 gm when weighted by means of a spring balance in a descending lift. The ace. Of the lift at time of weighing is a) 75.4 cm/sec²

b) 7.54 cm/sec2

d) none of these www.aieeepage.com

c) 754 cm/sec2 170. If

f[x]

a)

x 2

denotes the greatest integer ≤ x, then xlim →∞

1 n3

x

b) 3 

 3π

[1 x ]+ [2 x ]+ [3 x ]+ ...... + [n x ]= 2





2

2

x 6

c) 

2

π

d) 0 



4 4 6 6 171. The expression 3 sin  2 − α  + sin (3π + α) − 2 sin  2 + α  + sin (5π-α) is equal to        

a) 0

b) 1

c)

d) sin 4α + cos 6α

3 x +1

172. If

ω is

cube root of unity, then a root of the following equation

a) x = 1

c)

b) x = ω

ω ω2

x = ω2

PAGE

ω2

ω x+ω 1

2

1 =0 x+ω

d) x = 0

173. The maximum number of points with rational coordinates on a circle whose centre is a) one

is

( 3 ,0) is

b) two

c) four

d) infinite

174. If the sides of a triangle are in G.P and the largest angle is twice the smallest angle then the common ratio, which is greater then 1 ,lies in the interval b) www.aieeepage.com

a) (1 , 3 )

(1 ,4 3 )

 5 +1 c) 1 , 2  

d) none of these



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175. A man claims to have diving rod which locates hidden sources of oil. The Indian oil company conducts the following experiement to test his claim. He is taken into a room in which there are 10 sealed barrels. He is told that five of them contain oil and five contain water. His task is to decide which of the five contain water. His task is to decide which of the five contain oil and which do not. The probability that he locates all the barrels correctly just by chance is a) 1 / 10 !

b) (2! × 2!) / 10 !

c) (5! × 5!) / 10 !

d) none of these

176. A boat is rowed with a velocity of 6 km/hr. straight across a river which flows at the rate 2 km/h. If the breadth of the river is 300 m, then the boat will strike the opposite bank below the point, at which it was originally directed is : a) 75 m b) 85 m c) 90 m d) 100 m 177. A given force is resolved into components P and Q equally inclined to it. Then a) P = 2Q b) 2P = Q

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c) P = Q

d) none of these

G G G G G G G G G 178. Let a = ˆi − ˆj, b = ˆj − kˆ, c = kˆ − ˆi . If d is a unit vector such that aG ⋅ d = 0 = [b, c d] , then d equals :

a) ±

c) ±

ˆi + ˆj − 2kˆ

b) ±

ˆi + ˆj − kˆ

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6 ˆi + ˆj + kˆ

3

d) ± kˆ

3

179. The mean wages of 100 workers on a factory running two shifts of 60 and 40 workers is 38, the mean wage of 60 workers in the morning shift is Rs. 40, then the mean wage of 40 workers in the evening shift is : a) Rs. 37 b) Rs. 36 c) Rs. 35

d) Rs. 40

180. The smallest +ve integer n for for which a) 1

 n +1 n !<    2 

b) 2

n

c)

holds is 3

d) 4

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