Ai Aieee Modeltest 01

MODEL TEST TEST CODE - FEN

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. You are NOT allowed to use a calculator

PAGE

PAGE

TM

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1

Questions - 180 1.

PHYSICS

Dimensional formula for entropy is identical to that of a) Universal Gas constant b) Specific Heat c) Boltzmann constant

2.

d) Gravitational potential

A cylindrical bar magnet is kept along the axis of a circular coil. The magnet is rotated about its axis such that north pole faces the coil. The induced current in the coil a) is zero b) is clock - wise from magnet side c) may be clock-wise or anticlockwise

3.

Time - 180 Min

d) is anticlockwise from magnet side

A block of mass m is gently placed on a vertical spring of stiffness k. Identify the in-correct statement? a) The kinetic energy of the block remains constant b) The gravitation potential energy of the system decreases

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c) The spring potnetial energy of the system increases.

d) The rate of decreases in gravitational potential energy is equal to the increase in spring potential energy 4.

A nicol prism is based on the action of a) refraction c) dichroism

5.

b) double refraction

d) both (B) and (c) www.aieeepage.com

The fig shows a man of mass m standing at the end A of a trolley of mass M placed at rest on a smooth horizontal surface. The man starts moving towards the end B with a velocity u rel with respect to the trolley. The length of the trolley is L.

M

A

B

L Choose the correct statement a) As the man starts moving the trolley must move backward b) The distance moved by the trolley is independent of the speed of the man c) The distance moved by the trolley can never exceed L d) All the above 6.

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A rectangular door is supported only by two hinges along the vertical edge. Which of the following statement regrading the forces exerted by the two hinger on the door is incorrect ? a) Both forces cannot be vertical b) Both forces cannot be horizontal

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7.

The thermal conductivity of copper decreases significantly as the temperature is increased. This is because, at higher temperatures. a) Ionic, at higher temperatures b) Lattice vibrations travel more atoms decrease c) fewer conduction electrons are preasent d) The rate of collision between conduction electrons and copper atoms increases.

8.

Which of the following are not electromagnetic waves ? a) cosmic rays

9.

b) gammarays

c) β − rays

d) X - rays

Choose the correct statement by comparing the charging of the capacitors as shown in figure with the situation when there is no resistor.

R

PAGE C

E

a) It gets charged to the same magnitude

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b) Current through the battery never becomes zero c) Extra energy is dissipated in the resistor d) All the above. 10.

In a P-N junction diode a) Current in the reverse bias condition is generally small. b) Forward bias current is small as compared to reve c) Forward current is independent of the bias voltage d) Reverse bias current is independent of the bias voltage

11.

A car starts from rest to cover a distance s. The coefficient of friction between the road and tyres is µ. The minimum time in which the car can cover the distance is proportional to b)

a) µ 12.

c)

µ

1 µ

1

d) µ

A projectile of mass m is fired with velocity v pass a point A making an angle 45° with the horizontal. Neglecting air resistance, the magnitude of change in momentum between the starting point A and the arriving point B is a)

2 mv

c) (1/2) mv

PAGE b) 2 mv

d) (mv)1/2

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13.

Find the resultant resistance in this circuit across ‘AB’

10Ω

10Ω

B

A 10Ω

10Ω a) 10Ω 14.

b) 20Ω

c)

d) 40Ω

30Ω

A particle of mass m is fixed to one end of a light spring of force constant K and unstretched length 1. The system is rotated about the other end of the spring with an angular velocity ω, in gravity free space. The increase in length of the spring will be

PAGE ω

k

m www.aieeepage.com

mω2l K

a) 15.

m ω2 l

b)

K - m ω2

m ω2 l

c)

K + m ω2

b) t

t

c) t 2

d) 1/t

A point mass M is located at x = 0. Which one of the following graphs represents the variation of gravitation intensity ((A) with distance (x) from the mass I

I

a)

b) O

17.

none of these

If the displacement of a particle varies with time as x = t + 3, the velocity of the particle is proportional to a)

16.

d)

I

PAGE c)

O

O

I

d) O

The greatest thickness of a plano convex glass lens appear to be 2 cm when observed normally through the plane surface and when observed through the curved face, the greatest thickness is 20/9 cm. If the real thickness be 3 cm, the what is the refractive index of the lens ? a) 20/9 b) 2.0 c) 1.5 d) 1.3

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18.

A sphere of radius r is placed on a concave surface of radius of curvature 5r, which itself is placed on a horizontal table. See fig. When the sphere is displaced from the equilibrium position it describes SHM of period ?

1

1

 r 2 a) 2 π   g

19.

c)

1

 5r  2 2 π   g

 6r  2 d) 2 π   g

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The insulation property of air breaks down at E = 3 ×10 6 volts/metre. The maximum charge that can be given to a sphere of diameter 5 m is approximately a) 2 ×10 −2 coulomb

20.

1

 r 2 b) 4 π   g

b) 2 × 10 −3 coulomb

c)

2 ×10 −4 coulomb

d) 2 × 10 −5 coulomb

When a certain metallic surface is illuminated with monochromatic light of wave length λ, the stopping potential for photo-electric current is 3 V0 . When the same surface is illuminated with light of wave

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length 2λ, the stopping potential is V0 . The threshold wavelength for this surface is b) 6 λ

a) 8 λ 21.

PN

Circuit - 2

d) 2 λ

Circuit - 3

PN

NP

PN

N P

N P

a) circuit 1 and circuit 2

b) circuit 2 and circuit 3

c) circuit 3 and circuit 1

d) no two circuits have equal current

N moles of an ideal diatomic gas are in a cylinder at temperature T. Suppose on supplying heat to the gas, its temperature remain constant but n moles get dissociated into atoms. Heat supplied to the gas is : a) zero

23.

4λ

Two identical P-N junction may be connected in series with a battery in three ways as shown in the adjoining figure. The potentiak drop across the p - n junction are equal in Circuit - 1 Circuit -1

22.

c)

PAGE 1

3

b) 2 nRT

c) 2 nRT

3

d) 2 ( N − n) RT

An electron is projected at an angle θ with a uniform magnetic field. If the pitch of the helical path is equal to the its radius, then the angle of projection is a) tan -1π

c) www.aieeepage.com b) tan -1 2π

cot-1 π

d) cot -12π

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24.

If three bulbs of 40 w, 60 W and 100 w are connected in series with a 200 V power supply, then 1) the potential difference will be maximum across the 40 W bulb 2) the current will be maximum through the 100 W bulb 3) the 40 W bulb has the maximum resistance a) 1, 3 b) 2, 3

25.

c) 3, 4

d) 1, 3

A particle having a mass of 0.5 g carries a charge of 2.5 ×10 −8 C. The particle is given an intial horizontal velocity of 6 × 10 4 ms −1. To keep the particle moving in a horizontal direction 1) the magnetic field should be perpendicular to the direction of the velocity 2) the magnetic field should be along the direction of the velocity 3) magnetic field should have a minimum value of 3.27 T 4) no magnetic field is required

26.

PAGE

Study the diagram. As soon as the switch S is closed, the current through the cell is I1. After long time, the current through the cell is found to be I 2 , then

L

L R

L

E0

L www.aieeepage.com

S

27.

E E a) I1 = 0 , I 2 = 0 R 2R

E b) I1 = 0, I 2 = 0

E c) I1 = 0 , I 2 = 0 R

d) none of these

A particle with a specific charge S is fired with a speed v towards a wall at a distance d perpen dicular to the wall . What minimum magnetic field must exist in this region for patticle not to hit the wall v

2v

v

b) Sd

a) Sd 28.

R

v

c) 2Sd

d) 4Sd (n − n )

2 1 The number of particle crossing a unit area in a unit time is given by n = − D (x − x ) where n1 and n2 2

1

are number of particles per unit volume for the value of x meant to x1 and x2 . Find dimensions of D, the diffusion constant a) [M0 LT2 ] 29.

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b) [ML2T 4 ]

c)

[M 0 LT -3 ]

d) [M 0 L2T -1]

An earth satellite of mass m revolves in a circular orbit at a height h from the surface of the earth. R isthe radius of the earth and g is acceleration due to gravity at the surface of the earth. The velocity of the satellite in the orbit is given by a) g R 2 /(R + h)

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b) g R

g R/(R − h)

d)

[gR /(R + h)] 2

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30.

A block of mass M slides along the sides of a flat bottomed bowl. The sides of the bowl are frictionless and the base has a coefficient of friction 0.2. If the block is released from the top of the side which is 1.5 m high, where will the block come to rest, given, the length of the base is 15 m : a) 1 m from P b) Mid point of flat part PQ c) 2m from P

31.

A rod of mass M and length l is suspended freely from its end and it can oscillate in the vertical plane about the point of suspension. It is pulled to one side and then released. It passes through the equilibrium position with angular speed ω . What is the kinetic energy while passing through the mena position ? a) M l 2ω2

32.

b) M l 2ω2 / 4

c)

M l 2ω 2 / 6

d) M l 2ω2 / 12

Two particle are executing S.H.M. of same amplitude and frequency along the same straight line path. They pass each other when going in opposite directions, each time their displacement is half of their amplitude. What is the phase difference between them ? a) 5 π/6

33.

d) at Q

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b) 2 π/3

c)

π/3

d) π/6

In Young’s double slit expt., the sources S and two slits. A and B are lying in a horizontal plane. The slit A is above slit B. the friges are obtained on a vertical screen K. The optical path from S to B is increased by putting a transparent material of higher refractive index. The path from S to A remains unchanged. As a result of this the fringe pattern moves some what a) upwards b) downwards

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c) towards left horizontally 34.

A car, starting from rest, accelerates at a constant rate x for sometime after which it decelrates at a constant rate y to come to rest. If the total time elapsed is t, the maximum velocity attained by the car is given by: a)

35.

xy t x+ y

b)

xy t x− y

c)

x2 y2 2

x +y

2

t

d)

x2 y 2 2

x − y2

t

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 oroder that he catches the student just before the ground is reached (g = 10m/s 2 ) : a) 67.23 m/s

36.

d) towards right horizontally

b) 91.66 m/s

c) 102.91 m/s

d) None

An ideal gas is condensed adiabatically to 8/27 times of its present volume at 27oC. The increase in temperature of the gas is : ( γ = 5/3) a) 475oC

b) 402oC

c) 275oC

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d) 175oC

37.

A car battery of e.m.f. 12 V and internal resistance 5 x 10-2 Ω , receives a current of 60 amp from external source, then terminal path of difference of battery is : a) 12 V b) 9 V c) 15 V d) 20 V

38.

A step-up transformer operates on a 230V line and supplies a load current of 2A. The ratio of primary and secondary windings is 1 : 25. The turns in current in the primary is : a) 15 A b) 50 A c) 75 A d) 125 A

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39.

40.

 

4

A polyatomic gas  γ = 3  is compressed to 1/8th of its volume adiabatically. If its initial pressure is P0, 

its new pressure will be : a) 8P 0

b) 16p0

c) 6P 0

d) 2P 0

Two parallel-plate capacitors with different capacitance but the same plate separation are connected in series to a battery. Both capacitors are filled with air. The quantity that is the same for both capacitors when they are fully charged is : a) potential difference b) stored energy c) energy density

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d) charge on the positive plate 41.

A man beats drum at a certain distance from the mountain. He slowly increases the rate of beating and finds that the echo is not heard distinctly, when the drum beating is at the rate of 40 per minute. He moves by 80 m towards the mountain and finds that the echo is again not heard distinctly when the rate of beating of the drum is 1 per second. What is the original distance of the man from the mountain ? a) 120 m b) 240 m c) 270 m d) 340 m

42.

A swimmer can swim in still water with speed v and the river flowing with velocity v/2. To cross the river in shortest distance, he should swim making angle θ with the upstream. What is the ratio of the time taken to swim across in the shortest time to that in swimming across over shortest distance ?

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a) cos θ 43.

b) sin θ

c)

tan θ

d) cot θ

A copper ring is held horizontally and a bar magnet is dropped through the ring along axial line. The acceleration of magnet while is is passing through the ring is a) Equal to that due to gravity b) Less than that due to gravity c) More than that due to gravity d) Depends on the size of the ring and magnet.

44.

Two racing cars of masses m1 and m 2 are moving in circles of radii r1 and r2 respectively. Thier speeds are such that each makes a complete circle in the same length of time t. The ratio of the angulr speed of the first car to second car is a) m1 : m 2

b) r1 : r2

c) 1 : 1

d) m1r1 : m 2 r2

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45.

A spring balance, A reads 2 kg with a block m suspended from it. A balance B reads 5 kg when a beaker filled with liquid is put on the pan of the balance. The two balances are not so arranged that the hanging mass is inside the liquid as shown in figure. In the situation

A

B a) the balance A will read more than 2kg b) the balance B will read more than 5 kg

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c) the balance A will read less than 2 kg and B will read more than 5 kg d) the balnce A and B will read less than 2 kg and B will read more than 5 kg 46.

Two particles are executing SHMs of same amplitude and frequency along the same straight line. They crosos each other moving in opposite directions when their displacement is half of the amplitude. What is the phase difference between them ?

c) π/4 www.aieeepage.com

a) π/6 47.

b) π/3

The linear density of a vibrating string is 10-4 kgm −1. A transverse wave is propagating on the string. Which is described by the equation y = 0.02 sin (x + 30 t)where x and y are in meters and time t is in seconds. The tension in the string is a) 0.09 newton b) 0.36 newton c) 0.9 newton

48.

d) 2π /3

d) 3.6 newton

Two weights W1 &W2 are attached to the end of string which passes over a frictionless pulley. If the pulley is placed in a rocket accelerating upwards at 9.8 m/s 2 , what will be the tension in the string ? Take g = 9.8 m/s2 .

49.

a) W1W2 / 2(W1 + W2 )

b) 2W1 W2 /(W1 + W2 )

c) W1 W2 /(W1 + W2 )

d) 4W1 W2 /(W1 + W2 )

In the arrangement, shown in figure pulleys are massless and frictionless and threads are inextensible. Block of mass m1 will remain at rest, if : 1

1

1

4

1

1

a) m = m + m 1 2 3 b) m = m + m 1 2 3 c) m1 = m2 + m3 d)

1 2 3 = + m3 m2 m1

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50.

An electron accelerated through a potential difference of V volts has a wavelength λ associated with it. Mass of proton is nearly 2000 times that of an electron. In order to havhe the same λ for proton, it must be accelerated through a potential difference of a) V volt

51.

b) 2000 V volts

c) V/2000 volt

2000 V volt.

Half life of radioactive element is 12.5 hour and its quantity is 256 gm. After how much time its quantity will remain 1 gm : a) 50 hrs b) 100 hrs c) 150 hrs

52.

d)

d) 200 hrs

The current in the circuit will be :

PAGE

www.aieeepage.com a) 53.

5 A 40

b)

5 A 50

c)

5 A 10

d)

5 A 20

A horizontal plank has a rectangular block placed on it. The plank starts oscillating vertically and simple harmonically with an amplitude of 40 cm. The block just loses contact with the plank when the latter is monetary at rest. Then a) the period of oscillation is 2 π/ 5 sec b) the block weighs double its weight when the plank is at one of the positions of momentary at rest. c) the block weight 1.5 times its weight on the plank half way down. d) the block weighs its true weight on the plank, when the latter moves fastest.

PAGE

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54.

Two indentical glass bulbs are interconnected by a thin glass tube. A gas is filled in these bulbs at N.T.P. If one bulb is placed in ice and another bulb is placed in hot bath, then the pressure of the gas becomes x times. The temperature of the hot bath will be ___

Ke a) 55.

2-x T 2+x

Hot Water b)

PAGE xT 2−x

c)

2-x T x

d)

2+x T 2-x

A block is resting on a piston which is moving vertically with S.H.M. of period 1.0 s. At what amplitude of motion will the block and piston sepaprate ? a) 0.2 m b) 0.25 m c) 0.3 m

d) 0.35m

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56.

The magnitude of the sum of the two vectors is equal to the difference of their magnitudes. What is the angle between the vectors ? a) 0° b) 45° c) 90° d) 180°

57.

If in a photoelectric cell, the wavelength of incident light is changed from 4000Å to 3000Å then change in stopping potential will be a) 0.66 V b) 1.03 V c) 0.33 V

d) 0.49 V

58.

A current carrying coil is bent sharply so as to convert it into a double loop both carrying a current in the same direction. If B is the initial magnetic field at the centre, then the final concentric magnetic field will be a) zero b) 2 B c) 4 B d) 8 B

59.

An oil drop with charge q is held stationary between two plates with an external potential difference of 400 V. If the size of the drop is doubled without any charge of charge, the potential difference required to keep the drop stationary will be a) 400 V b) 1600 V c) 3200 V d) 4000 V

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60.

A thermodynamic process is shown in figure such that PA = 3 ×104 Pa, PB = 8 ×104 Pa VA = 2 ×10 −3 m 3 , VD = 5 × 10 −3 m 3 . In process AB, 600 J of heat is added to the system and in process

BC, 200 J of heat is added to the system. The change in internal energy of the system in process AC is

y P

B

C

A

D

O

V

a) 560 J CHEMISTRY 61.

X

PAGE

b) 800 J

c) 600 J

If two compounds have the same empirical formula but different molecular formulae, they must have a) different percentage composition b) different molecular weights

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c) same viscosity 62.

d) 640 J

d) same vapour density

Two containers P and Q of equal volume ( 1 litre each) contain 6g of O 2 and SO2 300 K and 1 atmosphere. Then a) Number of molecules in P is less than that in Q

respectively at

b) Number of molecules in P and Q are same c) Number of molecules in Q is less than that in P d) Either (a) or (b) 63.

If the nitrogen atom had electronic configuration 1s7 it would have energy lower than that of the normal ground state configuration 1s2 2s2 2p3 because the electrons would be closer to the nucleus.

64.

Yet 1s7 is not observed. It violates a) Heisenberg’s uncertainty principle

b) Hund’s rule

c) Pauli exclusion principle

d) Bohr postulate of stationary orbits

At low concentration, the statement that equimolal solutions under a given set of experimental conditions have equal osmotic pressure is true for a) All solutions b) Solutins of non-electrolytes only

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c) Solutions of electrolytes only 65.

d) None of these

Compounds with high heat of formation are less stable because a) it is difficult to synthesize them

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b) energy rich state leads to instability

c) high temperature is required to syntheside them d) molecules of such compounds are distorbed for IIT - JEE & AIEEE at the National PAGE- A Premier Institution www.iitjeepage.com www.bitsatpage.com

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66.

67.

A buffer solution changes its PH a) very rapidly

b) very slowly

c) does not changes

d) None of the above

Which of the following is a poor conducor of electricity ? a) CH 3COONa

68.

b) C 2 H 5 OH

c) NaCl

d) KOH

Boron compounds behaves as Lewis acids because of their a) acidic nature b) Covalent nature c) Electron deficient character Ionization property d) Ionization property

69.

Which of the following is an efficient catalytic converter ? a) A reagent which oxidizes CO and unburnt hydrocarbons to CO 2 and H 2 O and reduces NO and NO 2 to N 2

and O 2

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b) A reagent which oxidizes CO and NO to CO 2 and N 2 respectively c) A reagent which oxidizes CO and unburnt PbO to CO 2 and PbO 2 , and reduces SO 2 to H 2S . d) A reagent which reduces unburnt hydrocarbons to CO, CO 2 and H 2 O and oxidizes N 2 to NO and NO 2 . 70.

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The ionization energies of chlorine and hydrogen are 1256 and 1311 kJ/mole respectively. Hydrogen forms H+ (aqueous) ion, but chlorine does not form Cl+ (aqueous) ion, because : a) the enthalpy of hydration of Cl+ is low b) the enthalpy of hydration of H+ is low c) the electron affinity of Cl is high d) the electronegativity of Cl is high.

71.

72. 73.

The geometry of H 2S and its dipole moment are a) angular and non-zero

b) angular and zero

c) linear and non zero

d) linear and zero

The nuclear spins of hydgrogn, deuterium and helium - 4 are, respectively, a) 1/2, 0,2 b) 1,1/2. 1/2 c) 1/2, 1. 0

d) 1/2,1,2

The oxidation number of S is Na 2 S 4 O 6 is a) 2.5 b) +2 and +3 (two s have +2 and other 2 have +3)

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c) +2 nd +3 (three S have +2 one S has +30

d) +5 and 0 (two S havhe +5 and the other two have S = 0) 74.

Identify the correct statement ? a) Gypsum contains a lower percentage of calcium than plaster of pairs b) Gyspum is obtained by heating plaster of pairs

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c) Plaster of pairs can be obtained by hydration of gypsum

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75.

A metal which is not affected by conc. H 2SO 4 , HNO 3 or alkalies forms a compound X. This compound X can be used to give a complex which finds its application for toning in photography. the metal is a) Au b) Ag c) Hg d) Cu

76.

If a reaction A + B → C is exothermic to the extent of 30 kJ/mol and the forward reaction has an activation energy of 70 kJ/mol, the activation energy for the reverse reaction is a) 30 kJ/mol b) 40 kJ/mol c) 70 kJ/mol d) 100 kJ/mol

77.

In solid K[Cu(CN) 2 ] a) two CN- groups are bond through C, and the third (bridging) CN- group through C and N b) three CN- groups are bond through C, and the bridging CN- group through C and N c) one CN- group is bond through C, and the other through C and N

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d) one CN- group is bond through C, and two other CN- group through C and N 78.

In

[Cr (C 2 O 4 ) 3 ]3− ,

the isomerism shown is

a) Ligand 79.

X is converted into

b) Optical 14 7 N

a) 9 80.

c) Geometrical

by emitting two β -particles. Then the number of neutrons in X will be : c) 5 www.aieeepage.com

b) 7

d) 3

If 0.2 gram of an organic compound containing carbon, hydrogen and oxygen on combustion, yeilded 0.147 gram carbon dioxide and 0.12 gram water. What will be the content of oxygen in the substance ? a) 73.29% b) 78.45% c) 83.23%

81.

d) Ionization

d) 89.50%

Intramolecular hydrogen bonding is present in a) Nickel dimethyl glyoximate b) anti-pyridine-2-carboxaldoxime c) Maleic acid monoanion d) All the three

82.

Cyclopentadiene is unusually acidic for a hydrocarbon. This is because a) the carbon atoms of cyclopentadiene are sp-hybridized b) cyclo pentadiene is aromatic c) the removal of a proton from it yields n aromatic anion

PAGE

d) cyclopentadiene yields a highly stable free radical

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14

83.

Which chloro derivative of benzene among the following would undergo hydrolysis most redily with aqueous sodium hydroxide to furnish the corresponding hydroxy derivative ? NO 2

a)

O2 N

b)

Cl

O2 N

Cl

NO 2 c) 84.

Me 2 N

Cl

The following reaction

PAGE

OH

OH

Anhyd

+ HCN + HCl  → ZnCl 2

a) Perkin reaction c) Kolbe’s reaction 85.

d) C6H5Cl

is know as

CHO

b) Gattermann aldehyde synthesis

d) Gattermann-Koch reaction www.aieeepage.com

The rate of the conversion C 6 H 5 CH 2 Cl KCN → C 6 H 5 CH 2 CN can be increased by carrying out the reactoin. a) in an aqueoussolution by vigrous stirring. b) in the presence of an acid catalyst c) bystrringinan aquous medium in the presence of a small amount oftetrabutyl ammonium chloride d) by none of these methods.

86.

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

b) CH3 -- CH = CH -- CH3

c) CH 2 = C − −CH = CH 2

d) CH 2 = C − − − −C = CH 2

| CH 3

| CH 3

| CH 3

| CH 3

87.

Which of the following solutions can be titrated with HCl as well as NaOH? a) Glycine b) pyruvic acid c) Triethylamine d) Aniline

88.

The IUPAC name of the compound having the molecular formula Cl3C − CH2CHO is

PAGE

a) 3, 3, 3- trichloropropanal

b) 1, 1, 1-trichloropropanal

c) 2, 2, 2- trichloropropanal

d) Chloral

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15

89.

In the final answer of the expression

(29.2 − 20.2) (1.79 × 10 5 ) the number of significant figures is 1.37

a) 1

b) 3

c) 2

d) 4

90.

400 ml gas at 500 torr and 666.6 ml gas at 600 torr are taken in a container of 3 litre, then the total pressure of the mixture is : a) 200 torr b) 400 torr c) 600 torr d) 50 torr

91.

The line with maximum wavelength in the balmer series of spectrum is : a) 566 nm b) 656 nm c) 546 nm

92.

Correct order of 1st ionisation potential among the following elements Be, B, C, N, O is : a) B < Be < C < N < O b) B < Be < C < O < N c) Be < B < C < N < O

93.

PAGE

d) Be < B < C < O < N

Molarity of liquid HCl if density of solution is 1.17 gm/cc : a) 36.5 b) 18.25 c) 32.05

94.

d) 565 nm

d) 42.10

In the following exothermic reaction step I and step II are in favour of : A 2 (g) + B2 (g) º 3C(g) º D(g) step I setp II a) high pressure, low temperature and low pressure, high temperature

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b) high pressure, high temperature and low pressure, low temperature c) low pressure, low temperature and high pressure, low temperature d) low pressure, high temperature and high pressure, high temperature 95.

The beans are cooked earlier in pressure cooker, because a) boiling point increases with increasing pressure b) boiling point decreases with increasing pressure c) extra pressure of pressure cooker softens the beans d) internal energy is not lost while cooking in pressure cooker

96.

An element (X) forms compounds of the formula XCl3 , X2O5 and CaX2 but does not form XCl5 . Which of the following is the element X ? a) B b) Al c) N d) P C≡N

PAGE H O+

97.

OCH 3

+ CH 3MgBr → Q 3 → P

OH

CH

CH3

The product ‘P’ in the above reaction is

CO - CH 3

CHO

b)

a)

COOH

c)

www.aieeepage.com OCH OCH 3

d) 3

OCH 3

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16

98.

The reaction SO2 + Cl2 → SO2Cl2 is exothermic and reversible. A mixture of SO2 (g), Cl2 (g)

and SO 2Cl2 (l) is at equilibrium in a closed container. Now a certain quantity of extra

is introduced into the container, the volume remaining the same. Which of the following is/are true ? a) The pressure inside the container, will not change SO2

b) The temperature will not change c) The temperature will increase d) The temperature will decrease 99.

The Rubin number which was proposed by Ostwald as an alternative to the Gold number in order to measure the protective efficientcy of a lyophillic colloid may be defined as the a) Mass in milligrams of a colloid per 100 c.c of solution which just prevents the colour change of standard sol of dye Congo - Rubin from red to violet when 0.16 g eq. KCl is added to it

PAGE

b) Mass in grams of a colloid per 100 c.c. of solution which just prevents the colour change of standard sol of dye Congo - Rubin from red to violet when 0.1 M KCl is added to it c) Mass in grams of a colloid per 100 c.c of solution which just prevents the colour change of standard sol of dye Congo - Rubin from red to violet when 0.2 M KCl is added to it. d) Mass in grams of colloid per 100 c.c of solution which just prevents the colour change of standard sol of solid Congo - Rubin from red to violet when 1 M KCl is added to it

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100. A mixture of chlorides of copper, cadminum, chromium, iron and aluminum was dissolved in water acidifed with HCl and hydrogen sulphide gas was passed for sufficient time. It was filtered, boiled and a few drops of nitric acid were added hile boiling. To this solution ammonium chloride and sodium hydroxide were added and filtered. The filterate shall give test for a) Sodium and iron b) Sodium and aluminium c) Aluminium and iron d) Sodium, iron, cadmium and Al 101. When pieces of human hair are heated strongly with soda - lime, smell of ammonia can be detected. Which one of the following conclusion can be drawn from this observation ? a) Ammonia is present in the human hair b) Ammonium sal is present in hair c) Hair contains amino acids d) None of these

PAGE

102. The most unlikely representation of resonance structures of p-nitrophenoxide ion is -

O

+

O

N

a)

-

O

+

O−

-

-

O

+

c)

www.aieeepage.com O

O

−

O

+

O−

N

N

N

b) O−

O

d) O

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17

103. Consider the following statements : A hydrocarbon of molecular formula C5H10 is a I.monosubstitutedalkene II.

disubstituted alkene

III. trisubstituted alkene Which of the following statement(s) is (are) correct ? a) I, II and III b) I and II c) II and III d) I and III 104. Which one of the following is a free-radical substitution reaction ? a)

Anh.AlCl

+ CH 3Ci  3 →

b)

CH 2Cl + AgNO2 →

d)

CH3 + Cl2 Boiling  →

PAGE CH 3

c) CH3CHO + HCN → CH3CH(OH)CN

CH 2NO 2

CH 2Cl

105. Which of the following is the most suitable method for removing the traces of water from ethanol ? a) Heating with Na metal

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b) Passing dry HCl gas through it c) Distilling it d) Reaction with Mg

106. If one strand of DNA has the sequence ATGCTTGA , the sequence in the complimentary strand would be a) TACGAACT b) TCCGAACT c) TACGTACT

d) TACGTAGE

107. Which of the following compounds exhibits linkage isomerism ? a) [Co(en)2 ]Cl3

b) [Co(NH3 )6 ][Cr(en)3 ] c) [Co(en)2 NO2Cl]Br

d) [Co(NH3 )5 Cl]Br2

108. Standard electrode potential data are useful for understanding the suitability of an oxidatnt in a redoxtitration. Some half-cell reactins and their standard potentials are given below : − MnO 4(aq) + 8H + (aq) + 5e− → Mn 2 + (aq) + 4H 2O(I) , E 0 = 1.51V

Cr2O72 − (aq) + 14H+ (aq) + 6e− → 2Cr3+ (aq) + 7H2O(I),E 0 = 1.38V

PAGE

Fe3+ (aq) + e − → Fe 2+ (aq), E 0 = 0.77V

Cl2 (g) + 2e− → 2Cl− (aq), E 0 = 1.40 V

Identify the only incorrect statement regarding the quantitative estimation of aqueous Fe(NO3 )2 a) MnO-4 can be used in aqueous HCl

b) Cr2O72− can be used in aqueous HCl

c) MnO−4 can be used in aqueous H2SO4

d) Cr2O72− can be used in aqueous H2SO4

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18

109. Consider the reaction equilibrium 2SO2 (g) + O2 (g) 2SO3 (g); ∆H0 = −198 kJ. On the basis of Le Chatelier’s principle, the condition favourable for the forward reaction is a) lower of temperature as well as pressure b) increasing temperature well as pressure c) lowering the temperature and increasing the pressure d) any value of temperature and pressure 110. An aqueous solution of 6.3 g oxoalic acid dithydrate is made up to 250 mL. The volume of 0.1 N NaOH required to completely neutralize 10 mL of this solution is : a) 40 mL b) 20 mL c) 10 mL d) 4 mL 111.

Which of the following ions has the maximum magnetic moment ? a) Mn2+

b) Fe2 +

c) Ti 2+

d) Cr 2+

PAGE

112. The correct order of increasing ionic character is a) BeCl2 < MgCl2 < CaCl2 < BaCl2

b) BeCl2 < MgCl2 < BaCl2 < CaCl2

c) BeCl2 < BaCl2 < MgCl2 < CaCl2

d) BaCl2 < CaCl2 < MgCl2 < BeCl2

113. If E e , Eα and E p represents the kinetic energies of an electron alpha particle and a proton repectively,

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each moving with same de Broglie wavelength then ; a) Ee = Eα = E p

b) Ee > Eα > E p

c) Eα > Ep > Ee

d) Ee > Ep > Eα

114. The number of atoms present in a unit cell of a face centered cubic crystal is : a) 4 b) 6 c) 3 d) 8 115. The heats of solution of anhydrous CuSO4 and hydrated CuSO4. 5H2O are - 66.5 and 11.7 kJ/mole respectively. Calculate the heat of hydration of CuSO4 to CuSO4.5H2O a) 54.8 kJ b) - 54.8 kJ c) - 78.2 kJ

d) none of these

116. Boron has two isotopes 11 5 B

10 5 B

and

11 5 B.

If the atomic weight of boron is 10.81, then the ratio of

10 5 B

in nature is :

a) 19/81

b) 20/53

c) 15/16

d) 10/11

PAGE

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19

and

117. Order of acidic strength of the following compound will be :

(I)

(II)

(III)

(IV)

a) III > IV > II > I

b) IV > III > II > I

c) I > III > II > IV

d) II > I > III > IV

PAGE

118. The dipole moment of compound AB is 10.92 D and that of compound CD is 12.45D. The bond length of AB is 2.72 Å and that of CD is 2.56Å, then for these compound true statement is : a) more ionic nature in AB b) equal in both c) more ionic nature in CD

d) not predicted

119. Solubility of a M2S salt is 3.5 x 10-6, then find out its solubility product ? a) 1.7 x 10 - 6 b) 1.7 x 10 - 16 c) 1.7 x 10 - 18

www.aieeepage.com d) 1.7 x 10

- 12

120. MgO and NaCl has similar structure, In MgO, magnesium is surrounded by how many oxygen atoms : a) 2 b) 4 c) 6 d) 1

MATHS 121. Let z and w be two complex number such that | z | = 1, | w | = 1 and | z - i w | = 2 then z equals : a) 1 or i

b) i or -i

c) 1 or -1

d) i or -1

122. If p and q are the roots of x + px + q = 0, then : a) p = 1 b) p = 1 or 0 c) p = -2 2

d) p = -2 or 0

123. If the numerical coefficient of the pth term in the expansion of (2x + 3)6 is 4860, then the value(s) of p is (are) : a) 2 b) 3 c) 4 d) 5

PAGE

124. The differential equation (x + y) dx + x dy = 0 is : a) homogeneous but not linear b) linear but not homogeneous

c) both homogeneous and linear

d) neither homogeneous nor linear

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20

125. In a triangle ABC, 2ac sin

1 (A - B + C) = 2

a) a2 + b2 - c2

b) c2 + a2 - b2

c) b2 - c2 - a2

d) c2 - a2 - b2

126. The mean of 100 observations is 40. If one of observation 50 is replaced by 60. The resulting mean will be : b) 50 b) 30 c) 60 d) 40.10 GG

G

G

G

G

G

G

G

127. If a, b and c are unit coplanar vectors, then the scalar triple product [2a − b, 2b − c, 2c − a ] = a) 0

b) 1

c)

128. Let φ( x) be the inverse of the function f(x) and f ' ( x) = 1

1

c)

1 + x5

3

d

then dx φ(x ) is

PAGE 1

b) 1 + ( f ( x ))5

a) 1 + (φ( x ))5

d)

− 3

1 + (φ( x))5

d) 1 + ( f ( x))5

129. The equation of sphere concentric with the sphere x 2 + y 2 + z 2 − 2 x − 2 y − 2 x − 5 = 0 and passing through the point (1, 1, 1) is b) www.aieeepage.com

a) x + y + z − 2 x − 2 y − 3 = 0 2

2

2

x2 + y2 + z 2 − x − y − z = 3

c) x 2 + y 2 + z 2 − 2 x − 2 y − 2 z + 3 = 0

d) none of the above

130. Let A = {x, y, z}, B = {u, v, w} and f: A → B be defined by f(x) = u, f(y) = v, f(z) = v. Then f is : a) surjective but not injective b) injective but not surjective c) bijective

d) none of them

131. If the system of equations x + 2y - 3z = 1, (k + 2) z = 3. (2k + 1) y + z = 2 is inconsistent, then the value of k is a) 2 b) 0 c) −

1 2

d) -2

132. An n-digit number is a positive number with exactly n digits. Nine hundred distinct n-digit numbers are to be formed using only the three digits 2, 5 and 7. The smallest value of n for which this is possible is: a) 6 b) 7 c) 8 d) 9

a) R \ {-1, -2} c) R \ {-1, -2, -3}

log2 (x + 3)

PAGE

133. The domain of definition of F(x) =

x 2 + 3x + 2

is:

b) (-2, ∞ ) d) (-3, ∞ ) - {-1, -2}

134. The area bounded by the curves y = | x | - 1 and y = - | x | + 1 is : a) 1

b) 2

c)

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d) 4

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21

135. The equation of the plane passing through the point (-2, -2, 2) and containing the line joining the points (1, 1, 1) and (1, -1, 2) is : a) x + 2y - 3z + 4 = 0 b) 3x - 4x + 1 = 0 c) 5x + 2y - 3z - 17 = 0

d) x - 3y-6z+ 8=0

136. The graph of the equation y2 + z2 = 0 in three dimensional space is : a) x - axis b) y - axis c) z - axis

d) yz - plane

137. A man wishes to cross a river to an exactly opposite point on the other bank, if he can swim with twice the velocity of the current, then the inclination to the current of the direction in which he should swim is : a) 90o b) 120o c) 150o 138.

∫

d) none of them

PAGE

1 dx = log a. log(log x) + k x log a x

a) all x ∈ R

b)

is true for

c)

x>e

d) no real x

x >1

139. The values of a for which both the roots of the equation x 2 − (2a − 1) x + a = 0 are positive is 2− 3  a)  2 , ∞  



 2− 3 2+ 3  b)  2 , 2 

2+ 3   ,∞  2   

www.aieeepage.com 

c)



d) none of these

140. ABC is triangular park with AB = AC = 100 m. A Clock tower is situated at the mid point of BC. The angle of elevation of the top of the tower at A and B are α and β respectively. The height of the tower is a) 100 tan 2α + tan 2β

b)

c) 100 cot 2 α + cot 2β

d)

141. If a r > 0, r ∈ N and a1 , a2 , ......, a2 n are in AP then +

100 2

tan α + tan 2β 100 2

cot α + cot 2β

a1 + a 2n a1 + a2

+

a 2 + a2n −1 a 2 + a3

+

a3 + a 2 n − 2 a3 + a 4

+ .......

an + a n+1

a n + an +1 is equal to

c)

n −1

13

a) i

a1 + an +1

d) none of these

a1 + a n + 1

142. The value of the sum

n(a1 + a2n )

PAGE b)

a) n − 1

∑ www.aieeepage.com − 1 equals : n =1

(i n + i n +1 ) , where i =

b) i - 1

c) -i

d) 0

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22

143. Equation of the plane perpendicular to the plane x - 2y + 5z + 1 = 0 which passes through the points (2, -3, +1) and (-1, 1, -7) is given by : a) 4x - 4y + z + 7 = 0 b) 4x + 7y + 2z + 11 = 0 c) 2x + y - z = 0 d) none of them 144. The distance between the straight lines 6x +8y = 15 and 3x + 4y = 9 is : a) 1 b) 2 c) 3 145.

d) none

  lim  x + x − x  is equal to 

x →∞

a) 1

b) 0

c) 1 / 2

d) none of these

PAGE

146. If in a distribution each x is replaced by corresponding value of f ( x ) , then the probability of getting xi

Whose original probability is pi is a)

b) f( pi )

pi

d) none of these www.aieeepage.com

1

c) f  p   i

147. In a binomial distributation , the mean is 9 and S.D is 6 . The values of n and p are respectively : 1

1

b) 81 , 9

a) 27 , 3 1

1

c) 36 , 4 148. If

d) 18 , 2

x18 = y 21 = z 28 ( x ≠ y ≠ z ),

a) A.P

then 3, 3 logy x, 3logz y, 7 logx z are in

b) G.P

c) H.P.

d) none of these

149. Lines are drawn through ( - 4 , 5 ) such that the distance from ( 3 , -2 ) is a . The minium value of a is a) 2 7

b) 7 2

c)

3 6

d) 3 2

150. The solution of 1 − x 2 dy + 1 − y 2 dx = 0 is a) c = sin −1x + cos −1y c) c = tan −1x + tan −1y

b) c = sin −1x + sin −1y

PAGE

d) none of these

151. The left and derivative of f(x) = [x] sin ( πx ) at x = k, k an integer and [x] means the greatest integer ≤ x is : a) (-1)k (k - 1) π b) (-1)k - 1 (k - 1) π c) (-1)k k π d) (-1)k- 1 k π x 2   contains x , then r is equal to : www.aieeepage.com 3 x  10

152. If the r term in the expansion of  − th

a) 4

4

2

b) 3

c) 4

d) none

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23

153. A bag contains 2 red and 3 white balls. If two balls are drawn one by one without replacement, then the probability of the second ball being white is : a)

2 5

b)

3 5

c)

1 2

2 25

d)

154. A particle moves from rest at a distance c from a fixed O with an acceleration

µ x2

away from O at a

distance x. Then the velocity of the particle at distance 2c from is : µ c

a)

b)

µ

c)

µc

d) none

c

155. Equation of the curve through the point (1, 0) which satisfy the differential equation (1 + y2) dx -xy dy = 0 is : a) x2 + y2 = 1 b) x2 - y2 = 1

PAGE

c) 2x2 + y2 = 2

d) none

156. Forces of 1 and 2 units act along the lines x = 0, y = 0. The equation of the line of action of the resultant is : a) y - 2x = 0 b) 2y - x = 0 c) y + x = 0 →

→

d) y - x = 0 www.aieeepage.com → →

→

→

→

→

157. Let a = 2ˆi + ˆj − 2kˆ and b = ˆi + ˆj . If c is a vector such that a ⋅ c = | c |, | c − a | = 2 2 and the angle →

→

→

→

→

→

between ( a × b ) and c is 30o, then | {( a × b ) × c } | a) 2/3

b) 3/2

c) 2 a2

158. If a, b, c are sides of a triangle and

b2

d) 3 c2

(a + 1) 2

(b + 1) 2

(c + 1) 2

2

2

(c − 1) 2

(a − 1)

(b − 1)

= 0, then

a) ∆ABC cannot be equilateral triangle b) ∆ABC is a right angled isosceles triangle c) ∆ABC is an isosceles triangle d) None of these 1 159. The smallest interval in which the value of ∫ 0



1

a) 0, 17    160. If 0 ≤ α, β ≤ 90° and

x

x + 16

b) [0, 1] tan( α + β) = 3

1

a) − 2

b)

dx

lies is

PAGE 3

and

c)

tan( α − β) = 2

 1  0, 27   

d) None of these

then value of sin 2α is

c) www.aieeepage.com 1

1 2

2

d) None of these

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24

161. If α, β, γ are the rootos of the equation x 3 + mx 2 + 3x + m = 0. then the general value of tan −1 α + tan -1β + tan -1γ

is

π

a) (2n + 1) 2 c)

b)

nπ 2

nπ

d) dependent upon the value of p.

162. Let 0 < α < π/2 be a fixed angle. If P(cosθ, sinθ ) and Q{cos (α - θ), sin (α - θ)}, then Q is obtained from P by a) clockwise rotation around origin through an angle

α

b) anticlockwise rotation around origin through an angle c) reflection in the line through origin with slope tan

α

α

PAGE α

d) reflection in the line through origin with slope tan 2

163. The direction ratios of the diagonal of the cube joining the origin to the opposite corner are (when the 3 concurrent edges of the cube are coordinate axes) 2

a)

3

2

,

3

2

,

b) 1, 1, 1

3

c) 2, -2, 1

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d) 1, 2, 3

164. A point moves in a straight line so that its distance s from a fixed point at any time t is equal to kt (n > 1), where k is a constant. If v be the velocity and f acceleration at any time t, then a)

nv 2 − ( n − 1) fs

b)

c)

v 2 − nfs

d)

nv 2 − fs ( n − 1)v 2 − nfs

G G G G G G 165. The unit vector perpendicular to both the vectors aG = i + j + k and b = 2 i − j + 3k and making an acute

G

angle with the vector k is G G

1

G

a) - 26 (4 i − j − 3k) c)

1 26

1

b)

G G G (4 i − j + 3k)

26

G G G (4 i − j − 3k)

d) none of these

166. The sum of squares of deviations for 10 items from the mean (= 50) is 250. The coefficient of variation is a)

25

b)

50

c)

10

d)

none of these

PAGE

167. If twice the square of the diameter of a circle is equal to half the sum of the sides of the squares of the sides of the inscribed triangle ABC, then sin2 A + sin2 B + sin2 C is equal to : a) 1

b) 2 n

168. If an =

∑ r =0

1 n

Cr

n

then

a) (n - 1)an

∑ r =0

r n

Cr

c) 4

d) 8

equals :

www.aieeepage.com 1

b) na n

c)

2

nan

d) none

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25

169. If the roots of the equation x2 - 2ax + a2 + a - 3 = 0 are real less than 3, then : a) a < 2 b) 2 ≤ a ≤ 3 c) 3 < a ≤ 4 d) a > 2 170. If

n∈ N,

then (1 + i )2 n + (1 − i) 2n is a

a) purely imaginary number b) purely real number c) non-real complex number d) complex number in which real and imaginary parts are equal 171. The value of a)

∫

2π π

[2 sin x] dx , where [.] represents the greatest integer function, is :

−5π 3

b) − π

c)

5π 3

PAGE

d) -2x

172. The straight lines whose direction cosines are given by al + bm + cn = 0, fmn + gnl + hlm = 0 are perpendicular if : a)

c)

f g h + + =0 a b c

(af ) = ( bg) = (ch)

b)

f  + a

b c   +   = 0 g h  

www.aieeepage.com b a d)

c   =   =   f g   h  

173. If the line of action of the resultant of two forces P and Q divides the angle between them in the ratio 1 : 2, then the magnitude of the resultant is : a)

(P 2 + Q 2 ) P

b)

(P 2 + Q 2 ) Q

c)

(P 2 − Q 2 ) P

d)

(P 2 − Q 2 ) Q

174. The equation of the common tangent touching the circle (x - 3)2 + y2 = 9 and the parabola y2 = 4x above the x - axis is : a)

3 y = 3x +1

b)

3 y = -(x + 3)

c)

3y=x+3

d)

3 y = -(3x + 1)

PAGE

175. The volume of the tetrahedron included between the plane 2x - 3y + 4z - 12 = 0 and the three coordinate planes is a) 3 (29) c) 12

b) 6 (29)

d) none of these

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176. The transverse axis of a hyperbola is of length 2a and a vertex divides the segment of the axis between the centre and the corresponding focus in the ratio 2 : 1. If the transverse axis of the hyperbola lies along x-axis and the centre is at the origin then the equation of the hyperbola is a) 5x 2 − 4y 2 = 5a 2 b) 5x 2 − 4y 2 = 4a 2 c) 4x 2 − 5y 2 = 5a 2 d) 4x 2 − 5y 2 = 4a 2 177. Two weights W and W’ are connected by a light string passing over a light pulley. If the pulley moves with an upward acceleration equal to that of the gravity, the tension in the string is : a)

W W' W + W'

b)

2 W W' W + W'

3 W W' W + W'

PAGE c)

d)

4 W W' W + W'

178. Inorder that bigger sphere (with centre C1, radius R) may fully contain a smaller sphere (centre C2 , radius r), the correct relationship is a) C1C2 < r + R c) C1C2 < 2( R − r )

b) C1C2 < R − r

1 d) C1C2 < (R + r) www.aieeepage.com 2

179. m distinct animals of a circus have to be placed in m cages, one in each cage. If n(< m) are too small to accommodate p (n < p < m) animals, then the number of ways of putting the animals into cages is a) m−nCp

b) (m−nPp ) (m−n Pm− p )

c) (m−nC p ) (m− pCm− p )

d) None of these

180. If points A( x1, y1), B( x2 , y2 ) and C ( x3 , y3 ) are such that x1, x2 , x3 and y1, y2 , y3 are in G.P with same common ratio, then a) A, B are C are concylic points b) A, B and C are colliner points c) A, B, and C are vertical of an equilateral triangle d) none of these

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PAGE TM

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