Ai Aieee Modeltest 07

MODEL TEST TEST CODE - FNE

AIEEE 180 QUESTIONS TIME ALLOWED : 180 MINUTES

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STUDENT’S NAME :

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 4 12 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

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TM

Questions - 180

PHYSICS

Time - 180 Min

1.

Which of the following radiations form part of the electromagnetic spectrum? a) alpha rays b) beta rays c) gamma rays d) cathode rays

2.

Protons are found in the nucleus of the atom. The nuclear protons with the greatest mass are located in the a) hydrogen atom b) carbon atom c) iron atom d) radon atom

3.

If young’s double slit experiment is performed in still and clear water, instead of air, then pattern a) will shrink b) will disappear c) will be enlarged d) none of these

4.

An object is placed at a distance of 20 cm from the pole of a concave mirror whose focal length is 20 cm . Then image is formed at a) 20 cm from the pole of the mirror b) 40 cm from ther pole of the mirror

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c) at the pole of the mirror 5.

Photon A has twice the wavelength of photon B , then energy of photon A is a) half that of B b) twice that of B c) thrice that of B

6.

d) at infinity

d) four times that of B

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Dominant mechanism for motion of change carriers in forward and reverse biased silicon P -N junctions are a) diffusion in forward bias , drift in reverse bias b) Diffusion in forward bias as well as reverse bias c) drift in forward bias and diffusion in reverse bias d) drift in forward bias as well as reverse bias

7.

Mixed groups of cells will send the maximum current in the external circuit when total interanl resistance is a) less that external resistance b) more than external resistance c) equal to external resistance

8.

d) zero

In a full wave rectifier rms value of input ac signal is 10 volt .Transformer used is a step up ntransformer having turn ratio 1 : 2 DC voltage in the rectified output will be a) 18 V b) 22 V c) 15 V d) 21 V

9.

Sw,

PAGE

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The diagram above shows a battery and a variable resistor set at its midpoint resistance in series with a parallel light circuit. Switch 1 (SW1) is closed and the light bulbs illuminate. When the variable resistor is moved slightly to the left (L) the bulbs dim a little. When the variable resistor is moved slightly to the right (R) the bulbs brighten slightly for IIT - JEE & AIEEE at the National PAGE- A Premier Institution www.iitjeepage.com www.bitsatpage.com

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2

What happens in the circuit when the variable resistor is set all the way to the right ? a)

The lights brighten considerably

b) The total circuit resistance increases c) The total applied voltage increases d) The total power used in the circuit increases. 10.

Dimensionally which of the pairs is correct. Identify the pair a) torque and force b) angular momentum and work c) energy and Young’s modulus

11.

Let A, B, C. D be points on a vertical line such that AB = BC = CD. If a body is released from position A, the times of descent through AB, BC and CD are in the ratio a) 1 : 3 − 2 : 3 + 2

b) 1 : 2 − 1 : 3 − 2

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c) 1 : 2 − 1 : 3 12.

d) 1 : 2 : 3 − 1

A particle is projected at an angle of elevation α and after t second it appears to have an angle of elevation β as seen from point of projection. The initial velocity will be a)

13.

d) light year and wavelength

gt 2sin(α - β)

gt cos β

b) 2sin(α - β)

c)

sin (α - β) 2gt

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d)

2sin (α - β) gt cosβ

A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration a c is varying with time t as a c = k 2 rt 2 , where k is a constnat. The power delivered to the particle by the

forces acting on it is a) 2πmk 2r 2t 14.

c)

mk 4 r 2t 5 3

d) zero

A thin circular ring of mass M and radius R rotating about its axis with a constant angular speed ω . Two blocks each of m mass m are attached gently to opposite ends of a diameter of the ring. The angular speed of the ring will be a)

15.

b) mk 2r 2t

2Mω M + 2m

b)

(M - 2m)ω M + 2m

c)

Mω M + 2m

d)

(M + 2m)ω M

A particle starts with S.H.M. from the mean position as shown in figure below. Its amplitude is A and its time period is T. At one time, its speed is half that of the maximum speed. What is this displacement ?

PAGE u=

Umax 2

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2A 3

b)

3A 2

c)

2A 3

d)

3A 2

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16.

Equal charges q each are placed at the vertices A and B of an equilateral triangle ABC of side a. The magnitude of electric intensity at the point C is q

a) 17.

b)

4π ∈0 a 2

2q 4π ∈0 a

c)

2

2q

3q 4π ∈0 a

d) 4π ∈ a 2 0

2

Two walls of thickness d1 and d 2 and thermal conductivities K1 and K 2 are in the contact in the steady state, if the temperatures at the outer surfaces are T1 and T2 the temperature at the common wall is K1 T1d 2 + K 2 T2d1 K1d 2 + K 2d1

a) 18.

b)

 K1 d1 + K 2 d 2      T1 + T2  

d)

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b) 30 µF

K1 T1d1 + K 2T2 d 2 K1d1 + K 2d 2

c)

d) 10 µF

20 µF

Upon a six fold increase in the external resistance of a circuit, the voltage across the terminals of the battery has increased from 5 V to 10 V.The e.m.f of battery a) 15 V

20.

c)

A 10 µF capacitor is charged to a potential difference of 50 V and is connected to another unchrged capacitor in parallel. Now the common potential difference becomes 20 volt. The capacitance of second capacitor is a) 15 µF

19.

K1 T1 + K 2 T2 d1 + d 2

b) 18 V

c)

12.5 V

d) 11 V

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Two coils are wound on the same iron rod so that the flux generated by one also passes through the other. The primary has 100 loops and secondary has 200 loops. When a current of 2A flows through the primary the flux in it is 25× 10-4 wb. Determine value of M between the coils a) 25 mH

b) 24 mH

c)

26 mH

d) 23 mH

21.

The time period of oscillation of a magnet in a vibration magnetometer is 1.5 sec. The time period of oscillation of another magnet similar in size, shape and mass but having 1/4 magnetic moment than that of the 1 st magnet oscillating at the same place will be a) 0.75 sec b) 1.5 sec c) 3.0 sec d) 6.0 sec

22.

The figure shows the displacement-time graph of a body moving in a stright line

Y s O 1

X

3 4 t

2

Which of the graph shown in the fig., represents the velocity-time graph of the motion of the body ?

PAGE Y

Y

v

a)

v

O

1

2

3

b)

X

4

t

O

2

1

3

t

4

X

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Y

Y

v

v

c)

O

1

2

3

t

4

d)

X

O

1

t

2

3

4

X

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23.

Fig. represents two bulbs B1 and B2 , resistor R and an inductor L. When the switch is turned off -

R L

24.

S

B1 B2

a)

both B1 and B2 die out promptly

b)

both B1 and B2 die out with some delay

c)

B1

d)

B2 dies out promptly but B1 with some delay

dies out promptly but B2 with some delay

A cyclic process is shown in Fig. Work done during isobaric expansion is

PAGE 2 × 10 2

P

2 (N/m 2 ) 10

A

B

D

C

www.aieeepage.com 2 1 3 V (m 3 )

a) 1600 J 25.

b) 100 J

c)

400 J

d) 600 J

Two plates of same area ae placed in contact. Their thickness as well as thermal conductivities are in the ratio 2:3. The outer surface of one plate is maintained at 10°C and that of other at 0°C and that of other at 0°C. What is the temp. of the common surface ? a) 0°C

b) 2.5°C

c)

5°C

d)

6.5°C

26.

A wire 1 m along has resistance of 1Ω . If it is uniformly stretched, so that its length increases by 25% then its resistance will increase by a) 25% b) 50% c) 56.25% d) 77.33%

27.

Two masses each equal to m are lying on X-axis at (-a, 0) and (+a, 0) respectively as shown in fig. They are connected by a light string. A force F is applied at the origin and along the Y-axis. As result, the masses move towards each other. What is the accelreation of each mass ? Assume the instaneous position of the masses as (-x, 0) and (x, 0) respectively.

PAGE

F

-x

(a, 0)

(-a, 0)

m

O

x

x F . m (a 2 − x 2 )

a)

m www.aieeepage.com 2F

c) m

.

x 2

2

(a − x )

F

b) 2m

d)

.

x 2

(a − x 2 )

2F 2 F ( a 2 − x 2 ) . x m

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28.

A tangent galvanmeter has coil of 50 turns and a mean diameter of 22 cm. Calculate the current through it when the needle is deflected through 60° at a place where horizontal components of earth, H = 30 A/m a) 300 mA b) 130 mA c) 228 mA d) 158 mA

29.

A machinist starts with three identical square plates but cuts one corner from one them, two corners from the second, and three corners from the third. Rank the three plates according to the x coordinates of their centers of mass, from smallest to largest.

1 a) 1, 2, 3 30.

3

2

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b) 1 and 2 tie, then 3

c)

1, then 2 and 3 tie

d) 1 and 3 tie, then 2

A He 4 nucleus (atomic weight 4) moving with speed v breaks up into a neutron (atomic weight 1) and a He3 nucleus. The neutron moves off at right angles to the original He 4 as shown. If the neutron speed is 3v, the final speed of the He3 nucleus is :

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3v

neutron

v He 4 a) zero 31.

He 3

b) v

c)

4v/3

d) 5v/3

Two mirrors each 1.6 m long are facing each other. The distance between the mirrors is 20 cm. A light ray is incident on one end of the mirror at an angle of incidence of 30°. How many times is the ray reflected before it reaches the other end.

10 30°

PAGE

d

30°30°

a) there are 15 reflections counting the first one

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b) there are 13 reflections counting the first one c) there are 12 reflection counting the first one d) none of the above

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32.

In a thermodynamic process, a system absorbs 1 kilocallorie of heat and at the same time does 250 joule of work. What is the change in the internal energy of the system ? a) 250 J b) 3950 J c) 4200 J d) 4450 J

33.

Two blocks connected by a spring rest on smooth horizontal plane as shown in figure / a constant force F starts acting on the block m 2

m2

m1 a) length of spring increases continuously if m1 > m 2

PAGE

b) blocks start performing S.H.M. about center of mass of the system with increasing amplitude c) blocks start performing S.H.M about center of mass of the system which moves rectilinearly with constant acceleration. d) acceleration of m 2 is maximum at initial moment of time only 34.

When a stretched string of length L is vibrating in a particular mode, the distance between two nodes on the string is l. The sound produced in this mode of vibration constitutes the nth overtone of the fundamental frequency of the string.

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a) L = (n + 1)l 35.

b) L = (n − 1)l

c)

L = nl

(

)

d) L = n + 1 2 l

A capacitor of capacitance C is connected to two voltmeters A and B. A is ideal, having infinite resistancewhile B has resistance R. The capacitor is charged and then the switch S is closed. The readings of A and B will be equal A

a) at all times B

b) after time RC c) after time RC ln 2 d) only after a very long time

36.

A conducting rod of length l can slide without friction on two parallel conducting rails as shown in the fig. A resistance R is connected between the two rails, and the entire arrangement is kept perpendicular to a uniform and constant magnetic field B

B R

PAGE a)

no work is done by the external force

b)

positive work is done by the external force.

c) no work is done by Ampere’s force. www.aieeepage.com d) positive work is done by the Ampere’s force

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37.

Two similar pith balls are very near to one another, and each is charged with 2 excess electrons. The angle q between q1 and q2 is 5.5°. One electron is removed from q1 and placed on q2 , so that q1 has 1 electron and q 2 has 3 electrons. The angle between the pith balls changes to 4°. Which of the following statements is correct ? I. The amount of electrostatic charged has decreased. II. The electrostatic force between the pith balls has decreased. III. Both the electrostatic charge and force have decreased. a) I only

38.

b) II only

c)

I and III only

d) II and III only

If the potential barrier of the diode connected in the circuit shown below is 0.5 V. Then value of the current in the circuit is

+ 5v

PAGE D

150Ω

www.aieeepage.com A concave lens of glass, refractive index 1.5 has both surfaces of same radius of curvature R. On a) 20mA

39.

b) 30mA

c)

40mA

d) 50mA

immersion in a medium of refreactive index 1.75, it will behave as a a) convergent lens of focal length 3.5 R b) convergent lens of focal length 3.0 R c) devergent lens of focal length 3.5 R 40.

Binding energies of 1 H 2 , 2 He 4 , 26 Fe56 and 92 U 235 nuclei are 2.22 Mev, 28.3 MeV, 492 MeV and 1786 MeV respectively. Which of the following is more stable ? a) 1 H 2

41.

b) 2 He 4

c)

26 Fe

56

d)

92 U

235

Phase difference between two waves having same frequency (V) and same amplitude (A) is 2 π/3. If these waves superimpose each other, then resultant amplitude will be a) 2A

42.

d) devergent lens of focal length 3.0 R

b) 0

c)

A

d) A 2

An engine is moving on a circular track with a constant speed. It is blowing a whistle of frequency 500 Hz. The frequecy received by an observer standing stationary at the centre of the track is a) 500 Hz b) more than 500 Hz c) less than 500 Hz

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d) more or less than 500 Hz depending on the actual speed of the engine. 43.

Two identical vessels are filled with equal amounts of ice, The vessels are made from different materials. If the ice melts in the two vessels in times t1 and t 2 respectively, then their thermal conductivities are in the ratio a)

t1 t2

b)

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t 22 : t12

t1

d)

t12 : t 22

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44.

A ray of light travelling in a transparent medium falls on a surface separating the medium from air at an angle of incidnet 45°. The ray undergoes total internal reflection. If µ is the refractive index of the medium with respect to air, select the possible value (s) of µ from the following : 1) 1.3 2) 1.4 3) 1.5 4) 1.6 a) 1, 2

45.

b) 2, 3

c)

3, 4

d) 1, 3

The headlight of a train of length 200 m is switched on when it starts from rest with an acceleration of 0.5 m/s 2 . After 20 s, its tail-light is switched on. An observer in a frame moving with a constant

velocity parallel to the railway track observes that the two events occur at the same place. The velocity of this frame is a) 5 m/s in a direction opposite to the train’s motion b) 10 m/s in a direction opposite to the train’s motion c) 5 m/s in the same direction as the train’s motion

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d) 10 m/s in the same direction as the train’s motion 46.

A force acts on a particle of mass 3 g in such a way that the position of the particle as a function of time is given by x = 3t-4t 2 + t 3 where x is in metre and t is in seconds. The work done during the first 4 s is a) 570 mJ

47.

b) 450 mJ

c)

about 107 (Ω m ) −1

d) independent of A

Two rods with the same dimensions have thermal conductivities in the ratio 1 : 2. They are arrangned between heat reservoirs with the same temperature difference, in two different configurations, A and B. The rates of heat flow in A and B are I A and I B respectively. The ratio I A / I B is equal to

B

k

T2

T1

a) 1 : 2

2k

T1

T2

A

2k

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b) 1 : 3

c)

2:5

d) 2 : 9

A thin uniform rod of length l is pivoted at its upper end. It is free to swing in a vertical plane. Its time period for oscillations of small amplitude is a) 2π l/g

51.

d) infinity

A metal wire of length l and area of cross-section A is fixed between rigid supports at negligible tension. If this is cooled, the tension in the wire will be a) proportional to l b) inversely proportional to l

k

50.

d) 530 mJ

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b) about 103 (Ω m ) −1

c) independent of l 49.

490 mJ

At absolute zero of temperature, the electrical conductivity of a pure semiconductors is a) zero

48.

c)

b) 2π 2l/3g

c)

2π 3l/ 2g

d) 2π l/ 2 g

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Half-life period of a radiactive element X is same as the mean-life time of another radioactive element Y. If intially both have same number of atoms, then a) X decay faster than X b) Y decay faster than X c) X and Y decays at same rate

d) Initial decay rate of X and Y are same

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52.

When unit mass of water boils to become steam at 100°C, it absorbs Q amount of heat. The densities of water and steam at 100°C are ρ1 and ρ 2 respectively and the atmospheric pressure is p0 . The increase in internal energy of the water is  1

b) Q + p0 

a) Q

 ρ1

 1

c) Q + p0 

 ρ2

53.

−

1  ρ1 

−

1  ρ2 

 1 1  + ρ   1 ρ2 

d) Q − p0 

A sphere S rolls without slipping, moving with a constant speed on plank P. The friction between the upper surface of P and the sphere is sufficient to prevent slipping, while the lower surface of P is smooth and rests on the ground. Initially, P is fixed to the ground by a pin N. If N is suddenly removed.,

PAGE ω

N

S

v= ωt

r

P

www.aieeepage.com a) S will begin to slip on P b) P will begin to move backwards

c) The speed of S will decrease and its angular velocity will increase d) There will be no change in the motion of S and P will still be at rest 54.

Two blocks are connected over a massless pulley as shown in fig. the mass of block A is 10 kg and the coefficient of kinetic friction is 0.2. Block A slides down the incline at constnat speed. The mass of block B in kg is :

A

PAGE

30° a) 3.5 55.

B

b) 3.3

c)

3.0

d) 2.5

A uniform chain of mass M and length L lies on a frictionless table with length I0 hanging over the edge. The chain beings to slide down. Then the speed with which the end slides away from the edge is given by :

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a) v =

g (L + I0 ) L

b)

g (L - I0 ) L

c)

v=

g 2 2 (L - I0 ) L

d) v =

g 2 2 (L + I0 ) L

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56.

57.

A bullet of mass m moving horizontally with velocity v hits a block of wood of mass M, resting on a smooth horizontal plane. The fraction of energy of the bullet dissipated in the collision it self is (assume collision to be inelastic) a)

mv m+M

b) M + m

m

c)

Mm m+M

d) m + M

M

A body of mass 5 kg explodes at rest into three fragments with masses in the ratio 1 : 1 : 3. The fragments with equal masses fly in mutually perpendicular directions with speeds of 21 m/sec. The velocity of the heaviest fragment will be a) 11.5 m/sec b) 14.0 m/sec c) 7.0 m/sec

58.

d) 9.87 m/sec

PAGE

A semicircular lamina of mass m has radius r and centre C. Its centre of mass is at distance x from C. Its moment of inertia about an axis through its centre of mass and perpendicular to its plane is

C www.aieeepage.com r a) 59.

1 2 mr 2

b)

1 2 mr 4

c)

d)

1 2 mr − mx 2 2

In the figure, the block a of mass m is placed on the block B of mass 2m. B rests on the floor. The coefficient of friction between A and B as well as that betwen the floor and B is µ. Both blocks are given the same initial velocity to the right. The acceleration of A with respect to B is

µ

60.

1 2 mr + mx 2 2

µ

A

m

B

2m

a) zero

b) µg to the left

c) µg to the right

d)

1 µg to the right 2

PAGE

You are given several identiacl resistances each of value R = 10Ω and each capable of carrying a maximum current of 1A. It is required to make a suitable combination of these resistances to produce a resistance of 5Ω which can carry a current of 4A. The minimum number of resistances required is a) 4

b) 10

c)

8

d) 20

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CHEMISTRY 61. 62.

Mole ratio of H2 & O2 gas is 8 : 1. What will be the ratio of their weight : a) 1 : 1 b) 2 : 1 c) 4 : 1

The X-rays having wavelength 1.00 D are falling on metal from second order Bragg’s diffraction pattern on the angle of 60o. The distance between the planes will be : b) 1.00 D

a) 0.575 D 63.

d) 1 :2

c)

2.00 D

d) 1.15 D

For which set of four quantum number, the energy of an electron will be maximum : n

l

m

s

a)

3

2

1

1/2

b)

4

2

-1

1/2

c)

4

1

0

-1/2

d)

5

0

-1/2

0

PAGE

64.

The vapour pressure decreases by 10 mm of Hg when solute’s mole fraction in a solution is 0.2. If the vapour pressure decrease is 20 mm of Hg, then the mole fraction of solute will be : a) 0.2 b) 0.8 c) 0.6 d) 0.4

65.

The latent heat of vaporisation of a liquid at 500 K and 1 atm is 10.0K cal/mole. The change in internal energy ( ∆E ) of 3 mole liquid at the same temperature and pressure will be a) 13.0 K cal/mole b) -13.0 K cal/mole

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c) 7.0 K cal/mole 66.

d) -7.0 K cal/mole

For any reversible reaction the increase in concentration of reactant occur. Then effect on equilibrium constant will : a) depends on amount of reactant b) decrease c) unchange

67.

d) increase

Determine the value of Eo cell for the following reaction having equilibrium constant 106. Cu2 + Sn2+ → Cu + Sn4+

a) 0.1773 68.

b) 0.....01773

c)

0.2153

d) 0.02153

Activation energy can be determined : a) at two different temperature b) by changing concentration of reactant

PAGE

c) at a constant temperature d) none of these 69. 70.

First ionization potential of Be and B will be : a) 8.8 and 8.8 b) 6.6 and 6.6

c)

6.6 and 8.8

d) 8.8 and 6.6

The density of ice is less than water. The reason is : a) Induced dipole - induced dipole interaction b) Hydrogen bonding interaction c) Dipole - dipole interaction d) Dipole - induced dipole interaction

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71.

72.

73.

Which of the following pairs will not produce H2 gas on reaction : a) Fe + H2SO4 (dilute) b) Fe + steam c) Cu + HCl (dilute)

d) na + C2H5OH

Which compound has planar structure : a) XeOF2

b) XeO2F2

c) XeO4

d) XeF4

Aluminimum (III) chloride forms a dimer because : a) aluminimum can obtain high co-ordination b) ionization energy of aluminimum is high c) it cannot form trimer d) aluminium is related with third group

74.

PAGE

If helium is allowed to expand in vaccum, it librates heat because a) Helium is an ideal gas b) Helium is an inert gas

c) Critical temperature of He is very low

d) He has least boiling point of all the elements 75.

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Which of the following statements is/are not correct 1) A compound with D-configuration will always be dextrorotatory 2) A compound with D-configuration may be dextrorotatory or laevorotaiory 3) A compound with L-configuration will always be laevorotatory 4) A compound with L-configuration may be dextrorotatory or laevorotatory a) 1, 3

76.

b) 2, 1

c)

3, 4

d) 2, 3

H 2 SO4 + HgSO4 CaC 2 + 2H 2 O → X + Ca(OH) 2 X + H 2 O 60°c→ y

Identify X and Y in the above reaction sequence

77.

a) CH 4 and H 2C = O

b) C2H2 and CH3CHO

c) C2H4 and CH3COOH

d) C2H4 and HCOOH

An aromatic compound (X) was treated with alcoholic potash and another compond (y) when a foul smelling gas with the formula, C6H5NC was obtained. Y was also formed by reacting a compound (z) with Cl2 in presence of slaked lime. The compound (Z) is a) C6H5NH2

78.

b)

PAGE c)

CH 3OH

CH3COCH3

d) CHCl3

Best method to prepare trans-2-methyl-cyclohexanol form 1-methylcyclohexne is a) Oxo process b) Oxy mercuration-demercuration c) Hydroboration-oxidation

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d) Addition of H2O in presence of dil. H2SO4

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13

79.

Violet colour of iodine vapours is due to the excitation of an electron a) From the highest occupied M.O (the antibonding (the antibonding

π 2px or π 2py

to the lowest unoccupied M.O.

σ 2pz

b) From the lowest occupied bonding c) From the lower occupied bonding

σ 2pz

to the highest unoccupied antibonding σ 2 pz

π 2 px or π 2 py

to the highest unoccupied antibonding σ 2 pz

d) None of the above 80.

Identify the correct statement with respect to carbon monoxide; a) It combines with water to given carbonic acid b) It reacts with haemoglobin in red blood cells c) It is a powerful oxidizing agent

PAGE

d) It is used to prepare aerated drinks 81.

In the reaction I2 + XeF2 BF  3 → 2IF + Xe I 2 behaves as a/an a) Oxidising agent

b) Reducing agent

c) Both (a) and (b) 82.

d) None of these

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For nucleophilic substitution (S N 1) reaction the order of reactivity of following halides Cl

Cl

Cl

is : (A)

(B)

a) A > B > C 83.

(C)

b) B > A > C

c)

A>C>B

d) C > B > A

Which of the following is incorrect : a) FeCl3 is used in detection of phenol b) Fehling solution is used in detection of glucose c) Tollen’s reagent is used in detection of unsaturation d) NaHSO3 is used in the detection of carbonyl compound

84.

KOH A reduction  → B CHCl  3 / → C REDUCTION    → N - methyl anilline then A is :

a)

85.

NC

NO 2

NH 2

b)

PAGE c)

CH3NH2

d)

Synthetic rubber buna-S is : a) polymer of butadiene b) polymer of isoprene c) polymer of styrene d) polymer of butadiene and styrene

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14

86.

Which of the following is correct about H - bonding in nucleotide : a) A - GT - C b) A - TG - C c) G - TA - C

87.

d) A - AT - T

Aspirin can be prepared by reaction of acetyl chloride with : a) benzoic acid b) phenol c) p-hydroxy benzoic acid

88.

d) o-hydroxy benzoic acid

Which of the following period is suitable for “London smog” : a) Early morning of summer b) Early morning of winter c) Day time of summer

89.

The process of their extraction of Au and Ag is based on their solubility in a) NH 3 or NH 4 OH

90.

b) KCN or NaCN

d) H 2SO 4

HCl or HNO 3

PAGE

b) Protein + water

c) Soap + water

d) Hexane + chloroform

In a ccp arrangement of ‘N’ spheres, the number of tetrahedral holes is : a) N/2

92.

c)

Which of the following forms an example of miceller system ? a) Rubber + benzene

91.

d) Day time of winter

n) N

c)

2N

d) 2N 2

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Consider 1 M solutions of two solutes X and Y in a solvent. Solute ‘X’ undergoes 80% dimerisation while solute ‘Y’ is 90% trimerised in the solutions. Pick up the correct statement: a) Boiling point of ‘X’ < B.P. of Y b) Osmotic pressure of Y > O.P. of X c) Freezing point of X < F.P. of Y d) Colligative properties of solutions X and Y are equal

93.

When 500 ml of .0.2 M KOH reacts with 500 ml of 0.2 M HCl, rise in temperature is T1. When 250 ml of 0.2 M KOH react with 250 ml of 0.2 M HCl, rise in temperature is T2 . T1 and T2 are related as : a) T1 = T2

94.

b) T1 = 2T2

c)

T1 = 4T2

d) T2 = 9T1

100 ml of a clear saturated solution of silver sulphate (Ag 2SO 4 ) is added to 250 ml of a clear saturated solution of PbCrO 4 . Which of the following will be precipitated :

K sp [Ag 2SO 4 ] = 1.4 × 10 -5 ; K sp [PbCrO 4 ] = 2.8 × 10 −13

PAGE

K sp [Ag2 CrO4 ] = 2.4 × 10-12 ; K sp [PbSO 4 ] = 1.6 × 10−8 a) PbSO 4 95.

b) Ag 2 CrO 4

c)

d) PbCrO 4

Ag 2SO 4

Which of the following reactions occurs at the cathode of a common dry cell ? a) Mn → Mn 2 + + 2e −

b) 2MnO + Zn www.aieeepage.com 2

c) 2ZnO 2 + Mn 2+ + 2e − → MnZn 2 O 4

2+

+ 2e − → ZnMn 2 O 4

d) Zn → Zn 2 + + 2e −

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96.

For a general chemical change, 2A + 3B → Products, the rates with respect to A is r1 and that with respect to B is r2 . The rates r1 and r2 are related as : a) 3r1 = 2r2

b) r1 = r2

2r1 = 3r2

c)

d) r12 = 2r2

97.

Rock salt (NaCl) and quick lime (CaO) have the same crystal structure and approximately same ionic radii. If E is the lattice energy of NaCl, that of CaO approximately is : a) E b) 4E c) E/2 d) 2E

98.

If NaOH is added to an aqueous solution of Zn + + ions, a white precipitate appears and on adding excess NaOH, the precipitate dissolves. In this solution zinc exists in :

99.

a) Cationic part

b) Anionic part

c) Both in cationic and anionic parts

d) There is no zinc left in the solution

PAGE

In the metallurgical extraction of zinc from ZnO : a) Carnon monoxide is used b) sulphur dioxide is used c) Carbon dioxide is used

d) Nitric oxide is used

100. What is wrong about the complex [Pt (NH 3 ) 4 Cl 2 ]Br2 : a) Oxidation state of platinum is + 2

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b) Co-ordination number of platinum is 8

c) It gives the test of bromide as well as chloride d) All are wrong

101. In the transmutation of ab P to dc Q, the number of β - particles emitted is : a)

α-c 4

b-d 4

b)

c)

1 (α - c) - (b − d) 2

1 d) (c - a) + (b − d) 2

c)

NaCNS

d) None of these

102. In Lassaigne’s test, thiourea forms : b) NaCN

a) Na 2S

103. Which one of the folliwing compounds can not exists as enantiomers ? a) CH 3 − CH(OH)COOH

b)

CH 3 − CH 2 - CH - CH 2OH CH 3

c) C 6 H 5 CH 2 − CH 3

d)

C 6 H 5 CHClCH 3

PAGE

104. The compound ‘X’ (C 6 H10 ) does not react with ammoniacal AgNO 3 but gives a mixture of CH 3COOH and CH 3 - CH - COOH on reaction with excess of KMnO 4 . ' X' is :

CH 3 CH 3

b) CH − CH − CH www.aieeepage.com

a)

CH 3 − CH − C ≡ C − CH 3

c)

C 2 H 5 − CH − C ≡ CH

3

d)

2

2

− CH 2 − C ≡ CH

CH 3 − CH 2 − C ≡ C − C 2 H 5

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16

AlCl3 + CH 2 = CH − CH 2 − Cl  →(X) : (X) is :

105.

CH 3

CH

CH

CH 2Cl

a)

b)

CH 3

CH 3 Cl

CH 2 − CH = CH 2

c)

CH − CH = CH 2

d)

OH

106.

PAGE

When treated with CrO 3 followed by CH 3 MgBr and subsequent hydrolysis gives ?

OH a)

OH

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OH c)

d) None

Ni/H 2 KCN 107. CH 3CH 2 Cl  → X  → Y acetic anhydride  → Z

‘Z’ in the above reaction sequence is : a) CH 3CH 2 CONHCOCH 3

b) CH 3CH 2 CH 2 NHCOCH 3

c) CH 3CH 2 CH 2 CONHCH 3

d) CH 3CH 2 CH 2 NH 2

108. Which of the following is called a polyamide : a) Rayon 109. Lecitin is a a) Carbohydrate

b) Nylon

c)

Orlon

PAGE

b) Protein

c)

Phospholipid

d) Terylene d) Hormone

110. Streptomycin, a well known antibiotic, is a derivative of : a) Alkaloids

b) Peptides

c)

Terpenes

d) Carbohydrates

111. In a closed insulated container, a liquid is stirred with a paddle to increase the temperature. Which of the following is true : a) ∆E = W ≠ 0, q = 0

b) ∆E = W = q, q ≠ 0 www.aieeepage.com

c) ∆E = 0, W = q ≠ 0

d)

W = 0, ∆E = q ≠ 0

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17

112. Number of atoms is 558.5 gm of Fe [at. wt. of Fe = 55.85 gm mol −1 ] is : a) Twice that in 60 gm carbon

b)

6.023 × 10 23

c) Half that in 8 gm He

d)

558 .5 × 6.023 × 10 23

c)

Fe 3+

113. Which ion has maximum magnetic moment ? a) V 3+

b) Mn 3+

d) Cu + +

114. Polyphosphates are used as water softening agents because they : a) Form soluble complexes with anionic species b) Precipitate anionic species c) Form soluble complexes with cationic species d) Precipitate cationic species

PAGE

115. Alums help in purifying water by :

a) Forming Si complex with clay particles

b) Sulphate part which combines with dirt and removes it c) Aluminium ion which coagulates the mud particles d) Making mud water soluble

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116. The hybridisation of C in fullerene is : b) sp 2

a) sp

c)

sp 3

d) sp 3 d

117. The chemical processes in the production of steel from haematite ore involve :

118.

a) Reduction

b) Oxidation

c) Reduction followed by oxidation

d) Oxidation followed by reduction

KMnO 4 acts as an oxidising agent in :

a) Neutral and acidic medium

b) Neutral and alkaline medium

c) Neutral, acidic and alkaline medium

d) Acidic medium only

119. Wilkinson’s catalyst is used in which of the following processes : a) Isomerization b) Polymerisation c) Cyclisation

d) Hydrogenation

120. For the reaction system 2No(g) + O 2 ( g ) → 2 NO 2 (g) volume is suddently reduced to half its value by increasing the pressure on it. If the reaction is of first order with respect to O 2 and second order with respect to NO, the rate of reaction will : a) Diminish to one-fourth of its intial value b) Diminish to one-eight of its intial value

PAGE

c) Increase to eight-times of its initial value

d) Increase to four times of its intial value

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18

MATHEMATICS 121. If X and Y are two sets, then X ∩ (Y ∪ X) ' equals : a) X

b) Y

φ

c)

122. If z1, z2, z3 are complex numbers such that z1 = z 2 = z 3 =

d) none 1 1 1 + + = 1 , then z1 + z 2 + z 3 is : z1 z 2 z 3

a) equal to 1

b) less than 1

c) greater than 3

d) equal to 3

123. The mean of the n observations x1 , x2 , x3 ,....., xn be x.

Then the mean of n observations

2 x1 + 3, 2 x2 + 3, 2 x3 + 3,.....2 xn + 3 is :

a) 3x + 2

PAGE

b) 2 x + 3

c)

d) 2 x

x +3

124. The differential equation (4x - 3y) dx + (y - x) dy = 0 is of the following type : a) non-linear b) homogeneous of degree two

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c) homogeneous of degree one d) none of them

125. The probability that a leap year selected at random contains either 53 Sundays or 53 Mondays, is : a)

1 7

b)

126. If f(1) = 1 and

2 7

f ' (1) = 4, then

a) 9

the value of xlim →1

c) f ( x) − 1 x −1

b) 4

3 7

d)

4 7

is

c)

12

d) 1

c)

-1

d) does not exist

127. The derivative of f ( x) =| x | at x = 0 is a) 1

b) 0

G 128. If vector aG lies in the plane of vectors b and cG which of the following is correct ?

a) aG.(b × cG ) = 1

G

G b) aG.(b × cG ) = 0

G

G d) aG.(b × cG ) = −1

c) aG.(b × cG ) = 2

PAGE

129. General vlaue of x satisfying the equation 3 sin x + cos x = 3 is given by : π

a) nπ ± 6 π

c) nπ ± 3

π

π

π

π

n b) nπ + (-1) 4 + 3 n d) nπ + (-1) 3 − 6

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19

130. One of the two mutually exclusive events must occur. If the chance of one is 2/3 of the other, then odds in favour of the other are : a) 2 : 3 b) 1 : 3 c) 3 : 1

d) 3 : 2

131. If the system of equations x + 2y - z = 1, ( λ + 3) z = 3, (2 λ + 1) x + z = 0 is inconsistent, then the value of λ is equal to : a) −

1 2

b) -3

c)

2

d) 0

132. If b > a, then the equation (x - a) (x - b) - 1 = 0, has : a) both roots in (a, b) b) both roots in (- ∞ , a) c) both roots in (b, + ∞ )

PAGE

d) one root in (- ∞ , a) and other in (b, + ∞ )

133. The sum of the series 1 + 1 + 1.3 + 1.3.5 + . . . . . . is : 5

a)

b)

3

5.10

5.10.15

5 3

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5

3 5

d)

tan −1 x if | x | ≤ 1  is :  2 (| x | −1) if | x | > 1

134. The domain of the derivative of the function f (x) =  1 a) R - {0}

b) R - {1}

c)

R - {-1}

d) R - {-1, 1}

135. If a > 2b > 0 then the positive value of m for which y = mx - b 1 + m 2 is a common tangent to x2 + y2 = b2 and (x - a)2 + y2 = b2 is : 2b

a)

2

a − 4b

a 2 − 4b 2 2b

b)

2

c)

136. The foot of the perpendicular from (0, 2, 3) to the line a) (-2, 3, 4) 

x2

b) (2, -1, 3) x3





x4

2b a − 2b

d)

b a − 2b

x + 3 y −1 z + 4 = = is : 5 2 3

c)

(2, 3, -1)

x6



PAGE

d) (3, 2, -1) π

for 0 < | x | < 137. If sin −1  x + + − . . . . .  + cos−1  x 2 − + − . . . . .  =   2 2 4 2 4     equals : a)

1 2

b) 1

c)

−

1 2

2 , then x

d) -1

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138. The sum of the magnitudes of two forces acting at a point is 18 and the magnitude of their resultant is 12. If the resultant is at 90o with the force of smaller magnitude, then their magnitude are : a) 3, 15 b) 4, 14 c) 5, 13

d) 6, 12

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20

139. The speed of a swimmer in still water is 5m/min. He crosses a river of width 24 meter flowing with a speed 4m/min, to reach the opposite point on the other bank. The time taken by him is : a) 8 min b) 9 min. c) 19 min

d) 20 min

140. Let a1, a2, . . . . . . , a10 be in A.P. and h1, h2, . . . . . , h10 be in H.P. If a1 = h1 = 2 and a10 = h10 = 3, then a4h7 is a) 2 b) 3 c) 5 d) 6 141. How many different nine digit numbers can be formed from the number 223355888 by rearranging its digits so that the odd digits occupy even positions ? a) 16 b) 36 c) 60 d) 180 a 3 − 1 b3 − 1 c 3 − 1

142. If a ≠ b ≠ c such that

a a2

a) ab + bc + ca = 0 c) abc = 1

PAGE b b2

c c2

= 0 then

b) a + b + c =0 d) a + b + c = 1

143. If f(x) = aloge | x | +bx2 + x has extremums at x = 1 and x = 3 then

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1

3

a) a = − 4 , b = − 8 3

a=

1

c) a = 4 , b = 8

1 3 ,b = − 8 4

d) none of these

144. The combined equation of the lines 11 ,12 is 2x 2 + 6xy + y 2 = 0 and that of the lines m1 , m 2 is 4x 2 + 18xy + y 2 = 0 .If

π −α 2

a) 145.

∫

the angle between 11 and m2 be

α

then the angle between 12 and m1 will be

b) 2α

c)

π +α 4

d)

b) 1 + π /2

c)

π+3/ 2

d) none of these

α

2+x dx is equal to 2−x

2 0

a) π + 1

→

→

→

→

146. Let →a be a unit vector perpendicular to unit vectors b and c and if the angle between b and c be → →

b× c

is

→ a) cosα a

PAGE

→ b) cosecα a

c)

→ sinα a

α

then

d) none of these

147. If ω1 and ω2 are the complex cube roots of unity , then ω14 + ω24 equal : a)

-1 ω1ω 2

1 ω1ω2

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b) −2ω1ω2

c)

d) 2ω1ω2

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21

148. The upper part of a tree broken by the wind makes an angle of 30°with the ground . The distance from the foot to the point where the top of the tree touches the ground is 10 3 m . The height of the tree was a) 10 m

b) 30 m

c)

45 m

d) 60 m

149. If the interior angles of a polygon are in A.P with common difference 50 and the smallest angle is 1200 then the number of sides of the polygon is a) 9 or 16

b) 9

c)

13

d) 16

150. Two points (1, -1, 1) and (-2, 0, 5) with respect to the plane 2x + 3y - z + 7 = 0 lie on a) opposite sides b) same side c) on the plane

d) None of these

151. For real numbers x and y, we define x R y iff x − y + 5 is irrational number. The relation R is

PAGE

a) reflexive

b) symmetric

c) transitive

d) None of these A

C

152. If three sides a, b, c of a triangle ABC are in arithmetic progression, then the value of cot 2 cot 2 is : a) 4 b) 3 c) 2 d) 1

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153. The chord AB of the parabola y 2 = 4ax. cuts the axis of the parabola at C. if A = (at12 , 2at1), B = (at22 , 2at2 )

a) t2 = 2t1 154.

∫

d ( x 2 + 1) x2 + 2

and AC : AB = 1 : 3 then

b) t2 + 2t1 = 0

c)

1  x 2 + 2   

d) none of these

is equal to

a) 2 x 2 + 2 + k c)

t1 + 2t 2 = 0

3/ 2

b)

+K

x2 + 2 + k

d) none of these

155. The number of integral values of k for which the equation 7 cos x + 5 sinx = 2k + 1 has a solution is a) 4 b) 8 c) 10 d) 12 156. If

sin θ + cosθ > 0,



then θ lies in 

π

π









π





π

π

b)  nπ + 4 , nπ + 2 (n ∈ I )

a)  nπ - 2 , nπ + 4 (n ∈ I ) c)  0, nπ + 4 (n ∈ I )

PAGE



d) none of the above

157. If we consider only the principal valuesof the inverse trigonometric functions, then the value of  1 4   tan cos−1 − sin −1 2 17  

a)

29 3

is

b)

www.aieeepage.com 29 3

c)

3 29

d) none of these

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22

158. Which of the following pieces of data does not uniquely determine an acute-angle ABC (R being the radius of the circumcircle) ? a) a, sin A, sin B b) a, b, c c) a, sin B, R d) a, sin A, R 159. The equation of line parallel to lines L1 ≡ x + 2 y − 5 = 0 and L2 ≡ x + 2 y + 9 = 0 and dividing the distance between L1 and L2 in the ratio 1 : 6 (internally), is a) x + 2y - 3 = 0

b) x + 2y + 2 = 0

c) x + 2y + 7 = 0

d) none of these

160. The point (4, 1) undergoes the following three transformations successively : i) Reflection about the line y = x ii) Translation through a distance 2 units along the positive direction of x-axis π

PAGE

iii) Rotation through an angle 4 about the origin in the anticlockwise direction The final position of the point is given by the co-ordinates  1 7  a)  2 , 2   

b) (−2, 7 2 )

c)

 1 7   −  , 2 2  

d) (2, 7 2 )

161. Let T > 0 be a fixed real number. Suppose f is a continuous function such that for all

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x ∈ R,

f(x+T)=

f(x). If I = ∫T0 f(x)dx, then the value of ∫33+3T f (2 x)dx is a)

3 I 2

162. Real valued function a) −

1 3

b) 2I

c)

(a x − 1) x n (a x + 1)

3I

d) 6I

is even when n is equal to :

b) 2

c)

1 4

d)

2 3

163. In the expansion of (1 + x)50, let S be the sum of coefficients of odd power of x, then S is : a) 0 b) 249 c) 250 d) 251 164. The value of the integral a)

3 2

b)

∫

e2 e

−1

loge x dx is : x

5 2

c)

3

PAGE

d) 5

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

b) 2

c)

2 2

d) 4

166. The locus of the mid-point of the line segment joining the focus to a moving point on the parabola y2 = 4ax is another parabola with directrix : a) x = -a

c) x = 0 www.aieeepage.com 2

b) x = −

a

d) x =

a 2

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23

167. The locus of a point that moves such that the sumof the squares of its distances from the six faces of a cube is constant, is : a) a circle b) a plane c) a sphere

d) a straight line

168. If x = 9 is the chord of contact of the hyperbola x2 - y2 = 9, then the equation of the corresponding pair of tangents is : a) 9x2 - 8y2 + 18x - 9 = 0 b) 9x2 - 8y2 - 18x + 9 = 0 c) 9x2 - 8y2 - 18x - 9 = 0

d) 9x2 - 8y2 + 18x + 9 = 0

G G G G G G G G 169. Let λ = a × (b + c),µ = (b × c + a) and vG = cG × (aG + b). Then G G G

G

a) λ + µG = vG G

G

b) λ, µ, v are coplanar G

PAGE

d) none of these

c) λ + v = 2µ

170. If the angles of a triangle be in the ratio 1 : 4 : 5, then the ratio of its greatest side to the smallest side is : a) 5 : 1

b) ( 5 + 1) : 1

c) 1 : ( 5 − 1) 171. Let f(x) =

∫

x 1

d) none of the above

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2 − t 2 dt. Then the real roots of the equation x2 - f ′(x) = 0 are

a) ±1

b) ±

1

±

c)

2

1 2

d) 0 and 1

172. An unbiased die with faces marked 1, 2, 3, 4, 5 and 6 is rolled four times. Out of four face values obtained, the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5 is : a)

16 81

b)

65 81

1 81

c)

d)

80 81

173. The resultant of P and Q is R. If Q is doubled, R is also doubled and if Q is reversed, R is again doubled. Then P2 : Q2 : R2 is given by : a) 1 : 1 : 1 b) 2 : 2 : 3 c) 2 : 3 : 2

d) 3 : 2 : 2

174. A car is travelling at a velocity of 10 km/h on a straight road. The driver of the car throws a parcel with

PAGE

a velocity of 10 2 km/h when the car is passing by a man standing on the side of the road. If the parcel is to reach the man, the direction of throw makes the following angle with the direction of the car : a) 135o

b) 45o

c)

tan-1 2

 1    2

d) tan-1 

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175. The graph of the function cos x cos(x + 2) − cos2 (x + 1) is a a) straight line passing through the point (0 , − sin 21) with slope 2 b) straight line passing through the origin c) parabola with vertex (1 , − sin 21) d) straight line passing through the point (π /2 , sin 21) and parallel to the x - axis 176. The slope of the tangent of a curve y = f (x ) at ( x, f ( x)) is 2x + 1. If the curve pases through the point (1, 2), then area bounded by the curve, x-axis and the line x = 1 is a)

5 sq.units 6

c)

1 sq.units 6

6

b) 5 sq.units

PAGE d) 6 sq.units

177. A spherical rain drop evaporates at a rate Proportional to its surface area at any instant t. The differential equation giving the rate of change of the radius of the rain drop is a) proportional to radius b) proportional to surface area c) proportional to volume

d) none of these

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178. The vertices of a triangle ABC are A(-1, 0, 2) and B(1, 2, 0) and C(2, 3, 4). The momnet of a force of magnitude 10 acting at A along AB about C is a) c)

50 6 3

b) 20 6

50

d) none of these

3 x

2 179. The critical point of f ( x) = 1 + x + ∫ [log t ) + 2 log t ]dt is 1

a)

π 2

b)

π 6

c)

π 3

d) e

1

180. The number of values of x in the interval [0, 5 π ] satisfying the equation 3 sin2 x - 7 sin x + 2 = 0 is : a) 0 b) 5 c) 6 d) 10

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