Ai Aieee Modeltest 10

MODEL TEST TEST CODE - FVE

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

1.

PHYSICS

A semi conducting device is connected in series circuit with a battery and a resistance. A current is found to pass through the circuit. If the polarity of battery is reserved, the current drops to almost zero. The device may be a) a p - type semiconductor b) an p - type semiconductor c) an intrinsic semiconductor

2.

d) a p - n junection diode

Which of the following are true when the cells are connected in series ? a) Current capacity decreases b) Current capacity increases c) The e.m.f. decreases

3.

Time - 180 Min

d) The e.m.f. increases

Select wrong statement from the following, electromagnetic waves ____ a) are transverse b) travel with same speed in all media

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c) travel with the speed of light

d) are produced by accelerating charge

4.

When a material is placed in magnetic field B, a magnetic momnet proportional to B but opposite in direction is induced; the metal is a) diamagnetic b) paramagnetic c) ferromagnetic d) antimagnetic

5.

Particle having possitive charge occasionally come with high velocity from the sky towards the earth. On account of magnetic field of earth, they would be deflected towards the a) north b) south c) east d) west

6.

When a tuning fork vibrates, the vibrations of its two prongs have a phase difference of

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a) 7.

π

b) π /2

c) zero

d) 2 π

A body rests on a rough horizontal plane. A force is applied to the body directly towards the plane at ∠θ with the vertical. The body can moved along the plane only if θ is

θ

a) 45°

b) > 45°

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c) < Limiting angle of friction 8.

d) > Limiting angle of friction

A circular disc is to be made by using iron and aluminimum so that it acquired maximum moment of inertia about geometrical axis. It is possible with a) aluminimum at interior and iron surrounding it, b) iron at interior surrounded by aluminimum,

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c) using iron and aluminimum layers in alternate order,

d) sheet of iron is used at both external surfaces and aluminimum sheet as internal layer

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9.

A straight conductor carrying a direct current i amp. is split into circular loop as shown in figure. Then the magnetc induction at the centre of the circular loop of radius r meter is

r O

i a) 0 10.

b)

∞

i µ0 i 2π r

c)

d)

µ0 i 2r

A long which of the thermodynamic path shown in the following figure the heat given is more ? P

PAGE B

QB

QA

A

V

a) QA > QB 11.

b) QA < QB

c)

QA = QB

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d) none of these

Two bodies A and B of equal masses are suspended from two separate springs of spring constants K1 and K 2 respectively; If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude of vibration of A to that of B is a)

12.

K1/K 2

c)

K 2 /K1

b)

c)

eV/m

2eV/m

d)

2eV/m

A ring, a solid sphere and a thin disc of different masses rotate with the same kinetic energy Equal torques are applied to stop them. Which will make the least number of rotations before coming to rest ? a) Disc b) Ring c) Solid sphere

14.

d) K 2 /K1

K1/K 2

An electron of mass m and charge e is accelerated from rest through a potential differnece V in vacuum. The final speed of the electron will be a) V e/m

13.

b)

d) All will make same number of otations

In a cylindrical vessel containing liquid of density ρ , there are two holes in the side will at heights h1 and h 2 respectively such that the range of efflux at the bottom of the vessel is same. The height of a hole, for which the range of efflux would be minimum, will be

PAGE h2

www.aieeepage.com h1

a) (h 2 − h1)

b)

h 2 − h1 2

c)

h1 + h 2

 h1 + h 2    2 

d) 

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15.

The resultant of two forces, one double of the other magnitude, is perpendicular to the smaller of two forces. The angle between the two forces is _____ a) 60° b) 120° c) 10° d) 90°

16.

Figure shows V-T diagram for a gas heated at constant pressure. What happens to the mass of the gas when it goes from state 1 to state 2 ?

y V

2

1

PAGE 0

a) decreases 17.

T

b) increases

c) remains constant

d) cannot say

The network shown in figure is part of a complete cirucit. If at a certain instant, the current I is 5A, and is decreasing at a rate 103 A/s, then (VB − VA ) is

www.aieeepage.com 1Ω

A a) 20 V 18.

5mH

15V b) 15 V

c) 10 V

B d) 5V

A planet is observed by an astronomical refracting telescope having an objective of focal length 16 m and an eyepiece of focal length 2 cm. 1) The distance between the objective and the eyepiece is 16.02 m 2) The angular magnification of the planet is 800 3) The image of the planet is inverted 4) The objective is larger than the eyepiece a) 1, 2, 3, 4

19.

b) 1, 2, 3

d) 2, 3, 4

The Young’s double slit experiment is performed with blue and with green light of wavelengths 4360 Å and 5460Å respectively. If x is the distance of 4th maxima from the central one, then a) x (blue) = x (green) b) x (blue) > x (green) c) x (blue) < x (green) d) x(blue) /x (green)

20.

c) 1, 2, 4

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In a sample of radioactive material, what fraction of the initial no. of active nuclei will remain undisintegrated after half of a half life of the sample ? a)

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1 4

1

b) 2 2

2

d)

2 −1

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21.

A rectangular coil of wire rotates at a constant speed about one of its sides xy. The side xy is parallel to a long, straight current carrying conductor. The induced emf will be minimum when the coil is

i

22.

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a) perpendicular to the plane of the conductor

b) in the plane of the conductor

c) parallel to the plane of conductor

d) outside the plane of the conductor

A constant voltage is applied across a uniform wire, which produces some heat in the wire. If a second wire of the same material but of length twice that of the first wire is used, the heat produced in the second wire will the same as in the first wire if the area of cross-section of the second wire is a) increases by a factor of four b) decreases a factor of four

www.aieeepage.com d) decreased by a factor of two

c) increased by a factor of two 23.

In rising from the bottom of a lake to the top, the temperature of an air bubble remains unchanged, but its diameter is doubled. If h is the barometric height (expressed in metres of mercury of relative density ρ ) at the surface of the lake, the depth of the lake is (in metres) a) 8 ρ h

24.

25.

c) 7 ρ h

d) 2 ρ h

A circular coil is kept in a vertical position. A bar magnet is thrown with a velocity v towards the coil along the axis of the coil. After passing through the coil the magnet is stopped and again thrown with the same velocity from the same position towards the coil. If t1 and t 2 are time taken by the magnet to reach the coil in first case and second case respectively, then (assume heat produced in the coil is used in raising the temperature of coil) a) t1 = t 2

b) t1 > t 2

c) t1 < t 2

d) depends on size of magnet

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)

26.

b) 4 ρ h

xy t x+ y

b)

PAGE xy t x− y

c)

x2 y2

x2 + y

t 2

d)

x2 y 2 x2 − y2

t

Three equal charges q are placed at the corners of an equilateral triangle of side a. A charge Q is placed such that its distance from each charge is r. The force experienced by Q will be : qQ

a) 4π ε r 2 o

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qQ

b) 4π ε (r + a ) 2 o

4π ε o ( r − a ) 2

d) Zero

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27.

It is hotter for the same distance over the top of the fire than it is in the side of it, mainly because a) heat is radiated upwards b) air conducts heat upwards c) convection takes more heat upward d) conduction, convection and radiation all contribute significantly transferring heat upwards

28.

The factor on which the rise of liquid in a capillary tube doesnot depend is a) density of liquid b) atmospheric pressure c) radius of capillary

29.

A proton and will be :

α-

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

a) 1 : 2 30.

d) angle of contact

b) 2 2 : 1

c)

d) 2 : 1

2 :1

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Two rods A and B of the same material and the same length have raii r1 and r2 respectively. When they are rigidly fixed at one end and twisted by the same couple applied at the other end the ratio of  angle of twist at the end of A    is  angle of twist at the end of B 

a) r12 / r22 31. 32.

c) r / r www.aieeepage.com

b) r14 / r24

3 2

3 1

Which one of the following substances possesses the highest elasticity ? a) Rubber b) Glass c) Steel

d) r24 / r14 d) Copper

Two simple pendulum having lengths 0.5 m 0.2 m, They will be in same phase when shorter length pendulum completes oscillation : a) 5

b) 1

c) 2

d) 3

33.

A straight line conductor of length 0.4 m is moved with a speed of 7 m/s. perpendicular to a magnetic field of intensity 0.9 Wb/m2. The induced e.m.f. across the conductor is : a) 1.26 V b) 2.52 V c) 5.04 V d) 25.2 V

34.

A boat with a sail has a large powerful electric fan placed toward the sail. The boat will move in which direction ? The air is otherwise still. a) Direction of the breeze from the fan b) Direction opposite the breeze from the fan c) No direction

35.

d) Sideways, at a tangent

The rectangular blocks A, B, C and D are piled one above the other in such a way that each block projects a little beyond the block below it. If the length of each block is A , then the maximum possible projection for A is

PAGE A

B

C

D

a)

A 2

b)

A A www.aieeepage.com c) 6

4

d)

A 8

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36.

Two cars A and B are tavelling in the same direction with velocities v1 and v2 (v1 > v2 ) . When the car A is at a distance d behind the car B, the driver of the car A applies the breake producing uniform retardation a. There will be no collision when a)

37.

v −v  d <  1 2   2a 

 2

2

 v1 − v2  b) d >  2a  

c)



v2 − v2 d) d < 1 2

(v − v ) 2 d> 1 2 2a

2a

A projectile is moving at 60ms−1 at its highest point, where it breaks into two equal parts due to internal explosion. One part moves vertically up at 50ms−1 with respect to ground. The other part will move at a) 10 61 ms−1

b) 110 ms−1

c)

120 ms−1

d) 130 ms−1

38.

Two inductors of inductance L each are connected in series with opposite magnetic fluxes. What is the resultant indutance ? a) zero b) L c) 2L d) 3L

39.

Beats are produced by two progressive waves. Maximum loudness at the waxing is x times the loudness of each wave. The value of x is

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a) 4 40.

c)

d) 1

2

In an adiabatic expansion of a gas, initial and final temperatures are T1 and T2 respectively, then the change in internal energy of the gas is : a)

41.

b) 2

R (T2 − T1 ) γ -1

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b)

R (T1 − T2 ) γ -1

c) R(T2 - T1)

d) zero

In the circuit shown, some potential difference is applied between A and B. The equivalent resistance between A and B is

3Ω A

2Ω

5Ω

6Ω

B

4Ω a) 15Ω

b) 12.5 Ω

c)

3.6 Ω

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d) 2.1Ω

42.

A coil of area 100 cm2 having 50 turns is perpendicular to a magnetic field of intensity 0.02 weber/m². The resistance of the coil is 2 ohm. If it is removed in 1 sec from the magneticfield, the induced charge produceed is a) 5C b) 0.5 C c) 0.05 C d) 0.005C

43.

The length of the sum of the vectors a = 3ˆi and b = 4ˆj is ____ a) 3 b) 4 c) 5

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d) none of these

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44.

A coin is placed on a horizontal platform, which undergoes horizontal simple harmonic motion about a mean position. The coin does not slip on the platform. The force of friction acting on the coin is 1) zero when the coin and platform come to rest momentarily at the extreme position of the harmonic motion 2) maximum when the coin and platform come to rest momentarily at the extreme position of the harmonic motion 3) Is always directed towards mean position 4) Is directed towards mean position when the coin is moving away from mean position and away from mean position when the coin moves towards the mean positon. a) 2, 4

45.

b) 1, 2

c) 1, 3

d) 1, 4

G

Calculate the work done when a force F = 2ˆi + 3ˆj − 5kˆ units acts on a boyd, producing a displacement G S = 2ˆi + 4ˆj + 3kˆ

units

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a) 30 units

b) 45 units

c) 1unit

d) zero unit

46.

I c.c. of water at its boiling point (110oC) absorbs 540 calories of heat to become steam with a volume of 1571 c.c. If the atmospheric pressure is 1.013 x 105 N/m2, the energy spend (in calories) to overcome molecular attractive forces is nearly (mechanical equivalent of heat = 4.2 joule/calorie) : a) 540 b) 500 c) 40 d) zero

47.

A particle of mass m is executing osocillations about the originon the x-axis. Itis potential energy is U(x) = K | x |3 ,

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where K is a positive contant. If the amplitude of oscillation is a, then its time period T

is 1

a) proportional to a

b) independent of a

c) proportional to a

d) proportional to a3 / 2

48.

Two electric bulbs whose resistance are in the ratio of 1 : 2 are connected in parallel to a constant voltage source. The powers dissipated in them have the ratio : a) 1 : 2 b) 1 : 1 c) 2 : 1 d) 1 : 4

49.

Imagine an atom made up of a proton and a hypothetical particle of double the mass of the electron but having the same charge as the electron. Apply the Bohr atomic model and consider all possible transitions of this hypothetical particle to the first excited level. The longest wavelength of photon that will be emitted has wavelength λ (given in terms of the Rydberg constant R for hydrogen atom) equal to a) 9/(5R)

50.

c) 18/(5R)

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d) 4/R

A plono convex lens fits exactly into a plano concave lens. Their plane surfaces are parallel to each other. If the lenses are made of different material of refractive indices µ1 and µ2 and R is the radius of curvature of the curved surface of the lenses, then focal lengthof the combination is R

a) µ − µ 1 2 51.

b) 36/(5R)

2R

b) µ − µ 2 1

c)

R 2(µ1 − µ 2 )

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R

d) 2 - (µ + µ ) 1 2

Two point charges 2q and 8q are placed at a distance r apart. Where should a thrid charge -q be placed between them so that the electrical potential energy of the system is a minimum a) at a distance of r/3 from 2q b) at a distance of 2r/3 from 2q c) at a distance of r/16 from 2q d) none of these for IIT - JEE & AIEEE at the National PAGE- A Premier Institution www.iitjeepage.com www.bitsatpage.com

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52.

The ratio of magnetic field at the centre of current carrying circular coil to its magnetic moment is x. Ifthe currect and radius both are doubled the new ratio will become a) 2x b) 4x c) x/4 d) x/8

53

The same mass of copper is drawn into two wires 1mm and 3mm thick. These two wires are connected in series to the source of current. What is the ratio of heat produced in wires a) 1 : 9 b) 1 : 91 c) 9 : 1

d) 81 : 1

54.

The water drop falls at regular intervals from a tap 5m above the ground. The third top is leaving the tap at instant the first drop touches the ground. How far above the ground is the second drop at the instant : a) 1.25 m b) 2.50 m c) 3.75 m d) 4.00 m

55.

The velocity of a train increases uniformly from 20 km/h to 60 km/h in 4 hours. The distance travelled by the train during this period is : a) 100 km b) 120 km c) 160 km d) 180 km

56.

The period of revolution of planet A around the sun is 8 times that of B. The distance of A from the sun is how many times greater than that of B from the sun : a) 2 b) 3 c) 4 d) 5

57.

Two soap bubbles of radii 2 x 10-3 m and 4 x 10-3 m coalesce. If the surface tension of liquid is 7 x 10-2 N/m then the radius of curvature of the common surface will be :

PAGE

www.aieeepage.com 2X10-3m O R1

O

R2 4X10-3m

I

II R

a) 4 m

b) 4 × 10-3 m

c) 2 × 10-3 m

d) 6 × 10-3 m

58.

If the length of a simple pendulum is increased by 2%, then the time period : a) Increases by 2% b) Decreases by 2% c) Increases by 1% d) Decrease by 1%

59.

An air-column in a pipe, which is closed at one end, will be in resonance with vibrating t unning fork of frequency 264 Hz, if the length of the column is : (v = 330 m/sec) a) 31.25 cm b) 62.50 cm c) 93.75 cm d) 125.75 cm

60.

A solid copper sphere of radius R and a hollow copper sphere of equal internal and external radius R are heated to same temperature and are then allowed to cool in same atmosphere. Which of the following statement is correct : a) Both the spheres will cool simultaneously

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b) The temperature of two spheres will be same

c) The rate of cooling of solid sphere will be more than that of hollow sphere

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d) The rate of fall of temperature of hollow sphere will be more than that of solid sphere.

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9

CHEMISTRY

61.

Which one of the following statement is incorrect ? a) A mixture is not always heterogeneous. b) All elements are homogeneous c) Compounds made up of a number of elements are heterogeneous d) Air is a heterogeneous mixture.

62.

63.

The critical temperature of water is higher than of O2 because the H2O molecule has a) V-shape

b) dipole moment

c) two covalent bonds

d) fewer electrons then O 2

c) Solid Na Cl covalent 64.

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Solid NaCl is a bad conductor of electricity because a) in solid Na Cl there are no electrons b) in solid Na Cl there are no ions d) In solid Na Cl there is no mobility of ions

Which of the following statement is correct for a binary solution ? a) A solution in which heat is evolved exhibits positive deviations from Raoult’s law

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b) A solution in which heat isabsorbed negative deviations from Raoult’s law c) When one component in solution shows negative deviations from Raoult’s law ,the other exhibits positive deviation d) When one component in solution shows positive deciation deviation from Raoult’s law, so does the other 65.

66.

When water is added to conc. H 2SO 4 it gets very hot. This happens becaue dilution of conc H 2SO 4 is a) an exothermic reaction

b) an endothermic reaction

c) photochemical reaction

d) hydrolytic reaction

The equilibrium constant for the reaction H 2 (g) + l 2 (g) Then the equilibrium constant for the reaction Hl(g)

a) 7 67.

1 7

1 1 H (g)+ l2 (g) at the same temperature is 2 2 2 c) 24.5

d) 98

Whcih of the following statements is incorrect ? Oxidation state of oxygen is a) -1 in peroxide b) +2 in oxygen difluoride c) +

68.

b)

2Hl (g) at a certain temperature is 49.

1 in superoxides 2

PAGE d) -2 in CO 2

In the reaction A + B → Products, if B is taken in excess, then it is an example of a) second order reaction b) zero order reaction

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c) pseudounimolecular reaction 69.

Which of the following forms a colloidal solution in water ? a) NaCl b) Glucose c) Starch

d) Barium nitrate

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70.

If the atomic number of an element is 33 , it will be placed in the periodic table in the a) First group b) third group c) ftfth group d) seventh group

71.

Most covalent compounds have a very low solubility in water because of the a) low hydration energy due to the weak interaction between the polar water molecules and the nonpolar covalent molecules , which is insufficient to break the hydrogen bonds between the water molecues b) low dielectric constant of water c) high dipole moment of water d) high density of water

72.

73.

74.

Phosphorous has the oxidation state of +3 in a) Phosphorous acid

b) Orthophosphoric acid

c) Hypophosphorous acid

d) Metaphosphoric acid

PAGE

Each of the following is true of white and red phosphorus except that they a) are both soluble in CS 2

b) can be oxidised by heating in air

c) consist of the same kind of atoms

d) can be conveverted into one another

The order of solubility of lithium halides is non-polar solvents is : a) LiI > LiBr > LiC1 > LiF b) LiBr > LiCI > LiF > LiI

www.aieeepage.com d) LiF > LiI > LiBr > LiCI

c) LiCI > LiF > LiI > LiBr 75.

The blue colour of cupric salt solution in water is due to the formation of a hydrated cupric ion . The hydrated ion is a) octahedral with two long bonds trans to each other and four short bonds trans to each other b) tetrahedral with two long bonds trans to each other and two short c) octahedral with two long bonds cis to each other and four short bonds trans to each other d) octahedral with two short bonds cis to each other and four long bonds trans to each other

76.

In the manufacture of H2SO4 the nitrated acid form the Gay Lussnc’s tower is chemiscally a) H 2SO 4NO 2 b) H 2SO 4NO c) H2SO42NO d) HSO 4NO

77.

TlI 3 is an ionic compound which furnishes the following ions in solution

a) TI3+ and I− ions

b) TI+ and I3- ions

c)

Tl

+

and I

-

ions

d) TI+ , I− ions and I2

78.

The type of isomerism present in nitropentaam minechromium (II) chloride is a) Optical b) Linkage c) Ionization d) Polymerization

79.

The nucleus of an atoms is made up of X protons and Y neutrons. For the most stable and abundant nuclei a) X is even and Y is odd b) X is odd an Y is even c) X and Y are both even

80.

PAGE

d) X and Y are both odod

Which of the following technique is used for the purification of cyclohexanone from a mixture of benzoic acid, isoamyl alcohol, cyclohexane and cyclohexanone : a) crystallization b) gas - chromatography

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c) sublimation

d) infra - red spectroscopy

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81.

Among the following compounds (I - II) the correct order of reactivity with electrophile is CH 3

NO 2

I

III

II

a) II > III > I

b) III < I < II

c) I > II > III

d) I = II > III

82.

Which reaction sequence would be best to prepare 3-chloroanilne form benzene ? a) Chlorination, nitration, reduction b) Nitration, chlorination, reduction c) Nitration, reduction, chlorination d) Nitration, reduction, acetylation, chlorination, hydrolysis

83.

Finkelstein reaction is : a)

PAGE

2CH 3CH 2 CI + Ag 2 O → CH 3CH 2 OCH 2 CH 3 + 2 AgCI ( dry )

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Acetone → CH 3CH 2 I + NaBr b) CH 3CH 2 Br + NaI 

c)

CH 3CH 2 Br + Ag 2O → CH 3CH 2OH + AgBr ( Moist )

d) CH 3CH 2 CI + NaOCH 3 → CH 3CH 2 OCH 3 + NaCI 84.

An orgatnic compound (a) reacts with sodium metal and forms (b). On heating with conc. H 2SO 4 , (a) gives diethyl ether, (a) and (b) are a) C 2 H 5 OH and C 2 H 5 ONa b) C 3 H 7 OH and CH 3 ONa c) CH 3OH and CH 3ONa

85.

d) C 4 O 9 OH and C 4 H 9 ONa

Intermediate formed during reaction of R − C − NH 2 with Br2 and KOH are : || O

a) RCONHBr and RNCO c) RNH-Br and RCONHBr

b) RNHCOBr and RNCO d) RCONBr 2

86.

Secondary structure of protein refers to a) Mainly denatured proteins and structure of prosthetic groups b) Three-dimensional structure, especially the bond between amino acid residues that are distinct from each other in the polypetide chain c) Linear sequency of amino acid residuces in the polypetide chain d) Regular folding patterns of continuous protions of the polypetide chain

87.

The beta and alpha glucose have different specific rotations, when either is dissolved in water, their rotation changes until some fixed value results. This is called : a) Epimerisation b) Racemisation c) Inversion d) Mutarotation

88.

Aspirin is obtained by the reaction of salicylic acid with a) Acetone b) Acetaldehyde c) Acetyl chloride

PAGE

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d) Acetic acid

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89.

When rain is accompanied by a thunderstorm, the collected rain water will have a pH value : a) Slightly lower than that of rain water without thunderstorm b) Slightly higher than that when the thunderstorm is not there c) Uninfluenced by occurrence of thunderstorm d) Which depends on the amount of dust in air

90

Repeated use of which one of the following fertilizers would increase the acidity of soil ? a) Urea b) Potassium nitriate c) Ammonium sulphate d) Superphosphate of lime

91.

The reaction of Grignard reagent with formaldehyde followed by acidification gives a) An aldehyde b) A primary alcohol c) A carboxylic acid d) A ketone

92.

Which one of the following conditions will increase the voltage of the cell represented by the equation Cu(s) + 2Ag + (aq) → Cu 2+ (aq) + 2Ag (s) ?

PAGE

a) Increase in the concentration of Ag + ions

b) Increase in the concentration of Cu 2 + ions c) Increase in the dimensions of silver electrode d) Increase in the demensions of copper electrode 93.

Out of Ca +2 , Al−3 , Cr +3 , Mg2+ and Zn 2+ , the reagents NH4Cl and aqueous NH3 will precipitate c) Bl3+, Mg2+ www.aieeepage.com

a) Ca2+ , Al3+ 94.

b) Al3+, Cr3+

d) Mg2+, Zn2+

Arrange the following aqueous solutions in the order of their increasing boiling points i) 10−4 M NaCl ii) 10−4 M Urea a) (i) < (ii) < (iv) < (iii) c) (ii) < (i) < (iii) < (IV)

iii) 10−3 M MgCl2 b) (ii) < (i) = (iii) < (iv) d) (iv) < (iii) < (i) = (ii)

95.

The factor which does not affect the heat of reaction is a) Whether the reacton is carried out directly or indirectly b) Physical state of the reactants and products c) Whether the reaction is carred out in an open vessel or a closed vessel d) The temperature of the reaction

96.

The IUPAC name for the compound, CH3 − CH − C − CH 2CH3 is

iv) 10−2 M NaCl

CH3 CH2

a) 2-Ethyl-3-methybut - 1- ene c) 2 - Methyl - 3- ethyl - 3 butene

b) 2 - Isopropylbut -1-ene d) 2-(Methylehl) but -1 ene

97.

The raw material used in a Fisher Tropsch process for the manufacture of synthetic petroleum is a) Coal gas b) Producer gas c) Water gas d) Water gas + excess of hydrogen

98.

Which of following compounds on treatment with methanol in presence of potassium methoxide under pressure at 433 K will give methyl vinyl ether ? a) Propyne b) 1, 3, Butadiene c) Ethyne d) Ethene

99.

Erythro isomer among the following is

PAGE

www.aieeepage.com

CH3

a)

H

COOH

OH

b)

H

Br CH 3

PAGE

CHO

COOH

H

Cl

Cl

H

c)

H

H2N

H

CH 3

OH CH3

d)

OH

H H

OH CH 2 OH

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100. Which of the following solutions will have the highest boiling point ? a) 1% glucose in water b) 1% sucrose in water c) 1% NaCl in water

d) 1% CaCl 2 in water

101. The equilibrium constant for the reaction H 2 O(g) + CO(g)

H 2 (g) + CO 2 (g) is 0.44 at 1260 K.

The equilibrium constant for the reaction 2H 2 (g) + 2 CO 2 (g) equal to a) 0.44 b) 0.88 c) 5.16

2 CO(g) + 2H 2 O(g) at 1260 K is

d) 126

102. The volume of one mole of an ideal gas expands 1 litre to 10 litre on 300 K. The value of ∆E for this reaction will be : a) 163.7 cal b) zero c) 1381.1 cal d) 9 L. atm. 103. The number of significant figures in the following numbers will be : 1) 161 2) 0.0161 3) 1.61 a) 3, 3, 3 b) 3, 4, 3 c) 3, 2, 3

PAGE

104. Schottky defect represents : a) decrease of cation and anion in equal number

d) 3, 4, 4

b) removal of catio and anion from their sites

c) an ion leaves its site and occupies an interstitial d) increase in the density of crystal

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105. Which of the following compound gives p-cresol with p-methyl diazonium chloride : a) H 2 O b) H 3PO 2 c) HCOOH d) C 6H 5 OH 106. The conductance of a solution of an electrolyte is same as that of its specific conductance. The cell used can be said to have cell constant equal to a) 1 b) zero c) 100 d) 10 107. The weight of H 2 C 2 O 4 .2H 2 O required to prepare 500 ml of 0.2 N solution is a) 126 gm

b) 12.6 gm

108. isobutylene on hydroboration gives a) p - alcohol b) s - alcohol 109. For the reaction A(g) + B(g)

c) 63 gm

d) 6.3 gm

c) t - alcohol

d) Dihydric alcohol

C(g)

the equilibrium partial pressure are PA = 0.15 atm, PB = 0.10 atm and PC = 0.30 atm. The value of the pressure was so reduced that after attainment of equilibrim again, the partial pressures of A and B were doubled. The partial pressure of C would be a) 0.30 atm b) 0.60 atm c) 1.20 atm d) 1.80 atm 110. On the addition of mineral acid to an aqueous solution of borax , the following compounds is formed a) Boron hydride b) Orthoboric acid c) Metaboric acid d) pyroboric acid 111.

PAGE

If x is the specific resistance of the solution and N is the normality of the solution. The equivalent conductivity of the solution is given by a)

1000x N

b)

1000 Nx

c)

1000N x

d)

Nx 1000

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112. Which one of the following cannot be obtained from a mixture of ethanol and concentrated sulphuric acid, if the composition of the mixture and the reaction conditions are suitably adjusted ? a) C2H4

b) CH3CHO

c)

CH3CH2OCH2CH3

d) CH3CH2HSO4

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113. The degree of dissociation of dinitrogen tetroxide N2O4 (g) → 2NO2 (g) at temperature T and total pressure P is α . Which one of the following is the correct expression for the equilibrium constant α at this temperature ? 2α

a) (1 - α) 2

b)

α 2P 1- α

c)

4α 2

d)

2

(1 - α )

4α 2P (1 - α 2 )

114. When a biochemical reaction is carried out in laboratory from outside the human body in the absence of enzymes than rate of reaction obtained is 10-6 times, then activation energy of reaction in the presence of enzyme is : a) 6/RT b) P is required c) different from, Ea obtained in laboratory d) can’t say anything 115. 1.1. mole of A are mixed with 2.2 moles of B and mixture is then kept in 1 litre flask till the equilibrium

A 2B 2C D is attaied. At the equilibrium 0.2 moles ofC are formed. The equilibrium constant ofthe reation is a) 0.001 b) 0.02 c) .003 d) 0.004

PAGE

116. A compound C 6 H10 decolourizes bromine in carbon tetrachloride and reacts with Ag + in ammonia to given an insoluble salt . On treatment with excess hydrogen in the presence of an Ni catalyst, this compound given 2-methylpentane. The structure of the compound C 6 H10 is a)

b) CH C = C − CH = CHCH www.aieeepage.com

CH 3C = CH − CH = CH 2

2

3

CH 3

CH 3

H

c) CH 3CHC ≡ CCH 3

d) CH 3 - C - CH 2 C ≡ CH CH 3

CH 3

117. In a cubic lattice each edge of the unit cell is 400 pm. Atomic weight of the element is 60 and its density is 6.25 g/c.c. Avogadro number = 6 × 10 23. The crystal lattice is a) Face centred

b) primitive

c) Body centred

d) End centred.

118. Fructose on oxidation with HlO4 gives a) Two moles of formaldehyde + four moles of formic acid b) Two moles of formaldehyde + three moles of fromic acid + one mole of carbon dioxide c) One mole of formaldehyde + give moles of formic acid d) Three moles of formaldehyde +three moles of formic acid CH I

PAGE Ag O

3 → X 2→ Y the product Y may be NH 2  excess H O∆

119.

2

a)

b) (CH3 )3 N

+

N (CH3 )3 I −

c)

d) Both (a) and (b)

120. Equivalent weight of KMnO4 in acidic & neutral medium are respectively a)

M M & 3 5

b)

M M www.aieeepage.com M M & & c) 5

3

2

4

d)

M M & 5 7

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MATHEMATICS 121. In a class of 100 students, 55 students have passed in Mathematics and 67 students have passed in Physics. Then the number of students who have passed in Physics only is : a) 22 b) 33 c) 10 d) 45 122. Let A = { 2, 4, 6, 8} and define R = {(2, 4), (4, 2), (4, 6), (6, 4)} then R is : a) anti symmetric b) reflexive c) symmetric

d) transitive

123. Which of the following functions is not onto f : R → R + , f ( x) = x 2 + 2

a)

f : R → R , f ( x) = 3x + 4

b)

c)

f : R + → R + , f ( x) = x

d) none of these

13

124. The value of

∑ (i n =1

n

PAGE

+ i n +1 ), where i = − 1 equals

a) i

b) i - 1

h2

k2

d) 0

= 1 then (h 2 − a 2 ) x 2 − 2hkx + (k 2 − b 2 ) is a : a 2 b2 a) perfect square b) not a pefect square c) negative value

125. If

126.

+

c) - i

sin 6 x

∫ cos

8

x

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d) zero

dx =

a) tan 7 x + c

b)

tan 7 x +c 7

c)

tan 7 x +c 7

d) sec 7 x + c

127. The first and last terms of an A.P. are 1 and 11. If the sum of its terms is 36, then the numbers of terms will be : a) 5 b) 6 c) 7 d) 8 128.

n −2

a)

C r + n − 2Cr −1 + n− 2Cr − 2 is equal to n −1

Cr

b)

n +1

c)

Cr

n

d)

Cr

n

Cr +1

129. If m men and n women are to be seated in a row so that no two women sit together. If m > n, then the number of ways in which they can be seated is

m! n! a) (m - n + 1)!

b)

(m + 1)! (n + 1)! (m - n + 1)!

c)

m ! (m + 1)! (m - n + 1)!

PAGE

d) None of these

130. The standard deviation for variable x and y be 3 and 4 respectively and thier covariance is 8, then coefficient of correlation between them is a)

2 3

b)

3

c)

2 2

2 2 3

d)

2 9

www.aieeepage.com b) 2 cot 2α .(x + y ) = 1 + x

131. If α + iβ = tan -1 z, z = x + iy, α is constant, the locus of z is a) x 2 + y 2 + 2 x cot 2α = 1

2

c) x 2 + y 2 + 2 x sin 2 α = 1

2

d) x 2 + y 2 + 2 x sin 2α = 1

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132. If f be an injective map with domain {x, y, z} and range {1, 2, 3} such that exactly one of the following statements is correct and the remaining false. f(x) = 1, f(y) ≠ 1, f(z) ≠ 2. The value of f −1 (I) is : a) x b) y c) z d) Of is not a mapping 133. The determinant

13 + 3 ∆ = 15 + 26 3 + 65

a) 15 2 − 25 3 134. Solve (a)

2 5 5 65

equals

b) 25 3 − 15 2

3 x 2 − 7 x − 30 + 2 x 2 − 7 x − 5 = x − 5

−5 2

5 10 5

c)

3 5

d) − 15 2 + 7 3

(c)

−5 or 6 2

(d) none

:

(b) 6

135. If p (x) = ax² + bx +c and q(x) = - ax² +dx +c. Where ac ≠ 0 the p(x) , q(x) = 0 must have : (a) All are real roots (b) atleast one real root (c) atleast two real roots (d) no real roots 136. The sum of the seris 2, 5, 8, 11,..... is 60100, then n is : a) 100 b) 200 c) 150 d) 250

PAGE

137. If the sum of the coefficients in the expansion of (α2 x 2 − 2αx +1)51 vanishes, then the value of α is a) 2 b) -1 c) 1 d) -2 138. In the following two A.P.’s how many terms are identical ? 2, 5, 8, 11, ........to 60 terms 3, 5, 7, 9, ........to 50 terms a) 16 b) 17 c) 18 d) 20

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 2 1  139. Which term is independent of x in  3x −  3x   a) 6 b) 8 c) 5 d) 7 140. There are 4 balls of different colours and 4 boxes of colours same as those of the balls. The number of ways in which the balls, one each in a box could be placed such that a ball does not go to a box of its own colour is a) 3! b) 27 c) 4! d) 9 141. The number of different matrices that can be formed with elements 0, 1, 2(or ) 3 each matrix having 4 elements is

a) 3× 4 4

b) 2× 4 4

c)

3× 2 4

d) 4× 4 4

 B  = 142. If two events A and B are such that P(A C ) = 0.3, P(B) = 0.4 and P(ABC ) = 0.5, then P c  A∪B 

a)

1 2

PAGE

1 3

b)

1 d) can not be determined 4 143. An unbiased coin is tossed. If the result is a head, a pair of unbiased dice is rolled and the number obtained by adding the numbers on the two faces is noted. If the result is a tail, a card from a well shuffled pack of eleven cards numbered 2, 3, 4,......12 is picked and the number on the card is noted. Then the probability that the noted number is either 7 or 8 is c)

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a)

11 72

b)

193 792

c)

193 396

d) None

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17

144. The equations of the tangents, to the ellipse 3x 2 + 4 y 2 = 12, which are parallel to the line y + 2x = 4 are a) y + 2 x = ±12

b) y + 2 x = ± 17 c) y + 2 x = ±3 d) y + 2 x = ± 19 145. The curve described parametrically by x = 2 - 3 sec t, y = 1 + 4 tan t represents : a) An ellipse centred at (2, 1) & of eccentricity

3 5

b) A circle centred at (2, 1) and of radius 5 units c) A hyperbola centred at (2, 1) & of eccentricity

8 5

d) A hyperbola centred at (2, 1) & of eccentricity

5 3

146. The equation of the parabola with vertex at origin, which passes through the point (-3, 7) and axis along the x-axis is

PAGE

a) y 2 = 49 x

b) 3 y 2 = −49 x

c)

3 y 2 = 49 x

d) x 2 = − 49 y

147. The equation of the cirlce whose radius is 5 and which touches the circle x 2 + y 2 − 2 x − 4 y − 20 = 0 at the point (5, 5) is b) x 2 + y 2 − 18 x − 16 y + 120 = 0

a) x 2 + y 2 + 18 x + 16 y + 120 = 0

d) x + y + 18 x − 16 y + 120 = 0 www.aieeepage.com

c) x 2 + y 2 − 18 x + 16 y + 120 = 0

2

2

148. Let f : R → R be function defined by f ( x) = max{x, x3}. The set of all points where f(x) is not differentiable is a) {-1, 1} b) {-1, 0} c) {0, 1} d) {-1, 0, 1} 149.

d y ( x ) (where y is a function of x) is equal to dx

a)

y x (1 + y log x)

b)

y x (1 − y log x )

c)

y2 x (1 − y log x )

d) none of these

c)

φt f 2 − f t φ 2 3 f1

d) none of these

d2y 150. If x = f (t ), y = φ(t ), then 2 is equal to dx a)

151.

∫

( x − 1)e x

a) 152.

f t φ 2 − φt f 2 2 f1 ( x + 1) 3

b)

f t φ 2 − φt f 2 3 f1

dx

ex (x − 1) 2

+C

b)

∫ x 5 cos xdx

PAGE ex +C x +1

c)

ex

(x + 1) 2

+C

d) none

a) sin ( x 5 − 20 x 3 + 120x) + cos x(5 x 4 − 60 x 2 + 120) + C 5

3

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b) sin ( x − 20 x − 120x) + cos (5x 4 − 60 x 2 + 120) + C

c) sin ( x 5 + 20 x 3 − 120 x) + cos (5 x 4 − 60 x 2 + 120) + C d) none for IIT - JEE & AIEEE at the National PAGE- A Premier Institution www.iitjeepage.com www.bitsatpage.com

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18

153. The area of the region bounded by the curve y = 2 1 − x 2 and the x-axis a) π sq. units

b)

π sq. units 2

c) dy

2π sq. units

d) none

x2

154. The general solution of the differential equation dx = 2 is : y a) x 3 − y 3 = c

b) x 3 + y 3 = c

c)

155. The general solution of the differential equation 2

x2 + y2 = c

d) x 2 − y 2 = c

dy = 1 + xy is : dx

2

b) y = c e x / 2 c) y = ( x + c ) e − x / 2 d) none of these y = ce − x / 2 156. A particle starts from rest with acceleration f. After interval of time t the acceleration is increased by f units. So that after t, 2t, 3t, .... units of time the accelerations become 2f, 3f, 4f..... respectively. The velocity of the particle at time 8t, in appropriate unit is equal to : a) 40f b) 36f c) 32f d) 28f 157. A short is fired at an angle α to the horizontal up a hill of inclination β to the horizontal. Then it strikes the hill horizontally if : a)

2

PAGE

b) tan α = tan β c) tan α , tan β = 1 d) None a) tan α = 2tan β 158. The tower of a bridge, hung in the form of a parabola, have their tops 30 metres above the road-way are 200 metres apart. If the cable is 5 metres above the roadway at the centre of the bridge, then the length of the vertical supporting cable 30 metres from the centre is

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a) 100 m

b) 30 m

c)

9 m 4

d)

29 m 4

159. After a ball has been falling under gravity for 5 seconds, it passes through a plane of glass and looses half of its velocity, and now reaches the ground in 1 second. The height of the glass above the ground is a) 2900 cm b) 2543 cm c) 2943 cm d) None of these G G 160. If a = xiˆ + ( x − 1) ˆj + kˆ and b = ( x + 1)iˆ + ˆj + akˆ always make an acute angle with each other for every value of x ∈ R , then b) a ∈ (2, ∞ ) a) a ∈ (−∞, 2)

c)

a ∈ ( − ∞,1)

d) a ∈ (1, ∞)

161. If A = 30 0 , a = 7, b = 8 in ∆ ABC , then B has a) one solution b) two solutions c) no solution

d) none of these

n  π   π   + cos  = , then  2n   2n  2

162. Let n be a fixed positive integer such that sin 

PAGE

b) n = 5

a) n = 4

c)

n=6

d) none

a2 163. If a sin x + b cos x = c, b sin y + a cos y = d and a tan x = b tan y, then 2 is equal to b 2

2

(b - c)(d - b) a) (a − d)(c − a)

2

2

(a - d)(c - a) (d - a)(c - a) www.aieeepage.com b) c) (b − c)(d − b) (b − c)(d − b)

d)

(b - c)(b - d) (a − c)(a − d)

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19

164. The real roots of the equation cos 7 x + sin 4 x = 1 in the interval (− π , π ) are

π -π −π π −π π , ,0, b) c) 0, d) 0, 2 2 2 2 2 2 G G G G G G G G G 165. If a , b , c are unit coplanar vectors, then the scalar triple product [2a - b 2b - c 2c - a] = a)

a) 0

b) 1 c) − 3 d) 3 G G G 166. Let a = a i ˆi + a 2ˆj + a 3 kˆ, b = bi ˆi + b2ˆj + b3 kˆ and c = ci ˆi + c2ˆj + c3 kˆ be three non-zero vectors such π G G that c is a unit vector perpendicular to both aG and b if angle between aG and b is 3 , then the value

of

a1

b1

c1

a2

b2

c2

a3

b3

c3

2

is

a) 0

b)

PAGE 1 G 2 G 2 |a| |b| 4

c)

G G | a |2 | b |2

d) none of these

G G G G G G G G a×b b×c G c×a G G G G GGG 167. If P = G G G , q = G G G and r = G G G , where [a b c] ≠ 0 then the value of P • (a + b + c) is [a b c ] [a b c ] [a b c]

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equal to a) 0

b) 3

c) -1

d) 1

168. ABCD is a parallelogram with AC = ˆi − 2ˆj + kˆ and BD = −ˆi + 2ˆj − 5kˆ , area of the parallelogram is equal to 5 sq. units 2

a)

b) 2 5sq. units

c)

d)

4 5sq. units

5sq. units

169. Which of the triplet can not represent direction cosines of a line a)

 1 1 1     3, 3, 3  

b)

 3   50 , 

4 50

,

5   50 

170. Equation of plane which contains the line

c)

 4   77 , 

x −1 y − 2 z − 3 = − 1 3 2

5 77

,

6   77 

d)

 2   25 , 

3 25

,

4   25 

and which is perpendicular to the plane

2x + 7y + 5z = 2 is a) x + y + z = 6 b) -x + y + z = 2 c) 2x - y + z = 3 d) x - y + z = 2 171. The number of words that can be made by writing down the letters of the word CALCULATE such that each word starts and ends with a consonant, is a)

5(7 !) 2

b)

PAGE 3(7 !) 2

c) 2 (7!)

d) none of these

172. The total number of selections of at most n things from (2n + 1) differnet things is 63. Then the value of n is a) 3 b) 2 c) 4 d) none of these 173. If S1 , S2 , S3 are the sums of first n natural numbers, their squares, their squares, their cubes respectively, then a) 1

S3 (1 + 8S1 ) S2 2

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is equal to b) 3

c) 9

d) 10

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d2 7 174. If y = sin x, then 2 (cos x ) is equal to dy a) 35 cos 3 x − 42 cos 5 x c) 42 ' cos 3 x − 35 cos 5 x t

175. If x = t t and y = t t then

b) 35 cos 3 x + 42 cos 5 x d) None of these

dy is equal to dx t  1 t t 1 + log t +  t  b) (1 + log t )

t  1 t t (1 + log t)log t +  t  a) (1 + log t

c)

t  1 t t (1 + log t )log t +  t  2 (1 + log t )

PAGE

d) None of these

176. If for a real number y, [y] is the greatest integer less than or equal to y then the value of the integral 3π/2

∫ [2 sinx] dx is

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π/2

b) 0

a) -π x

177. Let g(x) =

∫ f (t ) dt

where f is such that

0

c)

-π 2

d)

π 2

1 1 ≤ f (t ) ≤ 1 for t ∈ [0, 1] and 0 ≤ f (t ) ≤ for t ∈ [1, 2] then 2 2

g(2) satisfies the in equality a)

−3 1 ≤ g ( 2) < 2 2

b) 0 ≤ g (2) < 2

c)

3 5 < g ( 2) ≤ 2 2

d) 2 < g (2) < 4

178. Area of a triangle with vertices ( a, b ), (x1 , y1 ) and (x 2 , y 2 ) where a, x1 and x 2 are in G. P. with common ratio r and b, y1 and y 2 are in G. P. with common ratio s is given by a) [ab (r − 1) (s − 1) (s − r)] c)

b)

1 [ab (r − 1) (s − 1) (s − r)] 2

1 [ab (r + 1) (s + 1) (s − r)] 2

d) [ab (r + 1) (s + 1) (r - s)]

PAGE

179. The centroid of the triangle formed by the points ( 0, 0 ), (cos θ , sin θ ) and (sin θ , − cos θ ) lies on the line y = 2x, then θ =

a) Tan -1 2 b) Tan −1 3 c) Tan −1 (−3) d) Tan −1 (−2) 180. A and B throw alternatively a pair of dice. A wins If he throws 6 before B throws 7 and B wins if he throws 7 before A throws 6. Their respective chance of winning if A begins a)

31 30 , 61 61

b)

30 30 30 31 www.aieeepage.com , , c) 61 61

61 61

d) None

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