Aieee Question Paper 4

8/2/2019 Aieee Question Paper 4

1/52

AIEEE Solved Paper 2005

1. A projectile can have the same rangeR for twoangles of projection. Ift1 and t 2 be the times offlights in the two cases, then the product of thetwo times of flights is proportional to

(a) R 2 (b)1

2

R(c)

1R

(d) R

2. An annular ring with inner and outer radii R1and R2 is rolling without slipping with auniform angular speed. The ratio of the forcesexperienced by the two particles situated on

the inner and outer parts of the ring,F

F1

2

is

(a)R

R2

1

(b)R

R1

2

2

(c) 1 (d)R

R1

2

3. A smooth block is released at rest on a 45

incline and then slides a distance d. The timetaken to slide is n times as much to slide onrough incline than on a smooth incline. Thecoefficient of friction is

(a) kn

= 1 12

(b) kn

= 1 12

(c) sn

= 1 12

(d) sn

= 1 12

4. The upper half of an inclined plane withinclination is perfectly smooth, while thelower half is rough. A body starting from rest atthe top will again come to rest at the bottom, ifthe coefficient of friction for the lower half isgiven by

(a) 2sin (b) 2 cos (c) 2tan (d) tan

5. A bullet fired into a fixed target loses half of its velocity after penetrating 3 cm. How muchfurther it will penetrate before coming to rest,assuming that it faces constant resistance tomotion ?

(a) 3.0 cm (b) 2.0 cm(c) 1.5 cm (d) 1.0 cm

6. Out of the following pairs, which one does nothave identical dimensions ?

(a) Angular momentum and Plancks constant

(b) Impulse and momentum(c) Moment of inertia and moment of a force(d) Work and torque

7. The relation between time t and distance xist ax bx = +2 , where a and b are constants. Theacceleration is

(a) 2 2abv (b) 2 3bv(c) 2 3av (d) 2 2av

8. A car, starting from rest, accelerates at the ratef through a distance S, then continues atconstant speed for time t and then deceleratesat the rate f /2 to come to rest. If the totaldistance travelled is 15 S, then

(a) S f t= (b) S f t=1

62

(c) S f t= 12

2 (d) S f t= 14

2

9. A particle is moving eastwards with a velocityof 5 1ms . In 10 s the velocity changes to5 1ms northwards. The average accelerationin this time is

(a)1

2ms 2 towards north-east

(b)12

ms 2 towards north

(c) zero

(d)12

ms 2 towards north-west

10. A parachutist after bailing out falls 50 m without friction. When parachute opens, itdecelerates at 2 m/s2. He reaches the ground

with a speed of 3 m/s. At what height, did hebail out ?

(a) 91 m (b) 182 m(c) 293 m (d) 111 m

1

Solved Paper 2005

AIEEE(All India Engineering Entrance Examination)

Physics


2/52


11. A block is kept on a frictionless inclined surfacewith angle of inclination . The incline is givenan acceleration a to keep the block stationary.Then a is equal to

(a) g/tan (b) g cosec (c) g (d) g tan

12. A spherical ball of mass 20 kg is stationary at

the top of a hill of height 100 m. It rolls down a

smooth surface to the ground, then climbs up

another hill of height 30 m and finally rolls

down to a horizontal base at a height of 20 mabove the ground. The velocity attained by the

ball is

(a) 40 m/s (b) 20 m/s(c) 10 m/s (d) 10 30 m/s

13. A bodyA of mass M while falling verticallydownwards under gravity breaks into two

parts; a bodyB of mass13

M and, a bodyCof

mass23

M. The centre of mass of bodiesB Cand

taken together shifts compared to that of bodyA towards

(a) depends on height of breaking

(b) does not shift(c) bodyC

(d) bodyB

14. The moment of inertia of uniform semicirculardisc of mass M and radius r about a lineperpendicular to the plane of the disc throughthe centre is

(a)14

2Mr (b)25

2Mr

(c) Mr2 (d)12

2Mr

15. A particle of mass 0.3 kg is subjected to a force

F kx = with k = 15N/m. What will be its

initial acceleration, if it is released from a point20 cm away from the origin ?

(a) 3 m/s2 (b) 15m s2/

(c) 5 m s2/ (d) 10 m s2/

16. The block of massMmoving on the frictionlesshorizontal surface collides with the spring of

spring constant k and compresses it by lengthL.The maximum momentum of the block aftercollision is

(a) Mk L (b)kL

M

2

2

(c) zero (d)ML

k

2

17. A mass m moves with a velocityv and collides

inelastically with another identical mass. After

collision the Ist mass moves with velocityv

3in

a direction perpendicular to the initial

direction of motion. Find the speed of thesecond mass after collision.

(a) v (b) 3 v

(c)2

3v (d)

v

3

18. A 20 cm long capillary tube is dipped in water.

The water rises upto 8 cm. If the entire

arrangement is put in a freely falling elevator,

the length of water column in the capillary tube

will be

(a) 8 cm (b) 10 cm

(c) 4 cm (d) 20 cm

19. If S is stress and Y is Youngs modulus of

material of a wire, the energy stored in the wire

per unit volume is

(a) 2 2S Y (b)S

Y

2

2

(c)2

2

Y

S(d)

S

Y2

20. Average density of the earth

(a) does not depend ong(b) is a complex function ofg(c) is directly proportional tog(d) is inversely proportional tog

21. A body of mass m is accelerated uniformly from

rest to a speedv in a time T. The instantaneouspower delivered to the body as a function of

time, is given by

(a)mv

Tt

2

2(b)

mv

Tt

2

22

(c)12

2

2

mv

Tt (d)

12

2

22mv

Tt

2

M

a


3/52

22. Consider a car moving on a straight road with aspeed of 100 m/s. The distance at which carcan be stopped, is [ . ]k = 0 5(a) 800 m (b) 1000 m(c) 100 m (d) 400 m

23. Which of the following is incorrect regardingthe first law of thermodynamics ?

(a) It is not applicable to any cyclic process

(b) It is a restatement of the principle ofconservation of energy

(c) It introduces the concept of the internalenergy

(d) It introduces the concept of the entropy

24. AT shaped object with dimensions shown in

the figure, is lying on a smooth floor. A force F

is applied at the point P parallel to AB, such

that the object has only the translationalmotion without rotation. Find the location ofPwith respect to C.

(a) 23 l (b) 32 l

(c)43

l (d) l

25. The change in the value ofg at a height h abovethe surface of the earth is the same as at a depthd below the surface of earth. When both d and hare much smaller than the radius of earth, then

which one of the following is correct ?

(a) dh=2

(b) dh= 32

(c) d h= 2 (d) d h=26. A particle of mass 10 g is kept on the surface of

a uniform sphere of mass 100 kg and radius10 cm. Find the work to be done against thegravitational force between them, to take theparticle far away from the sphere. (you maytake G = 6 67 10 11. )Nm /kg2 2 (a) 13.34 10 J10 (b) 3.33 10 J10

(c) 6.67 10 J9 (d) 6.67 10 J10

27. A gaseous mixture consists of 16 g of helium and

16 g of oxygen. The ratioC

Cp

V

of the mixture is

(a) 1.59 (b) 1.62(c) 1.4 (d) 1.54

28. The intensity of gamma radiation from a givensource isI. On passing through 36 mm of lead,it is reduced to I /8. The thickness of lead,

which will reduce the intensity toI/2 will be(a) 6 mm (b) 9 mm(c) 18 mm (d) 12 mm

29. The electrical conductivity of a semiconductorincreases when electromagnetic radiation of

wavelength shorter than 2480 nm, is incidenton it. The band gap in (eV) for thesemiconductor is

(a) 1.1 eV (b) 2.5 eV (c) 0.5 eV (d) 0.7 eV

30. A photocell is illuminated by a small bright

source placed 1 m away. When the same source

of light is placed12

m away, the number of

electrons emitted by photocathode would

(a) decrease by a factor of 4(b) increase by a factor of 4(c) decrease by a factor of 2(d) increase by a factor of 2

31. Starting with a sample of pure 66Cu, 7/8 of itdecays into Zn in 15 min. The correspondinghalf-life is

(a) 10 min (b) 15 min

(c) 5 min (d) 7

1

2 min32. If radius of the 13

27Al nucleus is estimated to be3.6 fermi, then the radius of 52

125 Te nucleus benearly

(a) 6 fermi (b) 8 fermi

(c) 4 fermi (d) 5 fermi

33. The temperature-entropy diagram of areversible engine cycle is given in the figure. Itsefficiency is

(a) 1/2 (b) 1/4

(c) 1/3 (d) 2/3

3

A B

C

P

F

2l

l

2T0

T0

S0 2S0S

T


4/52

34. The figure shows a system of two concentricspheres of radii r1 and r2 and kept attemperaturesT1 andT2, respectively. The radialrate of flow of heat in a substance between thetwo concentric spheres, is proportional to

(a)( )

( )r r

r r2 1

1 2

(b) ln

r

r2

1

(c)r r

r r1 2

2 1( )(d) ( )r r2 1

35. A system goes from A toBvia two processes Iand II as shown in figure. If U U1 2and arethe changes in internal energies in theprocesses I and II respectively, then

(a) U U1 2=(b) relation between U1 and U2 cannot be

determined(c) U U2 1>(d) U U2 1 Ifthe potential difference across the sourcehaving internal resistanceR2, is zero, then

(a) RR R R

R R= +

2 1 2

2 1

( )( )

(b) R R R= 2 1

(c) RR R

R R= +

1 2

1 2( )

(d) RR R

R R=

1 2

2 1( )

51. A fully charged capacitor has a capacitance C. It isdischarged through a small coil of resistance wire

embedded in a thermally insulated block ofspecific heat capacitys and mass m. If thetemperature of the block is raised byT, thepotential difference Vacross the capacitance is

(a)2mC T

s

(b)

mC T

s

(c)ms T

C

(d)

2ms TC

52. One conductingU-tube can slide inside anotheras shown in figure, maintaining electricalcontacts between the tubes. The magnetic field

B is perpendicular to the plane of the figure. Ifeach tube moves towards the other at aconstant speedv, then the emf induced in the

circuit in terms of B l v, and , where l is thewidth of each tube, will be

(a) Blv (b) Blv(c) zero (d) 2Blv

53. A heater coil is cut into two equal parts and

only one part is now used in the heater. Theheat generated will now be

(a) doubled (b) four times(c) one-fourth (d) halved

54. Two thin, long, parallel wires, separated by adistance d carry a current ofi ampere in thesame direction. They will

5

500

R

B12V

A

2VG

A B

D CX

X

X

X

X X XX

X

X

XX

XX

X

X X

v

v


6/52

(a) attract each other with a force of

0

2

2i

d( )

(b) repel each other with a force of

02

2

i

d( )(c) attract each other with a force of

0

2

22

i

d( )

(d) repel each other with a force of

0

2

22

i

d( )

55. When an unpolarized light of intensityI0 isincident on a polarizing sheet, the intensity ofthe light which does not get transmitted is

(a)12 0I (b)

14 0

I

(c) zero (d) I056. A charged ballB hangs from a

silk thread S, which makes an

angle with a large chargedconducting sheetP, as shown

in the figure. The surface

charge density of the sheet isproportional to

(a) cos (b) cot (c) sin (d) tan

57. Two point charges + 8 2q qand are locatedat x x L= =0 and respectively. The location ofa point on the x-axis at which the net electric

field due to these two point charges is zero is

(a) 2L (b) L/ 4

(c) 8L (d) 4L

58. Two thin wire rings each having a radiusR areplaced at a distance d apart with their axes

coinciding. The charges on the two rings are

+ q and q. The potential difference betweenthe centres of the two rings is

(a)qR

d4 02

(b)q

R R d21 1

0 2 2

+

(c) zero

(d)q

R R d41 1

0 2 2

+

59. A parallel plate capacitor is made by stacking nequally spaced plates connected alternatively.If the capacitance between any two adjacentplates is C, then the resultant capacitance is

(a) ( )n C 1 (b) ( )n C+ 1(c) C (d) nC

60. When two tuning forks (fork 1 and fork 2) aresounded simultaneously, 4 beats/s are heard.Now, some tape is attached on the prong of thefork 2. When the tuning forks are soundedagain, 6 beats/s are heard. If the frequency offork 1 is 200 Hz, then what was the originalfrequency of fork 2 ?

(a) 200 Hz (b) 202 Hz

(c) 196 Hz (d) 204 Hz

61. If a simple harmonic motion is represented by

d x

dtx

2

20+ = , its time period is

(a)2 (b)

2

(c) 2 (d) 2 62. The bob of a simple pendulum is a spherical

hollow ball filled with water. A plugged hole

near the bottom of the oscillating bob gets

suddenly unplugged. During observation, till

water is coming out, the time period of

oscillation would

(a) first increase and then decrease to theoriginal value

(b) first decrease and then increase to theoriginal value

(c) remain unchanged

(d) increase towards a saturation value

63. An observer moves towards a stationary source

of sound, with a velocity one-fifth of the

velocity of sound. What is the percentage

increase in the apparent frequency ?

(a) Zero (b) 0.5%

(c) 5% (d) 20%

64. IfI0 is the intensity of the principal maximum

in the single slit diffraction pattern, then what

will be its intensity when the slit width is

doubled ?

(a) 2 0I (b) 4 0I

(c) I0 (d)I02

65. Two concentric coils each of radius equal to

2 cm are placed at right angles to each other.3 A and 4 A are the currents flowing in each coil

respectively. The magnetic induction in Wb/m2

at the centre of the coils will be

( / ) 074 10= Wb Am

(a) 12 10 5 (b) 10 5

(c) 5 10 5 (d) 7 10 5

6

+

+

+

+

+

+

+

+

+

+

S

B

P


7/52

66. A coil of inductance 300 mH and resistance 2 is connected to a source of voltage 2V. Thecurrent reaches half of its steady state value in

(a) 0.05 s (b) 0.1 s

(c) 0.15 s (d) 0.3 s

67. The self-inductance of the motor of an electric

fan is 10 H. In order to impart maximum power

at 50 Hz, it should be connected to a

capacitance of

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

68. An energy source will supply a constant current

into the load, if its internal resistance is

(a) equal to the resistance of the load

(b) very large as compared to the loadresistance

(c) zero(d) non-zero but less than the resistance of theload

69. A circuit has a resistance of 12 and animpedance of 15 . The power factor of thecircuit will be

(a) 0.8 (b) 0.4

(c) 1.25 (d) 0.125

70. The phase difference between the alternating

current and emf is / .2 Which of the followingcannot be the constituent of the circuit ?

(a) Calone (b) R L,

(c) L C, (d) L alone

71. A uniform electric field and a uniform magneticfield are acting along the same direction in a

certain region. If an electron is projected along

the direction of the fields with a certain

velocity, then

(a) its velocity will decrease

(b) its velocity will increase

(c) it will turn towards right of direction ofmotion

(d) it will turn towards left of direction ofmotion

72. A charged particle of mass m and charge qtravels on a circular path of radius r that isperpendicular to a magnetic field B. The timetaken by the particle to complete onerevolution is

(a)2mq

B(b)

2 2q Bm

(c)2qB

m(d)

2mqB

73. In a potentiometer experiment the balancingwith a cell is at length 240 cm. On shunting the

cell with a resistance of 2 , the balancinglength becomes 120 cm. The internal resistanceof the cell is

(a) 1 (b) 0.5 (c) 4 (d) 2

74. The resistance of hot tungsten filament is about10 times the cold resistance. What will be theresistance of 100 W and 200 V lamp, when notin use ?

(a) 40 (b) 20 (c) 400 (d) 200

75. A magnetic needle is kept in a non-uniformmagnetic field. It experiences

(a) a torque but not a force(b) neither a force nor a torque(c) a force and a torque(d) a force but not a torque

76. The oxidation state of Cr in[Cr(NH ) Cl ]3 4 2+ is

(a) 0 (b) +1

(c) +2 (d) +3

77. Which one of the following types of drugs

reduces fever ?

(a) Tranquiliser (b) Antibiotic(c) Antipyretic (d) Analgesic

78. Which of the following oxides is amphoteric in

character ?

(a) SnO2 (b) SiO2(c) CO2 (d) CaO

79. Which one of the following species isdiamagnetic in nature ?

(a) H2 (b) H2

+

(c) H2 (d) He2+

80. If is the degree of dissociation ofNa SO2 4, the

vant Hoff factor ( )i used for calculating themolecular mass is

(a) 1 2 (b) 1 + 2(c) 1 (d) 1 +

81. Which of the following is a polyamide ?

(a) Bakelite (b) Terylene(c) Nylon-66 (d) Teflon

7

Chemistry


8/52

82. Due to the presence of an unpaired electron,free radicals are

(a) cations

(b) anions

(c) chemically inactive

(d) chemically reactive

83. For a spontaneous reaction the G, equilibriumconstant ( )K andEc lel

will be respectively

(a) ve, > 1, ve (b) ve, 1, ve (d) ve, > 1, +ve

84. Hydrogen bomb is based on the principle of

(a) artificial radioactivity(b) nuclear fusion(c) natural radioactivity(d) nuclear fission

85. An ionic compound has a unit cell consisting of

A ions at the corners of a cube andB ions on thecentres of the faces of the cube. The empirical

formula for this compound would be

(a) A B3 (b) AB3(c) A B2 (d) AB

86. The highest electrical conductivity of the

following aqueous solutions is of

(a) 0.1 M difluoroacetic acid(b) 0.1 M fluoroacetic acid(c) 0.1 M chloroacetic acid(d) 0.1 M acetic acid

87. Lattice energy of an ionic compound dependsupon

(a) charge on the ion and size of the ion(b) packing of ions only(c) size of the ion only(d) charge on the ion only

88. Consider an endothermic reaction X Y withthe activation energies Eb and Ef for thebackward and forward reactions respectively.In general

(a) there is no definite relation between EbandEf

(b) E Eb f=(c) E Eb f>(d) E Eb f H U (b) < H U(c) = H U (d) =H 0

92. The solubility product of a salt having general

formula MX2, in water is 4 1012 . The

concentration ofM2+ ions in the aqueoussolution of the salt is

(a) 4.0 10 M10 (b) 1.6 10 M 4(c) 1.0 10 M 4 (d) 2.0 10 M6

93. Benzene and toluene form nearly idealsolutions. At 20 C , the vapour pressure ofbenzene is 75 Torr and that of toluene is22 Torr. The partial vapour pressure ofbenzene at 20 C for a solution containing 78 gof benzene and 46 g of toluene in Torr is(a) 53.5 (b) 37.5

(c) 25 (d) 50

94. Which one of the following statements is nottrue about the effect of an increase intemperature on the distribution of molecularspeeds in a gas ?

(a) The area under the distribution curveremains the same as under the lowertemperature

(b) The distribution becomes broader

(c) The fraction of the molecules with themost probable speed increases

(d) The most probable speed increases95. For the reaction

2NO 2 NO + O2 2( ) ( ) ( ) g g ga

(Kc = 1.8 10 at 184 C)6

( = 0.00831 k J/(mol. K))RWhen Kp andKc are compared at 184C it isfound that

8


9/52

(a) whether Kp is greater than, less than orequal to Kc depends upon the total gaspressure

(b) K Kp c=(c) Kp is less thanKc

(d) Kp is greater thanKc96. The exothermic formation of ClF3 is

represented by the equation

Cl + 3 F 2 ClF ; 329 kJ2 2 3( ) ( ) ( ) g g g H ra = Which of the following will increase thequantity of ClF3 in an equilibrium mixture ofCl2, F2 and ClF3 ?

(a) Adding F2(b) Increasing the volume of the container(c) Removing Cl2(d) Increasing the temperature

97. Hydrogen ion concentration in mol/L in a

solution ofpH=5.4 will be

(a) 3.98 106 (b) 3.68 106(c) 3.88 106 (d) 3.98 108

98. A reaction involving two different reactants can

never be

(a) bimolecular reaction(b) second order reaction(c) first order reaction(d) unimolecular reaction

99. Two solutions of a substance (non electrolyte)are mixed in the following manner.480 mL of 1.5 M first solution +520 mL of1.2 M second solution.What is the molarity of the final mixture ?(a) 2.70 M (b) 1.344 M

(c) 1.50 M (d) 1.20 M

100. During the process of electrolytic refining ofcopper, some metals present as impurity settleas anode mud. These are

(a) Fe and Ni (b) Ag and Au

(c) Pb and Zn (d) Se and Ag

101. Electrolyte KCl KNO3 HCl NaOAc NaCl

(S cm2 mol )1 149.9 145.0 426.2 91.0 126.5

Calculate HOAc using appropriate molarconductances of the electrolytes listed above at

infinite dilution in H O2 at 25 C(a) 217.5 (b) 390.7(c) 552.7 (d) 517.2

102. If we consider that 1/6, in place of 1/12, massof carbon atom is taken to be the relativeatomic mass unit, the mass of one mole of asubstance will

(a) be a function of the molecular mass of thesubstance

(b) remain unchanged

(c) increase two fold(d) decrease twice

103. In a multi-electron atom, which of thefollowing orbitals described by the threequantum numbers will have the same energy inthe absence of magnetic and electric fields ?

(A) n l m= = =1 0 0, ,(B) n l m= = =2 0 0, ,(C) n l m= = =2 1 1, ,(D) n l m= = =3 2 1, ,(E) n l m= = =3 2 0, ,(a) (D) and (E) (b) (C) and (D)(c) (B) and (C) (d) (A) and (B)

104. Based on lattice energy and other considerations

which one of the following alkali metal chloridesis expected to have the highest melting point ?

(a) RbCl (b) KCl(c) NaCl (d) LiCl

105. A schematic plot ofln Keqversus inverse of

temperature for a reaction is shown below

The reaction must be(a) highly spontaneous at ordinary temperature(b) one with negligible enthalpy change(c) endothermic(d) exothermic

106. Heating mixture of Cu O2 and Cu S2 will give

(a) Cu SO2 3 (b) CuO + CuS(c) Cu + SO3 (d) Cu + SO2

107. The molecular shapes of SF , CF and XeF4 4 4 are

(a) different with 1, 0 and 2 lone pairs ofelectrons on the central atom, respectively

(b) different with 0, 1 and 2 lone pairs ofelectrons on the central atom, respectively

(c) the same with 1, 1 and 1 lone pair ofelectrons on the central atoms,respectively

(d) the same with 2, 0 and 1 lone pairs ofelectrons on the central atom, respectively

9

2.0

6.0

In Keq

3

1.5 10

3

2 1011/T(K )


10/52

108. The disperse phase in colloidal iron (III)hydroxide and colloidal gold is positively andnegatively charged, respectively. Which of thefollowing statements is not correct ?

(a) Coagulation in both sols can be broughtabout by electrophoresis

(b) Mixing the sols has no effect(c) Sodium sulphate solution causes

coagulation in both sols(d) Magnesium chloride solution coagulates,

the gold sol more readily than the iron (III)hydroxide sol.

109. The number of hydrogen atom(s) attached tophosphorus atom in hypophosphorous acid is

(a) three (b) one(c) two (d) zero

110. What is the conjugate base of OH ?

(a) O2 (b) O

(c) H O2 (d) O2111. Heating an aqueous solution of aluminium

chloride to dryness will give

(a) Al(OH)Cl2 (b) Al O2 3(c) Al Cl2 6 (d) AlCl3

112. The correct order of the thermal stability ofhydrogen halides (H )X is

(a) HI > HCl < HF > HBr(b) HCl < HF > HBr < HI(c) HF > HCl > HBr > HI(d) HI > HBr > HCl > HF

113. Calomel (Hg Cl )2 2 on reaction with ammoniumhydroxide gives

(a) HgO(b) Hg O2(c) NH HgHgCl2(d) HgNH Cl2

114. The number and type of bonds between twocarbon atoms in calcium carbide are

(a) two sigma, two pi

(b) two sigma, one pi

(c) one sigma, two pi

(d) one sigma, one pi

115. The oxidation state of chromium in the finalproduct formed by the reaction between KI andacidified potassium dichromate solution is

(a) +3 (b) +2(c) +6 (d) +4

116. In silicon dioxide

(a) there are double bonds between siliconand oxygen atoms

(b) silicon atom is bonded to two oxygenatoms

(c) each silicon atom is surrounded by twooxygen atoms and each oxygen atom isbounded to two silicon atoms

(d) each silicon atom is surrounded by fouroxygen atoms and each oxygen atom isbonded to two silicon atoms

117. The lanthanide contraction is responsible for

the fact that

(a) Zr and Zn have the same oxidation state(b) Zr and Hf have about the same radius(c) Zr and Nb have similar oxidation state(d) Zr and Y have about the same radius

118. The IUPAC name of the coordination compound

K [Fe(CN) ]3 6 is

(a) Tripotassium hexacyanoiron (II)(b) Potassium hexacyanoiron (II)(c) Potassium hexacyanoferrate (III)(d) Potassium hexacyanoferrate (II)

119. In which of the following arrangements the

order is not according to the property indicated

against it ?

(a) Li < Na < K < Rb : Increasing metallicradius

(b) I < Br < F < Cl : Increasing electron gainenthalpy (with negative sign)

(c) B < C < N < O : Increasing firstionisation enthalpy

(d) Al < Mg < Na < F :3+ 2+ + Increasing

ionic size

120. Of the following sets which one does notcontain isoelectronic species ?

(a) BO , CO , NO33

32

3

(b) SO , CO , NO32

32

3

(c) CN , N , C 2 22

(d) PO , SO , ClO43

42

4

121. 2-methylbutane on reacting with bromine inthe presence of sunlight gives mainly

(a) 1-bromo-3-methylbutane(b) 2-bromo-3-methylbutane(c) 2-bromo-2-methylbutane(d) 1-bromo-2-methylbutane

122. Which of the following compounds shows

optical isomerism ?(a) [Co(CN) ]6

3 (b) [Cr(C O ) ]2 4 33

(c) [ZnCl ]42 (d) [Cu(NH ) ]3 4

2+

123. Which one of the following cyano complexes

would exhibit the lowest value of paramagnetic

behaviour ?

10


11/52

(a) [Co(CN) ]63 (b) [Fe(CN) ]6

3

(c) [Mn(CN) ]63 (d) [Cr(CN) ]6

3

(Atomic no. Cr= 24,Mn= 25, Fe =26,Co =27)

124. The best reagent to convert pent-3-en-2-ol intopent-3-en-2-one is

(a) pyridinium chloro-chromate(b) chromic anhydride in glacial acetic acid(c) acidic dichromate(d) acidic permanganate

125. A photon of hard gamma radiation knocks a

proton out of1224Mg nucleus to form

(a) the isobar of1123Na

(b) the nuclide 1123Na

(c) the isobar of parent nucleus(d) the isotope of parent nucleus

126. Reaction of one molecule of HBr with one

molecule of 1, 3-butadiene at 40 C givespredominantly

(a) 1-bromo-2-butene under kineticallycontrolled conditions

(b) 3-bromobutene under thermodynamicallycontrolled conditions

(c) 1-bromo-2-butene underthermodynamically controlled conditions

(d) 3-bromobutene under kinetically controlledconditions

127. The decreasing order of nucleophilicity among

the nucleophiles

(A) CH C O

O

3

(B) CH O3

(C) CN

(D) H C S

O

O

O3

(a) (C), (B), (A), (D)

(b) (B), (C), (A), (D)

(c) (D), (C), (B), (A)

(d) (A), (B), (C), (D)

128. Tertiary alkyl halides are practically inert tosubstitution byS 2N mechanism because of

(a) steric hindrance (b) inductive effect

(c) instability (d) insolubility

129. In both DNA and RNA, heterocyclic base and

phosphate ester linkages are at

(a) C5 and C1 respectively of the sugar

molecule

(b) C1 and C5 respectively of the sugar

molecule(c) C2

and C5 respectively of the sugarmolecule

(d)C5 and C2 respectively of the sugar

molecule

130. Among the following acids which has thelowest pKa value ?

(a) CH CH COOH3 2 (b) (CH ) CHCOOH3 2(c) HCOOH (d) CH COOH3

131. Of the five isomeric hexanes, the isomer whichcan give two monochlorinated compounds is

(a) 2-methylpentane(b) 2, 2-dimethylbutane

(c) 2, 3-dimethylbutane(d) n-hexane

132. Alkyl halides react with dialkyl copper reagentsto give

(a) alkenyl halides(b) alkanes(c) alkyl copper halides(d) alkenes

133. Which one of the following methods is neithermeant for the synthesis nor for separation ofamines ?

(a) Curtius reaction

(b) Wurtz reaction

(c) Hofmann method(d) Hinsberg method

134. Which types of isomerism is shown by2, 3-dichlorobutane ?

(a) Structural (b) Geometric(c) Optical (d) Diastereo

135. Amongst the following the most basiccompound is

(a) p-nitroaniline (b) acetanilide(c) aniline (d) benzylamine

136. Acid catalyzed hydration of alkenes exceptethene leads to the formation of

(a) mixture of secondary and tertiary alcohols

(b) mixture of primary and secondary alcohols(c) secondary or tertiary alcohol(d) primary alcohol

137. Which of the following is fully fluorinatedpolymer ?

(a) PVC (b) Thiokol(c) Teflon (d) Neoprene

11


12/52

138. Elimination of bromine from 2-bromobutaneresults in the formation of

(a) predominantly 2-butyne(b) predominantly 1-butene(c) predominantly 2-butene(d) equimolar mixture of 1 and 2-butene

139. Equimolar solutions in the same solvent have

(a) different boiling and different freezingpoints

(b) same boiling and same freezing points(c) same freezing point but different boiling

point(d) same boiling point but different freezing

point

140. The reaction

R X R X C

O

Nu C

O

Nu

+

+s s

is fastest whenX is(a) OCOR (b) OC H2 5(c) NH2 (d) Cl

141. The structure of diborane (B H )2 6 contains

(a) four 2C-2e bonds and four 3C-2e bonds(b) two 2C-2e bonds and two 3C-3e bonds(c) two 2C-2e bonds and four 3C-2e bonds(d) four 2C-2ebonds and two3C-2e bonds

142. Which of the following statements in relationto the hydrogen atom is correct ?

(a) 3s, 3p and 3d orbitals all have the sameenergy

(b) 3s and 3p orbitals are of lower energy than3d orbital

(c) 3porbital is lower in energy than 3d orbital(d) 3s orbital is lower in energy than 3porbital

143. Which of the following factors may be regardedas the main cause of lanthanide contraction ?

(a) Greater shielding of 5d electron by 4felectrons

(b) Poorer shielding of 5d electron by 4felectrons

(c) Effective shielding of one of 4felectrons byanother in the sub-shell

(d) Poor shielding of one of 4f electron byanother in the sub-shell

144. The value of the spin only magnetic momentfor one of the following configurations is2.84 BM. The correct one is

(a) d5 (in strong ligand field)(b) d3 (in weak as well as in strong fields)(c) d4 (in weak ligand field)(d) d4 (in strong ligand field)

145. Reaction of cyclohexanone withdimethylamine in the presence of catalyticamount of an acid forms a compound. Waterduring the reaction is continuously removed.

The compound formed is generally known as(a) an amine (b) an imine(c) an enamine (d) a Schiffs base

146. p-cresol reacts with chloroform in alkalinemedium to give the compound A which addshydrogen cyanide to form, the compound B.The latter on acidic hydrolysis gives chiralcarboxylic acid. The structure of the carboxylicacid is

147. If the bond dissociation energies of XY X Y , and2 2 (all diatomic molecules) are inthe ratio of 1 : 1 : 0.5 and Hf for the formationofXYis 200 kJ mol1. The bond dissociationenergy ofX2 will be

(a) 400 kJ mol1 (b) 300 kJ mol1

(c) 200 kJ mol 1 (d) None of these

148. An amount of solid NH HS4 is placed in a flaskalready containing ammonia gas at a certaintemperature and 0.50 atm pressure.

Ammonium hydrogen sulphide decomposes toyield NH3 and H S2 gases in the flask. When thedecomposition reaction reaches equilibrium,the total pressure in the flask rises to 0.84 atm ?The equilibrium constant for NH HS4decomposition at this temperature is

(a) 0.11 (b) 0.17(c) 0.18 (d) 0.30

149. An organic compound having molecular mass60 is found to contain C = 20%, H = 6.67%and N = 46.67% while rest is oxygen. Onheating it gives NH3 alongwith a solid residue.The solid residue give violet colour withalkaline copper sulphate solution. Thecompound is

12

CH COOH2

CH3

(a)

OH

(b)

CH COOH2

CH3

OH

CH(OH)COOH

CH3

(c)

OH

CH(OH)COOH

CH3

(d)

OH


13/52

(a) CH CH CONH3 2 2 (b) (NH ) CO2 2(c) CH CONH3 2 (d) CH NCO3

150. t1 4/ can be taken as the time taken for the

concentration of a reactant to drop to 34 of its

initial value. If the rate constant for a first orderreaction is k, the t1 4/ can be written as

(a) 0.75/k (b) 0.69/k

(c) 0.29/k (d) 0.10/k

1. IfC is the mid point ofAB andP is any pointoutsideAB, then

(a) PA PB PC 0

+

+

=

(b) PA PB PC 0

+

+

=

2

(c) PA PB PC

+

=

(d) PA PB PC + = 22. LetP be the point (1, 0) and Q a point on the

locusy x2 8= . The locus of mid point ofPQ is(a) x y2 4 2 0 + = (b) x y2 4 2 0+ + =(c) y x2 4 2 0+ + = (d) y x2 4 2 0 + =

3. If in a frequency distribution, the Mean andMedian are 21 and 22 respectively, then itsMode is approximately

(a) 24.0 (b) 25.5(c) 20.5 (d) 22.0

4. LetR = {( , ),3 3 ( , ),6 6 ( , ),9 9 ( , ),12 12 ( , )6 12 ,( , ),3 9 ( , ), ( , )}3 12 3 6 be a relation on the setA = { , , , }3 6 9 12 . The relation is(a) reflexive and symmetric only(b) an equivalence relation

(c) reflexive only

(d) reflexive and transitive only

5. If A A I 2 + = O, then the inverse ofA is(a) I A (b) A I(c) A (d) A I+

6. If the cube roots of unity are 1 2, , , then theroots of the equation ( )x + =1 8 03 , are(a) + +1 1 2 1 2 2, , (b) 1 1 2 1 2 2, , (c) 1 1 1, ,

(d) + 1 1 2 1 22

, , 7. lim sec

n n n n n +

1 1 2 42

22 2

22

sec

+ +

. . . . secn

n22 1

equals

(a)12

1tan (b) tan 1

(c)12

1cosec (d)12

1sec

8. Area of the greatest rectangle that can be

inscribed in the ellipsex

a

y

b

2

2

2

21+ = is

(a) ab (b) ab

(c) ab (d) 2ab

9. The differential equation representing thefamily of curves y c x c2 2= +( ), where c > 0, isa parameter, is of order and degree as follows

(a) order 2, degree 2(b) order 1, degree 3(c) order 1, degree 1(d) order 1, degree 2

10. ABCis a triangle. Forces P Q R

, , acting along

I A IB IC , and respectively are in equilibrium,

where I is the incentre of ABC. Then

P Q R

: : is

(a) cos : cos : cos A B C

(b) cos : cos : cos A B C

2 2 2

(c) sin : sin : sin A B C

2 2 2

(d) sin : sin : sin A B C

11. If the coefficients ofr th, ( )r + 1 th and( )r + 2 thterms in the binomial expansion of( )1 + y m arein AP, then m and r satisfy the equation

(a) m m r r2 24 1 4 2 0 + + =( )(b) m m r r2 24 1 4 2 0 + + =( )(c) m m r r2 24 1 4 2 0 + + + =( )(d) m m r r2 24 1 4 2 0 + =( )

12. In a triangle PQR, =R 2

. If tanP2

and

tanQ

2

are the roots of

ax bx c a2 0 0+ + = , , then

(a) b a c= + (b) b c=(c) c a b= + (d) a b c= +

13

Mathematics


14/52

13. If the letters of the word SACHIN are arranged

in all possible ways and these words are written

out as in dictionary, then the word SACHIN

appears at serial number

(a) 602 (b) 603

(c) 600 (d) 601

14. The value of50 41

656

3C Cr

r+=

is

(a) 56 4C (b)56

3C

(c) 55 3C (d)55

4C

15. IfA =

1 01 1 andI

=

1 00 1 , then which one of

the following holds for all n 1, by the

principle of mathematical induction ?

(a) A A n I n n= + 2 11 ( )

(b) A n A n I n = + ( )1(c) A A n I n n= 2 11 ( )(d) A n A n I n = ( )1

16. If the coefficient ofx7 in axbx

211

1+

equals

the coefficient ofx7 in axbx

12

11

, then

a band satisfy the relation

(a) ab = 1 (b) ab

= 1

(c) a b+ = 1 (d) a b = 117. Let f B: ( , ) 1 1 , be a function defined by

f x xx

( ) tan= 1

221, then f is both one-one

and onto whenB is the interval

(a)

2 2

, (b)

2 2

,

(c) 02

,

(d) 02

,

18. Ifz z1 2and are two non-zero complex numbers

such that| | | | | | z z z z1 2 1 2+ = + , thenarg ( ) ( )z z1 2 arg is equal to

(a) 2

(b) 0

(c) (d)2

19. Ifwz

z i

= 1

3

and| |w = 1, thenz lies on

(a) a parabola (b) a straight line

(c) a circle (d) an ellipse

20. Ifa b c2 2 2 2+ + = and

f x

a x b x c x

a x b x c x

a x

( )

( ) ( )

( ) ( )

( )

=+ + ++ + +

+

1 1 1

1 1 1

1

2 2 2

2 2 2

2 ( )

,

1 12 2+ +b x c x then f x( ) is a polynomial of degree(a) 2 (b) 3(c) 0 (d) 1

21. The system of equations

x y z+ + = 1 x y z+ + = 1 x y z+ + = 1has no solution, if is(a) 1 (b) not 2(c) either 2or 1 (d) 2

22. The value ofa for which the sum of the squaresof the roots of the equation

x a x a2

2 1 0 =( ) assume the least valueis

(a) 2 (b) 3(c) 0 (d) 1

23. If the roots of the equation x bx c2 0 + = betwo consecutive integers, then b c2 4 equals(a) 1 (b) 2(c) 3 (d) 2

24. Suppose f x( ) is differentiable at x= 1 andlim ( )h h

f h

+ =0

11 5, then f ( )1 equals

(a) 6 (b) 5(c) 4 (d) 3

25. Let f be differentiable for all x. Iff( )1 2= and f x ( ) 2 forx[ , ]1 6 , then(a) f( )6 5= (b) f( )6 5 (b) I I3 4=(c) I I1 2> (d) I I2 1>

42. The area enclosed between the curve y x ee= +log ( )and the coordinate axes is(a) 4 (b) 3(c) 2 (d) 1

43. The parabolas y x x y 2 24 4= =and divide thesquare region bounded by the lines x= 4,y= 4and the coordinate axes. If S S S1 2 3, , arerespectively the areas of these parts numberedfrom top to bottom, then S S S1 2 3: : is

(a) 1 : 1 : 1 (b) 2 : 1 : 2(c) 1 : 2 : 3 (d) 1 : 2 : 1

44. If the plane 2 3 4 6 0ax ay az + + = passesthrough the mid point of the line joining thecentres of the spheres x y z x y z2 2 2 6 8 2 13+ + + = and x y z x y z2 2 2 10 4 2 8+ + + = , then a equals(a) 2 (b) 2(c) 1 (d) 1

45. The distance between the line

r i j k i j k = + + +2 2 3 4$ $ $ ($ $ $ ) and the

plane r i j k + + =($ $ $ )5 5 is

(a)103

(b)3

10

(c)10

3 3(d)

109

46. For any vector a

, the value of

( $) ( $) ( $ )a i a j a k + + 2 2 2 is equal to

(a) 4 a2

(b) 2a2

(c) a2

(d) 3a2

47.If non-zero numbers a b c, , are in HP, then thestraight line

x

a

y

b c+ + =1 0 always passes

through a fixed point. That point is

(a) 112

,

(b) ( , )1 2

(c) ( , ) 1 2 (d) ( , ) 1 2

48. If a vertex of a triangle is (1, 1) and the midpoints of two sides through this vertex are( , ) and ( , ) 1 2 3 2 , then the centroid of thetriangle is,

(a)13

73

,

(b) 173

,

(c)

13

73

, (d)

173

,

49. If the circles x y ax cy a2 2 2 0+ + + + = and x y ax dy 2 2 3 1 0+ + = intersect in twodistinct points P and Q, then the line5 0 x by a+ = passes throughP and Q for(a) exactly two values ofa(b) infinitely many values ofa(c) no value ofa(d) exactly one value ofa

50. A circle touches the x-axis and also touches thecircle with centre at (0, 3) and radius 2. Thelocus of the centre of the circle is

(a) a parabola (b) a hyperbola(c) a circle (d) an ellipse

51. If a circle passes through the point ( , )a b andcuts the circle x y p2 2 2+ = orthogonally, thenthe equation of the locus of its centre is

(a) 2 2 02 2 2ax by a b p+ + + =( )(b) x y ax by 2 2 2 3+ + =( )a b p2 2 2 0(c) 2 2 02 2 2ax by a b p+ + =( )(d) x y ax by 2 2 3 4+ + + =( )a b p2 2 2 0

52. An ellipse has OB as semi minor axis,FandFits foci and the angleFBF is a right angle. Then,the eccentricity of the ellipse is

(a) 1 3/ (b) 1 4/(c) 1 2/ (d) 1 2/

53. The locus of a pointP( , ) moving under thecondition that the line y x= + is a tangent

to the hyperbolax

a

y

b

2

2

2

21 = is

(a) a hyperbola (b) a parabola

(c) a circle (d) an ellipse

54. If the angle between the line x y z+ = = 1

11

22

2and the plane

2 4 0 x y z + + = is such that sin = 13.

The value ofis

(a) 43

(b)34

(c) 35

(d)53

16


17/52

55. The angle between the lines 2 3 x y z= = and6 4 x y z= = is(a) 30 (b) 45(c) 90

(d) 0

56. Let A and B be two events such thatP A B P A B( ) , ( ) = =1

614

and P A( ) = 14

,

where A stands for complement of event A.Then, eventsA andB are

(a) mutually exclusive and independent(b) independent but not equally likely(c) equally likely but not independent(d) equally likely and mutually exclusive

57. Three houses are available in a locality. Threepersons apply for the houses. Each applies forone house without consulting others. Theprobability that all the three apply for the same

house, is(a) 7/9 (b) 8/9(c) 1/9 (d) 2/9

58. A random variable X has poisson distributionwith mean 2. Then,P X( . )> 1 5 equals

(a)32e

(b) 132

e

(c) 0 (d)22e

59. Two points A Band move from rest along astraight line with constant acceleration f andf respectively. IfA takes m second more thanB and describes n unit more than B inacquiring the same speed, then

(a) ( ) f f n ff m = 12

2

(b)12

2( ) f f m ff n+ =

(c) ( ) f f m ff n+ = 2

(d) ( ) f f m ff n = 2

60. A lizard, at an initial distance of 21 cm behindan insect, moves from rest with an accelerationof 2 cm/s2 and pursues the insect which iscrawling uniformly along a straight line at aspeed of 20 cm/s. Then, the lizard will catchthe insect after

(a) 24 s (b) 21 s(c) 1 s (d) 20 s

61. The resultant R of two forces acting on aparticle is at right angles to one of them and itsmagnitude is one third of the other force. Theratio of larger force to smaller one is

(a) 3 2 2: (b) 3 2:

(c) 3 2: (d) 2 : 1

62. Let a i k b i j k

=

= + + $ $ , $ $ ( )$x x1 andc i j k

= + + + y x x y $ $ ( )$1 . Then, [ ]a b c

depends on(a) neitherxnory (b) bothxandy

(c) onlyx (d) onlyy

63. Let a b c, and be distinct non-negative

numbers. If the vectors a a c$ $ $ , $ $i j k i k + + + andc c b$ $ $i j k+ + lie in a plane, then c is(a) the harmonic mean ofa band

(b) equal to zero

(c) the arithmetic mean ofa band

(d) the geometric mean ofa band

64. If a b c

, , are non-coplanar vectors and isa real number, then

[ ( ) ] [ ] a b b c a b c b + = + 2

for

(a) exactly two values of(b) exactly three values of(c) no value of(d) exactly one value of

65. A Band are two like parallel forces. A couple ofmomentH lies in the plane ofA Band and iscontained with them. The resultant ofA Bandafter combining is displaced through adistance

(a)H

A B (b)H

A B2( )+

(c) HA B+ (d)

2HA B

66. The sum of the series

11

4 21

16 41

64 6+ + + +! ! ! K is

(a)e

e

+ 12

(b)e

e

12

(c)e

e

+ 1(d)

e

e

1

67. Let x x x n1 2, , . . . . . , be n observations such that x xi i

2 400 80= =and . Then, a possiblevalue ofn among the following is

(a) 12 (b) 9(c) 18 (d) 15

68. A particle is projected from a point O withvelocity u at an angle of 60 with thehorizontal. When it is moving in a direction atright angle to its direction atO, then its velocityis given by

17


18/52

(a)u

3(b)

23u

(c)u

2(d)

u

3

69. If both the roots of the quadratic equation x kx k k2 22 5 0 + + = are less than 5, thenk lies in the interval

(a) [4, 5] (b) ( , ) 4(c) ( , )6 (d) (5, 6]

70. If a a a an1 2 3, , , . . . . . , , K are in GP, then thedeterminant

=+ +

+ + +

+

log log log

log log log

log l

a a a

a a a

a

n n n

n n n

n

1 2

3 4 5

6 og loga an n+ +7 8

is equal to

(a) 2 (b) 4

(c) 0 (d) 1

71. A real valued function f x( ) satisfies thefunctional equation

f x y f x f y f a x f a y ( ) ( ) ( ) ( ) ( ) = +where a is a given constant and f( )0 1= , f a x ( )2 is equal to(a) f x( ) (b) f a f a x ( ) ( )+ (c) f x( ) (d) f x( )

72. If the equation

a x a x a x nn

nn+ + + =

1

11 0. . . . . ,

a n1 0 2 , , has a positive rootx= , then theequation

na x n a x ann

nn

+ + + =1 1

211 0( ) K has a

positive root, which is

(a) equal to

(b) greater than or equal to (c) smaller than (d) greater than

73. The value of + >

cos

,2

10

x

adx a

x, is

(a) 2 (b) a

(c)2

(d) a

74. The plane x y z+ =2 4 cuts the sphere x y z x z2 2 2 2 0+ + + = in a circle ofradius

(a) 2 (b) 2(c) 1 (d) 3

75. If the pair of lines ax a b xy by 2 22 0+ + + =( )lie along diameters of a circle and divide the

circle into four sectors such that the area of one

of the sectors is thrice the area of another

sector, then

(a) 3 2 32 2a ab b+ + = 0(b) 3 10 3 02 2a ab b+ + =(c) 3 2 32 2a ab b + = 0(d) 3 10 32 2a ab b + = 0

18


19/52

19

PHYSICS AND CHEMISTRY

1. (d) 2. (d) 3. (a) 4. (c) 5. (d) 6. (c) 7. (c) 8. (*)9. (d) 10. (c) 11. (d) 12. (a) 13. (b) 14. (d) 15. (d) 16. (a)

17. (c) 18. (d) 19. (b) 20. (c) 21. (a) 22. (b) 23. (a,d) 24. (c)25. (c) 26. (d) 27. (b) 28. (d) 29. (c) 30. (b) 31. (c) 32. (a)33. (c) 34. (c) 35. (a) 36. (b) 37. (d) 38. (a) 39. (b) 40. (a)41. (a) 42. (a) 43. (c) 44. (c) 45. (c) 46. (b) 47. (d) 48. (b)49. (b) 50. (b) 51. (d) 52. (d) 53. (a) 54. (a) 55. (a) 56. (d)57. (a) 58. (b) 59. (a) 60. (c) 61. (b) 62. (a) 63. (d) 64. (c)65. (c) 66. (b) 67. (c) 68. (c) 69. (a) 70. (c) 71. (a) 72. (d)73. (d) 74. (a) 75. (c) 76. (d) 77. (c) 78. (a) 79. (c) 80. (b)81. (c) 82. (d) 83. (d) 84. (b) 85. (b) 86. (a) 87. (d) 88. (d)89. (d) 90. (a) 91. (b) 92. (c) 93. (d) 94. (c) 95. (d) 96. (a)97. (a) 98. (d) 99. (b) 100. (b) 101. (b) 102. (b) 103. (a) 104. (c)

105. (d) 106. (d) 107. (a) 108. (b) 109. (c) 110. (a) 111. (b) 112. (c)113.

(d)114.

(c)115.

(a)116.

(d)117.

(b)118.

(c)119.

(c)120.

(b)121. (c) 122. (b) 123. (a) 124. (b) 125. (b) 126. (c) 127. (b) 128. (a)129. (a) 130. (c) 131. (c) 132. (b) 133. (b) 134. (c) 135. (d) 136. (c)137. (c) 138. (c) 139. (b) 140. (d) 141. (d) 142. (a) 143. (d) 144. (d)145. (c) 146. (c) 147. (d) 148. (a) 149. (b) 150. (c)

MATHEMATICS

1. (d) 2. (d) 3. (a) 4. (d) 5. (a) 6. (b) 7. (a) 8. (d)9. (b) 10. (b) 11. (b) 12. (c) 13. (d) 14. (a) 15. (d) 16. (a)

17. (a) 18. (b) 19. (b) 20. (a) 21. (d) 22. (d) 23. (a) 24. (b)25. (d) 26. (c) 27. (b) 28. (a) 29. (c) 30. (b) 31. (c) 32. (a,c)33. (b) 34. (d) 35. (b) 36. (d) 37. (c) 38. (a) 39. (a) 40. (a)41. (c) 42. (d) 43. (a) 44. (b) 45. (c) 46. (b) 47. (b) 48. (b)49. (c) 50. (a) 51. (a) 52. (d) 53. (a) 54. (d) 55. (c) 56. (b)

57. (c) 58. (b) 59. (a) 60. (b) 61. (a) 62. (a) 63. (d) 64. (c)65. (c) 66. (a) 67. (c) 68. (a) 69. (b) 70. (c) 71. (d) 72. (c)73. (c) 74. (c) 75. (a)

(*) No option is matching.

Answers


20/52


1. A projectile can have same range if angles ofprojection are complementary ie, and( )90 . Thus, in both cases

tu

g12= sin ...(i)

tu

g22 90= sin ( )

= 2ug

cos ...(ii)

From Eqs. (i) and (ii),

t tu

g1 2

2

2

4= sin cos

t tu

g

1 2

2

2

2 2= sin

= 2 22

g

u

g

sin

t t Rg1 22= =

R

u

g

2 2sin

Hence, t t R1 2 2. Since is constant,v would also be constant. So,

no net force or torque is acting on ring. The forceexperienced by any particle is only along radialdirection, or we can say the centripetal force.

The force experienced by inner part,F m R1

21= and the force experienced by outer

part,F m R22

2= F

F

R

R1

2

1

2

=

3. When friction is absent

a g1 = sin

s a t1 1 121

2= (i)

When friction is present

a g gk2 = sin cos

s a t2 2 221

2= (ii)

From Eqs. (i) and (ii), we have12

121 1

22 2

2a t a t=

or a t a nt1 12

2 12= ( ) (Qt nt2 1= )

or a n a12

2=

ora

a

g g

g n

k2

12

1= =sin cossin

org g

g n

ksin cossin

45 4545

12

=

or 1 12 =k n

or kn

= 1 12

4. According to work-energy theorem,

W K= = 0(Q Initial and final speeds are zero)

Work done by friction + work done by gravity= 0

+ =( cos ) sin mg l mgl2

0

or2

cos sin =

= 2tan5. According to work-energy theorem,W K=

Case I =

F m v mv3 12 2

12

02

02

where,Fis resistive force andv0 is initial speed.

20

O 90

u

u

v

R2 R1F

1

F2

Hints & Solutions

Physics


21/52


Case II Let, the further distance travelled bythe bullet before coming to rest iss.

+ = = F s K K mvf i( )312 0

2

or + = 18

3 120

202mv s mv( )

or14

3 1( )+ =s

or34 4

1+ =s

s = 1 cm6. I mr= 2

[ ] = [ML ]2Iand = moment of force =

r F

[ ] =

[L] [MLT ] = [ML T ]2 2 2

7. Given, t ax bx = +2

Differentiating w.r.t. tdt

dtax

dx

dtb

dx

dt= +2

vdx

dt ax b= = +

12( )

Again differentiating. w.r.t. t

d x

dt

a

ax b

dx

dt

2

2 2

2

2=

+( )

f d xdt

=2

2

= + +1

2

222( )

.( )ax b

a

ax b

orf

a

ax b=

+

2

2 3( )

f av= 2 3

8. The velocity time graph for the given situationcan be drawn as below. Magnitudes of slope ofOA f=

and slope ofBCf=2

v f tf

t= =1 22

t t2 12=In graph area ofOAD gives

distances, S f t= 1

2 1

2 ...(i)

Area of rectangle ABED gives distance travelledin time t.

S f t t2 1= ( )Distance travelled in time t 2

= =S f t3 121

2 22( )

Thus, S S S S1 2 3 15+ + =

S f t t f t S+ + =( )1 12 15

S f t t S S+ + =( )1 2 15 S ft=

12 1

2

( )f t t S1 12= ...(ii)

From Eqs. (i) and (ii), we have

12

12

1

1 1

S

S

f t t

f t t

= ( )

( )

t t1 6=

From Eq. (i), we get

S f t= 12 1

2( )

S f t f t=

=12 6

172

22

Hence, none of the given options is correct.

9. v i = +1 5$

v j2 5 = $

v v v j i

=

= 2 1 5 5^ ^

| | v

= 5 2

21

S

E

v1

v1

v2

v

N

W

x

y

O

C

A Bv

(m/s)

X

t (s)

Y

D Et1 t t2


22/52

at

=

= = | |v 5 210

1

2

2ms

For direction,

tan = = 55

1

Average acceleration is1

2ms2 towards

north-west.

10. Parachute bails out at height Hfrom ground.Velocity at A

v gh= 2

= 2 9 8 50.

= 980 m s/The velocity at groundv1 3= m s/ (given)

Acceleration = 2 m s2 / (given)

H h v v =

212

2 2

= 980 9

4 = =971

4242.75

H h242.75= + = + 242.75 50 293 m

11. In the frame of wedge, the force diagram ofblock is shown in figure. From free bodydiagram of wedge,

For block to remain stationary,

ma mgcos sin = a g= tan

12. According to conservation of energy,

mgH mv mgh= +12

22

or mg H h mv( ) =221

2

or v g= 2 100 20( )

v = 2 10 80 = 40 m/s

13. Since, the acceleration of centre of mass in boththe cases is same equal tog. So the centre ofmass of the bodiesB and Ctaken together doesnot shift compared to that of bodyA.

14. The mass of complete (circular) disc is

M M M + = 2The moment of inertia of disc about the given

axis is

IMr= 2

2

2

=Mr2

Let, the moment of inertia of semicircular discisI.The disc may be assumed as combination oftwo semicircular parts.

Thus,I I I 1 1=

I I Mr12

2 2= =

15. Given : m = 0 3. kg,x= 20 cm, andk = 15 N m/

F kx = ...(i)

and F ma= ...(ii) ma kx =

or a = 150 3

20 10 2.

a = =153

2 10 /m s

Initial acceleration a = 10 m s/ 2

22

ma cos N

mgsin

ma

mgcos+ ma sin mg

a

h =20 m2

h = 30 m1

H= 100 m

O

A

v= 2gh

Ground

h = 50m

H


23/52

16. Momentum would be maximum when KEwould be maximum and this is the case whentotal elastic PE is converted to KE.

According to conservation of energy12

12

2 2k L Mv=

k L MvM

22

= ( )

MkL p2 2= ( )p Mv= p L Mk=

17. Inx-direction

mu mvx1 0 0+ = + mv mvx= v vx =Iny-direction

0 03

+ =

m v mvy

vv

y =3

Velocity of second mass after collision

vv

v v =

+ =3

43

22 2

v v = 23

18. Water fills the tube entirely in gravity lesscondition.

19. Energy stored in wire

= 12

stress strain volume

and Youngs modulus = stressstrain

strain = SY

Energy stored in wireVolume

12

stress strai= n

= =12 2

2

SS

Y

S

Y

20. gGM

R=

2, M R=

43

3

g G RR

= 43

3

2

g G R=

43

( ) = average density g or g

21. F mamv

T= = =

av

T

0

Instantaneous power =Fv = mav

= = mvT

atmv

T

v

Tt

= mvT

t2

2

22. sv

gk= =

2

2100 100

2 0 5 10 .

= =100 100

5 21000 m

23. Statements (a) and (d) are wrong. Concept ofentropy is associated with second law ofthermodynamics.

24. For pure translatory motion, net torque aboutcentre of mass should be zero.

Thus, F

is applied at centre of mass of system.

OPm m l

m m= + +

1 2

1 2

0

where, m1 and m2 are masses of horizontal andvertical section of the object. Assuming object

is uniform,

m m OPl

2 1223

= =

PC l l l= +

23

=

=2 23

43

ll l

25. g gh

Rh=

12

(i)

g gd

Rd=

1 (ii)


gh

R g dR12

1 =

2 h d=

26. UGMm

ri=

Ui = 6 67 10 100 10

0 1

11 2..

23

C

P2l3

0,(

(0, 0)

(0, 2l)

Y

XlAfter collision

1 2Before collision

1 2

v/ 3mvx

vy


24/52

Ui = 6 67 100 1

11..

= 6 67 10 10. JWe know

W U= = U Uf i ( )Q Uf = 0 W Ui= =

6 67 10 10. J

27. C n C n C n nVV V= ++

1 2

1 2

1 2

For helium, n1164

4= = and 153

=

For oxygen, n21632

12

= = and 275

=

CR

V11 1

=

=

=R R53

1

32

CR R

RV22 1 7

51

52

= = =

CR R

V = +

+

4 32

12

52

412

.

=+6 5

492

R R

= =29 2

9 42918

R R

Now, CR

V = 1

=1 RCV

= + = +R

C

R

RV1 29

18

1

C

C

p

V

= +1829

1

= +18 2929

= 1 62.

28. I I e x =

= x II

log

=. log36 8II (i)

=x II

log2

(ii)


363

12

12

x =

log

log

x = 12 mm 29. E hg =

= =

h c

6.63 10 3 10

2480 10 1.6 10

34 8

9 19

= 0 5. eV

30. I

I

r

r

2

1

12

22

= ( )( )

asIr

12

II

2

1

2

2

1

12

=

( )

I I2 14= Now, since number of electrons emitted persecond is directly proportional to intensity, sonumber of electrons emitted by photocathode

would increase by a factor of 4.

31. N N e t= 0 1( )

N NN

e t0

0

=

18

= e t

8 = e t

3 2ln = t

= 3 0 69315

.

Half-life period

t1 20 693

3 0 69315/

..

=

t1 2 5/ = min

32. R R A= 0 1 3( )/

R

R

R A

R A

Al

Te

Al

Te

= 01 3

01 3

( )

( )

/

/

R

R

A

A

Al

Te

Al

Te

= ( )( )

/

/

1 3

1 3

24

3m = 1010 kg

M= 100 kg

R= 0.1 m


25/52

= =( )( )

/

/

27

125

35

1 3

1 3

RTe = 5

3

3 6.

RTe 6 fermi=33. According to the figure

Q T S T S T S1 0 0 0 0 0 0

1

2

3

2= + =

Q T S S T S2 0 0 0 0 02= =( ) Q3 0=

= WQ1

= Q QQ

1 2

1

= = 1 1 23

2

1

Q

Q

= 13

34. To measure the radial rate of heat flow, wehave to go for integration technique as here thearea of the surface through which heat willflow is not constant.

Let us consider an element (spherical shell) ofthickness dxand radiusxas shown in figure.Let us first find the equivalent thermal

resistance between inner and outer sphere.Resistance of shell = =

dR

dx

K x4 2

from where,

thermal conductivity

Rl

K A

K

=

dR R dxKxr

r

= =1

2

4 2

=

1

4

1 1

1 2K r r= r r

K r r

2 1

1 24 ( )Rate of heat flow =H

= T TR

1 2

= T T

r rK r r1 2

2 11 24 ( )

r r

r r1 2

2 1

35. The change in internal energy does not dependupon path followed by the process. It onlydepends on initial and final states.

Hence, U U1 2= .36. Here,y t= sin2

dy

dtt t t= = 2 2sin cos sin

d y

dtt

2

222 2= cos

For SHM, d ydt

y2

2

Hence, function is not SHM, but periodic.

From they- t graph, time period is

T =

38. Given :

y t1 0 1 100 3= +

. sin

dydt

v t1 1 0 1 100 100 3= = +

. cos

or v t1 10 100

3 2

= + +

sin

or v t1 10 10056

= +

sin

and y t2 0 1= . cos

dydt

v t t2 2 0 1 0 1= = = +. sin . sin ( )

25

x

T1

T2

r2

r1

dx

2T0

T0

S0 2S0S

1

2

3

y

O

2

3

4


26/52

Hence, phase difference

= 1 2

= + +100 56 t t( )

= 56 (at t = 0)

= 6

39. The situation is shown in figure.

sin C =1

tan CAB

AO=

AB OA C= tan

or ABOA=

2 1

=

12

43

12

= 36

7

40. We know

y

D d 1 22.

D y d1 22.

=

10 3 10

1 22 5 10

3 3

7.

= =306 1

5.

m

Dmax = 5 m

41. 1 1 1 1

1 2f R Ra=

( )

=

( . )1 5 11 1

1 2R R(i)

and1 1 1

1 2f R Rm

g m

m

=

1 1 5

1 61

1 1

1 2f R Rm=

.

.(ii)

Thus,f

f

m

a

=

= ( . )

..

1 5 1

1 51 6 1

8

f fm a= 8

= 8 15

( )Qfpa

= =1 15

m

= 1 6. m

Pfm m

= = = 1 61 6

1..

D

42. E Rhcn n

=

1 1

12

22

E Rhc( )4 3 2 21

3

1

4 =

=

=Rhc Rhc7

9 16 0 05.

E Rhc( )4 2 2 21

2

1

4 =

=

=Rhc Rhc316

0 2.

E Rhc( )( ) ( )

2 1 2 2

1

1

1

2 =

=

=Rhc Rhc34

0 75.

E Rhc( )( ) ( )

1 3 2 2

1

3

1

1 =

= = 89 0 9Rhc Rhc.

Thus, III transition gives most energy. I transitionrepresents the absorption of energy.

43. We know

= hmv

and K mvmv

m= =1

2 22

2( )

mv mK = 2

Thus, = hmK2

1

K

2

1

1

2

1

12= =

K

K

K

K(QK K2 12= )

12 1

2=

2 12

=

26

RA B

12 cm

O


27/52

44. In common base amplifier the input signal isamplified but remain in phase with outputsignal.

45. Given f = 50 Hz T = 150

For full wave rectifier TT

1 21

100= =

f1 100= Hz

46. ZAX n+ +0

137

24Li He

It implies that A + = +1 7 4 A = 10and Z+ = +0 3 2 Z= 5

Thus, it is boron 510 B.

47. Full scale de flection current

= =15010

15mA mA

Full scale deflection voltage

= =1502

75mV mV

Galvanometer resistance G = =75mV15mA

5

Required full scale deflection voltage,

V= =1 150 150 voltLet resistance to be connected in series isR.

V I R Gg= +( ) 150 15 10 53= + ( )R 10 54 = +R R = =10000 5 9995

48. We know m zq=

zq

1

zz

q

q2

1

1

2

=

Total charge q q q= +1 2

q

q

q

q2

1

21= +

qq

q

q

21

21

=+

qq

z

z

22

11

=+

49. The galvanometer shows zero deflection ie,current throughXYis zero

As a result potential drop acrossR is 2 V circuitcan be redrawn as

IR

= +12

500

Voltage across R V IR, =

2 12500

= + R R

1000 2 12 100+ = =R R R 50. R R R Req = + +1 2

I ER R R

= + +2

1 2

According to the question,

= ( )V V E I RA B 20 2= E I R

E I R= 2 E

E

R R RR= + +

2

1 22

R R R R1 2 22+ + = R R R= 2 1 51. E CV =

12

2 (i)

The energy stored in capacitor is lost in form ofheat energy.

H ms T = (ii)

27

R2V

12V

I

500

V

R GIgR1

A

R2

B

EE

R

500

R12V

2VG

X Y


28/52


ms T CV =

12

2

Vms T

C=2

52. Relative velocity = = =v v v dldt

( ) 2

Now, ed

dt=

eBldl

dt= dl

dtv=

2

Induced emf

e Blv= 2

53. HV

Rt1

2

=

HV

Rt2

2

2=

/

HH

2

12=

H H2 12= 54. The force per unit length between the two

wires is

F

l

i

d=

02

42

.

= 0

2

2i

d

The force will be attractive as currentdirections in both are same.

55. I I= 02cos

Intensity of polarized light

=I02

Intensity of untransmitted light

= =I I I0 0 02 256. Electric field due to a charged conducting sheet

of surface charge density is given byEo r

=

where, =0 permittivity in vacuum and rrelative permittivity of medium.

Here, electrostatic force onB

QEQ

o r

=

FBD ofB is shown in figure.In equilibrium, T mgcos =

and TQ

o r

sin =

Thus, tan = Q

mgo r

tan or tan

57. Suppose that a pointB, where net electric fieldis zero due to charges 8q and 2q.

E i

= BOq

a

14

8

02

$

E i

= ++

BAq

a L

14

2

02 ( )

$

According to condition E E

+

=BO BA 0

1

4

8 1

4

2

0

2

0

2

=

+

q

a

q

a L( )

2 1a a L

= +

2 2a L a+ = 2L a= Thus, at distance 2L from origin, net electricfield will be zero.

58. VA = potential due to charge + q on ring A+potential due to charge q on ringB

28

+

+

+

+

+

+

+

+

+

+

Tcos

B

Tsin

mg

F = QE

O

x = a x = 0 x = LA

2q

+ 8q

B

A B

R R

+q qd1d2


29/52

=

14 0 1

q

R

q

d, d R d1

2 2= +

=

+

1

4 0 2 2

q

R

q

R d

(i)

Similarly, Vq

R

q

R dB = + +

14 0 2 2

Potential difference V VA B

= +

1

41

40 2 2 0 q

R

q

R d

++

q

R

q

R d2 2

= + +1

41

41

40 0 0 2 2 q

R

q

R

q

R d

+1

4 0 2 2q

R d

= +

12 0 2 2

q

R

q

R d

59. Each plate is taking part in the formation of twocapacitors except the plates at the ends.

These capacitors are in parallel and n platesform (n 1) capacitors.Thus, equivalent capacitance between A Band = ( )n C1 .

60. The frequency of fork 2

= =200 4 196 204or HzSince, on attaching the tape on the prong offork 2, its frequency decreases, but now thenumber of beats per second is 6 ie, thefrequency difference now increases. It ispossible only when before attaching the tape,the frequency of fork 2 is less than thefrequency of tuning fork 1. Hence, the

frequency of fork 2 is 196 Hz.

61.d x

dtx

2

2= (i)

We know

ad x

dtx= =

2

22 (ii)


=2 =

or 2 T =

T = 2

62.

and T T1 2>

Hence, time period first increases and thendecreases to the original value.

63. Given : vv

o = 5 vo = =320

564 m/s

When observer moves towards the stationarysource, then

nv v

vno = +

n n = +

320 64320

n n =

384320

n

n

= 384

320Hence, percentage increase

n n

n

=

384 320320

100 %

=

64320

100 % = 20 %

29

A

B

Spherical hollow ballfilled with water

T= 2 lg

Spherical hollowball half filled with water

T = 21

l+lg

G

G

Sphericalhollow ball

T = 22 lg

l+l


30/52

64. I I=

0

2sin

and

=

ay

DFor principal maximumy= 0

= 0Hence, intensity will remain same.

65. BI

RP= 0 2

2

= =

4 10 4

2 0.024 10 Wb/ m

75 2

BI

RQ= 0 1

2

=

4 10 32 0 02

7. =

3 10 5 Wb m2/

B B BP Q= +2 2

= + ( ) ( )4 10 3 105 2 5 2

= 5 10 5 Wb/m2

66. The current at any instant is given by

I I e Rt L= 0 1( )/

I

I e Rt L0 021= ( )/

12

1= ( )/e Rt L

e Rt L =/ /1 2Rt

L= ln 2

tL

R= =

ln 2

300 10

2 0 693

3

.= 150 0 693 10 3.

= 0.10395 s 0.1 s=67. Given :L = 10 H, f = 50 Hz

For maximum power

X XC L=

1

= C L

CL

=

12

C=

14 50 50 102

C= =0 1 10 15. F F

68. IE

R r= +

IE

R= = constant

where,R = external resistance r = internal resistance = 0

69. Power factor

= =cos RZ

= =1215 45 = 0 8.

70. (i) In a circuit having Calone, the voltage lags

the current by2

.

(ii) In circuit containing R Land , the voltage

leads the current by2

.

(iii) InLCcircuit, the phase difference betweencurrent and voltage can have any value

between 0 to2

depending on the values of

L Cand .(iv) In a circuit containingL alone, the voltage

leads the current by

2.

71. When E

, v B

and are all along samedirection, then magnetic force experienced byelectron is zero while electric force is actingopposite to velocity of electron, so velocity ofelectron will decrease.

72. Magnetic force F q vB= (i)

Centripetal force

Fmv

r=

2

(ii)


mv

rqvB

2

=

30

2 V

L, R

v

l=3A1

P

BQ

Q

I= 4A2

B


31/52

rmv

qB=

The time taken by the particle to complete onerevolution,

Tr

v= 2

= 2 mvvqB

= 2 mqB

73. The internal resistance of the cell

rl l

lR=

1 2

2

= 240 120120

2 = 2

74. PV

R=

2

R V

Phot =

2

= 200 200100

= 400

Rcold =40010

= 4075. Magnetic needle is placed in non-uniform

magnetic field. It experiences force and torqueboth due to unequal forces acting on poles.

76. [Cr(NH ) Cl ]3 4 2+

Let oxidation state ofCr =x NH 03 =

Cl 1= Net charge 1= +

[ Cr(NH ) Cl ]3 4 2+

x+ + =+4 0 2 1 1( ) x= 3

77. Antipyretic drugs reduce fever. Analgesicrelieves in pain, antibiotics act against bacterial

infections while tranquilisers are used againstmental disorders.

78. A species is amphoteric if it is soluble in acid(behaves as a base) as well as in base (behavesas an acid).

SnO + 4HCl SnCl + 2H O2 4 2basic acid

SnO + 2NaOH Na SnO + H O2 2 3 2acid base

79. A species is said to be diamagnetic if it has allelectrons paired.

Species ElectronsMO

Electronicconfiguration

Magneticbehaviour

H2 3 1 12 1s s* Paramagnetic

H2+ 1 1 1s Paramagnetic

H2 2 12s Diamagnetic

He2+ 3 1 12 1s s* Paramagnetic

80. Na SO 2Na + SO2 4+

42

a

vant Hoff factor i y= + [ ( ) ]1 1 where yis the number of ions from one molesolute, (in this case = 3 ), the degree ofdissociation. i = +( )1 2

81. Nylon-66 is a polyamide of hexamethylenediamine (CH ) (NH )2 6 2 2 and adipic acid(CH ) (COOH)2 4 2.

(Each reactant has six-carbon chain hencetrade code (66) is used.)

82. Free radicals have unpaired electrons but areneutrals and are reactive.

CH + CH CH CH3 3 3 3

83. G RT K eq = 2.303 logG nFE = cell

If a cell reaction is spontaneous (proceeding inforward side), it means

Keq > 1 and Ecell ve = +

Thus G = ve

84. 4 H He 2 energy 11

24

10 + +e

It is the principal reaction of Hydrogen-bomb.

85. Unit cell consists ofA ions at the corners.Thus number of ions of the type

A = =88

1

Unit cell consists ofB ions at the centre of thesix faces.Thus number of ions of the type

31

Chemistry


32/52

B = =62

3

[Each corners is shared by 8 cubes and eachface is shared by 2 faces]

Thus formula isAB3.

86. Fluoro group causes negative inductive effectincreasing ionisation, thus 0.1 M difluoroaceticacid has highest electrical conductivity.

F C

F

H

C O

O

H

87. Greater the charge, smaller the radius, greaterthe polarising power and thus greater thecovalent nature. This leads to increase inlattice energy.

88. X Y is an endothermic reaction H= + ve

Eb = energy of activation of backward reactionEf = energy of activation of forward reactionH= heat of reactionThus E E H f b= + Thus E E

f b

>

89. Al Al3+ + 3e w zQ=

where w = amount of metal= = 5.12 kg 5.12 10 g3

z = electrochemical equivalent

Equivalent weight

96500

Atomic massElectrons

= = 96500

= 27

3 96500

5.12 103 = 27

3 96500Q

Q 5.12 10 3 96500

27 C

3

=

= 5.49 10 C7

90. Size of colloidal particles = 1 to 100 nm (say 10nm)

V rC =43

3 = 43

10 3( )

Size of true solution particles 1 nm

VS =43

1 3 ( )

Thus

V

V

C

S = 103

91. H U n RT g= +

H= enthalpy change (at constant pressure)U= internal energy change (at constant

volume) (given reaction is exothermic)ng = mole of (gaseous products gaseous

reactants) = ve

Thus H U< .

NOTE Numerical value of H U< in exothermicreaction and when ng < 0

92. MX M X S S

22 2

2a

+ +

K M X sp = + [ ][ ]2 2

If solubility be S then

K S Ssp = ( )( )22= 4 3S

4 4 103 12S =

S = 1 10 4 M M S2 41 10+ = = M

93. Mixture contains 78 g benzene = 1 mole benzeneand 46 g toluene = 0.5 mole tolueneTotal mole of benzene and toluene = 1.5 molMole fraction of benzene in mixture = =1

1 523.

VP of benzene pb = 75 Torr

Partial vapour pressure of benzene = p Xb b

= =75 23

50 Torr

94. Distribution of molecules (N) with velocity (u)at two temperatures T T1 2and ( )T T2 1> isshown below :

At both temperatures, distribution of moleculeswith increase in velocity first increases, reachesa maximum value and then decreases.

95. 2NO ( ) 2NO( ) O ( )2 2g g ga +Kc =

1.8 10 6 at 184 C ( 457 K) =

R 0.00831 kJ mol K1 1=

32

Energy

u

H

Eb

Ef

N

u

T1

T2


33/52

K K RT p cng= ( )

where, ng = (gaseous products gaseous reactants)

= =3 2 1 Kp =

1 8 10 0 00831 4576. .

= > 6 836 10 1 8 106 6. .Thus K Kp c>

96. Reaction is exothermic. By Le-Chatelierprinciple, a reaction is spontaneous in forwardside (in the direction of formation of more ClF3)ifF2 is added, temperature is lowered and ClF3is removed.

97. pH 5.4= [H ] 10 10 105.4 6 0.6+ = = Antilog of 0.6 is 4

[H ] 4 10 M6+

98. There are two different reactants (say

A Band ).

A B+ productThus it is a bimolecular reaction.

Ifdx

dtk A B= [ ][ ]

it is second-order reaction

Ifdx

dtk A

= [ ]

or = k B[ ]it is first order reaction.Molecularity is independent of rate, but is the

sum of the reacting substances thus it cannot beunimolecular reaction.

99. Total molarity = ++M V M V

V V1 1 2 2

1 2

= + +1.5 480 1.2 520

480 520

= 1.344 M100. During electrolysis, noble metals (inert metals)

like Ag,Au and Pt are not affected and separateas anode mud from the impure anode.

101. AcOH AcONa HCl NaCl = +

= + 91.0 426.2 126.5 = 3907.102. Remains unchanged.

103. (A) 1s (B) 2s

(C) 2p (D) 3d(E) 3dIn the absence of any field, 3d in (D) and (E)

will be of equal energy.

104. As we go down in the group, ionic characterincreases hence, melting point of halides shouldincrease but NaCl has the highest melting point(800C) due to its high lattice energy.

105. Variation ofKeq with temperature Tis given byvant Hoff equation.

logKH

RT

S

Req= +

2.303

A BSlope of the given line is + ve indicating thattermA is positive thus H is ve.Thus reaction is exothermic.

106. Following reaction takes place duringbessemerisation

2Cu O + Cu S 6Cu + SO2 2 2107.

Molecule StructureHybridisation

of centralatom

Lone pair

SF4 F S

F

F

F

sp d3 one

CF4 F C

F

F

F

sp3zero

XeF4F :Xe:

F

F

F

sp d3 2 two

108. Mixing the sols together can cause coagulationsince the charges are neutralised.

109. Hypophosphorus acid (H PO )3 2 is a monobasicacid and has only one ionisable H, two H-atomsare directly attached to phosphorus. Thus thecorrect statement is (c).

H P

O

H

O H

110. Conjugate base is formed by loss ofH+ .OH O + H 2 +

conjugatebase

O2 is the conjugate base ofOH.

33


34/52

111. Aqueous solution of AlCl3 is acidic due tohydrolysis.

AlCl + 3H O Al(OH) + 3HCl3 2 3aOn strongly heatingAl(OH)3 is converted into

Al O2 3

2Al(OH) Al O + 3H O3 2 3 2

112. In a group, G Xf( )H changes ve to + vedownwards.

HF( )g G = 273 .20 kJ mol1

HI( )g G 1.72 kJ mol1= +

Thus HF is thermally stable and HI not.Thus HF > HCl > HBr > HI

113. Hg Cl + 2NH HgNH Cl+ Hg + NH Cl2 2 3 2 4white black

114. CaC2 (Calcium carbide) is ionic.

CaC Ca +C22+

2

2

C CC2

2 has one and two bonds.

115. Cr O + 14H + 6I 2Cr + 7H O + 3I2 72 + 3+

2 2

Cr O2 72 is reduced to Cr3+ .

Thus final state of Cr is + 3.

116.

117. Lanthanide contraction, cancels almost exactlythe normal size increase on descending a groupof transition elements, thus Nb and Ta and, Zrand Hf have same covalent and ionic radii.

118. K [Fe(CN) ]3 6cation anion

Oxidation state of Fe in anion = + 3Thus it is potassium hexacyanoferrate (III).

119. (a) Metallic radii increase in a group from top

to bottom.

Thus Li < Na < K < Rb True

(b) Electron gain of enthalpy of Cl > F and

decreases along a group

Thus I < Br < F < Cl is true.(c) Ionisation enthalpy increases along a

period left to right but due to presence of

half-filled orbitals in N, ionisation enthalpy

of N > O.

Thus B < C < N < O is incorrect.

120.Species

Electron incentralelement

Electronsin otherelement

Chargegained

Total

BO33 5 3 8 24 = + 3 32

CO32 6 3 8 24 = + 2 32

NO3 7 3 8 24 = + 1 32

SO32 16 3 8 24 = + 2 42

CN 6 7 1 14

N2 7 7 0 14

C22 6 6 + 2 14

PO43 15 4 8 32 = + 3 50

SO42 16 4 8 32 = + 2 50

ClO4 17 4 8 32 = + 1 50

Thus (a) BO , CO , NO33

32

3 are isoelectronic.

(b) SO , CO , NO32

32

3 are not isoelectronic.

121. H C C

H

H

C

CH

H

CH3

3

3

Br3 2 3CH CH C

CH

Br

CH2

3

122.

Mirror image is not superimposable hence,optical isomerism is possible.

123. Hybridi-sation

Unpairedelectrons

Magneticmoment

(a) [Co(CN) ]63 d sp2 3 0 0

(b) [Fe(CN) ]63 d sp2 3 1 3 BM

(c) [Mn(CN) ]63 d sp2 3 2 8 BM

(d) [Cr(CN) ]63 d sp2 3 3 15 BM

Thus least paramagnetism is in (a).

34

|O|Si|O|

O O

|O|Si|O|

O

3 (CH) bond has minimum

bond energy hence easily cleaved

giving 2-bromo 2-methyl butane

C O2 4 Cr

C O2 4

C O2 4

3


35/52

124. CH CH

OH

CH==CH CH32

3

CH C||O

CH==CH CH3 3

Onlysuitable reagent is chromic anhydride in

glacial acetic acid. Other will also effect

(C ==C) bond.

125. 1224

11

1123Mg + H + Na

Thus nuclide of1123Na is formed.

126. CH == CHCH== CH + HBr2 2

CH CH|Br

CH==CH + CH CH==CHCH Br3 2 3 2

1,2-addition product 1, 4-addition product

Addition is through the formation of allylic

carbocation

CH ==CHCHCH CH CH==CHCH2 3 32 allylic

(more stable)( )

2

allylic(less stable)

( )1

Under mild conditions (temperature 80 C)kinetic product is the 1, 2-addition product and

under vigorous conditions (temp. 40 C)thermodynamic product is the 1, 4-addition

product.

Thus 1-bromo-2-butene is the major productunder given condition.

127. If acid is weak, its conjugate base (nucleophile)is strong andvice versa.

(A) CH C

O

O3

is a conjugate base of

CH COH(

O

I)3

(B) CH O3 is a conjugate base ofCH OH (II)3

(C) CN is a conjugate base of HCN (III)

(D) is a conjugate base

of

Acidic nature of IV > I > III > IIand nucleophilicity ofB C A D> > >

128. In S 2N reaction, nucleophile and alkyl halidereact in one step.

R

R

R

R

R R

+

C Br Nu Nu C Br. .. .. . . .. .. .

Thus tertiary carbon is under steric hindrancethus reaction does not take place until (CBr)bond breaks

R

R

R

R

R

C Br R C + Br

slow

which is then SN1 reaction.

129. Synthesis of RNA/DNA from phosphoric acid,ribose and cytosine is given below

Thus ester linkages are at C C5 1 and of sugarmolecule.

130. Out of the given acids, strongest is HCOOH.(highestKa value)

Since pK Ka a= logThus lowest pKa is of HCOOH.

131. (A) 2-methyl pentane Cl 2

five types of

monochlorinated compounds

(B) 2, 2-dimethylbutane Cl2

three types....

(C) 2, 3-dimethylbutane Cl2

two types .....

(D) n-hexaneCl2 three types .....

132. It is Corey House synthesis of alkanes.

133. Wurtz reaction is used to prepare alkanes fromalkyl halides :

2R X R R X + +2 2Na Nadryether

35

H C3

SO

3

H C3

SO H(IV)3

P

Dehydration

OHO

OH

HOCH2

HH

OH

H

OH

OOH

H

1

23

4

5N

N

O

NH2

H

2

345

6 1

2H O2

OH

P OO

OH

OH

CH2

HH

OH

H

OH

O

H

1'

2'3'

4'

5'

N

N

O

NH2

23

45

6 1


36/52

134. CH CH

Cl

CH

Cl

CH3* *

3

There are two chiral C-atoms (*)Thus optical isomerism is possible.

135. (a)

(b) CH CNH

O

3 2

CH C

O

3

group is also electron withdrawing.

(c) phenyl group is also electron

withdrawing.

(d) Benzyl is electron-repelling group increasesbasic nature.

Thus most basic compound is benzylamine.

136. CH CH CH CH OH2 2H O/H

3 2== +

2

CH CH CH CH CHCH

OH

3 2

H O/ H

3 3 ==

+2

(2 alcohol) through 2 carbocation CH CHCH3 3

CH C

CH

CH (CH ) COH3 2H O/ H

3 3 ==

+

3

2

(3 alcohol) through 3 carbocation (CH ) C3 3

CH CH

CH

CH CH3 2

==

3

CH C CH

CH

CH 3 alcohol3 2 32

carbocation

H O

3

3

Thus best alternate is (c).

137. Teflon is [CF CF ]2 2 n138. CH CH CHCH

|

Br

CH CH CHCH3 2 3 3 2 3 H +

CH CH CH==CH + CH CH==CHCH3 2 2 3 3less

IIsubstituted more

Isubstituted

Stability of I > II hence I is predominant.

139. Boiling point and freezing point depend on kb(molal elevation constant) and kf (molaldepression constant) of the solvent. Thusequimolar solution (of the non-electrolyte) willhave same boiling point and also same freezingpoint.

T kf f= molalityT kb b= molality

NOTE In question (139) set C, nature of solute hasnot been mentioned. Hence, we have assumed thatsolute is non-electrolyte.

140. R X R X

+

+ C

O

Nu C

O

Nu

Best leaving group (poorest nucleophile) isCl , thus fastest reaction is with Cl.

141. B H2 6 has structure

142. Hydrogen atom is in 1 1s and these3 3 3s p d, and orbitals will have same energy

wrt 1s orbital.

143. Lanthanide contraction is due to poor shieldingof one of 4f electron by another in thesub-shell.

144. (a) d5 in strong field

n = =unpaired electron 1

Magnetic moment BM= +n n( )2 = 3 BM = 1.73 BM

36

CH CH3

2 carbocation

CH CH3

+H O/H2

2 alcoholshift

1, 2 H

CH3

H O2

NO2

NH2

NO group (electron with2-drawing) decreases basicnature of aniline.

NH2

H

H

B

H

H

B

H

H

Bridging bonds(3C2e )

Terminalbond

2C2e

Bridging bonds(3C2e )

Boron electronHydrogen electron

Terminalbonds

(2C2e ) o

eg

t2g


37/52

(b) d3 in strong/weak field

n = 3Magnetic moment = 15 = 3.87 BM

(c) d4 in weak field

n = 4

Date post:	05-Apr-2018
Category:	Documents
Upload:	tina-dutta
View:	221 times
Download:	0 times

Aieee Question Paper 4

Documents