aieee question paper 4
TRANSCRIPT
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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
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AIEEE Solved Paper 2005
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
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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
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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
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(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
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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
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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
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(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 )
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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 ?
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(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
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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
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(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= +
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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
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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
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(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
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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
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AIEEE Solved Paper 2005
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
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AIEEE Solved Paper 2005
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
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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
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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)
From Eqs. (i) and (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
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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)
From Eqs. (i) and (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
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= =( )( )
/
/
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
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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
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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
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From Eqs. (i) and (ii), we have
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
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=
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)
From Eqs. (i) and (ii), we have
=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
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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)
From Eqs. (i) and (ii),
mv
rqvB
2
=
30
2 V
L, R
v
l=3A1
P
BQ
Q
I= 4A2
B
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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
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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
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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
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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
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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
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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
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(b) d3 in strong/weak field
n = 3Magnetic moment = 15 = 3.87 BM
(c) d4 in weak field
n = 4