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SOLUTION & ANSWER FOR
VITEEE-2008 VERSION - P PART
– 1 [PHYSICS] 1. In nature,
the electric charge of any system is always– Ans: Quantisation
of charge Choice
(D) 2. The energy stored in the capacitor as shown
in
Fig.
(a) is 4.5 ´
10-
6 J. If the battery is replaced by –
Ans:
=
4.5 ´
10-
6 J
Choice (B) 3. Equal amounts of a metal are converted into
cylindrical
wires of different lengths (L) and cross-sectional –
Ans: R
=
Choice (C) 4. If the force exerted by an electric dipole
on a
charge
q at a distance of 1 m is F, the force–
Ans:
Choice (D) 5. A solid sphere of radius R
1 and
volume charge density r
=
Ans: Q
in
=
=
=
4p
R22s
Choice (C) 6. A solid spherical conductor of radius R has
a
spherical
cavity of radius a9a < R) at its centre. A charge +Q is kept at
the center.–
Choice (B) 7. A
cylindrical capacitor has charge Q and length L. If both –
Ans: U
1
=
U
2
=
Choice (B) 8. Three
resistances of 4 W
each are connected as shown in
figure. If the point D divides the resistance –
Choice (C) 9. The
resistance of a metal increases with increasing –
Ans: Vibration
of lattice ions increases with
temperature Choice (B) 10. In the absence
of applied potential, the electric current flowing through-
Ans: Thermal
velocity of electrons is in random
directions Choice (C) 11. A meter bridge
is used to determine the resistance of an unknown wire by measuring the balance
point length l. If the wire is
replaced by –
Ans: 12. Identify the
INCORRECT statement regarding –
Ans: Supercurrent
always flows on the surface
of
the superconductor Choice (B) 13. A sample of
HCl gas is placed in an electric field of 3 ´
104 NC-
1. The
dipole moment of each HCl molecule is –
Ans: t
= pE Choice (C) 14. When a
metallic plate swings between the –
Ans: Lenz’s
law Choice (C) 15. When an
electrical appliance is switched on, it responds almost-
Ans: Electromagnetic
waves travel with the
speed
of light Choice (B) 16. Two identical
incandescent light bulbs are connected as shown in the figure. When the circuit
is an AC voltage source–
Ans: At
resonance XL = XC Choice (B) 17. A transformer
rated at 10 kW is used to connect a 5 kV transmission line to a 240 V circuit.
The ratio –
Ans: n
=
Choice (B) 18. Three solenoid
coils of same dimension, same number of turns and same number of layers of
winding are taken. Coil 1 with inductance L1 was wound using a Mn
wire of resistance 11 W
/ m; –
Ans: Alternate
winding in opposite direction
total
flux = 0 Choice (C) 19. Light travels
with a speed of 2 ´
108 m/s in crown glass of
refractive index 1.5. What is the speed of light –
Ans: n
1v1
= n2v2 Choice (B) 20. A parallel
beam of fast moving electrons is incident normally on a narrow slit. A screen is
placed at a large distance from the slit.–
Ans: sinq
=
Choice (C) 21. Two beams of
light will not give rise to an –
Ans: Since
the polarization vectors are
perpendicular
their vector sum ¹
0 Choice (C) 22. A slit of
width `a’ is illuminated with a monochromatic light of wavelength l
from a
distant source and the diffraction pattern –
Ans: sinq
=
Choice (B) 23. A thin film of
soap solution (n = 1.4) lies on the top of a glass plate (n = 1.5). When
visible light is incident almost normal to the plate, two adjacent reflection –
Ans: n
1l
1 = n2l
2
2n
1
= 3n2
Þ
n1
= 3
d
=
Choice (B) 24. If the speed
of a wave doubles as it passes from shallow water into deeper water, –
Ans: c
= fl
Choice (C) 25. A light whose
frequency is equal to 6 ´
1014 Hz is incident on a
metal whose work function is
Ans: hu
= f
+ K.E Choice (C) 26. An electron
microscope is used to probe the atomic arrangements to a resolution of
Ans:
Choice (D) 27. Which phenomenon
best supports the theory that matter –
Ans: Electrons
behave also as waves of l
=
Choice (B) 28. The
radioactivity of a certain material drops to
Ans: Activity
changes from A0 to A0/16 implies 4 half-lives. Choice (C) 29. An observer
`A’ sees an asteroid with a radioactive element moving by at a speed = 0.3 c
and measures the radioactivity decay time to be TA. Another observer
`B’ –
Ans: Moving
clocks are slower TB < TA Choice (A) 30. 234U
has 92 protons and 234 nucleons total in its nucleus. It decays by emitting an
alpha –
Ans:
234U92
à
230Th90 + a
Choice (C) 31. Ka
and Kb
x-rays are emitted when there is a transition of
electron –
Ans: K
series end in n = 1 Choice (A) 32. A certain
radioactive material ZXA starts emitting a
and b
particles successively such that the end product –
Ans:
ZXA
à
Z-
3YA-
8 + 2a
+ 1b
Choice (B) 33. In the circuit
shown above, an input of 1 V is fed into the inverting input of an ideal Op-amp
A. The output signal –
Ans:
Choice (B) 34. When a solid
with a band gap has a donor level just below its empty energy band, -
Ans: Knowledge
based Choice (D) 35. A p – n
junction has acceptor impurity concentration of 1017 cm-
3 in the P
side and donor impurity concentration of 1016 cm-
3 in the N
side. What is the contact potential at the –
Ans: V
contact
=
Choice (A) 36. A zener diode
has a contact potential of 1 V in the absence of biasing. It undergoes zener
breakdown for an electric field of 106 V/m at the depletion region
of p-n junction. If the width –
Ans: V
= Ed Choice (B) 37. In Colpitt
oscillator the feedback network –
Ans: a-c
equivalent circuit. Choice (B) 38. The reverse
saturation of p-n diode
Ans: Knowledge
based Choice (D) 39. A radio
station has two channels. One is AM at 1020 kHz and the other FM at 89.5 MHz. –
Ans: Knowledge
based Choice (A) 40. The
communication using optical fibers is –
Ans: Optic
fibre uses T.I.R. Choice (A) PART – II [CHEMISTRY] 41. The
oxidation number of oxygen ¾
Ans: KO
3:
+ 1 + 3x = 0, x =
Na
2O2: + 2 + 2x
= 0, x = -
1 Choice
(D) 42. Reaction
of I
Cl3 and PhMgBr ¾
Ans: Triphenyl phosphene
3C
6H5MgBr + PCl3
®
(C6H5)3P + 3MgClBr Choice
(C) 43. …….
not a characteristic of transition elements?
Ans: Choice (D) 44. Cl
-
P -
Cl bond ¾
Ans: Arial
bonds are 90° and Equatorial bonds are 120°. Choice
(A) 45. --- magnetic
moment ¾
Ans: No
unpaired electron. Choice
(A) 46. The
number of Formula units of calcium fluoride CaF2 ¾
Ans: Number
of moles =
Number
of formula units =
´
1023
=
1.129 ´
1024 Choice
(A) 47. The IUPAC name
of the given ¾
Ans: Choice
(C) 48. When SCN‑
is added to an aqueous ¾
Ans: Fe
3+
+ SCN‑ + H2O ®
[Fe(H2O)5SCN]2+ Choice(B) 49. Hair dyes
contain
Ans: Choice
(C) 50. Schottky
defects occurs ¾
Ans: Schottky
defect occurs when the ions have almost the same size Choice
(B) 51. The number of
unpaired electron ¾
Ans: [Co(NH
3)6]3+
-
Inner orbital complex
-
No unpaired electron [CoF
6]3‑ -
Outer
orbital complex
-
4 unpaired electrons Choice
(D) 52. The standard free energy change of a reaction ¾
Ans: -
D
G° =
2.303 RT log Kp
0.02016 ´
103
= log Kp
= log K
p = 20.16 Choice
(A) 53. If an endothermic reaction occurs spontaneously at ¾
Ans: For
an endothermic reaction D
H is positive, the reaction occurs
spontaneously when D
S > 0 Choice
(C) 54. If a plot of log10 C versus t fives a straight line ¾
Ans: t =
t ´
logC
= logC0 -
t ´
logC
is t in a stline with slope
Choice
(B) 55. A spontaneous process is one in which ¾
Ans: For
a spontaneous process D
G is negative. Choice
(B) 56. The half life period of a first order reaction ¾
Ans: t
½ =
100 sec.
For a first order reaction t
½ =
K =
Choice
(B) 57. The molar conductivities of KCl, NaCl and KNO3
are ¾
Ans:
= 128 + 111 -
152 =
87 S cm2 mol‑1 Choice
(B) 58. The electrochemical cell stops working ¾
Ans: When
both the electrode potentials become equal cell reactions stops. Choice
(B) 59. The amount of electricity required to produce ¾
Ans: 1 mole of copper is 2 equivalents
Current required = 2 Faraday Choice
(C) 60. Dipping iron article into a strongly alkaline ¾
Ans: Choice (C) 61. Hydroboration
oxidation of 4-methyl-octene ¾
Ans: Hydroboration
– oxidation of alkenes give alcohols containing the same number of carbon
atoms. Net reaction involves addition of H2O against Markownikoff’s
rule. Choice
(A) 62. When
ethyl alcohol is heated
Ans: Ethanol
undergoes dehydration when heated with conc.H2SO4 to form
ethylene. Choice
(D) 63. Anisole
is the product obtained from ¾
Ans: Anisole is phenyl methyl ether. Choice
(B) 64. Ethylene
glycol gives oxalic acid ¾
Ans: Choice (C) 65. Diamond
is hard ¾
Ans: Choice (A) 66. A
Wittig reaction with an aldehyde ¾
Ans: Carbonyl
compounds react with phosphorous yields to form alkenes. This is known as
Witting reaction. Choice
(C) 67. Cannizzaro
reaction is ¾
Ans: HCHO
does not contain a
-hydrogen atom. So it undergoes
Cannizzaro reaction. Choice
(A) 68.
Ans: C
6H6 + CO
This is known
as Gattermann-Koch aldehyde synthesis. Choice
(C) 69. Maleic
acid and Fumaric acids ¾
Ans: Maleic acid is the cis-isomer and fumaric
acid is the trans-isomer. Choice
(B) 70. The
gas evolved on heating ¾
Ans: HCOONa + NaOH
H
2
+ Na2CO3. Choice
(C) 71. CH
3CH3
+ HNO3 ¾
Ans: Choice (B) 72. When
acetamide is hydrolysed by ¾
Ans: Choice (A) 73. Which
will not go for diazotization?
Ans: Choice (B) 74. Secondary
nitroalkanes can be ¾
Ans:
Choice(A) 75. ……….
Stephen reduction to ¾
Ans: Alkyl
cyanides on reduction with SnCl2 and HCl will give aldehyde. Choice
(A) 76. The
continuous phase contains ¾
Ans: Choice (C) 77. The
number of hydrogen atoms present in ¾
Ans:
Choice
(B) 78. Milk
changes after digestion ¾
Ans: Choice (C) 79. ………
essential amino acids?
Ans: Choice (B) 80. …..
is a Ketohexose? Ans: Choice (C) PART – III [MATHEMATICS] 81. The system of equations -
Ans:
= 1(1 -
3) -
2(1 -
2) = -
2 + 2 = 0
Choice (B) 82.
Ans:
A
4 = I
A3 = I
A-
1 A2 = I
A-
2
=
A-
1 =
=
A-
2 =
ab =
Þ
a2b2 = 1 Þ
ab = 1 Choice (D) 83. If D = diag (d1, d2,
…….., dn) where -
Ans: Choice
(D) 84. If x, y, z are different from zero and D
= -
Ans:
=
Choice (D) 85. Probability of
getting positive integral roots of the equation, -
Ans: x
= ±
n
= 1, 4, 9, 16, 25, 36
Probability
=
Choice
(C) 86. The number of real roots of equation -
Ans:
x
4 + 20 = (22 -
x4)2 = 484 + x
8 -
44x4 x
8 -
45x4
+ 464 = 0 x
4 =
=
= 29, 16 x
4 = 29 is not admissible
Þ
x4 = 16 Choice
(B) 87. Let a
, b
be the roots of the equation -
Ans: a
2-
aa
+ b = 0
A
n+1
-
aAn + bAn-
1
= a
n+1 + b
n+1-
a(a
n + b
n) + b(a
n-
1 + b
n-
1)
=
a
n-
1(a
2-
aa
+ b) + b
n-
1(b
2-
ab
+ b)
=
0
Choice
(C) 88. If the sides of a right – angle
triangle -
a =
sin B =
Choice (A) 89. The plane through the point -
Ans: x + 3y -
z = 0 y + 2z = 0 Let the plane be A(x + 1) + B(y + 1) + C(z + 1) = 0 Plane passes through the origin A + B + C = 0 Choice (A) 90.
Ans:
=
Area =
=
Choice (D) 91. If
Ans
:
=
=
cos q
2 =
cos q
1 = 0 Þ
q
1 =
Choice (C) 92. The equation
Ans: Equation is
x
2 + y2 + z2
-
2xc1 -
2yc2 -
2zc3
+ h = 0
Choice (D) 93. The simplified expression of -
Let tan-
1 x be a
Þ
tan a
= x
Then from the figure sin a
=
Þ
sin (tan-
1 x)
= sin
Choice (B) 94. If
Ans:
Þ
z lies
on the line perpendicular to the real axis and divides the line segment between
1 and 25 in the ratio 1 : 5 Þ
z = (5, 0) Þ
|z| = 5 Choice (C) 95. Argument of the complex number -
Ans:
= -
(1 + i)
\
Arg
Choice
(C) 96. In a triangle ABC, the sides b and c
are -
Ans: x
2 -
61x + 820 = 0
x
2 -
41x -
20x + 820 =
0
Þ
x1,2 = 41, 20
A = tan-
1
Þ
cosA =
\
By
Cosine formula, a
2
= b2 + c2 -
2bc cos A a
2
= 412 + 202 -
2(41)(20)
=
2081 -
984 = 1097 Choice
(C) 97. The shortest distance between the
straight lines through -
Ans:
\
Shortest distance =
=
=
Choice
(D) 98. The center and radius of the sphere -
Ans: Centre is at
Choice (C) 99. Let A and B are two fixed points in a
plane then locus of another -
Ans: Ellipse
Choice (B) 100. The directrix of the parabola -
Ans: y
2 = -
4x -
3
= -
4
Equation of the directrix is
Choice
(D) 101. If g(x) is a polynomial satisfying g(x) -
Ans: g(x) . g(y) = g(x) + g(y) + g(xy) -
2 ¾
(1)
g(2) . g(y) = g(x) + g(y) + g(xy) -
2 5.g(y) = 5 + g(y) +
g(xy) -
2
Þ
4g(y) =
3 + g(xy)
\
g(0) = 1 g(x) is given in a polynomial, and by the
relation given g(x) cannot be linear. Let g(x) = x2 + k Since g(0) = 1 Þ
g(x) = x2 + 1 Verifying (1) Þ
(x2 + 1) (y2 + 1) = x
2
+ 1 + y2 + 1 + x2y2 + 1 -
2 (1) is satisfied by
g(x) = x2 + 1
= 10 Choice
(B) 102. The value of f(0) so that -
Ans:
=
= 2
0n2 -
1 = l
n2 -
1
= f(0)
Choice (D) 103.
Let [ ] denote the greatest integer -
Ans :
f(x) is continuous at x = 0
Choice (B) 104. A spherical balloon is expanding -
Ans : Let r be
the radius and V be the volume
\
\
V =
= 4p
(5)2 ´
(2)
= 200 p
Choice
(C) 105. The
length of the parabola -
Length
=
=
=
=
=
=
=
=
= 2
-
=
=
=
=
=
Choice
(A) 106. If I
=
Ans :
I
=
Put
1 + x3 = t Þ
x2 dx =
\
I
=
=
=
=
Choice
(D) 107. Area
enclosed by the curve -
Ans :
Þ
\
Area of ellipse = p
ab
= p
´
= 4 Choice
(D) 108.The value of -
Ans
:
x = a sin2 q
dx = 2a sin q
cos q
dq
x = 0 ®
q
= 0
x = a ®
q
=
=
= 2a ´
Choice (C) 109.
Let y be the number of people -
Ans :
l
n y = -
kt + c
y = ce-
kt,
c > 0
k ³
0
Choice (B) 110.
The differential equation of -
Ans: x
cos q
+ y sin q
= a ¾
(1)
differentiating cos q
+ y’
sin q
= 0 ¾
(2)
Eliminating sin q
and cos
q
from (1) and (2)
cos q
=
sin q
=
sin
2
q
+ cos2 q
= 1
Þ
Þ
a2y’
+ a2 = (xy’ -
g)2
Þ
Choice
(B) 111. The
differential equation
Ans:
Three
positive quantities cannot add to give zero.
\
No
solution. Choice
(B) 112.
Solution of the differential equation xdy -
Ans :
which is homogeneous put y = vx
\
\
(1) Þ
\
x
|
is enclosed by a hollow sphere of 
= 450
. What should be the electric potential –
of the initial value in 2 hours. The half –
= 
=
= 9.91 
, then 
= 
= 0
= 22 
=
are one of the sides 
be three unit vectors such that 
g(x) = g(3) (
= 2
, |y| > 0 , 3 > 0
