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[1] AIEEE 2011
1. Consider 5 independent Bernulli’s trails each with
probability of sucess p. If the probability of at least
one failure is greater than or equal to
31
32
, then p
lies in the interval
(1)
11
12
, 1 FH G
OQ P
(2)
1
2
3
4
, FH G
OQ P
(3)
3
4
11
12
, FH G
OQ P
(4) 0
1
2
, FH G
OQ P
Ans: [4]
2. The coefficient of x7 in the expansion of
(1 x x2 x3 )6 is
(1) 132 (2)144
(3) – 132 (4) – 144
Ans: [4]
3. lim
cos{ ( )}
x
x
x
F
H GG
I
K JJ
2
1 2 2
2
(1) equals
1
2
(2) does not exist
(3) equals 2 (4) equals 2
Ans: [2]
4. Let R be the set of real numbers
Statement -1
A {(x, y) R R : y x is an integer} is an
equivalence relation on R.
Statement -2
B {(x, y) R R : x y for some rational
number } is an equivalence relation on R.
(1) Statement -1 is false, Statement -2 is true
(2) Statement -1 is true, Statement -2 is true; Statement
-2 is a correct explanation for statement-1
(3) Statement-1 is true, Statement -2 is true, Statement-
2 is not correct explanation for Statement-1
(4) Statement -1 is true, Statement-2 is false
Ans: [4]
5. Let , be real and z be complex number. If
z2 z 0 has two distinct roots on the line
Re z 1, then it is necessary that
(1) (1, ) (2) (0, 1)
(3) (1, 0) (4) 1
Ans: [1]
6.
d x
dy
2
2 equal
(1) –
d y
dx
dy
dx
2
2
3 FH G
IK J
FH G
IK J
(2)
d y
dx
2
2
1 FH G
IK J
(3) –
d y
dx
dy
dx
2
2
1 3 FH G
IK J
FH G
IK J
(4)
d y
dx
dy
dx
2
2
2 FH G IK JFH GIK J
Ans: [1]
7. The number of values of k for which the linear
equations
4x ky 2z 0
kx 4y z 0
2x 2y z 0
possess a non-zero solutoin is
(1) zero (2) 3
(3) 2 (4) 1
Ans: [3]
8. Statement -1
The point A (1, 0, 7) is the mirror image of the
point B(1, 6, 3) in the line
x y z
1
1
2
2
3
Statement -2
The line
x y z
1
1
2
2
3
bisects the line
segment joining A (1, 0, 7) and B (1, 6, 3)
(1) Statement -1 is false, Statement -2 is true
(2) Statement -1 is true, Statement -2 is true; Statement
-2 is a correct explanation for statement-1
(3) Statement-1 is true, Statement -2 is true, Statement-
2 is not correct explanation for Statement-1
(4) Statement -1 is true, Statement-2 is false
Ans: [2]
Mathematics
[2] AIEEE 2011
9. Consider the following statements
P : Suman is brilliant
. Q : Suman is rich
R : Suman is honest
The negation of the statment “Suman is brilliant
and dishonest if and only if sumna is rich” can be
expressed as
(1) ~ (P ~ R)Q (2) ~ P (Q~ R)
(3) ~ (Q(P ~ R)) (4) ~ Q~ P R
Ans: [3]
10. The lines L y x 1 : 0 and L x y 2 : 2 0
intersect the line L y 3 : 2 0 at P and Q
respectivley. The bisector of the acute angle
between L1 and L2 intersects L3 at R.
Statement -1
The ratio PR : RQ equals 2 2 : 5 .
Statement -2
In any triangle, bisector an angle divides the trianle
into two similar triangles.
(1) Statement -1 is false, Statement -2 is true
(2) Statement -1 is true, Statement -2 is true; Statement
-2 is a correct explanation for statement-1
(3) Statement-1 is true, Statement -2 is true, Statement-
2 is not correct explanation for Statement-1
(4) Statement -1 is true, Statement-2 is false
Ans: [4]
11. A man saves Rs 200 in each of the first three months
of his services. In each of the subsequent months
his saving increases by Rs. 40 more than the saving
of immediately previous month. His total saving from
the start of service wil be Rs. 11040 after
(1) 21 months (2) 18 months
(3) 19 months (4) 20 months
Ans: [1]
12. Equations of the ellipse whose axes are the axes of
coordinates and which passes through the point
(3, 1) and has eccentricity 2
5 is
(1) 5×2 3y2 32 0 (2) 3×2 5y2 32 0
(3) 5×2 3y2 48 0 (4) 3×2 5y2 15 0
Ans: [2]
13. If A sin2 x cos4 x then for all real x.
(1)
3
4
13
16
A (2)
3
4
A 1
(3)
13
16
A 1 (4) 1 A 2
Ans: [2]
14. The value of
8 1
1 2
0
1
log( )
z x
x
dx is
(1) log2 (2) log2
(3)
8
log 2 (4)
2
log 2
Ans: [2]
15. If the angle between the line x
y z
1
2
3
and
the plane x 2y 3z 4 is cos FH G
IK J
1 5
14
(1) 5
3 (2) 2
3
(3) 3
2 (4) 2
5
Ans: [2]
16. For x FH G
IK J
0
5
2
,
, define
f x t
x
( ) z0
sint dt
Then f has
(1) local maximum at and local minimum at 2
(2) lcoal maximum at and 2
(3) lcoal minimum at and 2
(4) local minimum at and local maximum at 2
Ans: [1]
[3] AIEEE 2011
22. Let be the purchase value of an equaipment and
V (t) be the value after it has been used for t years.
The value V (t) depreciates at a rate given by
differential euqation
dV t
dt
k T t
( )
( ) , where
k 0 is a constant and T is the total life in years
of the equipment. Then the scrap value V(T) of the
equipment is
(1) ekT (2) T
k
2 1
(3) I
kT
2
2
(4) I
k T t
( )2
2
Ans: [3]
23. If C and D are two events such that C Dand
P(D) 0 , then the correct statement among the
following is
(1) P C D
P D
P C
( | )
( )
( )
(2) P(C|D) P(C)
(3) P(C|D) P(C) (4) P(C|D) P(C)
Ans: [3]
24. Let A and B be two symmetric matrices of order 3
Statement -1
A (BA) and (AB) A are symmetric matrices
Statement -2
AB is symmetric matrix if matrix multiplication of
A with B commutative.
(1) Statement -1 is false, Statement -2 is true
(2) Statement -1 is true, Statement -2 is true; Statement
-2 is a correct explanation for statement-1
(3) Statement-1 is true, Statement -2 is true, Statement-
2 is not correct explanation for Statement-1
(4) Statement -1 is true, Statement-2 is false
Ans: [3]
25. If ( 1) is a cube root of unity, and
(1)7 A B . Then (A, B) equals
(1) P C D
P D
P C
( | )
( )
( )
(2) P(C|D) P(C)
(3) P(C|D) P(C) (4) P(C|D) P(C)
Ans: [3]
17. The domain of the function
(1)
f x
x x
( )
1
is (2) (, ) {0}
(3) (0, ) (4) (, 0)
Ans: [4]
18. If the mean deviation about the median of the numbers
a, 2a, . . ., 50 a is 50, then a equals
(1) 5 (2) 2
(3) 3 (4) 4
Ans: [4]
19. If
ra
i k 1
10
e3$ $j and
rb
i j k 1
7
e2$ 3$ 6 $j , then
the value of 2 2
r r r r r r
a b a b a b LNM
OQP
e j e j e j is
(1) 3 (2) 5
(3) 3 (4) 5
Ans: [2]
20. The value of p and q for which the function
f x
p x x
x
q
x x x
x
x
x
x
( )
sin( ) sin
,
,
,
R
S
|||
T
|||
1
0
0
0
2
3
2
is continuous for all x in R, are,
(1) p q 1
2
3
2
, (2) p q 1
2
3
2
,
(3) p q 5
2
3
2
, (4) p q 3
2
1
2
,
Ans: [4]
21. The two circles x2 y2 ax and
x2 y2 c2 (c 0) touch each other if
(1) a 2c (2) 2 a c
(3) a c (4) a 2c
Ans: [3]
[4] AIEEE 2011
26 Statement -1
The number of ways of distributing 10 identical
balls in 4 distinct boxes such that no box is empty
is 9
3 C .
Statement -2
The number of ways of choosing any 3 places
from 9 different places is 9
3 C
(1) Statement -1 is false, Statement -2 is true
(2) Statement -1 is true, Statement -2 is true; Statement
-2 is a correct explanation for statement-1
(3) Statement-1 is true, Statement -2 is true, Statement-
2 is not correct explanation for Statement-1
(4) Statement -1 is true, Statement-2 is false
Ans: [3]
27 The shortest distance between line y x 1 and
curve x y2 is
(1)
4
3
(2)
3
4
(3)
3 2
8
(4)
8
3 2
Ans: [3]
28. The area of the region enclosed by trhe curves
y x, x e, y b1/ xg and the positive x-axis is
(1) 5/2 square units
(2) 1/2 square units
(3) 1 square units
(4) 3/21 square units
Ans: [4]
29. If
dy
dx
y 3 0 and yb0g 2, the ybln2g is equal
to:
(1) –2 (2) 7
(3) 5 (4) 13
Ans: [2]
30. The vectors a and
b are no perpendicular and c and
d are two vectors satisfying :
b c b d and
a d 0 . Then the vector
d is equal to:
(1)
c
a c
a b
b
FH G
IK J
(2)
b
b c
a b
c
FH GIK J
(3)
c
b c
a b
c
FH G
IK J
(4)
b
b c
a b
c
FH G
IK J
Ans: [1]
CHEMISTRY
[5] AIEEE 2011 / Code C
Part -B Chemistry
1. In context of the lanthanoids, which of the following
statements is not correct?
(1) Availability of 4f electrons results in the formation
of compounds in +4 state for all the members
of the series.
(2) There is a gardual decrease in the radii of the members
with increasing atomic number in the series.
(3) All the members exhibit +3 oxidation state.
(4) Because of similar properties the separation of
lanthanoids is not easy.
Ans: [1]
2. In a face centred cubic lattice, atom A occupies the
corner positions and atom B occupies the face centre
positions. If one atom of B is missing form one of the
face centred points, the formula of the compound is
(1) A2B5 (2) A2B
(3) AB2 (4) A2B3
Ans: [1]
3. The magnetic moment (spin only) of NiCl4
4 is
(1) 1.41BM (2) 1.82 BM
(3) 5.46 BM (4) 2.82 BM
Ans: [4]
4. Which of the following facts about the complex
Cr NH3 6 Cl3 b g is wrong?
(1) The complex gives which precipitate with silver
nitrate solution.
(2) The complex involves d2sp3 hybridisation and is
octahedral in shape.
(3) The complex is paramagnetic
(4) The complex is an outer orbital complex.
Ans: [4]
5. The rate of a chemical reaction doubles for every
10C rise of temperature. If the temperature is sraised
by 50C the rate of the reaction increases by aobut:
(1) 64 times (2) 10 times
(3) 24 times (4) 32 times
Ans: [4]
6. ‘a’ and ‘b’ are van der Waals’ constants for gases. Chlorine
is more easily liquefied than ethane because
(1) a for Cl2 a for C2H6 but b for Cl2 b for C2H6
(2) a and b for Cl2 a and b for C2H6
(3) a and b for Cl2 a and b for C2H6
(4) a for Cl2 a for C2H6 but b for Cl2 b for C2H6
Ans: [2]
7. The hybridisation of orbitals of N atom in NO3 NO2
,
and NH4
are respectively:
(1) sp2 , sp3, sp (2) sp, sp2 , sp3
(3) sp2 , sp, sp3 (4) sp, sp3, sp2
Ans: [3]
8. Ethylene glycol is used as an antifreeze in a cold climate.
Mass of ethylene glycol which should be added
to 4 kg of water to prevent it form freezing at 6C will
be: ( Kf foer water 1.86 K kg mol1 and molar mass
of ethylene glycol 62 g mol1 )
(1) 304.60 g (2) 804.32 g
(3) 204.30 g (4) 400.00 g
Ans: [2]
9. The outer electron configuration of Gd (Atomic No :
64) is
(1) 4f 7 5d1 6s2 (2) 4f 3 5d5 6s2
(3) 4f 8 5d0 6s2 (4) 4f 4 5d4 6s2
Ans: [1]
10. The structure of IF7 is
(1) pentagonal bipyramid
(2) square pyramid
(3) trigonal bipyramid
(4) octahedral
Ans: [1]
CHEMISTRY
[6] AIEEE 2011 / Code C
11. Ozonolysis of an organic compound gives
formaldehyde as one of the products. This confirms
the presence of:
(1) an acetylenic triple bond
(2) two ethylenic double bonds
(3) a vinyl group
(4) an isopropyl group
Ans: [3]
12. The degree of dissociation () of a weak electrolyte,
AxBy is related to van’t Hoff factor (i) by the expression:
(1)
x y
i
1
1
(2)
i
x y
1
b 1g
(3)
i
x y
1
1
(4)
x y
i
1
1
Ans: [2]
13. A gas absorbs a photon of 355 nm and emists at two
wavelengths. If one of the emissions is at 680 nm, the
other is at:
(1) 518 nm (2) 1035 nm
(3) 325 nm (4) 743 nm
Ans: [4]
14. Identify the compound that exhibits tautomerism.
(1) Phenol (2) 2-Butene
(3) Lactic acid (4) 2-Pentanone
Ans: [4]
15. The entropy change involved int he isothermal
reversible expansion of 2 moles of an ideal gas form a
volume of 10 dm3 to a volume of 100 dm3 at 27C is
(1) 42.3 J mol1 K1 (2) 38.3 J mol1 K1
(3) 35.8 J mol1 K1 (4) 32.3 J mol1 K1
Ans: [2]
16. Silver Mirror test is given by which one of the following
compounds?
(1) Benzophenone (2) Acetaldehyde
(3) Acetone (4) Formaldehyde
Ans: [2, 4]
17. Trichloroacetaldehyde was subjected to Cannizszaro’s
reaction by using NaOH . The mixture of the products
contains sodium trichloroacetate and another
compound. The other compound is:
(1) Chloroform (2) 2, 2, 2-Trichloroethanol
(3) Trichloromethanol (4) 2, 2, 2-Trichloropropanol
Ans: [2]
18. The reduction potential of hydrogen half cell will be
negative if:
(1) pbH2 g 2 atm and H 2.0 M
(2) pbH2 g 1 atm and H 2.0 M
(3) pbH2 g 1 atm and H 1.0 M
(4) pbH2 g 2 atm and H 1.0 M
Ans: [4]
19. Phenol is heated with a solution of mixture of KBr and
KBrO3 . The major product obtained in the above
reaction is:
(1) 2, 4, 6-Tribromophenol
(2) 2-Bromophenol
(3) 3-Bromophenol
(4) 4-Bromophenol
Ans: [1]
20. Among the following the maximum covalent character
is shown by the compound:
(1) MgCl2 (2) FeCl2
(3) SnCl2 (4) AlCl3
Ans: [4]
21. Boron cannot form which one of the following anions?
(1) BO2
(2) BF6
3
(3) BH4
(4) BbOHg4
Ans: [2]
CHEMISTRY
[7] AIEEE 2011 / Code C
22. Sodium ethoxide has reacted with ethanoyl chloride.
The compound that is produced in the above reaction
is
(1) Ethyl ethanoate (2) Diethyl ether
(3) 2-Butanone (4) Ethyl chloride
Ans: [1]
23. Which of the following reagents may be used to distinguish
between phenol and benzoic acid
(1) Neutral FeCl3 (2) Aqueous NaOH
(3) Tollen’s reagent (4) Molisch reagent
Ans: [1]
24. A vessel at 1000 K contains CO2 with a pressure of
0.5 atm. Some of the CO2 is converted into CO on the
addition of graphite. If the total pressure at equilibrium
is 0.8 atm the value of K is
(1) 0.18 atm (2) 1.8 atm
(3) 3 atm (4) 0.3 atm
Ans: [2]
25. The strongest acid amongst the following compounds
is
(1) ClCH2CH2CH2COOH
(2) CH3COOH
(3) HCOOH
(4) CH3CH2CH Cl CO2H b g
Ans: [4]
26. Which one of the following orders presents the correct
sequence of the increasing basic nature of the given
oxides?
(1) K2O Na2O Al2O3 MgO
(2) Al2O3 MgO Na2O K2O
(3) MgO K O Al O Na O 2 2 3 2
(4) MgO K O MgO Al O 2 2 3
Ans: [2]
27. A 5.2 molal aqueous solution of methyl alcohol,
CH3OH is supplied. What is the mole fraction of
methyl alcohol in the solution?
(1) 0.050 (2) 1.100
(3) 0.190 (4) 0.086
Ans: [4]
28. The presence or absence of hydroxy group on which
carbon atom of sugar differentiates RNA and DNA?
(1) 4th (2) 1st
(3) 2nd (4) 3rd
Ans: [3]
29. Which of the following statement is wrong?
(1) N2O4 has two resonance structures.
(2) The stability of hydrides increases form NH3 to
BiH3 in group 15 of the periodic table.
(3) Nitrogen cannot form d p bond.
(4) Single N– N bond is weaker than the single
P P bond.
Ans: [2]
30. Which of the following statements regarding sulphur
is incorrect?
(1) The oxidation state of sulphur is never less than +4
in its compounds.
(2) S2 molecular is paramagnetic
(3) The vapour at 200C consists mostly of S8 rings.
(4) At 600C the gas mainly consists of S2
Ans: [1]
[8] AIEEE 2011
PHYSICS
61. A Carnot engine operating between temperatures T1 and
T2 has efficiency
1
6
. When T2 is lowered by 62 K, its
efficiency increases to
1
3
. Then T1 and T2 are,
respectively:
(1) 310 K and 248 K (2) 372 K and 310 K
(3) 372 K and 330 K (4) 330 K and 268 K
Ans: (2)
62. A pulley of radius 2 m is rotated about its axis by a force
F e20t 5t 2 j newton (where t is measured in seconds)
applied tangentially. If the moment of inertia of the pulley
about is axis of rotationis 10kgm2 , the number of
rotations made by the pulley before its direction of motion
if reversed, is:
(1) more than 9
(2) less than 3
(3) more than 3 but less than 6
(4) more than 6 but less than 9
Ans: (3)
63. Three perfect gases at absolute temperatures T1,T2 and
T3 are mixed. The masses of molecules are m1,m2 and
m3 and the number of molecules are n1,n2 and n3
respectively. Assuming no loss of energy, the final
temperature of the mixtures is:
(1)
n T n T n T
n T n T n T
1
2
1
2
2
2
2
2
3
2
3
2
1 1 2 2 3 3
(2)
T1 T2 T3
3
b g
(3)
n T n T n T
n n n
1 1 2 2 3 3
1 2 3
(4)
n T n T n T
n T n T n T
1 1
2
2 2
2
3 3
2
1 1 2 2 3 3
Ans: (3)
64. A boat is moving due east in a region where the earth’s
magnetic field is 5.0105 NA1 m1 due north and
horizontal. The boat carries a vertical aerial 2 m long. If
the speed of the boat is 1.50ms1 , the magnitude of the
induced emf in the wire of aerial is:
(1) 0.15 mV (2) 1 mV
(3) 0.75 mV (4) 0.50 mV
Ans: (1)
65. A thin horizontal circular disc is rotating about a vertical
axis passing through its centre. An insect is at rest at a
point near the rim of the disc. The insect now moves along
a dimater of the disc to reach its other end. During the
journey of the insect, the angular speed of the the disc:
(1) first increases and then decreases
(2) remains unchanged
(3) continuously decreases
(4) continuously increases
Ans: (1)
66. Two identical charged spheres suspneded from a common
point by two massless strings of length are initially a
distance dbd g a part because of their mutual
repulsion. The charge begins to leak from both the spheres
at a constant rate. As a result the charges approach each
other with a velocity v. Then as a function of distance x
between them,
(1) v x (2) v x
1
2
(3) v x1 (4) v x
1
2
Ans: (2)
67. 100 g of water is heated fvrom 30 oC to 50 oC. Ignoring
the slight expansion of the water, the change in its internal
energy is (specific heat of water is 4184 J / kg / K):
(1) 2.1 kJ (2) 4.2 kJ
(3) 84 kJ (4) 8.4 kJ
Ans: (4)
68. The half life oa radioactive substance is 20 minutes. The
approximate time interval t2 t1 b g between the time t2
when
2
3
of it has decayed and time t1 when
1
3
of it had
decayed is
(1) 28 min (2) 7 min
(3) 14 min (4) 20 min
Ans: (4)
PART C — PHYSICS
[9] AIEEE 2011
PHYSICS
69. Energy required for the electron excitation in Li from
the first to the third Bohr orbit is:
(1) 122.4 eV (2) 12.1 eV
(3) 36.3 eV (4) 108.8 eV
Ans: (4)
70. The electrostatic potential inside a charged spherical ball
is given by ar2 b where r is the distance fromt he
centre ; a, b, are constants. Then the charge density inside
the ball is
(1) 6a 0 (2) 24 0 a r
(3) 6a 0r (4) 24 0 a
Ans: (1)
71. Work done in increasing the size of a soap bubble from a
radius of 3 cm to 5 cm is nearly (Surface tension of soap
solution 0.03Nm1 ):
(1) 0 4 . mJ (2) 4 mJ
(3) 0 2 . mJ (4) 2 mJ
Ans: (1)
72. A resistor ‘R’and 2 F capacitor in series is connected
through a switch to 200 V direct supply. Across the
capacitor is a neon bulb that lights up at 120 V. Calculate
the value of R to make the bulb light up 5 s after the
switch has been closed. blog10 2.5 0.4g
(1) 3.3107 (2) 1.3104
(3) 1.7 105 (4) 2.7 106
Ans: (4)
73. A current I flows in an infinitely long wire with cross
section in the form of a semicircular ring of radius R. The
magnitude of the magnetic induction along its axis is:
(1)
0
4
I
R
(2)
0
2
I
R
(3)
0
2 2
I
R
(4)
0
2
I
R
Ans: (2)
74. An object, moving with a speed of 6.25 m / s, is
decelerated at a rate given by
dv
dt
2.5 v
where v is the instantaneous speed. The time taken by the
object, to come to rest, woudl be:
(1) 8 s (2) 1 s
(3) 2 s (4) 4 s
Ans: (3)
75. Direction:
The question has paragraph fllowed by two statements,
Statement-1 and Statement-2. Of the given four
alternatives after the statements, choose the one that
describes the statements.
A thin air film is formed by putting the convex surface of
a plen-convex lens over a plane glass plate. With
monochromatic light, this film gives an interference
pattern due to light reflected from the top (convex) surface
and the bottom (glass plate) surface of the film.
Statement – 1:
When light reflects from the air-lgass plate interface, the
reflected wave surfers a phase change of .
Statement – 2:
The centre of the interference pattern is dark.
(1) Statement – 1 is flase, Statement – 2 is true.
(2) Statement – 1 is true, Statement – 2 is flase.
(3) Statement – 1 is true, Statement – 2 is true and
Statement – 2 is the correct explanation of Statement – 1
(4) Statement – 1 is true, Statement – 2 is true and
Statement – 2 is not the correct explantion of
Statement – 1.
Ans: (3)
76. Two bodies of masses m and 4m are placed at a distance
r. The gravitational potential at a point on the line joining
them where the gravitational field is zero is:
(1) 9Gm
r
(2) zero
(3) 4Gm
r
(4) 6Gm
r
Ans: (1)
[10] AIEEE 2011
PHYSICS
77. This equation has Statement – 1 and Statement – 2. Of the
four choices given afterthe statements, choose the one
that best decrribes the two statements.
Statement – 1:
Sky wave signals are used for long distance radio
communication. These signlas are in gneeral, less table
than ground wave signals.
Statement – 2:
The state of ionosphere varies from hour to hour, day to
day and season to season.
(1) Statement – 1 is flase, Statement – 2 is true.
(2) Statement – 1 is true, Statement – 2 is flase.
(3) Statement – 1 is true, Statement – 2 is true and
Statement – 2 is the correct explanation of Statement – 1
(4) Statement – 1 is true, Statement – 2 is true and
Statement – 2 is not the correct explantion of
Statement – 1.
Ans: (3)
78. A fully charged capacitor C with iniital charge q0 is
connected to a coil of self inductance L at t 0. The imt
at which the enrgy is stored equally between the electric
and the magnetic fiedls is:
(1) LC (2) LC
(3)
4
LC (4) 2 LC
Ans: (3)
79. This equation has Statement – 1 and Statement – 2. Of the
four choices given afterthe statements, choose the one
that best decrribes the two statements.
Statement – 1:
A metallic surface is irradiated by a monochromatic light
of frequency v v0 (the threshold frequency). The
maximum kinetic energy and the stopping potential are
Kmax and V0 respectively. If the frequency incident on
the surfaceis doubled, both the Kmax and V0 are also
doubled.
Statement – 2:
The maximum kinetic energy and the stopping potential
of photoelectrons emitted from a surface are linearly
dependent on the frequency of incident light.
(1) Statement – 1 is flase, Statement – 2 is true.
(2) Statement – 1 is true, Statement – 2 is flase.
(3) Statement – 1 is true, Statement – 2 is true and
Statement – 2 is the correct explanation of Statement – 1
(4) Statement – 1 is true, Statement – 2 is true and
Statement – 2 is not the correct explantion of
Statement – 1.
Ans: (1)
80. Water is flowing continuously from a tap having an
internal diameter 8 103 m. The water velocity as it
leaves the tap is 0.4ms1 . The dimaeter of the water
stream at a distance 2 101 m below the tap is close to:
(1) 3.6 103 m (2) 5.0103 m
(3) 7.5103 m (4) 9.6 103 m
Ans: (1)
81. A mass M, attached to a horizontal spring, executes SHM
with amplitude A1 . When the mass M passes through its
mean position then a smaller mass m is placed over it
and both of them move together with amplitude A2 . The
ratio of
A
A
1
2
FH G
IK J is:
(1)
M m
M
FH G
IK J
1
2
(2)
M
M m
(3)
M m
M
(4)
M
M m
FH G
IK J
1
2
Ans: (1)
82. Two particles are executing simple harmonic motion of
the same amplitude A and frequency along the axaxis.
Their mean positionis separated by distance
X0 X0 A b g . If the maximum separation between them
is X0 A b g , the phase difference between their motion
is
(1)
6
(2)
2
(3)
3
(4)
4
Ans: (3)
[11] AIEEE 2011
PHYSICS
83. If a wire is stretched to make it 0.1% longer, its resitance
will
(1) decrease by 0.05% (2) increase by 0.05%
(3) increase by 0.2% (4) decrease by 0.2%
Ans: (3)
84. A water fountain on the ground sprinkles water all around
it. If the speed of water coming out of the fountain is v,
the total area around the fountain that gets wet is:
(1) v
g
2
2 (2) v
g
2
(3) v
g
4
2 (4)
2
4
2
v
g
Ans: (3)
85. A thermally insulated vessel contains an ideal gas of
molecular mass M and ratio of specific heats . It is
moving with speed v and is suddenly brought to rest.
Assuming no heat is lost to the surroundings, its
temperature increases by:
(1)
1
2
2 b g
R
Mv K (2)
1
2 1
2 b g
b gR
Mv K
(3)
1
2
2 b g
R
Mv K (4)
Mv
R
K
2
2
Ans: (1)
86. A screw gauge gives the following reading when used to
measure the diameter of a wire
Main scale reading: 0 mm.
Circular scale reading: 52 dividison
Given tghat 1 mm on main scale corresponds to 100
dividions of the circular scale.
The dimater of wire from the above data is
(1) 0.005 cm (2) 0.52 cm
(3) 0.052 cm (4) 0.026 cm
Ans: (3)
87. A mass m hangs with the help of a string wrapped around
a pulley on a frictionless bearing. The pulley has mass m
and radius R. Assuming pulley to be a perfect uniform
ciruclar disc, the acceleration of the mass m, if the string
does not slip on the pulley, is
(1)
g
3
(2)
3
2
g
(3) g (4)
2
3
g
Ans: (4)
88. The transverse displacement ybx,tg of a wave on a string
is given by
y x t e
ax bt abxt
b , g e j 2 2 2
This represents a:
(1) standing wave of frequency
1
b
(2) wave moving in +x direction with speed
a
b
(3) wave moving in –x direction with speed
b
a
(4) standing wave of fcrequency b
Ans: (3)
89. A car is fitted with a convex side-view mirror of focal
length 20 cm. A second car 2.8 m behind the first car is
overtaking the first car at a relative speed of 15 m / s. The
speed of the image of the second car as seen in the mirror
of the first one is:
(1) 15 m / s (2)
1
10
m/ s
(3)
1
15
m/ s (4) 10 m / s
Ans: (3)
90. Let the x – z plane be the boundary between two
transparewnt media. Medium 1 in z 0 has a refractive
index of 2 and medium 2 with z < 0 has a refractive
index of 3. A ray of light in medium 1 given by the
vector A 6 3i 8 3 j 10k is incident on the plane
of separation. The angle of refraction in medium 2 is:
(1) 75o (2) 30o
(3) 45o (4) 60o
Ans: (3)