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.J/_IP/E/E 2011
Set
IMPORTANT INSTRUCTIONS
1. Immediate ly fill in the particulars on this page of the Test Booklet with Blue/Black Ball Po
Pencil is strictly prohibited.
2.
3
•
.
The Test
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consists
of90
questions.
The
maximum
marks are
360.
5
response.
6. Candidates will
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awarded marks as stated b o v ~ insp;yp on No. for correct response of each
question % (one fourth) marks will
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No
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es
p ns is indicated for
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item in the answer sheet.
7.
8.
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n } o
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writing particulars/
marking
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No
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0. Rough
work
is to one on the space prov
ided
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only. This space is
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1:>
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in 3 pages (Pages 21 - 23) at the end of the booklet.
11. On w m le ·o of the test, the candidate must
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AIEEE 2011 2
P RT A PHYSICS
1. The transverse displacement
y x,
t) of a wave on a string is given by y
x,
t) =e
a
x
2
+bt
2
+
2
.fabxt) .
2.
3.
4.
5.
6.
7.
This represents a
1) wave moving in x direction with speed 2) standing wave of frequency .Jb
3)
standing wave of frequency tJ
A screw gauge gives the following reading when used to measure the diamete r of a
WI
Main scale reading : 0
mm
Circular scale reading : 52 divisions
Given that 1 mm on main scale corresponds to 100 divisions of the ci molar> scale
The diameter
of
wire from the above date is :
1) 0.052 em 2) 0.026 em 3) 0.005 em .52 em
A mass m hangs with the help of a string wrapped around a pu ley on a frictionless bearing. The pulley
has mass m and radius
R.
Assuming pulley to be a peri e Rif
or-
rn
circular disc, the acceleration
of
the
mass m, if the string does not slip on the pulley, is
1) g 2) ~ g 3) g
3 3
3
4)
g
2
Work done in increasing the size of a soa b bble
fr-o
m a radius
of
3 em to 5 em is nearly Surface
tension of soap solution= 0.03 Nm-
1
:
1)
0.
2n
mJ 2) 2n
mJ 4 n mJ
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 r isc. insect now moves along a diameter of the disc to reach its
other end. During the journey of
~ E f i e c t
the angular speed of the disc:
1) continuously decreases \) 2) continuously increases
3) first increases and the rq ecreases 4) remains unchanged
Two particles are executing simple harmonic motion of the same amplitude A and frequency w along the
x-axis. Their me s i t i o n is separated by distance X
0
(
X
0
> A) . If the maximum separation between
them
is
phase difference between their motion is :
2) 2: 3) 2: 4) 2:
4 6 2
The gravitational potential at a point on the
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AIEEE 2011 3
9. A boat is moving due east in a region where the earth's magnetic field is 5.0x10-
5
NA-
1
m-
1
due north and
horizontal. The boat carries a vertical aerial 2m long. If the speed of the boat is 1.50
ms-\
the
magnitude of the induced emf in the wire of aerial
is:
1)
0.75 mV
2)
0.50 mV
3)
0.15 mV
4)
1 mV
10.
An object, moving with a speed of 6.25 m/s, is decelerated at a rate given by :
dv
=
-2.5../V
dt
where v is the instantaneous speed.
1)
2
s 2)
4
s
11.
A fully charged capacitor
C
with initial charge q
0
is
connected to a coil of self
in
The
time at which the energy is stored equally between the electric and the agnetic field is :
1)
:...Jlc
2) 2n../Lc 3) JLc 4)
n.Jlc
4
12. Let the x - z plane
be
the boundary between two t r a n s p a r e r : ~ t Medium 1 in z
; >
0 has a refractive
index of J2 and medium 2 with z < 0 has a refractive irnQJex J j . A ray of light in medium 1 given by
13.
14.
15.
the vector
A=
6.J3i + s.J3]-1
k
The angle of refraction in
medium 2 is
(1) 45° (2) 60°
The magnitude of the magnetic inducti
(1) (2)
t
2n
2
R 2nR
(4) 30°
A thermally insulated vess san ideal gas of molecular mass
M
and ratio of specific heats y It is
moving with speed u an is eJ
i
eVI Iy brought to rest. Assuming
no
heat is lost to the surroundings, its
temperature increases b
},
.
1) y-
1
)Mu
2
(2) yMu
2
K 3) y-
1
)Mu
2
K 4) (y -
1
) Mu
2
K
2yR 2R
2R 2 y+1)R
)
112
(3) M
m
4)
_M_
M+m
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AIEEE 2011 4
17.
18.
19.
20.
21.
22.
23.
This question has Statement - 1 and Statement -
2. Of
the four choices given after the statements,
choose the one that best describes the two statements.
Statement 1 : Sky wave signals are used for long distance radio communication. These signals are in
general, less stable than ground wave signals.
Statement 2 :
The state
of
ionosphere varies from hour to hour, day to day and season to seas
aR
.
(1) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation
of
Stateme flt
1.
(2) Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation
of St
tem t-1.
(3) Statement-1 is false, Statement-2 is true.
(4) Statement-1 is true, Statement-2 is false.
Three perfect gases at absolute temperatures T
1
T
2
and T
3
are mixed. The
m
0 molecules are m
1
m
2
and m
3
and the number of molecules are n
1
n
2
and n
3
respectively. Assu rm ing no loss of energy, the
final temperature
of
the mixture
is
:
(1) n1
T1
+ n2T2+ n3T3 (2) n1
T1
+ n2 i + n3 (3)
n
1
n
2
n
3
n
1
T
1
n
2
T
2
n
3
T
3
n2T
2+ n2T2+ n2T2
1 1 2 2 3 _a
n
1
T
1
n
2
T
2
n
3
T
A resistor
'R'
and
2 ~ L F
capacitor
in
series is co necte through a switch to 200
V
direct supply. Across
the capacitor is a neon bulb that lights up 2{ : 1 20 Calculate the value of R to make the bulb light up 5 s
after the switch has been closed. (log
2.5 : .4
(1)
1.7x10
5
0
(2)
2.7x
0
6
[
(3)
3.3x10
7
0
(4)
1.3x10
4
0
. . 1
temperatures T
1
and T
2
has
eff1c1ency
. When T
2
is lowered by 62
6
K,
its efficiency increases t - . ifhen T
1
and T
2
are, respectively :
3
(1) 372
K
and
330
330
K
and 268
K
(3) 310
K
and 248
K 4)
372
K
and 310
K
(4) increases by 0.05%
Directio
t\_
n t ~ ~ o n
has a paragraph followed by two statements, Statement - 1 and statement -
2. Of
the
giv
eKJ
fout alternatives after the statements, choose the one that describes the statements.
A h1 air film
is
formed by putting the convex surface of a plane - convex lens over a plane glass plate.
W th monochromatic light, this film gives an interference pattern due to light reflected from the top
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AIEEE 2011 5
24. A car is fitted with a convex side-view mirror of focal length 20cm. A second car 2.8 m behi?d tbe first
car is overtaking the first car at relative speed of 15 m/s. The speed of the image of the second c
e.c.
as
seen
in
the mirror of the first one is : li;)
1 1
1)
15
m/s 2) 10m/s 3) 15m/s 4)
1 0
m s
25.
Energy required for the electron excitation in
Li++
from the first to the third Bohr
1)
36.3 eV
2)
108.8 eV
3)
122.4 eV
4)
1 .1 eV
26. The electrostatic potential inside a charged spherical ball
is
given by
~
a p
2
+b where r is the distance
from the centre;
a, bare
constants. Then the charge density inside ba I is
+
27.
1)
6ac
0
r
2)
24nac
0
r
3)
6ac
0
4
)
24nac
0
r
A water fountain on the ground sprinkles water
all
around it.
fountain is
V,
the total area around the fountain that gets wet
I
v n v ~ 2
1) 2) 3)
g2 2 g2 g2
v
4) -
g
28.
1
DOg
of water
is
heated from 30°C to
5 0 ° C
~
g
n
o r i n g
e
slight expansion of the water, the change
in
its
internal energy is specific heat of water is 1 1 48 kg/K):
1) 8.4 kJ 2) 84 kJ 3 2.1 kJ 4) 4.2 kJ
29.
The half life of a radioactive subs .ance 1s
2
minutes. The approximate time interval t
2
- t
1
between
30.
. 2 . . 1 . .
the t1me t
2
when
3
of
1t
has de
cay:
e . t1me t
1
and
3
of
1t
had decayed
IS :
1) 14 min O 3) 28 min 4) 7 min
This question
h a s
~
t a t e
~
and Statement - 2. Of the four choices given after the statements,
choose the one \ e s t
s c r i b e s
the two statements.
Statement 1 : et surface is irradiated by a monochromatic light of frequency v
>
v
0
the threshold
frequency)
e
~ ~
a
x
m
u m kinetic energy and the stopping potential are
Kmax
and V
0
respectively. If the
frequency incide
to
n the surface doubled, both the
Kmax
and V
0
are also doubled.
State ·e t 2
· The maximum kinetic energy and the stopping potential of photoelectrons emitted from a
~ e ~
a r l y dependent on the frequency of incident light.
1
t s1atement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1.
tatement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1.
0).;statement-1 is false, Statement-2
is
true.
~ Statement-1 is true, Statement-2 is false.
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AIEEE 2011 6
P RT B MATHEMATICS
31. The lines L
1
:
y -
x =0 and L
2
: 2x
+
y =0 intersect the line L
3
:
y
+
2 =0
32.
33.
bisector of the acute angle between L
1
and L
2
intersect L
3
at R .
Statement 1 The ratio
PR : RQ
equals 2../2 : /5
.
Statement
2 In any triangle, bisector of an angle divides the triangle into two
1)
Statement
1 is true, Statement 2 is true;
Statement
2 is not a correct e
xp
l
1
2) Statement 1 is true,
Statement
2 is false.
3)
Statement
1 is false,
Statement
2 is true.
4) Statement -1 is true , Statement 2 is true; Statement 2 is a co
r
ect xp la ation for Statement -1
If A = sin
2
x +cos
4
x , then for all real x
1) ~ A
:;
1 2) 1
:;
A :; 2
6
3
4 ) - < ; A :; 1
4
4) 144
34
_ l i m [ ~ 1 c o s { 2 x 2 }
x ~ 2
35.
1) equals J2
1
3) equals J2
4) does not exist
Statement 1 The numser
of
ways of distributing 10 identical balls in 4 distinct boxes such that no
ox is empty is
9
C
3
Statement - 1:: e number
of
ways
of
choosing any 3 places from
9
different places is
9
C
3
1) Statement 1 · · true,
Statement
2 is true; Statement 2 is not a correct explanation for Statement
1
Statement 1
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37.
If dy =
y+3
> 0 and y O) =
2,
then y ln2) is equal to
dx
1)5
2)13 3)-2 4) 7
38.
Let R
be
the set of real numbers
39.
40.
41.
42.
Statement 1 A= { x,
y)
ER x R:
y xis
an integer} is an equivalence relation on R.
Statement- 2 B = {
x,
y) E R
x
R : x =
y
for some rational number } is an equivalem e
r
lation on
R.
(1) Statement - 1 is true, Statement - 2 is true; Statement- 2 is not a correct explam ation for Statement
1
(2) Statement- 1 is true, Statement- 2 is false.
(3) Statement- 1 is false, Statement- 2 is true.
(4)
Statement
1 is
true , Statement- 2
is
true; Statement- 2
is
a cor
r:ect
expla
tA
ation for Statement
1
1
81og 1+x)
The value of
2
dx is
1
X
7I
(1) -log2
8
7I
(2) -log2
2
Let a be real and z be a complex number.
Rez = 1, then it is necessary that
(1)
~ E - 1 , 0 )
(2)
~ ~ ~ =
1)
( ·
~ ~ ]
z + = 0 has two distinct roots on the line
4 ) ~ E 0 , 1 )
If the probability of
at
least
4)
]
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45.
46.
47
48.
49.
50.
51.
52.
1 (
A A
If a
=
.J10 3i + k
and 5= 2 i +3}- 6k)
,
hen the value of 2a- 5).[ ax
5)x
a+ 25)] is
(1) -3
2)
5
3)
3
4)
-5
Equation of the ellipse whose axes are the axes of coordinates and which passes through the point
( -3, 1) and has eccentricity s
1) 5x
2
+ 3y
2
- 48
= 0 2) 3x
2
+ 5y
2
-15 = 0 3) 5x
2
+ 3y
2
-
32 = 0
Let
I
be
the purchase value of an equipment and
V t)
be
the value after it h s
s
use for t years.
dV t)
The value V t) depreciates at a rate given by differential equation
=
f) , where k > 0 is a
dt
and P D) 0, then the correct statement among the
following is
(3)
P
C I D)= P(D)
P(C)
(4)
P(CID)=P(C)
(4) 3
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54. If the mean deviation about the median of the numbers a, 2a, ... , 50a is 50, then l l equals
55.
1)3
2)4
3)5 4)2
Statement-
1 The point
A 1,
0,
7)
is the mirror image of the point
8 1,
6,
3)
in
the line
x y-1 z 2
1 2 3
Statement- 2 : The line:
~ =
Y -
1
= z
2
bisects the line segment joining A
1
0,
7)
B 6, 3) .
1 2 3 \
1)
Statement- 1 is true, Statement-2 is true; Statement-2 is not a correct explanation for S
atement-
1
2) Statement- 1 is true, Statement- 2 is false.
3) Statement- 1 is false, Statement- 2 is true.
4) Statement 1 is true, Statement- 2 is true; Statement- 2 is a correct explana t
56.
Let A and B
be tvvo
symmetric matrices of order
3.
~ f i l l
Statement-1 : A BA) and
AB)A
are symmetric matrices
( J
57.
58.
59.
Statement- 2 : AB is symmetric matrix if matrix multiplication of
n d
B is commutative.
1)
Statement - 1 is true, Statement - 2 is true; State me - 2 correct explanation for Statement
1
2)
Statement- 1 is true, Statement- 2 is false.
3) Statement- 1 is false, Statement- 2 is true.
4) Statement 1
is
true, Statement- 2
is
tr , , n t 2
is
a correct explanation for Statement 1
The value of p and q for
sin p
+
1)x
+ sinx
X
q
~ - J X
x3t2
X
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P RT C HEMISTRY
61. Among the following the maximum covalent character is shown by the compound :
1) SnCI
2
2) AICI
3
3) MgCI
2
4) FeCI
2
62. The presence or absence of hydroxyl group on which carbon atom of sugar differentiates RNA
?
1) 2nd 2)
3rd
3)
4th
(4) 1st
63. Trichloroacetaldehyde was subjected to Cannizzaro s reaction by using NaOH.
products contains sodium trichloroacetate and another compound. The other campo
1) Trichloromethanol 2)
2,
2, 2-Trichloropropanol
3)
Chloroform
4)
2, 2, 2-Trichloroethanol
64. Sodium ethoxide has reacted with ethanoyl chloride.
reaction is :
1) 2-Butanone 2) Ethyl chloride
65.
66.
67. The degree of dissociation
expression :
is related to van t Hoff factor i) by the
68.
69.
1) ex= i -1
X+y+1
3) ex= x+y+1
1 1
(4)
ex=
i-1
x+y-1)
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EEE 2011 11
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72.
73.
74.
75.
76.
77.
78.
79.
80.
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
from freezing at -6°C will be :
[Kr for water
=
1.86 K kg mol-
1
, and molar mass of ethylene glycol
=
62g mol -
1
1)
204.30g
2)
400.00 g
3)
304.60 g
4)
804.32g
Which one of the following order represents the correct sequence
of
the increasing basic natl:l e of the
given oxides ?
1)
MgO < Kp <
lp
3
< Nap
3)
K p
< Nap < lp
3
< MgO
2)
Nap <
Kp
< MgO < lp
3
4)
lp
3
< MgO
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83. Ozonolysis of an organic compound gives formaldehyde as one of the products.
presence of :
(1) a vinyl group (2) an isopropyl group
(3) an acetylenic triple bond (4) two ethylenic double bonds
84. A gas absorbs a photon of 355 nm and emits at two wavelengths.
680 nm, the other is at :
(1) 325
nm
(2) 7 43
nm
(3) 518 nm
85. Silver Mirror test is given by which one
of
the following compounds ?
(1) Acetone (2) Formaldehyde (3) Benzophenone
86. Which of the following reagents may be used to distinguish between p e
nol
a nd benzoic
acid?
(1) Tollen s reagent (2) Molisch reagent (3) Neutral Fe [; l
3
:
) Aqueous NaOH
reaction is
(1) 3-Bromophenol (2) 4-Bromophenol (4) 2-Bromophenol
88. In a face centred cubic lattice, atom A occupies the
c o
e positions and atom B occupies the face centre
positions. If one atom
of
B is missing from 0 e f the face centred points, the formula
of
the compound is
89.
90.
The entropy change involved in ~ isothe mal reversible expansion of 2 moles
of
an ideal gas from a
volume of 10 dm
3
to a volume of at 2JCC is:
(1) 35.8J
moi
1
K-
1
2 3J
1
n0i
1
K
1
(3) 42.3J moi-
1
K-
1
(4) 38.3J moi-
1
K
1
Identify the compound that exhibits tautomerism.
(1) Lactic 2-Pentanone (3) Phenol
(4) 2- Butene
I
EEE 2011 13
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RE D THE FOLLOWING INSTRUCTIONS C REFULLY
1. The candidates should flll in the required particulars
on
the
Test Booklet and
Answer
Sheet
(Side-1) with
Blue/Black. Ball Point Pen.
3.
The
candidates should
not
write
their
Roll Numbers anywhere else (except
in
the sp
Test
Bookle
t/
Answer Sheet.
4. Out
of
the
four
options given for
each
question, only one option is the correct
5
For
each
incorrect response, one-fourth
1
/
4)
of the total marks allotted o
from the total score.
No
deduction from the total score , however,
will
for an item in the Answer Sheet.
e question would
be
deducted
e i
no response
is indicated
6.
Handle
the Test
Booklet and
Answer
Sheet
with care, as
un
deEn E
x:ru
mstances (except for discrepancy
in
Test
Booklet
Code
and
Answer Sheet Code), will anotheu
et
e rovided.
7.
The
candidates are
not
allowed to
do
any rougfl w
ork
GP
writing
work
on
the Answer Sheet. All
calculations/writing
work
are to
be done in
th:_p>ac pr ,/ ded for this
purpose
in the Test
Booklet
itself,
marked Space for Rough Work .
This
space s · en a e bottom
of
each page
and
in 4 pages (Pages
20
-
23) at the
end of
the booklet.
8.
On
completion of the test, the candid ,es st hand over the Answer Sheet to the Invigilator on duty in the
U
o
wed
to
take
away
this
Test
Booklet
with them.
9.
11. The candidates should no leave the Examination Hall without
handing
over their Answer Sheet to the
lnvigilator
on
·u
an
d sign the Attendance
Sheet
again. Cases where a candidate has
not
signed the
Attendanc S e
et
a se c
ond
time will
be deemed
not to have
handed over
the Answer
Sheet and
dealt with
as an ur
ua · eans ease.
The
candidates are also required to
put their
lefthand
THUMB
impression in the
space pre
de
in the Attendance
Sheet
13.
Th
e candidates are gov
emed
by all Rules
and
Regulations
of
the
Board
with regard to their
conduct
in
the
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EEE 2011 15
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8. 4
Sol. At any instant of separation between charges is x.
9.
Sol.
10.
Sol.
11.
Sol.
12.
·1·b . d·t· K Q
X
equ1 1
num
con 1
1on
= ) 2 =
2
£
=:: Q2= x3
=:: 2Q dQ =
C3x
2dx
dt
dt
dx x
3 2
=::
- oc - oc x-1 /2
dt x
3
E =BH£V =
0.15mV
1
dv =
-2.5../V
dt
Integrating the
above
equation.
=::
2../V = -2.5t+C
at
t = 0 v = 6.
25
=::
C = 5
at
v = 0 =:: t = ~ = 2s
2.5
1
1
q2
U
2C
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14. 3
Sol. W
=
..
U
1
-mv
2
= nCvdT
2
15.
Sol.
16.
Sol.
m ~ d T
M
y-1
dT
=
M y
-1
)v2
K
2R
3
Energy of simple harmonic oscillator
is
constant.
1
2 2
1 )
2 2
=>-Moo A
1
= m+M o A
2
2 2
M+m
---;;;- M
2
~ M ~ m
3
Equation
of
continuity
::::> axv)top= a x v)bottom
v - 0.4)
2
=
2x9.8
x
0.2[v
2
u
2
= 2g
vb = 2m/s nearly)
n[8 x10-
3
Jx 0.4 = nd
2
x 4
d RO 3. 6 X 1o
3
m
17.
1
Sol. Since ionospheric roperties cF ange with time, these signals are in general less stable than ground wave
signals. +
18. 1
Sol.
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EEE
11
17
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20.
S
ol
21 .
Sol
e
t
4
>
e = - - -
on integrat
ion)
3
12
8 in 6s) = 36rad
>
2
nn = 36
36
n =
- =< 6
21t
2
v
c = E 1 - e -t/R
c )
1
_
e t/Rc = 1 20
=
200 5
5
>
R
=
6
=
2 .7 x 10
6
Q
1 .8
4
x 1o
-
4
_ T
1
- T
2
_ 1
11
1-
- T-
- 6
1
T
1
- (T
2
-
62)
1
1
1
2 =
= -
T
1
3
T
1
-
T
2
62 1
=>
+ -
= -
T T
1
3
1
6 1
- + -
= -
6 T
1
3
62 1
T
1
6
+
:
T1= 62 X
6 = 3
7 K
T
1
- T
2
1
T1
6
1- T2
T
6
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13.
Sol. As light enters from air to glass it suffers a phase change
on n
and therefore at centre there will be
destructive interference.
24.
Sol.
25.
Sol.
26.
Sol.
1
1 1 1
- - =
v u f
1 dv 1 du _
0
~ d t ~ d t
= - J
f =
20
em
1 1 1
=
u
280 20
280
= :> v = -c m
15
280
J
V
1
= - x15
15x
280
1
= - m / s
15
2
So charge density is constant
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28
.
Sol
29 .
Sol
30
.
So
l
1
t Q =
U
+
t
W (ignoring e
xpansion)
t U
=
m st-.T
= 0.1x 4.184 x
20 = 8.368k
J
2
t
1
= 2
0 minutes
2
N = N
0
e
- J
2
At
1
= ln3
2
-
-)
. 2
t -
1
-N
0
N
0
e
1
- ln 3
3
_N
- N
- ).
2
3
o - ae
1 3
t
2
=
- I n
2
t - t =
2 1 2
=
In [ ]= 0.6
93
2
= 2
0 m in
3
KE
x
= hu -
hu
0
hu - hu
0
= e x
6 v
V _ hu _ hu
0
0
-
e e
'u'
is
doubl
ed
K
Ema
x =
2hu -
huo
Va
= (
t-.v ) = 2
u
e
e
KE
may not
be equa l to 2
KE
j18X
v
-
0
ma
y not equal to
2
Va
KE m
ax =hu - hu o
V
=
hu
_ hu
0
e e
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EEE 2011 21
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36.
Sol:
37.
Sol:
38
.
Sol:
d d x )
d [ 1
] 1
d
dy
J
dy
dy dy
= -
dy
dx
d y
2
1 d d
y J 2y )
dyJ-
3
= - d x
J x
dx = - d
x
2
dx
dy
= ~
dx
d x
y + 3
ln
y
+ 3 )
= X + C
=
=
0
c =
ln5
ln
y + 3 ) = x + ln5
y + 3 = eX In5 ~
y + 3 =
ln +
1n5
y
3
= 1 0 ~
=
7
x - y is an
in teger
As sum
of t
wo i
teg
ers is
an
intege
r
.
~ x
- y )+ ..y- z
= x z is an
in teger
~
A is tra
ns
iti
ve
. H ence
sta tement-
1 is true
.
is sym
metric
A
lso ~
1 is a ration
a l number
B is reflex ive
X
~
=
a
is rat iona
l
Y
need
not be rat ion
a l
y
X
0
1
1 e , - 1
s rat1onal 1s
not rat1on
al
1
0
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EEE 2011 23
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42.
Sol:
43.
Sol:
44.
Sol:
45.
Sol:
1
200
Sum= 11040
2
200
3
200
4
240
120 + 80 + 160 + 40 + 200 + 240 + = 11 040
[2a
+ n-1)d +80+ 40 = 11040
[240+ n-1)40J 10920
n 6 + n
-1
J
= 546
n n+5)=546
n = 21
2
1
x
=>
x
x
>
0
=>
lxl
>
x
=>
x
is
negative
X E - , 0
4
4
5
280
6
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53. 1
Sol: P =
y
2
,
y)
54.
Sol:
IY2- Y 11
Perpendicular distance from P to
x
y
+
1 = 0 is
J2
y
2
y
+
1 > 0 Vy
E
R
:
Coefficient y
2
>
0
. 1 [
4ac-
b
2
] 3
:
M1n value = J2
4
a =
4
[2
2
1
~ ~ x i
-AI
A= Median=
25
a
+
26
a = 25.5a
2
Mean deviation = -
1
{Ia-
25.5al
+
l2a-
25.5al} = _3_{ 24.5a
50 50
2
= -{312.5a} =50
50
=:::) 625a = 2500 =:::) a = 4
Given)
55. 1
Sol:
1, 2,
3
I
• A 1 ,0, 7)
Statement - 1 is perpendicular to given line and mid point of AB lies on line
S t a t e
is true but it
is
not correct explanation as it is bisector only.
If it ·s
l?e
, u l a r bisector then only
statement-
2
is
correct explanation.
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P RT
C
HEMISTRY
61. (2)
Sol
: Greater
charge and small size of cation cause more polarization and
more
covalent is that
compound
62. (1)
Sol :
In RNA,
the sugar
is Ribose,
where
as
in DNA the
Sugar is
-D-2-deoxy Ribose
63. (4)
Sol
64.
Sol
65.
Sol
66.
Sol
67
(2)
2H +
2e-
---
H
2
(g)
E E -
o
osg
log
[[
:] )
(here E is - •
•
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68. (3)
Sol
ease of liquefaction
a
X
b
for ethane a = 5.49, b=0.0638
for Cl
2
a=
6.49, b = 0.0562
69. (4)
Sol : C
2
(g) + C §
101
2CO(g)
70.
Sol
Initial moles p 0
Equilibriumm moles p-x 2x
Total pressure at equilibrium = 0.8 atm ; Total no.of
moles=
p +
x.
Therefore p rx n ;
0
·
5
=
_P_ :::> x
=
0.3
0 8 p X
K = P = 0 6 x 0 6 =
1 8
atm
P Pco 0 2
2
71. 2)
Sol
: [
Cr NH
3
)
6
] Cl
3
72.
Sol
73.
Sol
•
86
X W
2
X 1000
4 x 62
a period metallic strength decreases down the group
it
increases
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75.
Sol
76.
Sol
77.
Sol
78.
Sol
(2)
In [NiCI
4
t, n = 2
.1
=
~ n ( n + 2) BM
=
~ 2
2
2)
=
2.82BM
(1)
(3)
The general o.s of lanthanides is +3, only few elements exhibit
+4
o.s.
(2)
m
Molefraction of solute
X
2
) in aqueous solution=
1
0
0
7
0
m --
18
79. (4)
Sol
:
3
as M-H bond energy decreases.
80. (3)
81. (3)
Sol
:
S
can exhibit a minimum oxidation st te
Ex. H
2
S)
82. (3)
Sol : In IF
7
, I undergoes sp
3
d
3
oy
83. 1)
Sol
: Vinyl group
( CH
2
t
H-
•
84.
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86.
Sol
87.
Sol
88.
Sol
89.
Sol
90.
Sol
(3)
Phenol gives violet coloured comlex compound with neutral FeCI
3
ppt. with neutral FeCI
3
(3)
In acidic medium, KBr +
KBr0
3
in turn produces Br
2
. Phenol reacts with Br
trinitrophenol
(3)
Effective no of A
atoms=
. .x 8 = 1
Effective
no.
of B
atoms=
~
5
One s
m1ss1ng =
J
2
~ ; e r e f o r e formula s
A,B; • A, B, t
For an ideal gas, for Isothermal reversible process, '
V
~ 8 = 2 . 3 0 3
nR
l o g ~
J
~ ~
= 2 3 0 3 2 x 8 3 1 4 x l o g
~
~ ~
= 38.3 J mol-
1
.k-
1
•