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Roll No.:
Centre Code:
TEST No. 4
Test Date:
Test Booklet Code
JEE (Main) 2014
for
ALL
IND
IAAA
KASHTEST
SERIE
S
PAPER - I
INSTRUCTIONS FOR CANDIDATE1. Readeach question carefully.
2. It is mandatory to use Black Ball point PEN to darken theappropriate circle in the answer sheet.
3. Mark shouldbe dark andshould completely fill thecircle.
4. Rough work must notbe done on theanswer sheet.
5. Do not use white-fluid or any other rubbing material onanswer sheet.
6. Student cannot use log tables and calculators or any othermaterial in the examination hall.
7. Before attempting the question paper, student shouldensure that the test paper contains all pages and no pageis missing.
8. Before handing over the answer sheet to the invigilator,candidate should check that Roll No., Centre Code andDate of Birth havebeen filled and marked correctly.
9. Immediately after the prescribed examination time is over,the answersheetto be returned to theinvigilator.
There are parts in the question paper A, B and Cconsisting of , andhaving 30 questions in each part of equal weightage. Eachquestion is allotted 4 marks for each correctresponse.
three
Physics Chemistry Mathematics
(four)
10.
11. The Test booklet consists of 90 questions. The maximummarks are360.
12. One fourth () marks will be deducted for indicatingincorrect response of each question. No deduction fromthe total score will be made if no response is indicated foranyquestion in theanswer sheet.
13. Patternof the questions areas under:
Section I : Straight ObjectiveType Questions
Section II : Assertion ReasonType Questions
2 9 / 1 2 / 2 0 1 3
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TOPICS OF THE TEST
Test No. 4
Physics Waves, Kinetic Theory, Thermodynamics, Thermal Properties of Matter
Chemistry Hydrogen, The s-Block Elements, The p-Block Elements (Group-13 to
Group-18)
Mathematics Straight Lines, Conic Sections, Linear Inequalities, Mathematical Reasoning
Paper I
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PART - A (PHYSICS)
SECTION - IStraight Objective Type Questions
This section contains 25 multiple choice questions
numbered 1 to 25. Each question has 4 choices (1), (2),
(3) and (4), out of which ONLY ONE is correct.
Choose the correct answer :
1. Wavelength of a sound wave of frequency 707 Hz,
travelling inside water is (Bulk modulus of water =
2 109Pa)
(1) 1 m (2) 2 m
(3) 3.5 m (4) 7 m
2. Equation of a transverse wave travelling in a medium
is given by y= 10 sin (200 t 0.01 x). Where yand
x are expressed in cm and time in second. The
maximum transverse speed and maximum transverse
acceleration of a particle in the medium are
(1) 20 cm/s, 80 cm/s2 respectively
(2) 10 cm/s, 40 cm/s2 respectively
(3) 10 cm/s, 80 cm/s2 respectively
(4) 20 cm/s, 40 cm/s2 respectively
3. Figure shows a transverse travelling wave that
propagates with 100 m/s i . Velocity of point P
shown in figure is
j
i37
P
TEST - 4 (Paper-1)Time : 3 Hrs. MM : 360
(1) 75 m/s j (2) 75 m/s j
(3) 50 m/s j (4) 50 m/s j
4. Molar heat capacity at constant volume of an ideal
gas is 2R. Slope of (PVgraph) will be
(1) 2P (2) 2P
(3)3
2P (4)
3
2 P
5. In a stationary wave pattern that forms as a result of
reflection of waves from an obstacle, the ratio of the
amplitude at an antinode and a node is 4 : 1.Percentage of energy of wave passes across the
obstacle is
(1) 96% (2) 32%
(3) 48% (4) 64%
6. A standing wave is formed by two harmonic waves,
y1= a sin(bx ct) and y2= a sin(bx+ ct) travelling
on a string in opposite directions. Linear mass
density of the string is . Total mechanical energy
between two consecutive nodes on the string is
(1)
2 2
a cb
(2)2 2a c
b
(3)2 2a b
c
(4)2 2b c
a
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7. A sound absorber is fitted at a window of area
3 m2 which opens in a busy street. If the street
noise results an intensity level of 60 dB at the
window, amount of energy from street collected by
the sound absorber per second would be
(1) 2 J (2) 0.180 J
(3) 3 J (4) 0.10 J
8. A fighter jet moving in a vertical circle with constant
speed of radius R. The centre of the circle is at a
height h = 2R directly overhead of an observer
standing on the ground. The oiserver receives
maximum frequency of sound produced by the plane
when it is nearest to him. If speed of sound in air is
v0, speed of fighter jet is
(1) 03
v
(2) 03 3
v
(3) 02v (4)
0
3v
9. Two tuning forks with natural frequencies 170 Hz
each move relative to a stationary observer. One fork
moves away from the observer while the other moves
towards him at the same speed. The observer hears
beats of frequency 2 Hz. Speed of the tuning fork is
(velocity of sound in air is 340 m/s)
(1) 1 m/s (2) 1.5 m/s
(3) 2 m/s (4) 2.5 m/s
10. A tube 0.75 m long is closed at one end. A stretchedwire is placed near the open end. The wire is
0.25 m long and has a mass of 0.01 kg. It is held
fixed at both ends and vibrates in its fundamental
mode. It sets the air column in the tube into vibration
at its fundamental frequency by resonance. If speed
of sound is 330 m/s in air then tension in the wire is
(1) 55 N (2) 110 N
(3) 121 N (4) 165 N
11. Two tuning forks Aand Bwhen set in vibration, give
4 beats per second. If a prong of the fork Ais filled,
the beats are reduced to 5 beats per 2 second. If
frequency of fork Bis 250 Hz then frequency of Ais
(1) 246 Hz
(2) 254 Hz
(3) 252.5 Hz
(4) 247.5 Hz
12. Two waves of equal frequencies have their intensities
in ratio 9 : 25. If these two waves interfere, then the
ratio of the maximum and minimum possible
amplitudes in the resultant waves is
(1) 3 : 5 (2) 4 : 5
(3) 4 : 1 (4) 2 : 1
13. Filament of an incandescent bulb has length and
radius of cross-section r. Rating of the bulb is (P
watt, Vvolt). Emissivity of the filament is and
wein's constant is b. Wavelength of the most intense
radiation emitted by the filament, if the bulb is
operated at half of the rating voltage, is (= Stefan's
constant)
(1)
1
42 rb
P
(2)
1
44 r
b P
(3)
1
28 rb
P
(4)
1
48 rb
P
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14. Three rods AB, BC, CAare joined to form a triangle
ABC. Length of the rods ABand ACeach are equal
to band their coefficient of linear expansion is 1whereas length of rod BCis aand its coefficient of
linear expansion is 2. Ratio,
b
a such that the
height hdoes not change upon heating the rods by
same temperature, is
(1)2
1
1
2
(2)2
1
h
A
B C
(3)2
1
2
(4)2
1
1
3
15. A platinum resistance thermometer reads 0C when
resistance is 100 and 100C when its resistance
is 120 . Reading of thermometer, when its
resistance is 112 , is
(1) 50 (2) 55
(3) 60 (4) 56
16. One gram mole of hydrogen gas at temperature
T0K and pressure P0 pascal is enclosed in a vessel.
Assuming Boltzmann's constant to be k, Avogadro's
number to be NAand speed of molecules to be root
mean square speed (and m is molar mass), thenumber of collisions per second which the molecule
make with one square meter area of vessel wall is
(1)
20
024AP N
KT m(2)
2
0
012
AP N
KT m
(3)
20
0
500
3AP N
KT m(4)
2
0
02AP N
KT m
17. Assuming average molar mass of gases in the
Earth's atmosphere to be 29 g/mole, the temperature
at which Earth will be lack of atmosphere is (Radius
of Earth = 6.4 106m and g = 9.8 m/s2)
(1) 10 103K (2) 1.46 105K
(3) 0.73 105K (4) 2.92 105K
18. If the temperature of atmosphere Tvaries with height
has T= T0(1 h) where is a positive fraction.
Assuming average molar mass of air to be M and
the air to be an ideal gas, the variation of pressure
P with height h is (atmospheric pressure at Earth
surface = P0)
(1) 00 1Mg
RTP P h
(2) 00 1Mg
RTP P h
(3) 00 1Mg
RTP P h
(4)0
0(1 )
RTMgP P h
19. An ideal gasP
V
C
C
is taken through a process
in which the pressure and the volume vary such that
P = V. The value of , for which molar heat
capacity of gas is zero, is
(1) (2)
(3)1
(4) 2
20. 1.0 g of pure water vaporises isobarically at
atmospheric pressure such that its volume changes
from vliquid= 1.0 cm3to vvapour= 1671 cm
3. If latent
heat of vaporisation of water is LV= 2.26 106J/kg
and atmospheric pressure P0= 1.0 105Pa, the
change in internal energy of the system is
(1) 169 J (2) 2260 J
(3) 2091 J (4) 2009 J
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21. An ideal monoatomic gas undergoes a process such
that its internal energy relates to the volume as
U a V , where a is a constant. Molar specific
heat of the gas is
(1) 1.5 R
(2) 2.5 R
(3) 3.5 R
(4) 4.5 R
22. Pressure versus temperature (P T) graph of n
moles of an ideal gas is shown in figure.
Corresponding density versus volume ( V) graph
is
C
DB
T0
2T0
T
A
4P0
2P0
P0
P
(1)
B C,
A D,
V
(2)
V
C
D
AB
(3)
V
C B,
A D, (4)
V
B C
DA
23. Two moles of a diatomic ideal gas is taken through
a process, PT
, where a is a positive constant.
Temperature of gas is increased from T0to 2T0, work
done by the gas is
(1) 2 RT0
(2) 4 RT0
(3) 6 RT0
(4) 8 RT0
24. A bullet of mass 10 g moving with speed of 120 m/s
hits an ice block of mass 990 g kept on a
frictionless horizontal floor and gets embedded into
it. Temperature of ice block is 0C and its latent heat
of fusion is 80 calory/gram. If3
th4
of the energy lost
in collision is converted into heat, mass of ice
melted is
(1) 0.10 g (2) 0.11 g
(3) 0.42 g (4) 0.50 g
25. A cup of coffee cools down from 54C to 45C in
5 minute. How much further time in minutes it will
take to cool down to 36C, if the room temperature
is 18C?
(1) 5 (2) 7
(3) 9 (4) 11
SECTION - II
Assertion Reason Type Questions
Directions : Questions number 26 to 30 are Assertion-
Reason type questions. Each of these questions
contains two statements. Statement-1 (Assertion) and
Statement-2 (Reason). Each of these questions also has
four alternative choices, only one of which is the correct
answer. You have to select the correct choice.
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26. Statement-1 : Two waves y1= Acos(t + kx) and
y2 = Acos(t kx) are superimposed. At x = 0,
there forms a node.
and
Statement-2 : At node, net displacement due to two
waves should be zero.
(1) Statement-1 is True, Statement-2 is True;
Statement-2 is a correct explanation for
Statement-1
(2) Statement-1 is True, Statement-2 is True;
Statement-2 is NOT a correct explanation for
Statement-1
(3) Statement-1 is True, Statement-2 is False
(4) Statement-1 is False, Statement-2 is True
27. Statement-1 : A wire is stretched and then fixed at
two ends. It oscillates in its seventh overtone mode.
Number of nodes and antinodes on the wire are 9
and 8 respectively.and
Statement-2 : For a wire stretched and fixed at both
of ends, the length of wire and wavelength of wave
are related as = 7.5 corresponding to its
oscillation in seventh overtone mode.
(1) Statement-1 is True, Statement-2 is True;
Statement-2 is a correct explanation for
Statement-1
(2) Statement-1 is True, Statement-2 is True;
Statement-2 is NOT a correct explanation for
Statement-1(3) Statement-1 is True, Statement-2 is False
(4) Statement-1 is False, Statement-2 is True
28. Statement-1 : Transverse waves cannot be produced
in gaseous medium.
and
Statement-2 : Gaseous medium possess no
modulus of rigidity.
(1) Statement-1 is True, Statement-2 is True;
Statement-2 is a correct explanation for
Statement-1
(2) Statement-1 is True, Statement-2 is True;
Statement-2 is NOT a correct explanation for
Statement-1
(3) Statement-1 is True, Statement-2 is False
(4) Statement-1 is False, Statement-2 is True
29. Statement-1 : A cube of ice melts in open
atmosphere. Some amount of work is done by
atmosphere on (ice + water) system.
and
Statement-2 : Volume of water converted from melting
ice is lesser than its volume.
(1) Statement-1 is True, Statement-2 is True;
Statement-2 is a correct explanation for
Statement-1
(2) Statement-1 is True, Statement-2 is True;
Statement-2 is NOT a correct explanation for
Statement-1
(3) Statement-1 is True, Statement-2 is False
(4) Statement-1 is False, Statement-2 is True
30. Statement-1 : Deserts are hotter in the sunny days
but colder in nights.
and
Statement-2 : According to Kirchhoff's law, emissivity
of a body is equal to its absorptive power, this is why
deserts have high emissivity as their absorptive
power is high.(1) Statement-1 is True, Statement-2 is True;
Statement-2 is a correct explanation for
Statement-1
(2) Statement-1 is True, Statement-2 is True;
Statement-2 is NOT a correct explanation for
Statement-1
(3) Statement-1 is True, Statement-2 is False
(4) Statement-1 is False, Statement-2 is True
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SECTION - IStraight Objective Type Questions
This section contains 25 multiple choice questions
numbered 31 to 55. Each question has 4 choices (1), (2),
(3) and (4), out of which ONLY ONE is correct.
31. The order of Lewis acidic strength for boron halides
follow the order
(1) BBr3> BCl3> BF3
(2) BF3> BCl3> BBr3
(3) BCl3> BF3> BBr3
(4) BBr3> BF3> BCl3
32. Which of the following is not correct for diborane?
(1) Each boron atom has four bonds around it
(2) Each boron is sp3hybridized hence HBH bond
angles are of measure 10928
(3) Maximum number of atoms lie on a plane is
equal to 6
(4) B2H
6may act as reducing agent but can never
act as oxidising agent
33. When PCl3is hydrolysed then oxyacid of phosphrus
is formed. The basicity of oxyacid is
(1) 1 (2) 2
(3) 3 (4) 4
34. When ammoniacal solution of common salt is
saturated with CO2, then product formed is
(1) NH4HCO3 (2) (NH4)2CO3
(3) NaHCO3 (4) Na2CO3
35. Which of the following is the correct sequence of
dipole moment for MH3Cl, where M is the 14thgroup
element?
(1) C > Si > Ge (2) Ge > C > Si
(3) Si > C > Ge (4) C > Ge > Si
PART - B (CHEMISTRY)
36. What is the product when FeS2is oxidized by O
2?
(1) FeO and SO2
(2) Fe2O3and SO3
(3) FeO and SO3
(4) Fe2O3and SO237. 50% H2SO4on electrolysis produces the compound
around anode which on complete hydrolysis
produces one of the compound, which can act as
reducing agent, the compound is
(1) H2SO4 (2) H2S2O8
(3) H2O (4) H2O2
38. Which of the following is the correct order of bond
dissociation energy?
(1) F2> Cl2> Br2> I2
(2) Cl2> Br2> I2> F2(3) Cl2> Br2> F2> I2
(4) Cl2> F2> Br2> I2
39. Which of the following compound on hydrolysis form
two types of acids?
(1) N2O5 (2) N2O
(3) N2O4 (4) N2O3
40. XeF6on reaction with BF3donates one of its fluoride
to BF3 then what is the oxidation number of Xe in
final compound?
(1) 5 (2) 6(3) 7 (4) 4
41. Which of the following is used to block silicones
chain?
(1) MeSiCl3
(2) Me2SiCl2
(3) Me3SiCl
(4) Me4Si
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42. Which of the following bicarbonate is least
thermodynamically stable?
(1) KHCO3 (2) LiHCO3
(3) NaHCO3 (4) CsHCO3
43. When I2dissolves in KI it forms
(1) A compound which can reduce Na2S2O3
(2) Compound which is white in colour
(3) Compound has atom with linear shape
(4) I2in vapour phase
44. Which of the following can produce apple green
flame in flame test?
(1) Li+ (2) K+
(3) Ca2+ (4) Ba2+
45. KNH2with NH4Br on reaction to form product by using
(1) Acid base reaction
(2) Redox reaction
(3) Decomposition reaction
(4) Condensation reaction
46. Which of the following causes temporary hardness
to H2O?
(1) CaCl2
(2) MgCl2
(3) CaSO4
(4) Ca(HCO3)2
47. If a H2O2 sample has volume strength 10 V then
how many molecules of H2O2are present in 224 mL
solution of it?
(1) 6.022 1020
(2) 2 103
(3) 12.044 1022
(4) 103
48. When P4 (white phosphorus) reacts with SOCl2 it
does not form
(1) PCl5 (2) PCl3
(3) SO2 (4) S2Cl2
49. Which of the following can act as a reducing agent?
(1) H3PO4 (2) H4P2O7
(3) H3PO3 (4) (HPO3)3
50. Which of the following compound does not exist?
(1) SCl2 (2) SeCl2
(3) TeCl2 (4) OCl2
51. Which of the following nitrates on heating to lowest
temperature form metal oxide?
(1) LiNO3 (2) NaNO3
(3) KNO3 (4) CsNO3
52. Which of the following starred bond is most stable?
(1) Cl C H3 * *
(2) Cl C D3 * *
(3) Cl C T3 * *
(4) All of these are identically stable
53. Which of the following is not known?
(1) HOBr (2) HOBrO
(3) HBrO3 (4) HBrO4
54. In XeF2, the bond angle is
(1) 90 (2) 120
(3) 10928 (4) 180
55. In which of the following silicate, all four oxygen
around silicon are shared with other units?
(1) Pyrosilicate (2) Linear silicates
(3) Sheet silicates (4) 3-D silicates
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SECTION - II
Assertion Reason Type Questions
Directions : Questions number 56 to 60 are Assertion-
Reason type questions. Each of these questions
contains two statements. Statement-1 (Assertion) and
Statement-2 (Reason). Each of these questions also has
four alternative choices, only one of which is the correctanswer. You have to select the correct choice.
56. Statement-1 : F2 is a strongest oxidizing agent
among all halogens.
and
Statement-2 : Fluorine has highest electronegativity
among all elements.
(1) Statement-1 is True, Statement-2 is True;
Statement-2 is a correct explanation for
Statement-1
(2) Statement-1 is True, Statement-2 is True;
Statement-2 is NOT a correct explanation for
Statement-1
(3) Statement-1 is True, Statement-2 is False
(4) Statement-1 is False, Statement-2 is True
57. Statement-1 : NH3is highly water soluble.
and
Statement-2 : NH3forms hydrogen bond with H2O.
(1) Statement-1 is True, Statement-2 is True;Statement-2 is a correct explanation for
Statement-1
(2) Statement-1 is True, Statement-2 is True;
Statement-2 is NOT a correct explanation for
Statement-1
(3) Statement-1 is True, Statement-2 is False
(4) Statement-1 is False, Statement-2 is True
58. Statement-1 : H2O2has open book structure.
and
Statement-2 : H2O2 has H-bonding among
molecules.
(1) Statement-1 is True, Statement-2 is True;
Statement-2 is a correct explanation for
Statement-1
(2) Statement-1 is True, Statement-2 is True;
Statement-2 is NOT a correct explanation for
Statement-1
(3) Statement-1 is True, Statement-2 is False
(4) Statement-1 is False, Statement-2 is True
59. Statement-1 : Sodium in liquid ammonia (3 M) forms
a diamagnetic solution.
and
Statement-2 : Sodium in liquid ammonia (dilute
solution) shows reducing property.
(1) Statement-1 is True, Statement-2 is True;Statement-2 is a correct explanation for
Statement-1
(2) Statement-1 is True, Statement-2 is True;
Statement-2 is NOT a correct explanation for
Statement-1
(3) Statement-1 is True, Statement-2 is False
(4) Statement-1 is False, Statement-2 is True
60. Statement-1 : Cs can melt even on palm.
and
Statement-2 : Cs have very weak metallic bonding.(1) Statement-1 is True, Statement-2 is True;
Statement-2 is a correct explanation for
Statement-1
(2) Statement-1 is True, Statement-2 is True;Statement-2 is NOT a correct explanation for
Statement-1
(3) Statement-1 is True, Statement-2 is False
(4) Statement-1 is False, Statement-2 is True
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PART - C (MATHEMATICS)
SECTION - IStraight Objective Type Questions
This section contains 25 multiple choice questions
numbered 61 to 85. Each question has 4 choices (1), (2),
(3) and (4), out of which ONLY ONE is correct.61. A rectangle PQRS joins the points P, Q, R, S.
Co-ordinates of P and R be (2, 3) and (8, 11)
respectively. The line QSis known to be parallel to
the y-axis. Then coordinates of Qand Sare
(1) (0, 7) and (10, 7) (2) (5, 2) and (5, 12)
(3) (7, 6) and (7, 10) (4) (7, 2) and (7, 12)
62. The orthocenter of the triangle formed by pair of lines
3x2+ 5y2+ 8xy 5x 7y+ 2 = 0 and x y= 0 is
(1)1 1
,
2 2
(2)2 1
,
3 3
(3)1 1
,3 3
(4) (1, 1)
63. If the two feet of normals drawn from a point to the
parabola x2 6x 4y+ 5 = 0 be (7, 3) and (1, 3),
then the third foot is
(1) (1, 0) (2) (3, 8)
(3) (3, 1) (4) (5, 0)
64. Consider an ellipse with centre at the origin. From an
arbitrary point Pon the ellipse, perpendiculars PA
and PBare dropped on the axes of the ellipse. Thenthe locus of the point Qthat divides ABin the fixed
ratio m: nmay be
(1) Pair of straight lines (2) An ellipse
(3) A hyperbola (4) Parabola
65. Let ABCbe a triangle whose vertices are A(5, 5)
and B(7, 1). If vertex C lies on the circle whose
director circle has equation x2+ y2= 100, then the
locus of orthocenter of ABCis
(1) x2+ y2 4x 8y 30 = 0
(2) x2+ y2+ 4x 8y 30 = 0
(3) x2+ y2+ 4x+ 8y 30 = 0
(4) x2+ y2+ 4x+ 8y= 0
66. Let A, B, Cbe three points on a straight line suchthat B lying between A and C. Consider all circlespassing through Band C. The points of contact of
the tangents from Ato these circles lie on
(1) A straight line (2) A parabola
(3) A circle (4) Ellipse
67. The eccentricity of the curve1
2
ax t
t and
1
2
ay t
t , where tis a parameter, is
(1)1
2(2)
1
2(3) 2 (4) 2
68. The four sides of a quadrilateral are given by equation
(xy+ 12 4x 4y)2= (2x 2y)2. The equation of a
line with slope 3 which divides area of
quadrilateral in two equal parts is
(1) 3( 4) y x (2) 3 4 y x
(3) 3( 4) 4 y x (4) 3( 4) y x
69. From any point P on the hyperbola2 2
1
9 4
x y ,
tangents are drawn to the hyperbola2 2
118 8
x y
.
The area cut-off by the chord of contact and theasymptotes of the first hyperbola
(1) Depends only on abscissa of the point P
(2) Depends only on ordinate of point P
(3) Is 48 sq. unit
(4) Is 24 sq. unit
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70. Tangents are drawn from (, ) to the hyperbola
3x2 2y2= 6 and are inclined at angles 1,
2to the
positive x-axis. If tan1.tan2 = 2, then value of
(22 2) is equal to
(1) 7 (2) 11
(3) 5 (4) 6
71. PQis the chord passing through centre of the ellipse2 2
2 21
x y
a b. If the square of its length is the H.M.
of the squares of length of major and minor axes,
then slope of line may be equal to
(1) 2 (2)1
2
(3) 1 (4) 3
72. Line y= x+ 2 is a tangent to the parabola y2= 8x. Let
Mbe the point on this line from where other tangent is
drawn which is perpendicular to this tangent. The
distance of Mfrom ( 1, 2 2)N is
(1) 2 (2) 3
(3) 1 (4) 5
73. A tangent to the hyperbola2 2
14 1
x y
meets the
ellipse x2+ 4y2= 4 at two distinct points. The locus
of mid point of this chord is
(1) (x2+ 4y2)2= 4(x2 4y2)
(2) (x2
4y2
)2
= x2
+ 4y2
(3) (x2+ 4y2)2= (x2 4y2)
(4) (x2+ 4y2)2= 4(x2+ 4y2)
74. Let PQ be double ordinate of the hyperbola
2 2
2 21
x y
a b. If Ois the centre of the hyperbola and
OPQ is an equilateral triangle, then its eccentricity
must be
(1) Greater than1
3
(2) Less than or equal to 2
(3) Greater than2
3
(4) Less than or equal to2
3
75. Equation of the parabola with latus rectum 2 2 units
and axis as the line x y=0 and tangent at the vertex
as x+ y= 1, is (origin lies outside of parabola)
(1) x2+ y2 2xy+ 4x+ 4y+ 4 = 0
(2) x2+ y2 2xy+ 8x+ 8y 8 = 0
(3) x2+ y2 2xy 4x 4y+ 4 = 0
(4) x2+ y2 2xy 2x 2y+ 2 = 0
76. The number of points with integral coordinates that
lie in the interior of the region common to the circlex2+ y2= 16 and the parabola y2= 4xis
(1) 10 (2) 16
(3) 17 (4) 13
77. On the ellipse2 2
118 8
x y
, the point Mnearest to the
line 2x 3y+ 25 = 0 is
(1) (3, 2) (2)8
2,3
(3) (3, 2) (4) ( 3 2, 0)
78. Given a circle (x + 4)2 + (y 2)2 = 25. Another
circle is drawn passing through (4, 2) and touching
the given circle internally at the point A(4, 7). AB
is the chord of length 8 units of the larger circle
intersecting the other circle at the point C. Then AC
will be
(1) 4 units (2) 17 units
(3) 5 units (4) 3 units
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79. The equation of the hyperbola whose foci aresymmetrically situated on the x-axis with respect to
the origin, the equation of the asymptotes as
4
3 y xand distance between foci being 20, is
(1)2 2
164 36
x y
(2)2 2
116 9
x y
(3)2 2
19 16
x y
(4)2 2
136 64
x y
80. If normal at the point P() to the ellipse2 2
114 5
x y
intersects it again at the point Q(2), then cos isequal to
(1)1
3
(2)
1
2
(3)2
3
(4)
1
6
81. If the circumference of the circle
x2+ y2+ 8x+ 8y b= 0 is bisected by
x2+ y2 2x+ 4y+ a= 0, then a+ bis equal to
(1) 56 (2) 2
(3) 64 (4) 14
82. A, Band Care 3 points on a circle with centre O.
The chord BAis extended to point T such that CTbecomes a tangent to the circle at point C. IfATC= 20 and ACT= 40, then BOAis
(1) 120 (2) 150
(3) 160 (4) 170
83. The equation of the base of an equilateral triangle is
2x+ y= 3 and vertex is (2, 3), then length of itsside is
(1)8
15(2)
4
3 5
(3)4
15(4)
8
3 5
84. An incident ray (L1) is reflected by the mirror (L2)
3x + 4y= 5 and equation of reflected ray (L3) is
x+ y= 1, the equation of L1is
(1) x y= 3 (2) 17x+ 31y= 45
(3) 17x 31y= 77 (4) 31x+ 17y= 3
85. If origin is moved to a point such that the
transformed expression for the expressionf(x, y) = x2 4y2 6x+ 8y+ 3 will be free from first
degree terms, then the point is
(1) (3, 1) (2) (1, 3)
(3) (3, 1) (4) (3, 1)
SECTION - II
Assertion Reason Type Questions
Directions : Questions number 86 to 90 are Assertion-
Reason type questions. Each of these questions
contains two statements. Statement-1 (Assertion) and
Statement-2 (Reason). Each of these questions also has
four alternative choices, only one of which is the correct
answer. You have to select the correct choice.
86. Statement-1 : Equation of tangent passing through
(1, 1) to the circle x2 + y2 4x + 2y 1 = 0 is
x(1) + y(1) 2(x+ 1) + (y+ 1) 1 = 0
i.e., 2y x 2 = 0.
and
Statement-2 : Equation of tangent passing through
(0, 0) to the circle x2+ y2 x y= 0 is x+ y= 0.
(1) Statement-1 is True, Statement-2 is True;
Statement-2 is a correct explanation for
Statement-1
(2) Statement-1 is True, Statement-2 is True;
Statement-2 is NOT a correct explanation for
Statement-1
(3) Statement-1 is True, Statement-2 is False
(4) Statement-1 is False, Statement-2 is True
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87. Statement-1 : Tangent of the angle intercepted by
the tangents drawn to the ellipse x2 + 4y2= 4 at
(0, 2) is 4 3 .
and
Statement-2 : Angle intercepted by the tangents from
(x1, y1) to any ellipse is acute if (x1, y1) lies outside
the director circle and obtuse if (x1, y1) lies inside the
director circle and outside the ellipse.(1) Statement-1 is True, Statement-2 is True;
Statement-2 is a correct explanation for
Statement-1
(2) Statement-1 is True, Statement-2 is True;
Statement-2 is NOT a correct explanation forStatement-1
(3) Statement-1 is True, Statement-2 is False
(4) Statement-1 is False, Statement-2 is True
88. Statement-1 : For ellipse2 2
2 21
x y
a b (a > b) and
hyperbola2 2
2 21
x y
a b. If e1 and e2 represent the
eccentricities of ellipse and hyperbola respectively
then e12+ e2
2= 2.
and
Statement-2 : If e1 and e2 are eccentricities of
hyperbola and conjugate hyperbola respectively, then
2 21 2
1 11
e e.
(1) Statement-1 is True, Statement-2 is True;
Statement-2 is a correct explanation forStatement-1
(2) Statement-1 is True, Statement-2 is True;
Statement-2 is NOT a correct explanation for
Statement-1
(3) Statement-1 is True, Statement-2 is False
(4) Statement-1 is False, Statement-2 is True
89. Statement-1 : The equation x2+ y2 2xy+ x+ 1 = 0
represents pair of straight lines if 2 2 .
and
Statement-2 : The point P on the line x + y = 1
such that PA + PB is minimum, where A(2, 0),
B(0, 1) is 4 1,3 3
.
(1) Statement-1 is True, Statement-2 is True;
Statement-2 is a correct explanation for
Statement-1
(2) Statement-1 is True, Statement-2 is True;
Statement-2 is NOT a correct explanation for
Statement-1
(3) Statement-1 is True, Statement-2 is False
(4) Statement-1 is False, Statement-2 is True
90. Statement-1 : Triangle formed by the vertex and end
points of double ordinate of the parabola y2= 4xis
an equilateral triangle, then area of triangle is 48 3
sq. units.
and
Statement-2 : Area formed by the vertex and latus
rectum of the parabola y2= 4xis 2 sq. units.
(1) Statement-1 is True, Statement-2 is True;
Statement-2 is a correct explanation for
Statement-1
(2) Statement-1 is True, Statement-2 is True;
Statement-2 is NOT a correct explanation for
Statement-1
(3) Statement-1 is True, Statement-2 is False
(4) Statement-1 is False, Statement-2 is True
8/10/2019 JEE Main 2014_Test 4 (Paper I) Code A
15/16
Test Booklet Code
Test No. 3
Paper I
JEE (Main) 2014
for
ALL
INDI
AAA
KASHTEST
SERIE
S
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ANSWERS
1. (1)
2. (3)
3. (4)
4. (1)
5. (4)
6. (4)
7. (3)
8. (2)
9. (3)
10. (4)
11. (2)
12. (3)
13. (3)
14. (3)
15. (2)16. (4)
17. (Deleted)
18. (3)
19. (3)
20. (4)
21. (3)
22. (3)
23. (3)
24. (1)
25. (2)
26. (2)
27. (1)
28. (1)
29. (2)
30. (3)
PHYSICS CHEMISTRY MATHEMATICS
31. (1)
32. (3)
33. (4)
34. (2)
35. (1)
36. (3)
37. (1)
38. (3)
39. (2)
40. (1)
41. (2)
42. (1)
43. (1)
44. (2)
45. (2)46. (4)
47. (3)
48. (4)
49. (2)
50. (3)
51. (1)
52. (2)
53. (3)
54. (3)
55. (4)
56. (3)
57. (4)
58. (3)
59. (1)
60. (3)
61. (2)
62. (3)
63. (2)
64. (2)
65. (3)
66. (2)
67. (4)
68. (2)
69. (2)
70. (4)
71. (1)
72. (4)
73. (1)
74. (3)
75. (2)76. (3)
77. (3)
78. (4)
79. (3)
80. (3)
81. (1)
82. (2)
83. (2)
84. (2)
85. (3)
86. (1)
87. (1)
88. (1)
89. (4)
90. (4)
TEST - 3 (Paper-I)
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