JEE Main 2014_Test 4 (Paper I) Code A

8/10/2019 JEE Main 2014_Test 4 (Paper I) Code A

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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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Space for Rough Work

Test - 4 (Paper-I) All India Aakash Test Series for JEE (Main) 2014

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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




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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All India Aakash Test Series for JEE (Main) 2014 Test - 4 (Paper-I)

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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


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.



Statement-1



Statement-1(3) Statement-1 is True, Statement-2 is False


28. Statement-1 : Transverse waves cannot be produced

in gaseous medium.

and

Statement-2 : Gaseous medium possess no

modulus of rigidity.



Statement-1



Statement-1



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.



Statement-1



Statement-1



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-1



Statement-1




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(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






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.



Statement-1



Statement-1



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



Statement-1



58. Statement-1 : H2O2has open book structure.

and

Statement-2 : H2O2 has H-bonding among

molecules.



Statement-1



Statement-1



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



Statement-1



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-1

(2) Statement-1 is True, Statement-2 is True;Statement-2 is NOT a correct explanation for

Statement-1




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PART - C (MATHEMATICS)




(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






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.



Statement-1



Statement-1




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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-1


Statement-2 is NOT a correct explanation forStatement-1



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.


Statement-2 is a correct explanation forStatement-1



Statement-1



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

.



Statement-1



Statement-1



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.



Statement-1



Statement-1




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Test Booklet Code

Test No. 3

Paper I

JEE (Main) 2014

for

ALL

INDI

AAA

KASHTEST

SERIE

S


16/16

Test - 3 (Paper-I) (Answers & Hints) All India Aakash Test Series for JEE (Main)-2014

1/8

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)

JEE Main 2014_Test 4 (Paper I) Code A

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Transcript of JEE Main 2014_Test 4 (Paper I) Code A