JEE Main-2014_Test-5 (Paper-I) - Code-A.pdf

8/19/2019 JEE Main-2014_Test-5 (Paper-I) - Code-A.pdf

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Roll No.:

Centre Code:

TEST No. 5

Test Date:

Test Booklet Code

JEE (Main) 2014

for

A L L

I N D

I A A A

K ASH T E S T

S E R I E

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 other material 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 (¼) marks will be deducted for indicatingincorrect response of each question. No deduction fromthe total score will be made if no response is indicated for anyquestion in theanswer sheet.

13. Patternof the questions areas under:

Section – I : Straight ObjectiveType Questions

Section – II : Assertion– ReasonType Questions

1 9 / 0 1 / 2 0 1 4


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TOPICS OF THE TEST

Test No. 5

Physics Electric Charges and Field, Electrostatics Potential and Capacitance,Current Electricity

Chemistry General Principles & Processes of Isolation of Elements, The d & f - Block

Elements, Coordination Compounds, Qualitative Analysis

Mathematics Sets, Relations & Functions (XI & XII), Limits & Derivatives, Continuity and

Differentiability

Paper I


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Space for Rough Work

Test - 5 (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. Figure shows two concentric shells. Whose radii are

a and b . If outer shell has charge +q , charge oninner shell would be

b

O

a

(1) Zero (2) q

(3)2

2

qb

a (4)

aq

b

2. Maximum rate of heat dissipation in the resistance

R is2 V

12 V

4 V

R

4

4

(1) 2 W (2) 1 W

(3) 4.5 W (4) 0.25 W

TEST - 5 (Paper-1)Time : 3 Hrs. MM : 360

3. The dimensional formula for rate of change of

electrical flux per unit current is(1) [ML3T–4A–2] (2) [ML2T–4A–2]

(3) [ML3T–2A–2] (4) [ML3T–2A–1]

4. Which is the correct representation of the chargeson the surface of a conductor at the bend whencurrent is flowing?

(1)

(2)

(3)

(4)

5. Electric field which is directed along y -axis. Variesalong x-axis as shown in figure. Potential differencebetween x = 1 m to x = 3 m is

100

75

E (N/C)

1 2 3 4x (m)

(1) 250 V (2) 0 V

(3) 375 V (4) 333.5 V


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All India Aakash Test Series for JEE (Main) 2014 Test - 5 (Paper-I)

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6. A resistance wire is connected across the voltmeter,

which is in series of an ammeter and a battery.

Choose the correct statement.

(1) Ammeter reading decreases and voltmeter

reading increases

(2) Ammeter reading increases and voltmeter

reading decreases

(3) Readings of both meters will increase

(4) Readings of both meters will decrease

7. A small dipole is directed along Y -axis is centered

at point P (a, 0). There is point charge fixed at origin.Work done in moving dipole from large distance to

point P is W 1 and from P to Q (–a, 0) keeping

same orientation is W 2. Choose the correct

statement.

(1) W 1 > W 2 (2) W 2 > W 1

(3) W 1 = W 2 (4) W 1 > 0, W 2 < 0

8. Two parallel plates A and B are having 12 C and

4 C charges. Their arrangement forms capacitance

of 2 F. It is connected with resistance of 1 at

t = 0. Choose correct statement.

R

B A

(1) Charge on the plate A is 4e –t /2 C, where t is

time in S

(2) Charge on the plate B is –4e –t /2 C, where t is

time in S

(3) Charge on the plate A is 8 + 4e –t /2 C, where t is time in S

(4) Charge on the plate B is 8 + 4e –t /2 C, where t

is time in S

9. A proton is either released at rest or launched withcertain velocity in a uniform electric field. Which ofthe following graph could not represent possiblevariation of kinetic energy with time?

(1)

KE

t (2)

KE

t

(3)

KE

t

(4)

KE

t

10. Eight small spheres of mercury, each with adiameter of 1 mm and a charge of 5 nC unite to forma large sphere. Potential energy stored in the largesphere is

(1) 72 mJ

(2) 7.2 mJ

(3) 0.72 mJ

(4) 0.072 mJ

11. A point charge of 1 nC is placed at 50 cm from thecentre of a thin conducting shell of 20 cm radiushaving –1nC charge. Net potential at point

P (AP = 10 cm) would be.

A P

B

(1) –27 V

(2) –45 V

(3) –49.5 V

(4) –22.5 V


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12. Three particle charges of same magnitude and

different nature are placed at some distance along a

line evaluate correct variation of potential along line

joining of separation.

+q +q –q

(1)

v

(2)

v

(3)

v

(4)

v

13. A long cylinder with uniformly charged surface and

cross sectional area a moves with constant velocityv along its axis. An electric field strength at the

surface of cylinder is equal to E . The current due to

mechanical transfer of charge would be

(1) Eav

(2) 2 0Eav

(3) 2 Eav

(4) Zero

14. Each plate of a parallel plate air capacitor has an

area S . How much work has to be performed to

slowly increase the distance between the plates form

x 1 to x 2, if potential difference across plates V is kept

constant ?

(1)

20

1 2

1 1

2

SV

x x

(2)

20

2 1

1 1

2

SV

x x

(3)2

0

1 2

1 1SV

x x

(4) Zero

15. Two rectangular frames (2 m × 30 cm) and

(2 m × 40 cm) are joined along the common length.Their planes are perpendicular to each other. A long

charged wire of linear charge density 40 C/m is

placed at 25 cm from common length of planes. Net

electric flux through both the frames

(1) 4 Nm2 /C (2) 8 Nm2 /C

(3) 0.4 Nm2 /C (4) 0.8 Nm2 /C

16. A system consists of a uniformly charged sphere of

radius R and surrounding medium filled by a charge

with the volume charge density

r

, where is a

positive constant and r is the distance from the

centre of the sphere. Find charge on the sphere for

which electric field intensity outside sphere is

independent of r 2

1

R

(1) 20 C (2) 2.0 C

(3) 5.0 C (4) 4.0 C


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17. An uniformly charged and long thin wire is kept

along x -axis as shown in figure. Linear charge

density is . Electric field at P : (x, y, z ) would be

(where x 0, y 0, z 0)

------++++++++++++++++++++------- x

y

x

(1) 2 2

0

ˆ ˆ2

yj zk y z

(2) 2 2 2

0

ˆ ˆ ˆ2

xi yj zk x y z

(3) 2 2

0

ˆ ˆ2

yj zk y z

(4) 2 2 2

0

ˆ ˆ ˆ2

xi yj zk x y z

18. A point charge q is placed inside cavity of a

spherical conductor as shown in figure. Electric field

at a point lying outside the conductor due to charge

on surface of cavity would be

q

C P

r 1

r 2

(1) 21

kq

r

(2) 22

kq

r

(3) Cannot be determined

(4) Zero

19. In the measurement of resistance by a meter-bridgepercentage error is minimum when the null point is

(1) Close to 0 cm

(2) Close to 50 cm

(3) Close to 75 cm

(4) Close to 100 cm

20. A semicircular frame of radius R is having charge q and –q in the respective quadrants. Frame is free torotate about C in uniform electric field E . The workdone to rotate the frame in the given sense to bring

diameter AB parallel to electric field.

E B

q

–q A

C

R

(1)2R

qE

(2)2

R qE

(3)4R

qE

(4)4

R qE


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21. A rod of mass m length l uniformly distributed with

charge density – is placed horizontally on the

support O and P in electric field 0ˆ( )E x j . For what

value of E 0 rod is about to topple?

O x P

y

(1) 2mg

l(2) 22

mg

l

(3) 23mg

l(4) 2

3

2

mg

l

22. Time constant of circuit would be

12 V R 3 = 2

R 1 = 3

R 2 = 6

C = 5 F

(1) 20 s (2) 10 s

(3) 5 s (4) 1 s

23. An electric filed 2Nˆ ˆ ˆ, , 2 2 3C

E x y z x i yj k exists

in space. Charge density at (1, 0, 1) would be

(1) 0 (2) 20

(3) 60 (4) –60

24. Two thin conductors of same length and same area

are connected in series as shown in figure. An

electric current i flows through them. The total

charge accumulated at junction would be ( and 2

are their resistivity)

i i 3

(1) i 0 (2) 2i 0

(3) 3 i 0 (4) Zero

25. A slide wire of linearly varying radius from a to 2a of

the cross-sections and uniform resistivity with 12 V

source is applied in the experimental circuit.

Unknown emf E of the source is balanced at

mid-point of the wire. The value of E .

G

12 V

E

J

(1) 6 V (2) 8 V

(3) 10 V (4) 4 V

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 : A parallel plate capacitor at constant

potential is being filled by a long dielectric slab,

moves with constant speed after some time.

and

Statement-2 : After some time moving dielectric slab

will interact with fringing field on both sides.

(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 conducting sphere cannot be

charged beyond a definite potential.

and

Statement-2 : Dielectric strength of the medium

surrounding conductor it does not allow infinite

charge.


Statement-2 is a correct explanation for

Statement-1


Statement-2 is NOT a correct explanation for

Statement-1



28. Statement-1 : Electrostatic field lines never form

closed loop.

and

Statement-2 : Electrostatic field is conservative field.

(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 forStatement-1


(4) Statement-1 is False, Statement-2 is True29. Statement-1 : A uniform resistance wire of thermal

coefficient of resistivity is divided in three equallength and joined parallel to each other. Equivalentthermal coefficient of resistivity (e ) is .

and

Statement-2 : e R

R

∑

∑, where R is the resistance

of the segments connected in parallel and is itscoefficient of thermal resistivity.





30. Statement-1 : Coulomb's law obeys Gauss theorem.

and

Statement-2 : Coulomb's law obeys inverse square

law.(1) Statement-1 is True, Statement-2 is True;

Statement-2 is a correct explanation forStatement-1





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SECTION - IStraight Objective Type Questions

This section contains 25 multiple choice questionsnumbered 31 to 55. Each question has 4 choices (1), (2),(3) and (4), out of which ONLY ONE is correct.

31. An inorganic carbonate salt is strongly heated. Theresidue is yellow while hot and white when cold. Thesalt contains

(1) Pb+2 (2) Zn+2

(3) Hg+2 (4) NH4+

32. On being heated, a salt gives a gas which turns limewater milky and an acidified dichromate solutiongreen. The salt may be a

(1) Carbonate (2) Sulphide

(3) Nitrate (4) Sulphite

33. Which of the following pairs of cations turns boraxbeads blue in a oxidising flame?

(1) Fe+2 and Co+2 (2) Co+2 and Cu+2

(3) Cu+2 and Mn+2 (4) Cu+2 and Cr+3

34. Which of the following pairs of cations can beseparated by adding NH4Cl and NH4OH to themixture?

(1) Fe+3, Al+3 (2) Cr+3, Ni+2

(3) Al+3, Cr+3 (4) Fe+3, Cr+3

35. Which of the following pairs of cations cannot beseparated by adding NH4Cl, NH4OH and then(NH4)2CO3 to the mixture?

(1) Ca+2, Sr2+ (2) Sr+2, Mg+2

(3) Ca+2, Mg+2 (4) Ba+2, Mg+2

36. Which of the following cations will form an insolublered-brown compound with [Fe(CN)6]

4–?

(1) Hg2+ (2) Pb+2

(3) Cu+2 (4) Cd+2

PART - B (CHEMISTRY)

37. Following ligands can show linkage isomerism

(1) CNS (2) NO2

(3) CN (4) All of these

38. Which of the following compounds show optical

isomerism?i . cis [Co(en)2Cl2]

+ ii. trans [Co(en)2Cl2]+

iii. cis-[Co(en)2] iv. [Co(en)3]+

Select the correct answer using the codes givenbelow

(1) (i) & (ii) (2) (ii) & (iii)

(3) (iii) & (iv) (4) (i), (iii) & (iv)

39. EAN of Ni in [Ni(CN)4]2– is

(1) 34 (2) 36

(3) 32 (4) 35

40. The co-ordination number of Pt in the complexion[Pt(en)2Cl2]

2+ is

(1) 3 (2) 4

(3) 5 (4) 6

41. Spin only magnetic moment of the Hg[Co(SCN)4] is

(1) 3 BM (2) 15 BM

(3) 24 BM (4) 8 BM

42. Which is not the square planar complex?

(1) [Cu(NH3)4]2+ (2) [PtCl4]

2–

(3) [NiCl4]2– (4) [AuCl4]

–

43. The number of unpaired electrons expected for thecomplexion [Cr(NH3)6]

3+ is

(1) 2 (2) 3

(3) 4 (4) 5


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57. Statement-1 : Cryolite is used in electrolyticextraction of Al from alumina.

and

Statement-2 : It dissolves alumina.





58. Statement-1 : In acidic medium, Zn+2 is notprecipitated by S–2 ions.

and

Statement-2 : Common ion effect reduces theconcentration of S–2 ions to the minimum level.





59. Statement-1 : K3[Fe(CN)6] is more stable thanK4[Fe(CN)6].

and

Statement-2 : In K4[Fe(CN)6], effective atomicnumber of Fe is 36.





60. Statement-1 : Ce+4 is used as an oxidising agent involumetric analysis.

and

Statement-2 : Ce+4 has the tendency to attain +3oxidation state.





PART - C (MATHEMATICS)

SECTION - I

Straight Objective Type QuestionsThis 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. Set A has 10 elements. The number of subsets of

A having 2 or 3 elements is

(1) 165 (2) 45

(3) 120 (4) 100

62. Let n (S ) represents the number of elements in set 'S '

and n (A) = 4, n (B ) = 6, n (C ) = 3. If n ((A B ) C )

is maximum, then

(1) A B (2) B A

(3) A B and B C (4) C A B

63. Let n (X ) represents the number of elements in set X .

If n (A × B × C ) = 6, then the maximum value of

n (A × B B × A) is

(1) 1 (2) 9

(3) 4 (4) 36


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64. A relation 'S ' is defined on the set of real numberssuch that S = {(x , y ): x (x – 2y ) + |y |2 0} then 'S 'is

(1) Reflexive only (2) Symmetric only

(3) Not transitive (4) Equivalence

65. Let f : R R , f (x ) = x 3 + x 2 + 2kx + 6 is one-onefor all x R , then the least integral value of k is

(1) 4 (2) 2

(3) 1 (4) –3

66. If { } and [ ] represents fractional function andgreatest integer function respectively, then the

domain of {2 }( ) (log [ ])x f x x is

(1)3

[1, 2]2

(2)

3(1, 2)

2

(3)3

(1, 3)2

(4)

3(1, 4)

2

67. The range of| | 3| | 3

( )| | 4| | 4

x x x x f x

x x x x

is (–, ) – A.

The sum of all elements of set A is

(1)37

15(2)

37

17

(3)37

12(4)

37

8

68. Let f : R R defined as f(x ) = x 3 + x + 1, 1 x 2.The graph of y = g (x ) is the reflection of graph ofy = f (x ) through the line y = x . If the domain of g (x ) is[a, b ], then a + b is equal to

(1) 3 (2) 12

(3) 15 (4) 14

69. The graph of y = f (x ) is symmetric about the curvesrepresented by x 2 – 6x + 8 = 0, then the period off (2x ) is

(1) 1 (2) 2

(3) 3 (4) 4

70. Consider that f (x ), g (x ) and h (x ) are functions definedfrom R to R such that f (x ) = g (h (x )) and f (x ) is evenfunction. Now consider the following statements S 1,

S 2, S 3, S 4 .

S 1: g (x ) may even function

S 2: g (x ) is odd function and h (x ) is even

S 3: g (x ) is even function and h (x ) may be odd function

S 4: g (x + y ) = g (x ) + g (y ), h ( + ) = h () + h ()

The incorrect statement is

(1) S 4 (2) S 3

(3) S 2 (4) S 1

71.4 6 3

7 3 4–

( 1) 1lim

1x

x x x

x x x

is equal to

(1) 1 (2) –1

(3) 2 (4) 3

72. If { } represents fractional function, then the value

of 0

lim tan cot2x

x x x x

is

(1) 0 (2) 1

(3) 2 (4) Not in existence

73. 4 24

0

1– cos 4 sin 4limx

x x

x

(1) Is –29/4

(2) Is 29/4

(3) Does not exist as LHL does not exist

(4) Does not exist as LHL RHL

74. If [ ] represent greatest integer function, then sum ofvalues of 'x ' at which f (x ) = min{2x – [2x ], – 2x – [–2x ]}

is not differentiable in (0, 1) is

(1)5

2(2)

3

2

(3)7

2(4) 2


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75. The value of

2

lim (cot )[2 tan ]x

x x

, where [ ] represents

greatest integer function, is

(1) 1 (2) 2

(3) 3 (4) Not in existence

76. If { } and [ ] represents fractional function and greatest

integer function respectively, then the number ofpoints where f (x ) = [{x 2 + |x – 2|}] + {[|x 2 – 4x + 3|]}is not continuous is

(1) 0 (2) 2

(3) 3 (4) 4

77. The number of point(s), where

2 2( ) | 5| ( 6 5) 2 1f x x x x x x is notcontinuous is

(1) 4 (2) 2

(3) 3 (4) 0

78. If y = 8sinx cosx cos2x cos4x and10

10

d y

dx = ky , then

the value of (k + 810) is

(1) 1 (2) 810

(3) 0 (4) 108

79. Let f (x ) be a function defined on the set of realnumbers. If and are any two real numbers suchthat (–| – |5) (f () – f ()) | – |5, then f (x ) is

(1) One one function

(2) f (x ) is always odd function

(3) f (x ) is always even function(4) The fundamental period of f (x ) is 2

80. The sum of values of x satisfying the equation[log

2x ]2 – log

2x – 2 = 0, where [ ] representsgreatest integer function, is

(1) 5 (2)9

2

(3)7

2(4)

5

2

81. The number of elements in sets A, B and C are 2,

3 and 4 respectively. Then

(1) Number of functions from A to B is 6

(2) Number of surjective functions from B to C is 36

(3) Number of surjective functions from C to B is 36

(4) Number of one-one function from A to B is 2

82. A relation R is defined on the set of real numbers. If

{ } and [ ] represents fractional and greatest integer

function respectively and aRb such that

R = {(a, b ) : {a + 2} > [a + 2] > {b + 3}}, then

(1) R is reflexive

(2) Number of ordered pairs in R is 2

(3) R is symmetric relation

(4) R is null relation

83. The range of 22

2 1( )

2 2f x x

x x x

, where x > 0,

is equal to [a, b ) then a is equal to

(1) 1 (2) 2

(3) 3 (4) 4

84. Let f : R R defined by f (x ) = x + sin x . If g (x ) is

the inverse of f (x ), then the value of g (0) is equal to

(1) 1 (2) 2

(3) 12

(4) 13

85. Consider that1

2 ( ) 3 5 1f x f x x

, then the value

of f (1) is

(1) 1 (2) 2

(3) 3 (4) 4


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SECTION - IIAssertion – 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 : Set A has two elements, then numberof reflexive relations from A to A is 4.

and

Statement-2 : If [ ] represents greatest integer

function, thenlog [ ] sin

lim 0[ ]x

x x

x x

.



Statement-2 is NOT a correct explanation forStatement-1



87. Statement-1 :

2 2

20

2 sin cos cos cos2 2

limsinx

x x

x

.

and

Statement-2 :

1

sin 2

0

5lim tan

4

x

x x e

.





88. Statement-1 : If [ ] represents greatest integer

function, then4

lim([2 3] [3 2 ] 6) 4x

x x

.

and

Statement-2 :2 4

0

1 coslim

sinx

x x

x

= 0.





89. Statement-1 : f (x ) = |x – 4|, then f (1) = –1.

and

Statement-2 : f (x ) = |x – 4|, is not continuous at x = 4.

(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



90. Statement-1 :4 2

4 3

1 1lim

22 1x

x x

x x

.

and

Statement-2 : If

3

1 4 0

0

x x x f x k x

is

continuous at x = 0, then k = 12.






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Test Booklet Code

Test No. 4

Paper I

JEE (Main) 2014

for

A L L

I N D I

A A A

K ASH T E S T

S E R I E

S


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

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ANSWERS

1. (2)

2. (4)

3. (2)

4. (Deleted)

5. (4)

6. (1)

7. (3)

8. (2)

9. (3)

10. (3)

11. (1)

12. (3)

13. (4)

14. (1)

15. (3)

16. (2)

17. (2)

18. (3)

19. (2)

20. (3)

21. (3)

22. (1)

23. (2)

24. (Deleted)

25. (2)

26. (4)

27. (3)

28. (1)

29. (1)

30. (1)

PHYSICS CHEMISTRY MATHEMATICS

31. (1)

32. (2)

33. (2)

34. (3)

35. (1)

36. (4)

37. (4)

38. (3)

39. (3)

40. (2)

41. (3)

42. (2)

43. (3)

44. (4)

45. (1)

46. (4)

47. (3)

48. (1)

49. (3)

50. (2)

51. (1)

52. (3)

53. (2)

54. (4)

55. (4)

56. (2)

57. (1)

58. (2)

59. (4)

60. (1)

61. (2)

62. (1)

63. (3)

64. (2)

65. (1)

66. (3)

67. (4)

68. (3)

69. (4)

70. (1)

71. (3)

72. (2)

73. (1)

74. (3)

75. (3)

76. (4)

77. (1)

78. (1)

79. (4)

80. (3)

81. (1)

82. (3)

83. (1)

84. (2)

85. (4)

86. (4)

87. (4)

88. (2)

89. (4)

90. (2)

TEST - 4 (Paper-I)

JEE Main-2014_Test-5 (Paper-I) - Code-A.pdf

Documents

Transcript of JEE Main-2014_Test-5 (Paper-I) - Code-A.pdf