JEE Main-2014_Test-6 (Paper-I) - Code-A.pdf

8/19/2019 JEE Main-2014_Test-6 (Paper-I) - Code-A.pdf

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Roll No.:

Centre Code:

TEST No. 6

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

0 2 / 0 2 / 2 0 1 4


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TOPICS OF THE TEST

Test No. 6

Physics Moving Charges and Magnetism, Magnetism & Matter, Electromagnetic

Induction,Alternating Current, Electromagnetic Waves

ChemistryOrganic Chemistry (Some Basic Principles and Techniques),

Hydrocarbons, Environmental Chemistry, Haloalkanes and Haloarenes,

Alcohols, Phenols andEthers

Mathematics Application of Derivatives, Integrals, Applications of Integrals

Paper I


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Space for Rough Work

Test - 6 (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. Which one of the following circulation is correct?

i 1

X i 2

C 1

C 2

C 3

(1)

1

0 1.C

B dl i ∫

(2)

2

0 2.C

B dl i ∫

(3)

3

0 2 1. ( ) ∫

C

B dl i i

(4)

3

0 1 2. ( )C

B dl i i ∫

TEST - 6 (Paper-1)Time : 3 Hrs. MM : 360

2. Figure shows a regular hexagon made of uniform

wire. If a battery is connected across the ends AB ,magnetic field at O is B 0. If the same battery is

connected across A and C , the magnetic field at O

will be

O F C

A B

D E

(1) Equal to B 0

(2) Greater than B 0(3) Less than B 0

(4) May be less or greater than B 0

3. Figure shows two coils carrying equal currents. The

ratio of magnetic field at P due to coil-1 to coil-2 is

2R R

i

R

2

1

P i

R

(1)1

2(2) 1 : 2

(3)1

4(4)

1

41

2


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All India Aakash Test Series for JEE (Main) 2014 Test - 6 (Paper-I)

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4. The arrangement shown here is a Faraday's disc of

radius a which is rotating in a uniform magnetic field

B perpendicular to the plane of disc. The current

passing through the resistance is

(1)2B a

R

(2)

2

2

B a

R

R

B

(3)

2

2

B a

R

(4)2B a

R

5. In the cylindrical region shown, magnetic field is

diminishing at the rate of (T/s). The force on theelectron at a distance r along y -axis is

Y

X

B

e P

(1) ˆ( )2

r e i (2) ˆ( )

2

r e i

(3)2

ˆ( )2

r e i (4)

2ˆ( )

2

r e i

6. A solenoid has an inductance L and a resistance R .

If the solenoid is connected to a battery, the time it

will take to reach half of its final equilibrium value is

(1) ln22

L

R (2)

2ln3

L

R

(3) ln2LR

(4) ln3LR

7. A wire forms a closed circular loop of radius 2 m and

resistance 6 . The circle is centred on a long

straight wire. (The straight wire is insulated). The

current changes according to i = (5 – 2 t 2)A.

The magnitude of current induced in the loop at

t = 1 s is

R

i

(1) 1 A (2) 2 A

(3) 3 A (4) Zero

8. Wire AB is moved with a velocity 2 m/s. Wire is

kept near a long current carrying conductor, as

shown. Emf induced in the wire is

(1) 0 ln32

(2) 05

ln32

3 m

5 A

2 m/s

B A

1 m

(3)05 ln3

(4) Zero


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9. EMF of the battery shown in the circuit varies withtime, so that the current is given by i = 3 + 5t ,where i is in ampere and t is in second. Theexpression for battery emf as a function of time is

E

R = 4

L = 6 H

(1) 10t + 32

(2) 20t + 42

(3) 20t + 18

(4) 10t + 22

10. The current density J inside a long, solid cylindrical

wire of radius a is along central axis and its

magnitude varies linearly with r as 0r

J J a

. The

magnetic field at2

ar is

(1)0 0

3

J a(2) 0 0

6

J a

(3)0 0

9

J a(4)

0 0

12

J a

11. An ideal choke takes a current of 8 A whenconnected to an a.c. source of 100 V and 50 Hz. Apure resistance under the same conditions takes acurrent of 10 A. If two are connected in series to ana.c. supply of 100 V and 40 Hz, then current in thecircuit is

(1) 10 A (2) 8 A

(3) 5 2 A (4) 10 2 A

12. I f a direct current of value "a" ampere issuperimposed on an ac i = b sint flowing through awire, the effective value of resulting current in thecircuit is

(1)2

b (2)

2

b a

(3)

2

22

b a (4)

2 2

2

a b

13. An electron moves in a uniform magnetic field andfollows a spiral path as shown in figure. Which of thefollowing statement is incorrect?

(1) Angular velocity of electron remains constant

(2) Magnitude of velocity of electron decreasescontinuously

(3) Net force on the particle is always perpendicularto direction of motion

(4) Magnitude of net force on the electrondecreases continuously

14. A bar magnet is moved between two circular coils Aand B with a constant velocity v as shown. Then thecoils

v

A B

(1) Repel each other

(2) Attract each other

(3) Neither attract nor repel each other

(4) May attract or repel depending upon size of coils


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15. Slider of length 1 m moves with velocity 2 m/s in auniform magnetic field of 2T. Resistance of the slideris 2 . The magnitude of external force required tomaintain the velocity is

3 6 v

× B

(1) 1 N (2) 2 N

(3) 4 N (4) 6 N

16. A copper rod is bent into a semicircle of radius a andis being rotated with an angular velocity in themagnetic field shown. Resistance of the circuit is

negligible. Amplitude of current through the circuit is

× B

C

O ×

a O

(1)2 21

2 B a C

(2)2 21

4Ba C

(3)2 21

8Ba C

(4) 2 22 Ba C

17. A particle of mass m and charge q is released fromrest at the origin as shown in figure. The speed ofthe particle when it has travelled a distance d alongthe z axis is given by

(1)02qE d

m

(2) 00

E d B

E 0

y

x

B 0

z

m q ,

(3)0

m

qE d

(4)0

2m

qE d

18. A magnetic needle of negligible width and thicknessas compared to its length oscillates in horizontalplane with period T . If it is broken into n equal parts,then the time period of each part in same field

will be

(1) T n (2) nT

(3)T

n (4)

T

n

19. Current in R 3 just after closing the switch and insteady state respectively, will be

R 1

R 2

R 3

LE

C

S

(1) 0, 0 (2)3

,0E

R

(3)3

0,E

R (4) Indeterminate


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20. In the arrangement shown, maximum current that will

flow in the circuit is

(1) 06C

V L

(2) 0C

V L

– + + –4

0V V

0

S

L

2C C

(3)0

2 6

V L

C

(4)0 6

2

V C

L

21. In the figure shown I L = 0.8 A and I

C = 0.6 A. The

current drawn from the source is

L

C

I L

I C

I ~V

(1) 0.2 A (2) 0.4 A

(3) 0.6 A (4) 1 A

22. A parallel plate capacitor with plate area A and

separation between the plates d, is charged by a

constant current i . Consider a plane surface of area

2

A parallel to the plates and drawn symmetrically

between plates. The displacement current through

this area is

(1) i (2)2

i

(3)4

i (4) Zero

23. An E.M. wave going through vacuum is described by

E = E 0sin(kx – t ); B = B 0sin(kx – t ) then

(1) E 0k = B 0

(2) E 0B 0 = k

(3) E 0 = B 0k

(4) E 0 = B 0

24. A paramagnetic material is kept in a magnetic field.

The field is increased till the magnetization becomes

constant. If the temperature is now decreased, the

magnetization

(1) Will increase

(2) Will decrease

(3) Remains constant

(4) May increase or decrease

25. A toroid has a mean radius20

cmR

and a total

of 400 turns of wire carrying a current of 2 A.

A metallic ring at 300 K inside the toroid provides

the core. If the magnetization I = 4.8 × 10–2 A/m,

the susceptibility of metal at this temperature is

(1) 2.4 × 10–5 (2) 4.2 × 10–5

(3) 2.4 × 10–4 (4) 4.2 × 10–4

SECTION - IIAssertion – 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 : Co-axial cable containing equal andopposite current in wire and hollow conductingcylinder is used to produce zero magnetic fieldsoutside the cable.

and

Statement-2 : Net current enclosed for the cable bya concentric outer circular loop is zero.

(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

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

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

27. Statement-1 : In an a.c. series circuit, the appliedinstantaneous voltage is not equal to the algebraicsum of instantaneous voltage across the differentelements of the circuit.

and

Statement-2 : The RMS voltage across differentelements are not in phase, only their phasor sum isequal to the applied RMS voltage.

(1) Statement-1 is True, Statement-2 is True;Statement-2 is a correct explanation forStatement-1




28. Consider two small elements of current carrying wire

as shown.

i 1

i 2

12

Statement-1 : The force on 1 due to 2 is downwardsin the plane of paper but the force on 2 due to 1 iszero.

and

Statement-2 : Electromagnetic waves carrymomentum with them.





29. An inductor is connected to a battery through aswitch.

Statement-1 : The emf induced in the inductor ismuch larger when the switch is opened ascompared to the emf induced when the switch isclosed.

and

Statement-2 : When the switch is opened, the currentsuddenly tends to drop to zero. But when the switchis closed, due to finite resistance of the circuit, thecurrent does not suddenly build up to the maximumvalue.





30. Statement-1 : In electromagnetic waves energy isequally shared between electric field and magneticfield.

and

Statement-2 : Unit vector of E B

gives thedirection of propagation of electromagnetic wave.






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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.

NO2

Cl

+ OH– (X) (Y)

H O3+

Identify the product (Y)

(1)

OH

NO2

(2)

Cl

OHO N2

(3)

NO2

NO2

(4)

NO2

OH

32. In which of the molecules all the effects namely

inductive, resonance and hyperconjugation operate?

(1) CH3 – CH = CH2

(2) ClCH2CH2OH

(3) CH3 – CH = CH – CHO

(4) CH2 = CH – CH = CH2

PART - B (CHEMISTRY)

33. 2 52 5

C H ONaHOCl KOH

3 2 in C H OHCH CH CH (A) (B) (C)

The product (C) formed in the given sequence ofreactions will be

(1) CH3 – CH = CH – OC2H5

(2) CH – CH – CH3 2

OH

OC H2 5

(3) CH – CH – CH3 2

OC H2 5

OH

(4) CH3 – CH2 – CH = O

34. Which of the following hydrocarbon gives thefollowing compounds on ozonolysis followed byreductive hydrolysis?

I. CH3 – CO – CH3

II. CH3CHO

III. CH3 – CO – CHO

(1) CH – CH = C – C = CH – CH3 3

CH3

CH3

(2) CH – C = C – CH = CH – CH3 3

CH3

CH3

(3) CH – CH = C – CH = C – CH3 3

CH3 CH3

(4) Both (2) & (3)


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35. Arrange the following compounds in the decreasing

order of their basic strength

N

H

NH2

N

I II III IV

C H – NH – C H2 5 2 5

(1) IV > I > III > II

(2) II > III > IV > I

(3) I > IV > II > III

(4) IV > II > III > I

36. Consider the following base induced elimination

reactions

CH – CO – CH – CH3 3

Br

CH – CO – CH – CH23 2

B / –

B / –

CH – CO – CH = CH3 2

(X)

Br(Y)

(Z)

Which one of the following statements is true?

(1) (X) reacts faster than (Y)

(2) (Y) reacts faster than (X)

(3) Both (X) and (Y) react at the same rate

(4) Both (X) and (Y) do not react

37. Identify the product (B) in the following reaction

18

2 2 2 2HOCH C C CH CH OH H

Lindlar 's H /

Catalyst(A) (B)

(1) HOCH – CH2

O – CH2

CH2

CH2

18

(2) CH – CH – CH – CH OH2 2 2

18

CH – O2

(3)O

18

(4)O

38. Find out the reagent (X) used in the followingreaction

MeBaeyer's

Reagent(A)

(X)Me

OH

O

(1) NaBH4 (2) (i) O3, (ii) Zn/H2O

(3) K2Cr2O7 /H+ (4) NH2 – NH2 /KOH

39. Name the product formed in the following reaction

CH – CH – CH – CH – CH – CH3 2 2 3

Cl Cl

+ alcoholic Na S

2

(1) CH – CH – CH – CH – CH – CH3 2 2 3

SH SH

(2) CH – CH – CH – CH3 3

CH – CH2 2

(3) CH – CH CH – CH3 3

S

CH – CH2 2

(4) CH – CH – CH – CH – CH – CH3 2 2 3

SH Cl


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40. Arrange the following compounds in the increasing

order of their acidic strength

HCOOH CH3 – COOH C6H5 – COOH

I II III

(1) II < III < I (2) II < I < III

(3) III < II < I (4) III < I < II

41. (+) mandelic acid has a specific rotation of +158º.What would be the specific rotation of a solution

containing 35% of (–) mandelic acid and 65% of (+)

mandelic acid?

(1) (–) 55.3° (2) (+) 47.4°

(3) (+) 102.7° (4) (–) 102.7°

42. Identify the reagent (X) in the following reaction

OH

CH3

(X)

Br

CH3

(1) PBr3 (2) SOBr2

(3) HBr (4) Both (1) & (2)

43. Arrange the following compounds in the decreasing

order of their reactivity towards SN2 reaction

I. CH3 – CH2 – CH2 – Cl

II. CH2 = CH – CH2 – Cl

III. CH3 – CH = CH – Cl

(1) II > I > III (2) I > II > III

(3) II > III > I (4) I > III > II

44. Which one of the following compounds is most

acidic?

(1)

OH

(2)

COOH

(3)

O OH

OHO

(4) C

O

OHHO

45. Which one of the following statements is incorrect?

(1) m-cresol when treated with Br2(H2O) gives

tribromoderivative

(2) Picric acid and phenol can be distinguished by

FeCl3

(3) o-nitrophenol is steam volatile

(4) Phenol and benzyl alcohol can be separated byNaOH

46. Identify the missing reactant in the following reaction

CH3CH2NH2 + (X) + KOH CH3CH2NC + KCl + H2O

(1) CH3Cl (2) CH2Cl2

(3) CHCl3

(4) CCl4

47. What is the major product formed in the following

reaction?

OH

+ K S O2 2 8 Major productOHH O

–

2

(1)

OH

OH

(2)

SO H3

OH

(3)

OH

SO H3

(4)

OH

OH

48. Pesticides consist of

(1) Insecticides (2) Herbicides

(3) Fungicides (4) All of these

49. Which of the following is not a greenhouse gas?

(1) CO2 (2) N2O

(3) CO (4) CH4


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50. Which of the following free radicals is most stable?

(1)

CH2(2)

CH3

(3)

CH3

(4)

CH3

51. 2CH CH C CH HBr A(Major) ,

The product 'A' is

(1) CH3 CH CHC

Br

(2) CHC

Br

CH2 CH2

(3) CH2C

Br

CH2 CH

(4) CHCH

Br

CH2 CH

52. The number of optically active isomers of the following

compound is

CH – C – CH = CH – C – CH3 3

H H

Cl Cl

(1) 2

(2) 4

(3) 6

(4) 8

53. The decreasing order of stability of carbocations is

I.3 3

CH CH CH

II.3 2

CH O CH

III. 3 2CH S CH

(1) III > II > I (2) II > III > I

(3) I > III > II (4) I > II > III

54. Which one of the following compounds gives instantprecipitate with aqueous AgNO3?

(1) Cl (2)

Cl

(3) CH2 = CH – Cl (4)

Cl

55. Identify the major product formed in the followingreaction

OH

OH+

Major product

(1)O

(2)

O

O

(3)

O

O

(4)O


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SECTION - II

Assertion – Reason Type Questions







56. Statement-1 : Neopentyl chloride undergoes

nucleophilic substitution by SN1 mechanism only.

and

Statement-2 : Neopentyl chloride is a primary alkyl

halide.


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



57. Statement-1 : Dipole moment of CH3 – F is greater

than that of CH3 – Cl.

and

Statement-2 : C – F bond is more polar than C – Cl

bond.

(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



58. Statement-1 : Butan-1-ol and butan-2-ol can bedifferentiated by I2 /NaOH.

and

Statement-2 : Butan-2-ol is more acidic thanbutan-1-ol.





59. Statement-1 : If BOD level of water in a reservoir isgreater than 5 ppm, it is highly polluted.

and

Statement-2 : High biological oxygen demandmeans low activity of bacteria in water.






60. Statement-1 : The nitro group of nitrobenzene isdeactivating and mata directing towards electrophilicaromatic substitution.

and

Statement-2 : Nitrobenzene reacts with CH3 – Cl in

presence of AlCl3 to give m-nitrotoluene.






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This section contains 25 multiple choice questionsnumbered 61 to 85. Each question has 4 choices (1), (2),(3) and (4), out of which ONLY ONE is correct.

61. If

4 2

22

4log

x dx

x

∫ , then

(1) + 2 is irrational number

(2) = 2 (1 – )

(3) (, ) lies on x 2 – 4y 2 = 2(x – 1)

(4) (, ) lies on x 2 – 4y 2 = 4(x + 1)

62. If23 , 2

( )

14 48 , 2

x x f x

a x x

and f (x ) has a local maxima at x = 2, then

(1) Least value of 'a' is 2011

(2) Greatest value of 'a' may be 2011

(3) a can not be determined

(4) The greatest value of 'a' may be 2345

63. Iflog (1 )

( )1

x e

x

x e dx f x c

e

∫ , then f (x ) =

(1) –log(1 + e x )

(2)1 x

x

e

(3) 21

log(1 )2

x e

(4) 21

log(1 )2

x e

64. If

2

2

03

3 cos sin 0,y x

t dt tdt

∫ ∫ thendy

dx

(1) 23 cos x

(2) 21

2 .sin( )y y

(3)2

2

3 cos

2sin( )

x

y

(4) 2

2

3 cos

2 sin( )

x

y y

65. Tangent to a curve xy = a2 at point P meets the

x -axis in A and y -axis in B . Then, the ratio AP : PB is

(1) 1 : 2 (2) 2 : 1

(3) 1 : 1 (4) 2 : 3

66. For the curve y = a log(x 2 – a2), where a is positivenumber. The algebraic sum of the tangent and

subtangent at any point on curve is

(1)xy

a(2)

2xy

a

(3)2

xy

a(4)

x y

a

67. On the interval [ 2, 2] , one of the value of 'c ' in

Rolle's theorem for f (x ) = 2x 3 + x 2 – 4x – 2 is

(1)3

5(2)

4

5

(3)2

3(4)

2

3

PART - C (MATHEMATICS)


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68. The sum of an infinitely decreasing geometricprogression is equal to the least value of the function

2 25( ) 312

f x x x and the first term of the

progression is equal to the square of its commonratio. Then, the common ratio is

(1)2 1

(2)3 1

(3) 2 3 (4)2 2

3

69. Let f (x ) = |x 2 – 5x + 6|,12

0,5

x

. Then, the sum

of the maximum and minimum values of f on12

0,5

is

(1) 6 (2) 5

(3)13

2(4)

11

2

70. The value of 2 20

logx dx

x

∫ is equal to

(1) loge ()2 (2)

(3) log ( )e (4) 22

71. The area bounded by x 3 = 4(x – y )2 and x = 1 is

(1)4

5 sq. units (2)

2

5 sq. units

(3) 1 sq. unit (4) 2 sq. unit

72. If 1/3

7 4 4 4/3 41 ( 1) (4 3)x x dx k x x c ∫ , then

the value of k is equal to

(1)1

112(2)

1

28

(3)3

112(4)

1

56

73. If y (x – y )2 = x , then the value of3

dx

x y ∫ equals

(1) 2log ( ) 12 e x

x y c

(2) 21

log ( ) 12 e

x y c

(3) 21log ( ) 12 e x x y c

(4) 2log ( ) 1e x y c

74. The value of 2sec (2 sec )

(1 2sec )

x x dx

x

∫ is equal to

(1) 2cosecx + cotx + c

(2) (2cotx + cosecx )–1 + c

(3) 2cosecx – cotx + c

(4) (2cosecx + cotx )–1 + c

75. The value of

log 5

0

1

3

e x x

x

e e dx

e

∫ is equal to

(1) 3 + (2) 3 –

(3) 4 + (4) 4 –

76. The maximum value of2

1( 1)

1

ax

a

e dx

∫ , aR, is

attained at

(1) a = 2 (2) a = 1

(3) a = –1 (4) a = 0

77. If [ t ] stands for the integral part of t , then the value of

5 /12

0

[tan ]x dx

∫ equals

(1)2

(2)

(3)4

(4) 2


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78. The funct ion

/6

( ) (4sin 3cos )x

F x t t dt

∫ attains

least value on3

,4 4

at x equals

(1)3 (2)

2

(3)3

4

(4)

4

79. The area bounded by the curve y = 2x – x 2 and the

straight line y = –x is

(1) 3 (2)7

2

(3) 92

(4) 4

80. The area bounded by the curve y 2 = 4a(a – |x – a|),

a > 0, is

(1)28

3

a(2)

216

3

a

(3)219

3

a(4)

213

3

a

81. The area of the region bounded by the curves y = x 2,

1y

x and

1

2x is log

e 2 – p , then p equals to

(1)5

24(2)

5

24

(3)7

24(4)

7

24

82. The graph of y = f (x ), where f (x ) 0, meets x -axis

in two points (0, 0) and (2, 0) and encloses an area

of3

4 square units with the axes. Then the value of

2

0

( ) ,xf x dx ∫ equals to

(1)3

2(2)

3

4

(3)3

4

(4) 1

83. If2

1 1 1.....

1 2 2n S

n n n n

, then the

value of limn S n is equal to

(1) loge 2

(2) 2 + 2loge 2

(3) 2 + loge 2

(4) 2loge 2

84. The number of critical points for the function

31 2( ) sin tan (sin 1)tan ,3 8

f x x x

where < < 2, 2 1 ,2

x n

where n is a integer, is

(1) 4

(2) 2

(3) 1

(4) 0


17/20



15/16

85. For x (0, ), the least value of2

2 cos( )

sin

x f x

x

is

(1) 2

(2) 3

(3) 4

(4) 3

SECTION - II

Assertion – Reason Type Questions







86. Statement-1 : The function f (x ) = x 3 + bx 2 + cx + d,

where 0 b 2 < 3c , is strictly increasing in (–, ).

and

Statement-2 : If f is continuous on [a, b ],

differentiable in (a, b ) and f (x ) > 0 x (a, b ),

then f is strictly increasing in (a, b ).


Statement-2 is a correct explanation for

Statement-1


Statement-2 is NOT a correct explanation for

Statement-1



87. Statement-1 : The function f (x ) = 2 – (x – 1)2/3

attains maximum value 2 at x = 1.

and

Statement-2 : If f x does not exist at a point x 0but f x exists in a neighbourhood of x 0 and

changes its sign at x 0, then x 0 may be a point of

local extremum for f (x ).





88. Statement-1 : The function

2 12 2 sin , 0( )

2, 0

x x f x x

x

has local maximum at x = 0.

and

Statement-2 : If f (x ) is a real valued function suchthat f (x + y ) = f (x ) + f (y ) then

2

2

4f x f x dx

∫






18/20



16/16

89. Statement-1 :

2tan sec tan ,x e x x x x dx f x c ∫ thenf (0) = 2

and

Statement-2 : 21

1x x x

e x dx e f x c

x

∫

then f (1) = 2.





90. Statement-1 : If [ ] represents the greatest integer

function then0

4sin cos cos 04 4 2

x x x dx

∫

and

Statement-2 :

20

10

2sin cos 302 2

x x dx

∫ (1) Statement-1 is True, Statement-2 is True;


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

Statement-1




19/20

Test Booklet Code

Test No. 5

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


20/20

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

ANSWERS

1. (4)

2. (3)

3. (1)

4. (1)

5. (2)

6. (2)

7. (3)

8. (3)

9. (4)

10. (2)

11. (3)

12. (2)

13. (2)

14. (1)

15. (1)16. (2)

17. (1)

18. (2)

19. (2)

20. (3)

21. (4)

22. (3)

23. (3)

24. (2)

25. (2)

26. (1)

27. (1)

28. (1)

29. (3)

30. (1)

PHYSICS CHEMISTRY MATHEMATICS

31. (2)

32. (4)

33. (2)

34. (2)

35. (1)

36. (3)

37. (4)

38. (4)

39. (1)

40. (4)

41. (2)

42. (3)

43. (2)

44. (1)

45. (4)46. (2)

47. (4)

48. (3)

49. (3)

50. (3)

51. (4)

52. (3)

53. (2)

54. (1)

55. (4)

56. (3)

57. (1)

58. (1)

59. (2)

60. (1)

61. (1)

62. (4)

63. (3)

64. (4)

65. (3)

66. (2)

67. (1)

68. (4)

69. (2)

70. (1)

71. (2)

72. (1)

73. (4)

74. (2)

75. (2)76. (1)

77. (4)

78. (3)

79. (3)

80. (2)

81. (3)

82. (4)

83. (2)

84. (3)

85. (1)

86. (2)

87. (2)

88. (4)

89. (3)

90. (3)

TEST - 5 (Paper-I)

JEE Main-2014_Test-6 (Paper-I) - Code-A.pdf

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