JEE Main 2014_Test 2 (Paper I) Code A

8/10/2019 JEE Main 2014_Test 2 (Paper I) Code A

1/20

Roll No.:

Centre Code:

TEST No. 2

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 ObjectiveQuestions

Section II : Assertion ReasonType Questions

17/11/2013


2/20

TOPICS OF THE TEST

Test No. 2

Physics Work, Energy & Power, System of Particles and Rotational Motion

Chemistry States of Matter, Thermodynamics, Equilibrium, Redox Reactions

Mathematics Permutations and Combinations, Sequences and Series, Matrices,

Determinants

Paper I


3/20

Space for Rough Work

Test - 2 (Paper-I) All India Aakash Test Series for JEE (Main) 2014

1/14

PART - A (PHYSICS)

SECTION - IStraight Objective Type Questions

This section contains 25 multiple choice questionsnumbered 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. A system acted on by a force Fmove along x-axisfrom x = 2R to x = R. The force has only

x-component whose variation with x is shown in

figure. The curves are arcs of circle of radius R. Findthe work done on the system

R O2R

R

R

R

x(m)

(N)FxDirection ofmotion of system

(1)23

4

R (2)

2

4

R

(3)2

4

R(4)

23

4

R

2. A 2 kg body moves under the action of force such

that its position xas a function of time tis given by

x= 5t, xis in metre and tin second. Find the workdone by force in the first one second

(1) Zero (2) 5 J

(3) 2.5 J (4) 10 J

TEST - 2 (Paper-1)Time : 3 Hrs. MM : 360

3. A block is projected upward from the bottom of an

incline, having inclination , with initial speed u. Theblock reaches maximum height and then comesback to initial position with half speed.

u

L

The distance (L) travelled by the block, while goingup on the incline is

(1)25

8 sin

u

g (2)

25

16 sin

u

g

(3)24

sin

u

g (4)

2

4 sin

u

g

4. A pendulum bob of mass mwith string length lcanswing in a vertical plane. The bob is given an initialvelocity uat the lower most position. At what initial

velocity, tension in thread and velocity of bobbecome zero simultaneously

(1) 2g

(2) 4g

(3) 5g

(4) g


4/20


All India Aakash Test Series for JEE (Main) 2014 Test - 2 (Paper-I)

2/14

5. A block of mass m is released from a height h1along a smooth track as shown in figure. Find the

safe value of radius of curvature at point 3, so thatthe block does not fly off the track (Given

h1> h2)

h1

h2

3

2

1

(1) 1 21

( )2

h h (2) 1 22( )h h

(3) 2(h1 h2) (4)1 2

2

h h

6. A force acting on a certain particle depends on theparticles position in the xy-plane. This force Fis given

by the expression 2 N/mF xyi xyj . Where xand

y are expressed in metre. The work done as theparticle moves along the straight line OCis

C

O(0, 0)(1, 0) (m)x

(1, 1)(1, 0)

y(m)

(1) 2 J (2)3

J2

(3)1

J2

(4)2

J3

7. A small marble ball is released from point A on asmooth parabolic surface y= x2as shown in figure.

The velocity of ball at point Bis [g= 10 m/s2]

x= 2 m x= +1 m

A

hA B

(1) 15 m/s (2)15

2 m/s

(3) 2 15 m/s (4)15

2m/s

8. A single conservative force F(x) acts on a 1.0 kgparticle that moves along the x-axis. The potentialenergy U(x) is given by U(x) = 20 + (x 2)2, where

x is in meters. At x = 5.0 m the particle has a

kinetic energy of 20 J. Find the greatest value of x1up to which particle can move

(1) 8.37 m (2) 3.38 m

(3) 7.38 m (4) 5.24 m

9. In the given figure mass of block Ais mand that of

Bis 2m. They are attached at the ends of a springand kept on a smooth horizontal surface. Now, thespring is compressed by x0 and released. Find

displacement of block Bby the time compression of

the spring is reduced to 02

x

m 2m

A B

(1)0

3

x

(2)0

2

x

(3)0

6

x

(4)0

4

x


5/20



3/14

10. Two blocks of masses mand 2mare connected by

a relaxed spring with a spring constant K. The blocks

rest on a smooth horizontal table. At t= 0, the block

on the right is given a sharp impulse J towards the

left, and the blocks begin to slide along the table.

Find the maximum compression in the spring

m 2m

J

(1)2

3J

mk(2)

1

6J

mk

(3)3

2J

mk(4)

6J

mk

11. Mass Aof 2mand mass Bof mare connected with

an inextensible string of length lie on a smooth

horizontal plane. Ais given a velocity of vm/s alongthe ground perpendicular to line AB as shown in

figure. Find the tension in string during their

subsequent motion

A m(2 )v

B m( )

(1)23

2

mv

(2)

2

2

mv

(3)22

3

mv

(4)

2

3

mv

12. A block of mass m is released at the top of a

hemispherical wedge of mass Mas shown in figure.

Find the displacement of wedge, when the block

reaches the angular position . All surfaces are

smooth

M

R

m

m

(1)sinmR

m M

(2)cosmR

m M

(3) sinMRm M

(4)cosMR

m M

13. A block Bof mass mis projected with velocity vas

shown. The ground is smooth but there is friction

between Aand B. The resulting collision is elastic.

Assume that Adoes not fall off B, the final common

velocity of Aand Bis

m 2mv

m AB

B

(1)2

v(2)

3

v

(3)4

9

v(4)

3

4

v


6/20



4/14

14. Two identical discs initially at rest are in contact on

a table. A third disc of same mass but of double

radius strikes them symmetrically and itself comes

to rest after impact. The speed of any of the smaller

disc after impact is

2R

m

m

mR

R

(1)2

v

(2)3

2

v

(3)2

4

v

(4)3

4 2

v

15. Angular momentum of projectile, about point of

projection, when it strikes the ground is

u

x

R Range on ground

(1) sinmuR k

(2) sinmuR k

(3) cosmuR k

(4) cosmuR k

16. Initial angular velocity of the system is 0and framelength is a.System is rotating on the vertical axleand frame has negligible mass as compared to thefour masses each of mass m. Due to an internalmechanism the spokes in the frame lengthen to 2a.Find new angular velocity of the system

m

0

m

mm

a

(1) 0 (2)03

4

(3) 02

(4) 0

4

17. A particle of mass 2 kg is just dropped from a certain

height. At the same time another particle of mass1 kg is projected upwards with velocity 60 m/s. After

2 second, find the velocity of centre of mass (Take

g= 10 m/s2)

(1) 10 SI Units

(2) 20 SI Units

(3) Zero

(4) 15 SI Units

18. A particle of mass 2 kg has a velocity 21v t j and

another particle of mass 1 kg has a velocity 22v t i .

Find the net force on centre of mass at 2 s

(1) 8 units

(2) 10 units

(3) 2 units

(4) 68 units


7/20



5/14

19. The body is released from A. Length ABin the figure

shown is 5 m. Friction is sufficient for pure rolling to

take place. Find the maximum time which any

uniform body (which can roll) can take to reach the

bottom is

5 m

= 30

A

B

(1) 2 s (2) 3 s

(3) 1 s (4) 4 s

20. A solid sphere of mass 2 kg and radius 1 m is

moving on a smooth ground with linear velocity

v0 = 4 m/s and angular velocity 0 = 9 rad/s asshown in figure

v0

0

R= 1m

m= 2 kg

It collides elastically with a rough wall of coefficientof friction and after collision with the wall rolls

without slipping in opposite direction. Find the

coefficient of friction

(1)3

4(2)

3

5

(3)1

4(4)

1

2

21. The disc rolls without slipping on a smooth horizontalsurface as shown. The speed of the centre C is v.

The speed of point A on the disc at the instantshown is

(1) v

(2) vcos

(3) 2v

C A

(4) vsec

22. A small sphere of mass 1 kg is rolling without

slipping with linear speed200

m/s7

v . It leaves

the inclined plane at point C. Find the kinetic energy

at top just before leaving the inclined planeneglecting any impact at Band assuming no slippinganywhere.

30

C

1 m

BA

v

(1) 20 J (2)100

J7

(3) 10 J (4) 15 J

23. The moment of inertia of a straight wire about an axisperpendicular to the wire and passing through one of

its end is I. This wire is framed into a circle (a ring)of single turn. The moment of inertia of this ringabout an axis passing through centre andperpendicular to its plane would be

(1) 23

I

(2) 24

I

(3) 24

3

I

(4) 2

3

4

I


8/20



6/14

24. As shown in figure a small block of mass m= 1kg

is placed over a wedge of mass M = 4 kg. All

surfaces are smooth. Mass m is released from rest

from top position of wedge. Find the velocity of block

at the instant, it is leaving the wedge.

4 m

M = 4 kg 2 m

m

(1) 2

(2) 4

(3) 4 2 m/s

(4) 2

25. Three identical rods of mass M and length L areplaced on one another on the table so as to produce

the maximum overhang as shown in figure. The

maximum possible overhang will be

(1)2

3

L

(2)11

12

L

(3)3

L

(4)13

12

L

SECTION - IIAssertion Reason Type Questions

Directions : Questions number 26 to 30 are Assertion-

Reason type questions. Each of these questionscontains two statements. Statement-1 (Assertion) and

Statement-2 (Reason). Each of these questions also hasfour alternative choices, only one of which is the correct

answer. You have to select the correct choice.

26. Statement-1 : The net work done by the non-conservative forces in an isolated system equals the

change in the system's total mechanical energy.

Wnoncon= (K+ U)

and

Statement-2 : The total work done by all forces(conservative + non-conservative) equals the change

in the kinetic energy of the system.

Wcons+ Wnoncons = K

(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

27. Statement-1 : The work done by spring forcedepends on the initial and final state of spring only.

and

Statement-2 : The net work done by the spring force

is zero for any path that returns to the initial position.



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




9/20



7/14

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.

Choose the correct answer :

31. When Cr2O72 ion acts as an oxidant in acidic

medium, Cr3+ion is formed. The number of mole ofSn+2 that are oxidised to Sn+4 by one mole ofCr2O7

2ion would be

(1) 3 (2) 2

(3)2

3(4)

3

2

PART - B (CHEMISTRY)

28. Statement-1 : In an oblique collision between twosmooth balls, along tangential axis (along tangent to

surfaces in contact) velocity of each particle remainsunchanged.

and

Statement-2 : No contact force acts along tangentialaxis for oblique collision between smooth surface.

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




29. Statement-1 : The angular velocity of a rotating body

is the same relative to any point on it.

and

Statement-2 : The sense of angular velocity andangular acceleration is always same.





30. Statement-1 : When a wheel rolls on a horizontalsurface, any point on its circumference moves alonga curved path called cycloid.

and

Statement-2 : Distance moved by the centre in onerevolution, when a wheel rolls on a horizontal surfaceis 2r.



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


32. Fe0.94O Fe+3, equivalent weight of reactant will

be (molecular mass of Fe0.94O is M)

(1)M

2(2)

M

3

(3) 3M8

(4) M0.82

33. Which of the following gas has higher value of thevan der Waals constant 'b'?

(1) N2

(2) O2

(3) O3

(4) B2


10/20



8/14

34. Which of the following options is correct regardingvan der Waal's constants a and b?

(1)3 2 3 2NH N NH N

a a and b b

(2)3 2 3 2NH N NH N

a a and b b

(3)3 2 3 2

NH N NH Na a and b b

(4)3 2 3 2NH N NH N

a a and b b

35. A vessel containing 1.0 gm of oxygen at a pressure

of 10 atm and a temperature of 47C. The pressure

drops to5

th8

of its original value and temperature

falls to 27C due to leakage of the gas, then mass

of oxygen leaked out will be

(1) 0.432 gm (2) 0.333 gm

(3) 0.232 gm (4) 0.123 gm

36. At constant pressure what would be the percentage

decrease in the density of an ideal gas for an

increase in the temperature by 10%

(1) 9.1% (2) 8.1%

(3) 7.1% (4) 6.1%

37. The molar heat capacity of water in equilibrium with

ice at constant pressure is

(1) Zero

(2) Infinity ()

(3) 40.45 kJ K1mol1

(4) 75.48 J K1mol1

38. One mole non-ideal gas undergoes change of state

(1 atm, 2 L, 90 K) (2 atm, 3 L, 300 K) with a

change in internal energy 35 L atm. H for the

change will be

(1) 29 (2) 39

(3) 49 (4) 59

39.ogasH of a liquid is 1.437 kcal mol

1 and omS is

5.26 cal mol1K, melting point will be

(1) 0C (2) 273C

(3) 273C (4) 0 K

40. The enthalpy of combustion of H2(g) at 298 K to give

H2O(g) is 249 kJ mol1 and bond enthalpies of

H H and O = O are 433 kJ mol1

and 492 kJ mol1

respectively. The bond enthalpy of O H would be

(1) 464 kJ mol1

(2) 464 kJ mol1

(3) 232 kJ mol1

(4) 232 kJ mol1

41. The maximum work done by the gas, when pressure

on 10 g of H2 is reduced from 20 atm to 2 atm at

a constant temperature 300 K reversibly is (the gas

behaves ideally)

(1) 2.872 J (2) 28.72 kJ

(3) 28.72 kcal (4) 28.72 erg

42. The difference in H and U for combustion of

benzoic acid (solid) at 300 K is equal to

(1) +1.247 kJ

(2) 1.247 kJ

(3) 1.99 kJ

(4) +1.99 kJ

43. In standardisation of Na2S2O3 using K2Cr2O7 by

iodometry, the equivalent mass of K2Cr2O7 is (At.mass K = 39, Cr = 52, O = 16)

(1) 147 (2) 94

(3) 49 (4) 74

44. If a 0.1 M solution of HCN is 0.01% ionised, the

ionisation constant for HCN is

(1) 105 (2) 106

(3) 1 108 (4) 1 109


11/20



9/14

45. The solubility product of a salt having generalformula MX

2in water is 4 1012. The concentration

of M+2 ions in the aqueous solution of the salt is

(MX2 M+2+ 2X)

(1) 2 106M

(2) 1 104M

(3) 6 104M

(4) 4 1018M

46. Which of the following buffer solution turns invalid onaddition of 10 ml of 1 M HCl?

(1) 100 ml having 0.15 M NH3and NH4Cl each

(2) 100 ml having 0.2 M NH3and NH

4Cl each

(3) 100 ml having 0.2 M NH3and 0.1 M NH4Cl each

(4) 100 ml having 0.05 M NH3and NH4Cl each

47. At the half way in titration of a weak acid with strongbase the pH was measured as 5. What is the pH ofthe weak acid solution that is 0.01 M is the acid?

(1) 4.2 (2) 6.7

(3) 3.5 (4) 7.6

48. Which of the following is most soluble?

(1) Bi2S3(Ksp= 1 1020)

(2) MnS (Ksp= 7 1016)

(3) CuS (Ksp= 8 1037)

(4) Ag2S (Ksp= 6 1051)

49. The percentage of dissociation of 0.5 M NH3at 25Cin a solution of pH = 12 is

(1) 2%

(2) 20%

(3) 4%

(4) 40%

50. The acid ionisation constant for

22 2Zn H O Zn(OH) H

is 1 109 the pH

of 0.001 M solution ZnCl2is

(1) 4 (2) 6

(3) 8 (4) 9

51. Which salt has highest extent of hydrolysis?

(1) CH3COONa

(2) NH4Cl

(3) NH4CN

(4) NaCl

52. For the process H2O(l) (1 bar, 373 K) H2O(g)

(1 bar, 373 K), the correct set of thermodynamicsparameters is

(1) G = 0, S = +ve (2) G = ve, S = ve

(3) G = +ve, S = +ve (4) G = 0, S = ve

53. For, N2 NH3, the equivalent weight of N2 is

(M is the mol.wt. of N2)

(1)M

3(2)

M

4

(3)M

6(4)

M

8

54. 10 ml of H2O2 solution (vol. strength x) required

10 ml of 41

N MnO

0.56

solution in acidic medium.

Hence x is

(1) 0.56 (2) 5.6

(3) 0.1 (4) 10

55. Which of the following can be oxidised further witha strong oxidising agent?

(1) SO3 (2) MnO2

(3) Al2O3 (4) CrO3


12/20



10/14

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 correct

answer. You have to select the correct choice.

56. Statement-1 : Absolute zero is the theoretically

minimum possible temperature.

and

Statement-2 : At any temperature, less thanabsolute zero, the volume of an ideal gas becomesnegative, which is impossible.





57. Statement-1 : There is no change in enthalpy of anideal gas during compression at constanttemperature.

and

Statement-2 : Enthalpy of an ideal gas is a functionof temperature and pressure.





58. Statement-1 : Enthalpy and entropy of any perfectlycrystalline substance in the standard states aretaken as zero.

and

Statement-2 : At absolute zero, particle of theperfectly crystalline substance become completelymotionless.





59. Statement-1 : The value of van der Waal's constant'a' is larger for NH3than PH3.

and

Statement-2 : Hydrogen bonding is present in NH3.





60. Statement-1 : NaCl can be hydrolysed.

and

Statement-2 : It is a salt of strong acid and strong

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






13/20



11/14

PART - C (MATHEMATICS)

SECTION - I

Straight 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. The number of integers lying between 3000 and 8000

(including 3000 and 8000) which have at least two

digits equal is

(1) 4384 (2) 2755

(3) 1977 (4) 2481

62. Let x ky z= 0, kx y z= 0, x+ y z= 0.

If x= 1 is one of solution then the value of kis

(1) 2, 1

(2) 1, 0

(3) 1, 0, 1

(4) 1

63. P(x), Q(x), R(x) be polynomials of degree 3, 4, 5

respectively and

( ) ( ) ( )

( ) ( ) ( ) ( ) ,

( ) ( ) ( )

P x Q x R x

F x P Q R R

P Q R

F(x) = 0 has

(1) At least 2 real roots

(2) At least 3 real roots

(3) Exactly 1 real roots

(4) Exactly 2 real roots

64. Number of values of in [0, 2] for which equation

(cos3)x y+ z= 0, (cos2)x+ 4y+ 3z= 0 and

x+ 7y+ 7z= 0 has non-trivial solution is

(1) 4 (2) 3

(3) 5 (4) 2

65. The number of distinct 6 digit number between 1 and300000 which are divisible by 4 and obtained byrearranging the digits of 11 22 33 is

(1) 12 (2) 15

(3) 18 (4) 90

66. A student preparing for IIT-JEE at Aakash Institute isgiven 6 targets numbered for 1 to 6 of each subjectPhysics, Chemistry and Mathematics, He or shekeeps all his books in different shelves (for each

subject) in order. Number of ways to select all 18books one by one such that books of each subjectmust be selected in order (i.e. all books of onesubject to the selected one after another, then ofsecond subject and then of third subject) is

(1)18!

6!6!6!(2)

18!3!

6!6!6!

(3) 6!6!6!3!

(4) 18!6!6!6!3!

67. Six numbers are in A.P. such that their sum is 3 andthe first number is four times the third number. Thefifth term is equal to

(1) 15

(2) 3

(3) 9

(4) 4

68. Let a1, a2, a3, ....., an be in A.P., 'd' being the

common difference. Let the arithmetic mean of thesquares of these quantities exceed the square of thearithmetic mean of these quantities by quantity pthen 'p' is equal to

(1)2

21

12

nd

(2)

221

12

nd

(3)2

12

nd(4)

2 1

12

n


14/20



12/14

69. If nis multiple of 4, the sum S= 1 + 2i+ 3i2+ .....

+ (n+ 1)inwhere 1i is

(1) 1 i (2)2

2

n

(3)2 8 4

8

n ni (4)

( 2)

2

n ni

70. The number of integers between 1 and 10,000. Bothinclusive which are neither perfect square nor perfect

cube is

(1) 9283 (2) 9883

(3) 9281 (4) 9887

71. Let set 's' be the set of points whose co-ordinates

x, yand zare integers that satisfy 0 x 2, 0 y 3 and 0 z 4. Number of ways to select twodifferent points such that the mid point of thesegment also belongs to 's' is

(1) 885

(2) 1770

(3) 230

(4) 665

72. 10.39C9 30.39C8is equal to

(1) 42C9 (2)40C9

(3) 41C9 (4) 10.40C9

73. Sum of the series

2 2 2 2 2 2

3 5 7.....

1 1 2 1 2 3

upto 100 terms is

equal to

(1)100

0.06(2)

600

101

(3)606

100(4)

101

600

74. a, b, care non real numbers such that the equation(a 1)x = y + z, (b 1)y = x + z = 0, (c1)z =

x+ yhas a non-trivial solution, then ab+ bc+ cais equal to

(1) abc (2) a+ b+ c

(3) 0 (4) 1

75. Ifcos sin 0

( ) sin cos 0

0 0 1

x x

f x x x

. then A1is equal to

(1) f(x) (2) f(x)

(3) f(x) (4) f(x)

76. If f(x) = x2+ 4x 5 and1 2

4 3A

, then f(A) is

equal to

(1) 0 48 8

(2)2 1

2 0

(3)1 1

1 0

(4)8 4

8 0

77. There are 100 students in a row. Number of ways toselect 3 students such that at least two student mustbe present between is each selected students is

(1) 24C3 (2)98C3

(3) 95C3 (4)96C3

78. The highest power of 18 contained in 50C25is

(1) 3 (2) 0

(3) 1 (4) 2


15/20



13/14

79. If 12 + 22 + 32 + ..... + 20142 = x and 1.2014 +2.2013 + ..... + 2014.1 = ythen xis equal to

(1) 2015.10072 y

(2) 1007 20152 y

(3) 1007 20152+ y

(4) 2015.10072+ y

80. If a1= 0 and a1, a2, a3, ....., an+1are real numbersuch that |ai| = |ai 1+ 1| i, then the A.M. of thenumber a1, a2, .....anhas value xwhere

(1)1

2x

(2)1

2x

(3)1

2x

(4) x1

81. Ai(xi, yi), i = 1, 2, ....., n are npoints on the curve

2y x . If x1, x2, ....., xn are in G.P. with x1 = 1,

x2= 2 then yn=

(1) ( 2)n (2) 1( 2)n

(3) 2n (4) 2n1

82. For any 2 2 metrix A, if A(adjA) =100 0

0 100

,

then |A| is equal to

(1) 1000(2) 10

(3) 100

(4) 10000

83. If A= [aij]44and |A| = 10, N= |adjadjadjA|. Numberof divisors of Nwhich is perfect square is

(1) 256 (2) 225

(3) 196 (4) 169

84.

2 3 21 3 2

2 1 3 2 1

1 2 0

x x x

x x x

= A0 + A1x + A2x2 + .....

the value of A1is

(1) 2 (2) 1

(3) 0 (4) 385. Letters of word 'NEWTON' is arranged in all possible

ways and written as a dictionary. The rank of word'NEWTON' is

(1) 76 (2) 84

(3) 82 (4) 80

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) andStatement-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.

86. Statement-1 : Let f(x) = (x)75(3 x)25, x(0, 3) then

f(x) is maximum at9

4x .

and

Statement-2 : a1, a2, ....., an > 0 then

1/1 21 2 3

.....( . . ....., ) nn n

a a aa a a a

n

.

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

Statement-1





16/20



14/14

87. Statement-1 : x = 7 is a root at equation

2 5

2 5 0

2 5

x

x

x

and

Statement-2 : If x= amakes mrows or mcolumns

of determinant (x) = 0 identical then (x a)m1

is itsfactor.



Statement-1



88. Statement-1 : If 22aA

a

and |A3| = 1728 then a

= 4

and

Statement-2 : det(AB) = detA.detB.

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

Statement-1


Statement-1



89. Statement-1 : The value of expression

537 42

4 31

J

j

C C

is equal to42C4.

and

Statement-2 : nCr +nCr+1 =

n+1Cr+1, 0 r,

r+ 1 n.





90. Statement-1 : Let 31 22 3 5N . Number of positive

integers p, q such that L.C.M. of p, q is N, is

1 2 3(2 1)(2 1).(2 1) 1

2

.

and

Statement-2 : Number of ordered pairs of (p, q) suchthat L.C.M. of p, q is N, is (21 + 1) (22 + 1)(23+ 1).



Statement-2 is NOT a correct explanation forStatement-1




17/20


18/20


19/20

Test - 1 (Paper-I) (Answers & Hints) All India Aakash Test Series for JEE (Main)-2014

1/10

ANSWERS

1. (4)

2. (3)

3. (4)

4. (3)

5. (3)

6. (1)

7. (1)

8. (2)

9. (2)

10. (2)

11. (1)

12. (1)

13. (3)

14. (2)

15. (3)

16. (3)

17. (4)

18. (1)

19. (1)

20. (3)

21. (2)

22. (2)

23. (1)

24. (2)

25. (2)

26. (4)

27. (1)

28. (3)

29. (2)

30. (4)

PHYSICS CHEMISTRY MATHEMATICS

31. (2)

32. (3)

33. (1)

34. (2)

35. (4)

36. (3)

37. (1)

38. (3)

39. (2)

40. (4)

41. (3)

42. (2)

43. (3)

44. (3)

45. (2)

46. (4)

47. (1)

48. (4)

49. (4)

50. (1)

51. (4)

52. (2)

53. (3)

54. (1)

55. (3)

56. (1)

57. (3)

58. (4)

59. (2)

60. (1)

61. (3)

62. (3)

63. (1)

64. (3)

65. (4)

66. (4)

67. (2)

68. (3)

69. (1)

70. (3)

71. (2)

72. (3)

73. (1)

74. (4)

75. (3)

76. (4)

77. (1)

78. (2)

79. (2)

80. (1)

81. (3)

82. (3)

83. (3)

84. (3)

85. (2)

86. (3)

87. (4)

88. (3)

89. (1)

90. (4)

TEST - 1 (Paper-I)


20/20

JEE Main 2014_Test 2 (Paper I) Code A

Documents

Transcript of JEE Main 2014_Test 2 (Paper I) Code A