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Test - 1 (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 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. At a distance L = 550 m from the traffic signal,brakes are applied to a rail road train moving at avelocity v = 72 km/hr. Determine the distance of railroad train from the traffic signal, one minute after theapplication of brakes if its acceleration a = –0.4 m/s2

(1) 70 m (2) 30 m

(3) 40 m (4) 50 m

2. A boy runs away from a pole in a straight line sothat its velocity is inversely proportional to thedistance from the pole. When boy is at a point A ata distance x1 = 100 m from the pole, its velocity isv1 = 2 m/s. What time will boy take to run awayfrom point A to point B which is at a distancex2 = 200 m from the pole?

(1) 50 s (2) 60 s

(3) 75 s (4) 90 s

3. A lift whose floor to ceiling distance is equal to 2.7 mstarts ascending with constant acceleration1.2 m/s2, 2.0 s after the start a bolt begins fallingfrom the ceiling of the car. Find the distance coveredby bolt as seen by observer on ground.

(g = 9.8 m/s2)

(1) 1 m (2) 1.7 m

(3) 2.7 m (4) 1.3 m

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

4. A point object moves along straight line withretardation a v , where a is constant and v is thespeed of particle. Initially the speed of the particlewas v0. Then select correct statement

(1) The body never stops

(2) The body stops after covering a distance 3/20

3

v

a

and time taken to cover this distance is 02 v

a

(3) In time 02 v

a body covers a distance

3/202

3v

a

(4) Total distance travelled by body till it stops is

3/20

3v

a

5. A particle moves along x axis. Its velocity timegraphs is given below. The distance travelled by theparticle in 0 to 3 s is

–3 m/s

1s 2s3 sO t

v

Parabola

(1) Zero (2) 4 m

(3) 8 m (4) 12 m


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

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6. A cannon fires successively two shells with speed250 m/s, the first at an angle 60° and second at anangle 45° to the horizontal in same plane. Find timeinterval between firings leading to the collision of shells.(g = 10 m/s2)

(1) 11 s (2) 5 s

(3) 7 s (4) 6 s

7. A ball is thrown from a point A with a speed v0 at anangle with horizontal from a point A. A smooth wallis approaching the ball with speed v as shown infigure, after colliding with the wall it bounces back onthe point of projection A. Then its time of flight is

v0

A

v

(1)02 sinvg

(2)02 sin vg

(3)02 sin vg

(4) Information is not sufficient to decide time offlight

8. If there is no air drag in the ascent of a projectile,

(1) The magnitude of tangential accelerationincreases while magnitude of normal accelerationdecreases

(2) The magnitude of tangential accelerationdecreases while magnitude of normalacceleration increases

(3) Both increases

(4) Both decreases

9. x hits a ball along the ground with a speed u in adirection which makes an angle 30° with the linejoining him and fielder y. Fielder y runs to intercept

the ball with a speed 23u

. At what angle should he

run to intercept the ball in the shortest time?

x y

u

30°

23u

(1) 1 3sin

2 ⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠

(2) 1 3sin

4 ⎛ ⎞⎜ ⎟⎝ ⎠

(3) 1 4sin

5 ⎛ ⎞⎜ ⎟⎝ ⎠

(4) 1 2sin

3 ⎛ ⎞⎜ ⎟⎝ ⎠

10. An athlete jumps to throw a javelin from a height of3 m with a speed of 15 m/s. Then find the maximumpossible range on the ground (g = 10 m/s2)

(1) 22.5 m

(2) 25.3 m

(3) 21 m

(4) 28.1 m

11. A man can swim in still water with a speed of

3 3 m/s and flow velocity of water is 3 m/s. He

wants to move along a line at an angle 60° with theflow direction. At what angle from flow directionshould he start swimming?

(1) 90° (2) 75°

(3) 120° (4) 74°



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12. A particle starts from the origin at t = 0 second,

with a velocity of ˆ10 m/sj and moves in the x-y

plane with a constant acceleration of 2ˆ ˆ(8 2 ) m/si j .

Find the speed of the particle when x = 16 m

(1) 21.26 m/s

(2) 13 m/s

(3) 16.4 m/s

(4) 25.2 m/s

13. A particle is moving in a vertical circle under theaction of a force that gives a tangential accelerationof 4 m/s2 in addition to the radial acceleration. At the

position P, its speed is 3 m/s and acceleration is

horizontal. The value of is

P

(1) 37° (2) 30°

(3) 53° (4) 60°

14. The position vector of a particle is

ˆ ˆ[cos sin ] �

r a t i t j . The acceleration of the

particle is

(1) Parallel to velocity vector

(2) Directed towards origin

(3) Directed away from origin

(4) Perpendicular to position vector

15. Initially the system shown in figure is in equilibrium.Find the acceleration of block C immediately afterlower string is cut

m

m

m

2m

A

B

D

C

E

Q

(1) g upward (2) g downward

(3) Zero (4)2g

downward

16. In the system shown the triangular wedge is fixed,mass of block A is 50 kg and mass of block B is75 kg. The tension in the string is (g = 10 m/s2)

50 kg A75 kgB

37°

(1) 500 N (2) 400 N

(3) 300 N (4) 600 N



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17. At the instant shown in figure, the block movesdownwards with velocity u1, the wedge movesrightwards with velocity u2. The correct relationbetween u1 and u2 is

u1

u2

(1) u2 = u1 (2) u2 = u1sin

(3) 2u2sin = u1 (4) u2(1 + sin) = u1

18. In the figure shown A and B are free to move. All thesurfaces are smooth. Mass of A is m, then

B M

m A

(1) The acceleration of A will be more than gsin

(2) The acceleration of A will be less than gsin

(3) Normal reaction on A due to B will be more thanmgcos

(4) Normal reaction on A due to B will be equal tomgcos

19. A solid uniform 45 kg ball of diameter 32 cm issupported against a vertical wall (smooth) using a30 cm massless string. The normal reaction of thewall on the ball is nearly (g = 9.8 m/s2)

30 cm

g

(1) 163 N (2) 221 N

(3) 140 N (4) 240 N

20. A ball is held at rest in position A and anotheridentical ball is released from rest in position B. The

ratio of tensions 1

2

TT

is given by

(1) 1

(2)12

30°

30°

T1 T2

A B

(3)43

(4)34

21. In the arrangement shown in figure

1 = 0.1

2 = 0.4

M = 20 kg

Find the maximum value of m so that arrangementis in equilibrium

1M

2

m

(1) 4 kg (2) 5 kg

(3) 6 kg (4) 3 kg

22. In the figure shown, there is exist friction betweenthe blocks but the ground is smooth. The frictionforce acting between the blocks is (g = 10 m/s2)

Smooth

3 kg

2 kg

20 N

= 0.65 N

(1) 12 N (2) 11 N

(3) 6 N (4) 5 N



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23. A cylinder of mass m rest in a supporting block asshown. If = 60º and = 30º, calculate themaximum acceleration which the block may be givenup the incline so that the cylinder does not losecontact at P (neglect friction everywhere)

= 60°

QP

= 30º

(1) g (2)2g

(3)4g

(4) 2g

24. A block of mass m is stationary relative to a trolleycar which moves with an acceleration a. The frictionalforce acting on the block is

ma

(1) mg

(2) ma in forward direction

(3) ma in backward direction

(4) Zero

25. A horizontal force F pushes a block of mass m sothat it moves up the plane with a constant velocity.Assume = coefficient of kinetic friction. The valueof F is

mF

(1) mgsin + mgcos

(2)(sin cos )(cos sin )

mg

(3)(sin cos )cos sin

mg

(4) mgtan

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) andStatement-2 (Reason). Each of these questions also hasfour alternative choices, only one of which is the correctanswer. You have to select the correct choice.

26. Two blocks of masses m1 and m2 (m1 > m2) arekept over a rough horizontal plank whose inclinationwith horizontal is increased slowly. The coefficient offriction for all surface in contact is same

Plank

m1 m2

Statement-1 : m1 will begin to slip before m2 does.

and

Statement-2 : The force causing m1 to slip is morethan that for m2.

(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



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27. Statement-1 : For a particle moving in a curved path,

�

dvdt

must be greater than dvdt

.

and

Statement-2 : The magnitude of rectangular

component of a vector cannot be more than

magnitude of a vector.

(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



28. Statement-1 : A particle moves so that its coordinate

vary with time as x = acost and y = asint. The

trajectory of the particle is circular.

and

Statement-2 : Two mutually perpendicular velocities

when added, give rise to a circular motion.


Statement-2 is a correct explanation for

Statement-1


Statement-2 is NOT a correct explanation for

Statement-1



29. Statement-1 : If a body is moving on a curved pathand it is speeding then angle between velocity andacceleration is always acute.

and

Statement-2 : Rate of change of velocity isacceleration.





30. In the figure shown.

2 kg

3 kg

A

B

Statement-1 : Block B will exert greater force onstring in comparison to block A.

and

Statement-2 : Block A will exert a force on stringgreater than 2g and block B will exert a force lessthan 3g on the string.







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31. Overlap of which of the following atomic orbitalswould be maximum to give the strongest covalentbond?

(1) 2p – 2p() (2) 2p – 2p()

(3) 1s – 2s() (4) 1s – 2p()

32. The vapour density of a mixture of NO2 and N2O4 is33.35, at 25°C. Calculate the number of moles ofNO2 in 10 mole of the mixture.

(1) 3.0 (2) 4.5

(3) 5.5 (4) 7.0

33. The correct order of second ionisation energy ofcarbon, nitrogen, oxygen and fluorine is

(1) O > F > N > C (2) F > O > N > C

(3) C > O > N > F (4) O > N > F > C

34. Which one of the following orders of bond angles iscorrect?

(1) NH3 < NF3 (2) PH3 < PF3

(3) BF3 < BCl3 (4) H2O < OF2

35. The maximum F – Xe – F bond angle in XeOF2 is

(1) 90° (2) 120°

(3) 150° (4) 180°

36. What mass of HNO3 is needed to convert 12.7 g ofI2 to HIO3 according to the following reaction?[Atomic mass : N = 14, I = 127]

I2 + HNO3 HIO3 + NO2 + H2O

(1) 24.8 g (2) 13.5 g

(3) 31.5 g (4) 48.2 g

PART - B (CHEMISTRY)

37. The mass of carbon that contains same number ofatoms as are present in 2.4 g of S is

(1) 0.90 g (2) 1.8 g

(3) 1.35 g (4) 2.15 g

38. The radius of 4th orbit in He+ is X times the radiusof first orbit of H-atom. What is the value of X?

(1) 4.5 (2) 6

(3) 8 (4) 9.25

39. The difference between nth and (n + 1)th Bohr'sradius of H-atom is equal to its (n – 1)th Bohr'sradius. The value of n is

(1) 5 (2) 4

(3) 2 (4) 1

40. Which of the following species has one lone pair ofelectrons in the valence shell of the central atom?

(1) XeF4 (2) SiF4

(3) BrF3 (4) SF4

41. Which of the following is most covalent?

(1) Na2S

(2) MgCl2

(3) MgS

(4) NaCl

42. The uncertainty in momentum of an electron is halfof uncertainty in position. What is the value ofuncertainty in velocity?

(1)1 hm

(2)1 h

2m 2

(3)1 hm 4 (4)

h2m



8/13

43. The specific gravity of a solution is 1.4 g/ml. It has54% (mass/mass) of a salt. What is the mass of saltin 750 ml of the solution?

(1) 537 g (2) 555 g

(3) 567 g (4) 586 g

44. The first four ionisation energies of an element (M)are 8.30 eV, 25.15 eV, 37.93 eV and 259.30 eV.What would be the formula of its chloride?

(1) MCl (2) MCl2

(3) MCl3 (4) MCl4

45. Which one of the following elements/ions haspositive electron gain enthalpy?

(1) B (2) N

(3) S (4) O

46. Which of the following oxides is/are amphotericoxide(s)?

(1) BeO (2) Al2O3

(3) ZnO (4) All of these

47. 2.74 g of a mixture of NaHCO3 and Na2CO3 lost0.62 g of its weight on strong heating. The molefraction of NaHCO3 in the original mixture is

(1) 0.67 (2) 0.33

(3) 0.55 (4) 0.40

48. A sample containing H3PO4 and P4O10 is labelled inthe analogous manner as oleum. The mass of P4O10in a sample labelled as 127%, would be (Atomicmass : O = 16, P = 31)

(1) 24 g (2) 37 g

(3) 53 g (4) 71 g

49. Which one among the following species has longestbond length?

(1) N2 (2) N2+

(3) N2– (4) N2

2–

50. An electron comes back from 4th excited state ofH-atom. How many lines will appear in the visibleregion of its emission spectrum?

(1) 3 (2) 4

(3) 10 (4) 2

51. In 6th period of periodic table the electrons fill theorbitals in the order of

(1) 6s, 4f, 5d, 7s

(2) 4s, 3d, 4p

(3) 5s, 4d, 5p

(4) 6s, 4f, 5d, 6p

52. Which one of the following has highest dipolemoment?

(1) CH3 – F (2) CH3 – Cl

(3) CH3 – Br (4) CH3 – I

53. Which of the following is correct order of bondangle?

(1) NF3 < PH3 < NH3

(2) PH3 < NH3 < NF3

(3) PH3 < NF3 < NH3

(4) NF3 < NH3 < PH3

54. What is the hybridisation of S-atom in S8 molecule?

(1) sp3 (2) sp2

(3) sp (4) dsp2

55. Pick out the isostructural species having similarshape from the following

I. NH2II. OF2

III. XeF2 IV. CS2

(1) II and III

(2) III and IV

(3) I and II

(4) II, III and IV



9/13



56. Statement-1 : A metal is heated in an atmosphere ofoxygen to form its oxide having 53.33 % oxygen.The equivalent weight of metal is 7.

and

Statement-2 : In the above reaction 7 parts of metalhave combined with 8 parts of oxygen.





57. Statement-1 : The shape of ICl2– is linear.

and

Statement-2 : Hybridisation of I in ICl2– is sp.





58. Statement-1 : Atomic radius of aluminium is lowerthan that of gallium.andStatement-2 : Aluminium and gallium belong to thesame group of periodic table.





59. Statement-1 : NO2 is paramagnetic and undergoesdimerisation to form N2O4 which is diamagnetic.andStatement-2 : NO2 is mixed anhydride.





60. Statement-1 : Orbital 4d has one radial node andtwo angular nodes.andStatement-2 : Number of radial nodes is given byn–�–1 and number of angular nodes is given by �.







10/13

PART - C (MATHEMATICS)



61. The radius of the circle

2 (3 2 ) (3 2 ) 6 0 z z i z i z is

(1) 5 (2) 4

(3)52

(4) 1

62. Consider the quadratic equation 2 0ax bx a ,

where a, b, C (set of complex number) such thatIm(a) 0 and Im(b) = 0. Then

(1) Both roots of the equation are always real

(2) Both roots of the equation are complex numbersand conjugate of each other

(3) Both roots of the equation are always complexnumbers, but not the conjugate of each other

(4) Roots may be real as well as complex numbers

63. Let z1, z2, z3, ....., z11 be the roots of the equationz11 – 1 = 0, where z1 = 1. If is the fifth complexroot of unity (Im () 0) then

2 2 22 3 11

2 3 11

( ) ( )..... ( )( ) ( )...... ( )

z z zz z z

is equal to

(1) 1 (2)

(3) 2 (4) –1

64. The term independent of x in the expansion of

7 81 1⎛ ⎞ ⎛ ⎞ ⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠x x

x x is

(1) 35 (2) 6

(3) 0 (4) –35

65. If the quadratic equation (ln a) x2 + 2(ln a)2x – 3 = 0,a > 1, has exactly one root in (1, 2), then ln a liesin

(1)1

0,2

⎛ ⎞⎜ ⎟⎝ ⎠

(2) (1, )

(3)1

1,2

⎛ ⎞⎜ ⎟⎝ ⎠

(4)1

, 12

⎛ ⎞⎜ ⎟⎝ ⎠

66. Let A(z1), B(z2), C(z3) be three points in the argandplane such that z1 + 7z2 – 8z3 = 0. Then

(1) ABC is right angled triangle

(2) ABC is a triangle whose area is 212

sq. unit

(3) A, B, C are collinear and B divides AC in theratio 7 : 1 internally

(4) A, B, C are collinear and B divides AC in ratio8 : 1 externally

67. The least value of |z| satisfying 4

3 zz is

(1) 0 (2) 1

(3) 2 (4) 4

68. Let , be the roots of x2 + 2x + 3 = 0. Then theroots of x2 – 2x (1 – x) + 3(1 – x)2 = 0 are

(1) ,1 1 (2) ,

1 1

(3) ,1 1

(4)

1 1,

69. If x1, x2 are the roots of x2 + x – 2 = 0 andy1, y2 are the roots of y2 + y + 2 = 0, then (x1 – y1)(x2 – y2) (x1 – y2) (x2 – y1) is equal to

(1) 16 (2) 8

(3) 4 (4) 2



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70. The greatest term in the expansion of (3 + 5x)15

when 925

x , is

(1) T6 only (2) T7 only

(3) T6 and T7 only (4) T5 and T6 only

71. 5[(2 3) ] , where [.] represents the greatest integer

function, is equal to

(1) 722 (2) 723

(3) 724 (4) 725

72. Let be the 7th root of unity. Then

2 3 4 53

8log 1

is equal to

(1) 0 (2) 1

(3) 2 (4) 3

73. The least argument of the complex number z

satisfying | 2 3 6 | 2 3 z i , is

(1)6

(2)4

(3)3

(4)23

74. If and ( > ) are the roots of the equationx2 – px – q = 0, where p > 0, q > 0. Then

(1) || > > 0 > (2) > > 0

(3) || > > 0 > (4) > || > 0 > 75. If , , are the roots of x3 + 3x2 – 1 = 0, then

1 1 1( ) ( ) ( )

is equal to

(1) 0 (2) –3

(3) 3 (4) –1

76. The sum of the series 10C0 + (10C0 + 10C1) + (10C0+ 10C1 + 10C2) + ..... + (10C0 + 10C1 + ..... + 10C10)is equal to

(1) 1536 (2) 5120

(3) 5632 (4) 6144

77. The first negative term in the expansion of (1 + x)35/3,0 < x < 1, is

(1) 14 (2) 13

(3) 12 (4) 11

78. The co-efficient of x4 in the expansion of

52 1

3⎛ ⎞ ⎜ ⎟⎝ ⎠

xx

is

(1) 254 (2) 260

(3) 270 (4) 280

79. Let z and be two complex numbers such that

arg( ) arg( ) , | | 2 | |4 z z . Then z equals

(1) (1 ) i (2) 2(1 ) i

(3) 2 (1 ) i (4) 2 (1 ) i

80. The number of real roots of the equation 4x3 – x2 +2x – = 0, R, > 1, is

(1) 1

(2) 3

(3) Dependent on

(4) Dependent of both and

81. 35C0.35C15 – 35C1.35C16 + 35C2.35C17 – ..... +35C20.

35C35 is equal to

(1) 0 (2) –35C25

(3) 35C25 (4) 1



12/13

82.12

1

2 2sin cos

13 13

⎛ ⎞⎜ ⎟⎝ ⎠

∑k

k ki is equal to

(1) 0 (2) 1

(3) –i (4) i

83. Let origin, z1 and z2 are the vertices of an equilateraltriangle. If z1 and z2 are the roots of the quadraticx2 + 2x – b = 0. Then b is

(1) 1 (2)23

(3)43

(4) 2

84. The sum of the real values of x satisfying theequation |x – 1|2 + 4|x – 1| – 5 = 0 is

(1) –4 (2) 0

(3) 2 (4) 4

85. If n > 1, then (1 – 2x)n – 1 + 2nx is always divisibleby (for all n)

(1) x2 (2) 2x2

(3) x – 1 (4) x + 1



86. Statement-1 : The 4th term from the end in the

expansion of 11

13 5

3

⎛ ⎞⎜ ⎟⎝ ⎠

is 275 5 .

and

Statement-2 : The rth term from the end in theexpansion of (1 + x)n is (n – r + 1)th term from thebeginning.





87. Statement-1 : P(n) : ( 1)!2

⎛ ⎞ ⎜ ⎟⎝ ⎠

nn

n holds for all

natural numbers n.

and

Statement-2 : P(1) is true.





88. Statement-1 : Origin, 2 + 3i, 4 65 5 i are collinear.

and

Statement-2 : If origin, z1 and z2 are collinear then|z1 + z2| = |z1| + |z2| for all complex numbers z1 andz2.







13/13

� � �

89. Statement-1 : For all nN, P(n) : 64n/2 – 7n – 1 isdivisible by 7.

and

Statement-2 : If P(k + 1) is true wherever P(k) istrue and P(1) is true then P(n) is true for all kN.





90. Statement-1 : The number of points of intersection of

|z – 2| = 2 and arg ( 3 )4 z i is 1.

and

Statement-2 : Point 3 + i lies on the circle

| 2 | 2 z .





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