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Space for Rough Work
Test - 1 (Paper-I) All India Aakash Test Series for JEE (Main) 2014
1/13
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
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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
(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
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.
(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
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.
(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
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.
(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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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. 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
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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
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SECTION - IIAssertion – Reason Type Questions
Directions : Questions number 56 to 60 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.
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.
(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
57. Statement-1 : The shape of ICl2– is linear.
and
Statement-2 : Hybridisation of I in ICl2– is sp.
(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
58. Statement-1 : Atomic radius of aluminium is lowerthan that of gallium.andStatement-2 : Aluminium and gallium belong to thesame group of periodic table.
(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
59. Statement-1 : NO2 is paramagnetic and undergoesdimerisation to form N2O4 which is diamagnetic.andStatement-2 : NO2 is mixed anhydride.
(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
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 �.
(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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PART - C (MATHEMATICS)
SECTION - IStraight Objective Type Questions
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. 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
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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
SECTION - IIAssertion – Reason Type Questions
Directions : Questions number 86 to 90 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.
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.
(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
87. Statement-1 : P(n) : ( 1)!2
⎛ ⎞ ⎜ ⎟⎝ ⎠
nn
n holds for all
natural numbers n.
and
Statement-2 : P(1) is true.
(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
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.
(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
Space for Rough Work
Test - 1 (Paper-I) All India Aakash Test Series for JEE (Main) 2014
13/13
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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.
(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
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 .
(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